Theoretical studies on the lineage specification of hematopoietic stem cells

Transcription

1 Theoreticl studies on the linege specifiction of hemtopoietic stem cells Ingmr Gluche Ph.D. thesis University of Leipzig, Germny, 2010

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3 To my dughters Elisbeth Kthrin nd Henriette Mrie

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5 Contents 1. Introduction nd objective Stte of reserch Motivtion Objective Biologicl bckground: Stem cells nd linege specifiction Stem cells: history nd definitions Hemtopoietic stem cells nd hemtopoiesis Linege specifiction of hemtopoietic stem cells Phenomenology Moleculr spects of linege specifiction Reversibility of linege decisions Heterogeneity nd linege bis Anlysis of single cell developments Experimentl techniques nd mesures Technicl chllenges nd ethicl considertions Theoreticl bckground: Conceptul nd mthemticl models Generl spects Models in the nturl sciences Quntittive models in stem cell biology Models of stem cell self-renewl nd differentition Comprtment models with fixed stem cell chrcteristics Models of dptive nd self-orgnizing stem cell systems Conceptul pproches on linege specifiction The concept of developmentl lndscpes The concept of stte spce Fluctutions nd robustness Reduction of complexity Phenomenologicl models of linege specifiction Functionl models of linege specifiction Integrtion of linege specifiction nd self-mintennce Roeder nd Loeffler model of hemtopoietic stem cell orgniztion Methods I: Modeling the linege specifiction of HSCs Ctlog of criticl phenomen IX

6 Contents 4.2. The intrcellulr linege specifiction model Mthemticl representtion of the intrcellulr model Linege specifiction s cellulr property Dynmics of the competition process Phenotypic mpping Regultion of linege specifiction Integrtion of linege specifiction in the model of HSC self-mintennce Results I: Dynmics of linege specifiction Linege specifiction in the regressive nd the dissiptive control regime Dynmics in the regressive control regime Dynmics in the dissiptive control regime Dynmics of the extended stem cell model Modeling the in vivo sitution Adpting the model to the in vitro sitution Instructive versus selective linege specifiction Fluctutions of the ground stte nd linege bis Experimentl vlidtion Linege contribution of single differentiting cells Comprtive differentition of pired dughter cells Linege specifiction in differentiting cell cultures Summry nd dditionl remrks Methods II: Chrcteristics of single cell development Records of single cell development Forml chrcteristics of cellulr genelogies Topologicl mesures for cellulr genelogies Assignment of linege ftes Results II: Quntittive nlysis of in silico cellulr genelogies Compring cellulr genelogies under different growth conditions Genertion of cellulr genelogies under different growth conditions Topologicl chrcteriztion nd comprison Linege fte ssignment Compring cellulr genelogies under different modes of linege specifiction Genertion of cellulr genelogies under different modes of linege specifiction Anlysis of structurl differences in the topologies Summry nd dditionl remrks X

7 8. Discussion nd conclusion Summry of results Amended model of HSC self-renewl nd linege specifiction Trcing the ncestry of single cells Conclusions Outlook Acknowledgement 161 Bibliogrphy 163 Appendix A. Detils of the updte procedure 183 A.1. The Póly urn model A.2. Renormliztion of the vector of linege propensities B. Modifictions of the originl HSC model 185 C. Computtionl spects of the model of linege specifiction 187 C.1. Extension of the SCMuni code C.2. Anlysis of the cellulr genelogies C.3. Sttisticl nd grphicl nlysis of the results D. Simultion protocols nd prmeters 191 D.1. Studies on the regressive control regime D.2. Studies on the dissiptive control regime D.3. Studies on the extended model system D.4. Simultion results: Linege contribution of single differentiting cells192 D.5. Simultion results: Comprtive differentition of pired dughter cells D.6. Simultion results: Linege specifiction in differentiting FDCPmix cells D.7. Simultion results: Scenrios for the genertion of cellulr genelogies194 D.8. Simultion results: Instructive versus selective linege specifiction 195 E. Selected mthemticl bbrevitions 205 XI

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9 Denken und Wissen sollten immer gleichen Schritt hlten. Ds Wissen bleibt sonst tot und unfruchtbr. Wilhelm von Humboldt ( )

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11 1. Introduction nd objective 1.1. Stte of reserch Stem cells nd their therpeutic pplictions. Tissue stem cells re found in ll multi-cellulr orgnisms tht retin the bility to renew themselves through mitotic cell division. In order to mintin or reconstitute prticulrtissuethese cells cn specilize into wide rnge of mture cell types through process of differentition nd linege specifiction. Given the developmentl potentil of stem cells, it is not surprising tht the interest in their therpeuticl use is continuously growing. Adistinctionbetweentissuestemcellsndembryonicstemcells is pproprite in the first plce. Tissue stem cells, which re lso clled dult or somtic stem cells, re typiclly found within prticulr tissue or orgn. There, the tissue stem cells gurntee the sustined function of the tissue by the mintennce of their own popultion nd by the genertion of the specilized celltypesofthe tissue which re needed for replcement nd repir [1, 2]. Generlly, their differentition potentil is nrrowed to the cell types of the prticulr tissue. In contrst, embryonic stem cells re derived from the cells of the inner cell mss of blstocyst nd re mintined in in vitro cultures [3, 4, 5]. These cells re defined by their bility to differentite into ll cell types of the orgnism. However, they represent fixtion of trnsient cell stge (corresponding tothecellsoftheinner cell mss of the blstocyst) nd therefore do not hve stble in vivo counterprt. Although embryonic stem cells hve superior differentition potentilcompred to tissue stem cells, their ppliction for medicl therpy imposes number of technicl problems nd ethicl questions which re more extensively discussed in Section 2.6 of this thesis. Acompletenewperspectiveinexperimentlstemcellreserch ws recently opened by the observtion tht somtic cells cn be reprogrmmed to stte closely similr to embryonic stem cells [6, 7, 8, 9] thus circumventing nucler trnsfer techniques. Although the pproches re bsed on the trgeted overexpression of set of relevnt genes using gene vectors, the results gined gret ttention. In the very first plce, these results showed tht reprogrmming of complete somtic cell is in principle possible. Additionlly, these techniques do not require the utiliztion of humn egg cells nd the generted cells re ofthesmegenotype s the donor ones. These dvntges, to circumvent the ethicl discussion using embryonic stem cells or humn eggs s well s the identity with thegenotypeof the donor, put gin highest expecttions on stem cell reserch. Potentil p- 1

12 1. Introduction nd objective plictions in the clinicl setting depend very much on the understnding of the underlying process to successfully tune the reprogrmming nd the subsequent differentition. So fr, only tissue stem cells re successfully used for medicl tretment or re t lest studied in the clinicl sitution. The most prominent exmple is the use of hemtopoietic stem cells (HSCs) for the tretment of severe mlignnciesofthe blood generting system. As in most leukemis norml hemtopoiesis is displced by rpidly expnding clone of mlignnt cells with impired function. Current trnsplnttion tretments im on n erdiction of the complete hemtopoietic system of the effected ptient nd the subsequent replcement of the HSC source provided from helthy donor. Given the successful engrftment of the donor stem cells in the bone mrrow of the host they cn completely reconstitute the hemtopoietic system nd provide ll types blood cells s there re lymphocytes, erythrocytes nd grnulocytes. However, there is still number of uncertinties with stem cell trnsplnttion, e.g. concerning the chncesofdonorengrftment nd the risk of immunorections between host nd donor tissue. Further fesible pplictions of stem cells include the use of epiderml stem cells nd the resulting kertinocytes in wide spectrum of different techniques for the tissue-engineering of rtificil skin (see [10] nd references therein). Such cultured skin substitutes re regulrly used for burn-injured ptients nd for the tretment of chronicl wounds. By reducing the demnd for utologous skin trnsplnts the cultured skin substitutes hve significntly enhnced the survivl rtes for mjor burns nd reduced the efforts for skin biopsies in ptients with chronic wounds. Novel therpeutic pproches hve identified tissue stem cells s possible trgets for the insertion of genes which re corrupted or deficient in ptients suffering from severe genetic, often inheritble mlignncies. This pproch, commonly clled gene therpy, wssuccessfullyppliedforthetretmentofseverecombined Immunodeficiency Disorder (SCID) [11], further subform clled X-SCID [12] nd for the tretment of Chronic Grnulomtous Disese (CGD) [13]. These studies showed tht the integrtion of the missing or corrupted gene in HSCs using virl vectors cn contribute to the corrected tissue function over extended time periods. However, since the integrtion site of the corrected geneisrndom, the trnsfected cell smple might contin cells in which other functions re corrupted nd potentilly induce tumors. Such effects hve to ccount for number of secondry hemtopoietic mlignncies with lethl consequences [14] nd re the gretest limittion to the present ppliction of gene therpy. Current limittions nd novel concepts. The limited number of vilble medicl pplictions is cler indictor tht mny questions bout generl principles of stem cell orgniztion, culturing nd differentition re not fully nswered. Even from the perspective of bsic reserch mny detils bout the intrinsic reg- 2

13 1.1. Stte of reserch ultion of stem cells, their interctions with the locl environment, their differentition decisions nd even their identifiction re still unknown. The limittions in the understnding of bsic principles becme even more obvious when the clssicl view on tissue stem cells ws chllenged by experimentl observtions demonstrting the bility of such cells to contribute to functionl cell types of completely different tissues. It hs for exmple been shown tht HSCs hve the generl bility to differentite into hert tissue ([15], see lso the criticl discussion in [16]), liver [17], brin [18, 19] nd muscle [20, 21]. This phenomenon, generlly referred to s plsticity, hsginincresedtheinterestintissuestem cells since it offers n lterntive pproch to circumvent the ethiclly questionble use of embryonic stem cells. Even more importnt, these findings chllenge to whole concept of perceiving tissue stem cells s rther fixed nd homogeneous popultion of cells with well defined chrcteristics nd predetermined differentition potentil. It ppers tht these stem cells re much more flexible thn previously nticipted nd tht they re generlly ble to respond to chnging environmentl conditions. This is not only true for the unexpected plsticity of these cells to switch between tissue, but lso for their popultion-inherent heterogeneity. It could be shown tht stem cell popultions re rther heterogeneous with respect to the cycling sttus or with respect to the expression of surfce mrkers [22, 23]. It is therefore not surprising, tht prospective identifiction of HSC could not be ccomplished so fr. Even the most rigorous isoltion protocols bsed on the expression of chrcteristic surfce mrkers result in heterogeneous popultions tht re enriched for HSCs but in which significnt number of cells fil to demonstrte long-term reconstitution of depleted niml [24]. For the prospective identifiction of stem cells this isoltion strtegy might not be the ultimte tool since the flexible nd reversible expression of the surfce mrkers s well s their limited functionl correltion to the stem cell ctivity re principle objections. But lso on the underlying genetic level it is not yet cler whether there exist unique stem cell signture or not [25]. Even more, it might be just the defining chrcteristic of stem cells to not express strict pttern uniquely encoding pluripotency nd the potentil for sustined self-renewl. It seems much more plusiblethtthe stem cell stte is chrcterized by different fcets of flexibility, reversibility nd robustness, nd tht this stte is highly dependent on the environmentl conditions, defined by the tissue, the signling context nd the metbolic options. In this sense stemness is not specific cellulr property but rther n inherent function of prticulr heterogeneous cell popultion. In the sme line of rgument it is questionble whether the process of linege specifiction, which describes the trnsition of originlly undifferentited(stem) cells into functionl mture cell types, is predetermined sequence of decision steps or whether linege specifiction needs to be understood sflexiblend dptive process tht is only predictble on the popultion level. As erly s 3

14 1. Introduction nd objective in the 1980s, Ogw nd coworkers [26, 27, 28] studied the linege specifiction potentil of hemtopoietic progenitor cells nd concluded tht committed cells re derived from multipotent progenitors through progressive restriction of linege potentil, in which the restriction in type nd number of linegesoccurs in stochstic fshion. Although mny detils on the moleculr mechnisms of linege specifiction hve been elucidted since then it remins uncler how the specific gene expression dynmics re generted nd how they re controlled by cell-cell nd cell-environment interctions. Even on more generllevelitisnot well understood how processes like dhesion, migrtion nd poptosis influence the cell fte development. However, there is n incresing number of reports tht gree upon generl phenomenology of the linege specifiction process: wheres the undifferentited stte is chrcterized by low level coexpression of mny linege specific nd potentilly ntgonistic genes in erly progenitorcells,this coexpression, commonly referred to s priming, disppersinthecourseofdifferentition, when certin linege restricted genes re up-regulted while others re down-regulted [29, 30, 31, 32]. Theoreticl pproches in stem cell biology. The bove criticism is not in plce to discredit more thn 40 yers of successful reserch on stem cells. It is the motivtion to study stem cell orgniztion in comprehensive, conceptul fshion in which different nd diverse phenomen cn be uniquely represented nd linked to ech other. It is evident, tht every experimentl design requires t lest conceptul perception of the underlying biologicl processes in order to either embed the results in the existing frmework or to modify or even flsify the existing model. Prominent exmples of such conceptul models re the hierrchy of hemtopoietic cell differentition or the interction mps tht outline the interply of genes nd trnscription fctors. However, beyond the level of conceptul models is the level of mthemticl vlidtion whichrepresents more rigorous description of the conceptul frmework in terms of quntittively ccessible mesures nd predictions. There is little rgument tht stem cell orgniztion is complex regultion process emerging from the collective interction of multitude of components. However, complexity is not just gme of mny plyers tht need to be identified. One could even rgue tht the identifiction of the plyers hs nothing to do with complexity t ll but it is the interctions, i.e. the rules of the gme, tht mke up complexity. In this cse, it is not sufficient to nlyze rtherisolted components or pthwys since the orgniztionl principles onlypperinthe context of mny interction prtners. This perception leds tonunderstnding in which determinism is replced by the notion of dynmiclly stbilizedsystems. It is here tht the plsticity nd reversibility of cellulr fetures tht re controlled by interctions with the environment gurntee for robustnddptive 4

15 1.1. Stte of reserch orgniztion. Such systems re generlly referred to s self-orgnizing. The smll number of quntittive modeling pproches in the field of stem cell biology does not compre to the importnce of this reserch field. Besides the obstcles in identifiction nd mesurement of this rre cell clss,mnymodels re rther descriptive in nture nd stick to the trditionl ctegoriesofstemcell orgniztion s deterministic process. However, there is lso few quntittive models tht pply the ide of complex intercting systems to the stem cell field nd tht contributed to the development of novel conceptul ides bout stem cell orgniztion [1, 33, 34]. Within such models it is possible to consistentlydescribe widerngeofexperimentlfindingsndtocouplethemtoperspective which perceives stem cell orgniztion s n dptive nd flexible process. New chllenges in stem cell reserch. Within the lst yers the systems biologicl dvnces mde the field of stem cell biology more ttrctive for novel theoreticl pproches. Especilly the vilbility of vst mounts of moleculr dt such s mrna nd protein screens s well s the rpid increse of computtionl resources fostered the development of mny new nlyticl methods for dt mining nd representtion. Driven by the experimentl reserch mny such pproches im t the identifiction of moleculr key plyers thtinfluencestem cell development nd orgniztion. Trnslting these findings from the moleculr level to the phenotypic level is still mjor chllenge. Aprt from the moleculr dt, the vilbility of new monitoring techniques such s high-resolution time lpse video microscopy fcilittes the observtion of cell cultures over time. Anlyzing the development of individul stem cells nd their progeny within such cultures yields informtion bout thedivisionlhistory, the timing of differentition events like symmetric cell ftes nd the role of cellulr interctions. Regrding ech cellulr trjectory s possible reliztion of the developmentl potentil of the originl (stem) cell, multitude of such trjectories should provide n impression bout the diversity of possible developments. Such pproches re suited to couple observed phenomen on the popultion level to the relevnt processes on the cellulr level. However, the interprettion nd generliztion of such cellulr trjectories requires rigorous nlyticl foundtion, which is in mny prts still lcking. Model pproches in stem cell biology re importnt tools to connect cell intrinsic regultions like signling pthwys nd gene expression ptterns on one side with the popultion behvior on the other side. The scope ofsuchmodels ims t the identifiction of generl principles tht define the ppernce of the tissue, e.g the regultory principles leding to self-mintennce of the stem cell popultion, the system inherent heterogeneity or the mechnisms tht govern the differentition process into different types of functionl cells. Given the necessry simplifictions from the rther complex biologicl system, these models re in- 5

16 1. Introduction nd objective dequte for the understnding of moleculr detils. However, such bstrctions re often key to understnding the fundmentl properties of suchcomplexsystems nd llow to put different experimentlly observed phenomen in common conceptul nd quntittively ccessible context. This helps to identify common regultory principles, nd therefore in the design of future experimentlstrtegies Motivtion Phenomenology. Undifferentited stem cells re defined by their bility to differentite into distinct somtic cell types. For the hemtopoietic system, HSCs cn generlly contribute to red nd different types of white blood cells. This differentition process, generlly involving sequence of decision steps, is referred to s linege specifiction nd is chrcterized by number of biologiclly relevnt fetures: Loss of linege potentil. In seminl series of experiments in the 1980s, Ogw nd coworkers [26, 27, 28, 35] studied the linege specifiction potentil of hemtopoietic stem nd progenitor cells. It could be demonstrted tht the potentil for the contribution to multiple lineges (multipotency) is progressively lost while the cells undergo differentition. This led to the conclusion tht linege specifiction is chrcterized s progressive restriction of linege potentil until distinct mture cell fte is finllyrelized. Genertion of diversity. Anlyzing single cell-derived colonies in number of closely similr studies [26, 27, 36] it could be furthermore shown tht originlly undifferentited cells cn give rise to heterogeneous colonies contining multiple different cell types. Together with the bove mentioned loss of multi-linege potentil this genertion of diversity is commonly ssocited with hierrchy of stem cell differentition. In this conceptul picture the stem cell t the origin gives rise to ll linege restricted progenitors nd mture cells in hierrchic sequence of decision steps (compre Figure 2.2). Regultion of linege specifiction. Linege specifiction is not sttic process but cn be regulted both in vivo nd in vitro. Commonexmples include the dpttion to higher demnds of erythrocytes in high-ltitude conditions [37] or the trgeted differentition of primry cells nd cell lines in vitro (see e.g. [38, 39]). Temporl extension. The process of linege specifiction hs temporl extension. As illustrted e.g. in [39, 40] the proportion of undifferentited cells decreses continuously s function of time while the proportions of functionl cells increses over the sme period. 6

17 1.2. Motivtion Reversibility. Generlly it ppers tht reversibility plys minor role under homeosttic conditions but might be essentil in cses ofinjurynd repir. Experimentl evidence suggests tht linege specifiction is t lest prtillyreversibleprocess[22,41,42]. Priming. On the moleculr level, the undifferentited stte is chrcterized by coexpression of mny, potentilly ntgonistic genes nd trnscription fctors [29, 31, 43]. This low-level coexpression, commonly referred to s priming, disppersinthecourseofdifferentitionwhencertinlinegerestricted genes re up-regulted while others re down-regulted. Linege bis. Experimentl evidence suggests tht HSCs cn mintin n inheritble linege bis in the sense tht they preferentilly contribute to one cell type s compred to nother [44, 45]. The mechnisms introducing this dditionl level of heterogeneity mong multipotent stem nd progenitor cells re still specultive. For further detils of the discussed phenomen the reder is referred to Chpter 2ofthiswork. Conceptul pproch. Besides their bility to provide multitude of distinct functionl cell types for replcement nd repir, stem cells refurthermorechr- cterized by their bility to preserve the regenertive potentil of tissue by sustined mintennce of their stem cell popultion. To gurntee both these functions certin mechnisms re required tht on one hnd regulte the selfmintennce of the stem cell popultion, even under chnging demnds,ndon the other hnd generte stble, lthough tunble, composition of different functionlly differentited cells. Adopting criticl nd unprejudiced view on stem cell orgniztion it seems obvious to sk whether such system cn be envisioned in the context of selforgniztion nd rective dptiveness, in which stemness is not cellulr property of single cells but systemic feture. Approching this subject from the perspective of theoreticl biologist, these questions hve to be ddressed in well defined nd mthemticlly founded fshion. On this level it needs to be sked which generl types of rules re required to estblish self-orgnizing system stisfying the experimentlly imposed criteri. In turn, these generlprincipleshve implictions for the interprettion of the system behvior nd even more direct impct on mesurble experimentl outcomes. For the mthemticl description of the sustined mintennce of the stem cell popultion, n elegnt pproch hs been dvocted by Ingo Roeder nd Mrkus Loeffler [33, 46, 47]. This pproch, which is estblished for the well studied hemtopoietic system, is build on the ide tht ech cells is subject to different 7

18 1. Introduction nd objective environmentl signls which in turn induce different directions for the developments of these cells. For simplified system with just two opposing signling contexts, one inducing differentition nd loss of stem cell function, the other inducing self-mintennce nd regenertion, it could be shown tht the mjor experimentl results cn be reproduced s there re the sustined mintennce of the HSC popultion, the dynmic response to system depletion, the heterogeneity of the stem cell popultion nd the estblishment of cellulr chimerisms. A detiled ccount of the model is given in Section 3.4. However, the model by Roeder nd Loeffler does not ccount for the second functionlity of tissue stem cells: the sustined, lthough dptive supply of different types of mture cells for mintennce nd repir of the functionl tissue Objective It is the objective of this work to estblish theoreticl model which ccurtely represents the phenomenology of stem cell differentition nd linege specifiction nd to study its implictions on the interprettion of cellulr behvior both on the single cell s well s on the popultion level. In prticulr, the following issues re ddressed in this thesis: Agenerlizednlyticlfrmeworkhstobedevelopedtounderstnd linege specifiction s n intrcellulr, temporlly extended processbsed on the interction of competitive differentition progrms. This concept needs to be discussed on the bsis of generlized understnding of the moleculr process involved in linege specifiction of HSCs. The proposed intrcellulr linege specifiction dynmics hve to be embedded in the model for HSC orgniztion proposed by Roeder nd Loeffler [33]. To do so, the interprettion of n instructive microenvironment hs to be extended to the sitution of linege specifiction, thus inducing correltion between the regultion of self-renewl nd linege specifiction. The intrcellulr model of linege specifiction needs to represent different possible mechnisms for the regultion of linege contribution (i.e. instructive nd selective linege specifiction). To verify the proposed theoreticl model, the simultion results need to be compred to severl sets of experimentl dt covering different spects of the linege specifiction process. In the second prt of the thesis the extended model pproch is ppliedtothe trcing of individul cell ftes including the cell s complete progeny. Therefore, the following spects hve to be covered: 8

19 1.3. Objective Estblishment of topologicl chrcteriztion for the tree-like structures resulting from the single cell-bsed pproch. This needs tobesupplemented by the proposition of suitble mesures for their nlysis nd comprison. The ppliction of these mesures nd their robustness needs tobedemon- strted under different (rtificil) conditions. In prticulr, it hs to be ddressed how different modes of linege specifiction cn be inferred from the single cell trcking dt. The thesis is structured s follows. Chpter 2 provides brod overview of the experimentl notion of stem cells nd illustrtes in more detil the phenomenology of linege specifiction. Chpter 3 continues with n introduction to the relevnt conceptul nd mthemticl models. Bsed on ctlogue of criteri theoreticl concept of linege specifiction is proposed in Chpter 4ndcomplemented by sensitivity nlysis nd comprison with experimentl dt in Chpter 5. Extending the focus towrds the nlysis of single cell ftes Chpter6introduces the relevnt nomenclture nd proposes pproprite mesures. Chpter 7 nlyses the suitbility of these mesures for different in silico situtions. The thesis is concluded with comprehensive summry nd outlook in Chpter 8. 9

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21 2. Biologicl bckground: Stem cells nd linege specifiction 2.1. Stem cells: history nd definitions It ws s erly s in 1868 tht the biologist Ernst Heckel used the term Stmmzelle (germn for stem cell) torefertotheunicellulrncestorfromwhichmulticellulr orgnisms developed during evolution. By mpping such n evolutionry Stmmbum (germn for pedigree or fmily tree) ontonembryologicltree he dvocted the view tht the founding fertilized egg cn lso be clled stem cell. It ws round the turn of tht century tht the term stem cell ws lso used to identify common progenitor cell tht gives rise to different cell types of the peripherl blood. However, the notion of one common type of stemcelltht regenertes the complete hemtopoietic system remined controversil. It ws not until the erly 1960s tht Cndin scientists round Ernest McCulloch nd Jmes Till could prove the existence of common undifferentited hemtopoietic (stem) cell tht is cpble of self-renewl nd differentition. In series of experiments it could be shown tht single, undifferentited bone mrrow cells yield the potentil to developed into spleen colonies of irrdited mice [48, 49, 50]. An excellent review bout the historicl usge of the term stem cell wspublished recently by Rmlho-Sntos nd Willenbring [51]. After the lndmrk experiments by Till nd McCulloch modern stem cell reserch took up speed. Using trnsplnttions experiments whole body of knowledge bout the repopultion potentil of certin bone mrrow derivedcells,their differentition hierrchy s well s their contribution to multiple hemtopoietic lineges hs been estblished. Beyond the hemtopoietic system, somtic stem cells could lso be identified in other tissues, e.g. in the skin [52], gut [53], liver [54], neurl tissue [55]. The pprent proximity between the processesofsomtic stem cell differentition nd differentition during embryonic development estblished the reserch on erly embryonic cells s n dditionl brnchofstemcell reserch. After the first stble embryonic stem cell line hs be derivedfromthe inner cell mss of mouse embryo in 1981 [3, 4], this reserch quickly expnded, resulting in the first humn embryonic stem cell line derived in 1997 [56]. In contrst to tissue stem cells, embryonic stem cells re defined in vitro nd re chrcterized by their bility to self-renew in culture nd to contribute to ll tissues of the three primry germ lyers, ectoderm, endoderm nd mesoderm. In 2006, Shiny Ymnk nd collegues showed the possibility toreprogrmtissue 11

22 2. Biologicl bckground: Stem cells nd linege specifiction cells into n embryonic stem cell-like stte by trgeted overexpression of four specific trnscription fctors Sox-2, Oct-4, c-myc, nd Klf4 [6, 8]. Thevilbility of these so clled induced pluripotent stem (ips) cells opened completely new perspective for stem cell reserch nd its pplictions in the 21nd century. These recent dvnces re lso bsed on the rpid biotechnicl developments in the lst decdes tht opened the window for the understnding of moleculr processes in stem nd progenitor cells. Using these techniques it ws possible to identify mny importnt genes tht re required for stem cell mintenncend differentition s well s their regultion by trnscription fctorsndsignling pthwys. Especilly the vilbility of microrrys, tht couldidentifythewhole rnge of mrnas trnscribed within certin cell popultion, rised the hope for unique trnscriptionlsignture ofstemcells[57,58]. However, such unique signture could not be obtined so fr [25], nd it is questionble whether such n stble signture exists or if the stem cell stte is dynmiclly defined [59]. Similrly, much effort hs been mde to prospectively isolte stem cellsbsedonthe expression of certin surfce ntigens. But lso these techniques only enrich for stem cells nd it is not yet possible to prospectively decide whether prticulr cell will ct s stem cell in functionl ssy or not. Therefore, the gold stndrd for defining stem cell is functionl chrcteriztion evluting the cell s bility for long-term tissue regenertion in vivo. There is n bundnce of definitions tht commonly chrcterize stem cells by their bility to mintin their own popultion (self-mintennce) s well s their bility to contribute to different types of functionl cells (multipotency). However, such working definitions do mostly not ccount for the full spectrum of phenomen ssocited with stem cells nor do they clerly outline whether the ssigned fetures pply to isolted cells or to cell popultion. Potten nd Loeffler [1], s well s other scientists [60, 61] illustrted tht stem cell function needs to be understood s concerted ction of mny different cells including stem cells nd their locl environment. This in turn implies tht functionl definition of stem cell is not chrcteriztion of single cell but of heterogeneous popultion. Aiming on comprehensive representtion of the full functionl spectrum of tissue stem cells nd bsed on previous work [1], Loeffler nd Roeder proposed more sophisticted definition of stem cells [46]. They define tissue stem cells s potentilly heterogeneous popultion of functionlly undifferentited cells, cpble of: homing to n pproprite growth environment prolifertion production of lrge number of differentited progeny 12

23 2.1. Stem cells: history nd definitions self-renewing or self-mintining their own popultion regenertion of the functionl tissue fter injury with flexibility nd reversibility in the use of these options. Adetiledccountofthechrcteristicfeturesisprovided in the originl publiction [46], however some spects re of prticulr relevnce for the focus of this thesis nd re briefly discussed below. First, the definition is bsed on cpbilities which is linguistic synonymous of potentil : certin functionl tsks cn be ccomplished in principle. Whetherthepotentilisctullyused,ishighlydependent on the prticulr sitution (e.g. homeostsis, injury). Here, nd second, nother spect comes into ply, which is the role of the prticulr environment. It could be shown for different tissues tht stem cell regultion ishighlydependent on the supportive function of the locl environment which is commonly referred to s niche. Within these niches stem cells re subject to different environmentl signls, which re generlly supportive in nture nd llow them to dptively rect on chnging demnds. The fct tht it hs not been possible to expnd HSCs in vitro is most likely due to the incomplete understnding of the complex signling tht occurs in the in vivo niches. Third, the production of lrge number of differentited progeny includes the option for unipotent stem cells tht only give rise to one mture cell type, like certinstemcellsoftheepidermis. Forth, thetermsself-renewl nd self-mintennce re often used interchngeble, lthough they might refer to slightlydifferentphenomen [62]. Self-mintennce generlly refers to the property of stem cell popultion to preserve their functionlity to ct s stem cells, which is the generl cse in homeosttic sitution. In contrst, self-renewl does lso include the repopultion of tissue nd the reestblishment of the corresponding stem cell popultion fter serious stress. However, it is more philosophicl questions, whether these re relly distinct processes nd if just one of bothissufficientto fulfill the definition criteri. Fifth, there is strong emphsize on the flexibility in the use of the ssigned cpbilities. Since the list of criteri postultes number of different potentils, prticulr cell does not necessrily hve to mke use of ll of them. It might well be the cse tht under certin environmentl conditions just one of the cpbilities is used (e.g. the differentition intolrgenumber of functionl cells) wheres other cpbilities (e.g. the self-mintennce) remin unused. It might even be the cse tht the use of the potentils chngeswith time including reversible developments. At this point it is most evident tht ny functionl definition of stem cells generlly refers to popultion of such cells. Since the criteri re functionl chrcteristics, single stemcellcnnotfulfill them ll t the sme time. In this respect it is pproprite to bndon the view of stem cell entities nd to refer to the stemness of cell popultions. 13

24 2. Biologicl bckground: Stem cells nd linege specifiction 2.2. Hemtopoietic stem cells nd hemtopoiesis Hemtopoietic stem cells re responsible for the production of blood cells throughout thelife of n orgnism. Theorigin of these cells duringembryonic development is not completely elucidted. However, it could be demonstrted tht the formtion of hemtopoietic stem cells occurs in complex developmentl process tht involves severl ntomicl sites including the yolk sc, the plcent nd the fetl liver [63]. Finlly, t birth, pool of HSCs is estblished in the bone mrrow [64], in mice especilly in the femur, in humns lso in the pelvis, sternum nd vertebr. The bone mrrow contins prticulr micro-environment which on one hnd supports the mintennce of the stem cell popultion nd ontheotherhnd provides surplus of cells for differentition nd the production of mture blood cells. In the post-ntl, homeosttic sitution, HSCs re generlly in quiescent stte nd re only rrely ctivted into cell cycle [65, 66, 67]. Hemtopoietic stem cells re rre subpopultion mong the cells in the bone mrrow. Estimtes in mice reveled tht between one to eight HSCs cn be found within 10 5 nucleted bone mrrow cells [68, 69]. However, HSCs re morphologiclly undistinguishble from other cells in the bone mrrow whichdonothve the stem cell functionlity. Although, the expression of certin surfce mrkers hs successfully been used to enrich for HSCs up to purity of one stem cell in two selected cells it is still not possible to prospectively identify stem cell with certinty [70]. Unlike other stem cell systems with well-structured sptil rrngement(e.g. the smll intestine or the hir follicle), the identifiction of HSCs bsed on sptil informtion is not possible. It is the semi-liquid composition of the bone mrrow tht mkes it very chllenging to study HSCs nd their interctions with the locl micro-environment in the in vivo sitution [71]. This is lso the reson why precise identifiction of the hemtopoietic niche s complex of locl nd systemic growth fctors, strom cells, nd extr-cellulr mtrix components, is such difficult tsk. However, it is well estblished fct tht the interction of stem cells with is locl environment re indispensble for the functionlity. Originlly, the perception of n inductive microenvironment ws introduced in erly 1970s by John Trentin [72, 73], however it is generlly Rymond Schofield [74] who is credited with the concept of stem cell niche. In this interprettion niche corresponds to defined ntomicl site tht regultes stem cell function by mens of secreted nd cell surfce molecules, mechnicl signls, sptil rrngements nd prticulr metbolic conditions [75, 76]. Although precise knowledge bout the sptil structures is missing, schemtic visuliztion of theconceptisprovided in Figure 2.1. Meticulous work reveled tht osteoblst cells ply crucil role in the construction of the hemtopoietic niches. Osteoblsts potentilly medite the dhesion of HSCs to the prticulr niches by the formtion of N-cdherin/β-ctenin dherens 14

25 2.2. Hemtopoietic stem cells nd hemtopoiesis Figure 2.1.: The hemtopoietic niche. In the picture, stem cells re shown in close proximity to the osteoblst nd sheltered by stroml cells nd extrcellulr mtrix components. Picture reproduced from [77] with kind permission from Kteri Moore. complexes. N-cdherin function is decresed in the course of differentition which in turn might promote the displcement from osteoblstic niche. A mjor role to fcilitte connection between osteoblsts nd HSCs hs been demonstrted for the Ang-1/Tie2 signling, which is importnt for sustined quiescence nd longterm repopultion bility [78]. Similr regulting functions hve been ssigned to the Notch nd Wnt pthwys, however the exct regultion needs further investigtion. An excellent overview bout the stte of reserch hs been published in reviewrticlebymoorendlemischk[77]. The vilbility of osteoblst niches seems to be mjor regultor of the bsolute stem cell number [79]. However, besides the dominnce of the osteoblst niches in the bone mrrow lso other tissues, like spleen nd liver, cn provide similr functionlity [80, 81] nd might replce the bone mrrow nichesinsitutions of stress [82]. In this context, it hs recently been shown tht lso sinusoidl endothelil cells in bone mrrow estblish n lterntive, so clled vsculr niche for HSCs [83]. Wheres in the osteoblst niches stem cells re primrily mintined in the quiescent stte, vsculr niches seem to be involved in the regultion of stem cell prolifertion, differentition nd mobiliztion. However, the mutul regultion between these different supportive environments isonlyinsufficiently understood. 15

26 2. Biologicl bckground: Stem cells nd linege specifiction Asurplusofcellsthtisnotnecessryforthemintennceofthestemcell pool undergoes differentition. These cells progressively lose their potentil to ct s stem cells, undergo mssive expnsion nd develop into mture cell types tht re finlly relesed into the peripherl blood. Specificlly, threedifferenttypes (lineges) of blood cells re ll derived from common clss of HSCs, nmely erythrocytes, leukocytes nd pltelets. Erythrocytes re responsible for the oxygen trnsport from the lungs to the different orgns nd tissues. This trnsport is fcilitted by the protein hemoglobin, which is uniquely present in erythrocytes nd the corresponding precursor cell stges. Furthermore, erythrocytes re chrcterized by the loss of their nucleus which hs been dischrged during the lte normoblst stge. In humns, erythrocytes circulte in the peripherl blood for bout 120 dys. Leukocytes re composed of mixture of different cell types, most of which re primrily involved in the immunorections of the orgnism. The mutul interction of these cells is importnt for n optiml immuno-defense, lthough the different leukocytes differ significntly in their ppernce nd function. It is generlly distinguished between grnulocytes (neutrophils, eosinophils, nd bsophils), lymphocytes nd monocytes / mcrophges. Leukocytes persist in the peripherl blood between few hours (neutrophils) up to months nd yers (lymphocytes). Thrombocytes, lsoknownspltelets,reresponsibleforblood cogultion nd wound closure. The verge life spn for thrombocytes is bout 10 dys. The intermedite developmentl stges leding to the production of the mture blood cells re often comprised in hierrchicl tree structure. Besides the finl, mture cell types mny precursor stges cn be identified bsed on morphology or the expression of chrcteristic surfce mrkers. The prticulr processes tht regulte the development of the distinct cell types re generlly referred to s linege specifiction. Since it is the focus of the thesis to provide principle understnding of linege specifiction, this subject is more extensivelydiscussed in the Section 2.3. In the light of the definition of stem cells provided in the previous section, HSCs re primry exmple to fit the stted criteri. For this system, trnsplnttion experiments hve been estblished s the most rigorous proof ofstemcellfunction since ll criteri need to be fulfilled in order to gurntee long-term reconstitution. In such experiments, donor-derived HSCs re trnsplnted in lethlly irrdited nimls tht do not hve functionl hemtopoiesis nymore. It hs been shown tht lredy one HSC is sufficient to reestblish complete hemtopoiesis to norml levels nd to rescue the niml [84]. However, the ppliction ofrepopultion experiments lso hs serious limittions. E.g. the process of irrdition cuses number of side effects tht re hrd to quntify. Furthermore, thereestblishment of hemtopoiesis requires the support of functioning micro-environment but lso the contribution of other blood cells to gurntee the niml s survivl briefly fter trnsplnttion. 16

27 2.3. Linege specifiction of hemtopoietic stem cells 2.3. Linege specifiction of hemtopoietic stem cells Besides the developmentl options of self-renewl, differentition, migrtion nd poptosis, stem cells nd their progenitors undergo decision process to select the type of functionl cells to which they contribute. The question, how stem cells specify this cell type, is long-stnding nd will be elucidted from conceptul perspective within this thesis. Throughout the thesis the term linege specifiction is used to chrcterize the sequence of decision steps tht finlly leds to linege commitment, mnifested by the cquisition of prticulr linege specific fetures. The term differentition refers to the ctul process of cquisition of these linege specific fetures nd does lso include the loss of self-renewl bility. Linege potentil describes the generl bility of stem or progenitor cell to produce certin number of different types of mture functionl cells. In contrst, the linege contribution of prticulr cell describes the cell types ctully produced in prticulr differentition process, nd my therefore comprise only prt of the cell s linege potentil Phenomenology The hemtopoietic system is commonly perceived s hierrchy with the stem cell t the origin giving rise to linege restricted progenitors nd finlly to terminlly differentited end cells [85, 86, 87, 88], see lso Figure 2.2. Different developmentl stges within in this tree-like differentition sequence hve been chrcterized s follows: The pool of multipotent HSCs consists of long-term reconstituting hemtopoietic stem cells (LT-HSCs) tht cn repopulte n lethlly irrdited niml nd estblish life-long supply of ll hemtopoietic lineges. Furthermore, the multipotent HSCs lso include the so clled short-term repopulting hemtopoietic stem cells (ST-HSCs) tht lso give rise to ll hemtopoietic lineges, but do so for only 8-10 weeks. It is commonly ssumed tht ST-HSCs re n intermedite cell stge between LT-HSCs nd the more linege restricted progenitors s they re the common myeloid progenitor (CMP) nd the common lymphoid progenitor (CLP). In further set of decisions CLPs giverisetothe different cells of the lymphtic lineges: B- nd T-lymphocytes nd nturl killer cells. In contrst, CMP normlly differentite to cells of the myeloidlineges, mong them grnulocytes, mcrophges, erythrocytes nd thrombocytes. The hemtopoietic system is ble to propgte chnges in the demnd of peripherl blood cells using feedbck mechnisms tht ct on erlier cell stges. Such regultions re fcilitted e.g. by the relese of cytokines ndchemokines[89,90]. By djustments of erly linege decisions nd incresed expnsion the system is ble to dptively respond to such chnging needs which re introduced e.g. by injuries, infections or high ltitudes. In series of experiments in the 1980s, Ogw nd coworkers [27, 28, 35] studied 17

28 2. Biologicl bckground: Stem cells nd linege specifiction Figure 2.2.: The hemtopoietic system. Different, prominent cell types of the hemtopoietic system re rrnged in clssicl hierrchicl ordering tht represents the mjor lines of development. Picture tken from [91]. the linege specifiction potentil of hemtopoietic progenitor cells. In prticulr they used hemtopoietic, spleen-derived mouse cells [27] nd humn umbilicl cord blood cells [28] to exmine nd compre the developmentl fte of two dughter cells derived from one prent cell. From their results the uthors concluded tht committed cells re derived from multipotent progenitors through progressive restriction of linege potentil, in which the restriction in type nd number of lineges occurs in stochstic fshion. In their interprettion, which still holds tody, the contribution of lineges which is observed in the progeny of single differentiting cell cn only be predicted in sttisticl sense. The prticulr experiments will serve s primry reference to verify the proposed modeling pproch. The question remins, how the phenomenologicl view on linege specifiction cn be mpped on n pproprite moleculr bsis in which linege specifiction is interpreted s shift in gene expression ptterns nd correlted to epigenetic modifictions. 18

29 2.3. Linege specifiction of hemtopoietic stem cells Moleculr spects of linege specifiction Although mny detils on the moleculr mechnisms of linege specifiction re still unknown, it ppers tht certin moleculr processes fcilitte linege specifiction of multipotent progenitor cells to select nd to commit to one out of finite number of predefined lineges. Since linege committed, mture cells re chrcterized by discrete nd robust genetic progrms supporting the functionl nd morphologicl requirements, linege specifiction is the process of estblishing the prticulr cell type-specific gene expression pttern [92]. The processes involved do not necessrily ct on the trnscriptionl level lone but potentillyincludell kinds of moleculr regultions, e.g. post-trnscriptionl ndtrnsltionlmodifictions, phosphoryltions, signling pthwys nd epigenetic ltertions. Becuse of this complexity of possible interctions comprehensive, conceptul understnding of the nture of multipotency nd the dynmic processes tht initite nd regulte linege specifiction is still incomplete. Priming. Although gret effort hs been mde to obtin chrcteristic trnscriptionl profiles of vrious stem cells [57, 58, 93]), no consensus of unique, stble stem cell stte could be reched. It becomes incresingly evident tht multipotency, s one of the defining chrcteristics of stem cells, is dynmiclly stbilized feture ssocited with the simultneous coexpression of linege specific, potentilly ntgonistic genes [29, 31, 93, 43, 59]. Such promiscuous coexpression of genes specific for lterntive lineges ftes, commonly referred to s priming, hsbeenreportedformultipotentcelltypesofthehemtopoietic system [30, 32]. It cn be envisioned s the moleculr representtion of the potentil for different developmentl options which disppers in the course of differentition when certin linege restricted genes re up-regulted while others re down-regulted. A sketch is provided in Figure 2.3. Regultion of linege specifiction. The regultion of specifiction is ultimtely required to respond to chnging demnds of mture blood cells. Such control mechnisms re commonly fcilitted by the ction of regultory molecules, such s cytokines, chemokines nd growth fctors like erythropoietin or G-CSF [89, 90] tht medite chnging demnds nd skew the linege specifiction process. For the ction of such externl signls two generl modes of regultion re discussed [94, 95, 87, 96]: In the instructive mode the externl signls do directly impose their regultion on the trnscriptionl level by promoting or repressing certin gene ctivities vi signl trnsduction cscdes. This mens tht the cellintrinsic linege decision is skewed. In contrst, in the selective mode, the externl signls lck linege-determining cpcity nd the cells rndomly decide between preexisting developmentl ftes. This wy, the cell intrinsic decision is not skewed nd the externl signls exert their ction by promoting the survivl of lredy 19

30 2. Biologicl bckground: Stem cells nd linege specifiction differentited cells stem cells Figure 2.3.: Priming. The priming behvior of the HSCs is depicted by the equl sized symbols indicting linege specific gene expression ptterns. In the course of differentition one linege specific progrm is finlly up-regulted while others re down-regulted. This chnge in the expression ptterns is encoded in the symbol sizes nd the corresponding color-coding of the cell membrne. committed cells. In prticulr it ppers tht certin cytokines support the survivl of cells expressing subset of linege specific receptors while in the bsence of the cytokines the cells undergo cell deth. Using such regultion it is possible to skew n initilly blnced cell popultion to preferentilly contribute to some but not ll vilble lineges. These modes of linege specifiction re briefly outlined in Figure 2.4 in which the linege decision process is seprted from the survivl under pproprite conditions. The ltter, selective mode of linege specifiction is often referred to s stochstic (or intrinsic) s compred to deterministic (or extrinsic) which is lso used s n lterntive description for the instructive mode. However, this terminology is confusing nd not suited to distinguish properly between these modes of linege specifiction. Perceiving the cell-intrinsic regultion in theinstructive mode s shiftofprobbilities(rtherthnthedeterministicon-off mechnism) for the different vilble cell ftes, the ctul cell fte decisions cn still be stochstic. Therefore, the more discrimintive terms instructive (regulted cell-intrinsic decision) nd selective (unregulted cell-intrinsic decision nd selective survivl) will be used throughout this thesis. 20

31 2.3. Linege specifiction of hemtopoietic stem cells A instructive decision survivl B selective decision survivl Figure 2.4.: Modes of linege specifiction. (A). In the instructive mode of linege specifiction the linege decision is intrinsiclly skewed to commit to one cell type insted of nother (indicted by the block). Selective survivl plys minor role. (B). In the selective mode the intrinsic linege decision is rther blnced giving rise to cells of different lineges. However, externl signls selectively promote the survivl of some lineges wheres others re discrded (indicted by the block). Temporl extension. The process of linege specifiction is not relized llof- sudden but involves temporl extension in which the cells pss through severl intermedite stges (see Figure 2.5). On the moleculr level, this refers to the time which is necessry to remodel the genetic expression ptternincluding the corresponding chnges on the epigenetic level. Furthermore, the expression pttern needs to be stbilized by the ctivtion of down-strem trget genes nd the subsequent chnges in cellulr morphology. In this concept, in which linege specifiction is understood stemporlly extended sequence of moleculr ltertions, it is immeditely evident tht n understnding of the underlying process requires the mesurement of time courses of the development. Such time structured experiments tht nlyze the phenotypicl chnges of cell cultures re rther well estblished [39, 97], lthough homogeneous cell popultions re still difficult to chieve. The vilbility of high-throughput methods llows to extend these pproches towrds the moleculr level [40, 98]. Nevertheless, these experiments suffer from structurl insufficiency of stem cell 21

32 2. Biologicl bckground: Stem cells nd linege specifiction stem cells differentited cells time Figure 2.5.: Temporl extension. Linege specifiction is described s temporlly extended process in which cell trnsits through different intermedite steps. Strting from primed stem cells the up-regultion of linege specific gene expression ptterns involves different stges of remodeling, indicted by the chnging sizes of the colored symbols. cultures since they re bsed on cell popultions rther then onindividulcells. Given the inherent heterogeneity of such cultures the experimentl findings re lwys verges of distinct cells t potentilly different developmentl stges nd cn hrdly be ttributed to prticulr cell. However, for the exmple of the PU.1-GATA-1 interction on the level of common myeloid progenitors (CMP), the high-throughput dt hs been used to nlyze the dynmics of the moleculr switch in time dependent mnner [92]. Key regultors nd switches. It could be shown successfully tht number of trnscription fctors re ctively involved in the process of linege specifiction [43, 99, 100, 101]. Although comprehensive understnding of theirinterctions is still missing, it hs been proposed tht such key regultors ct on prticulr switch points of the developmentl sequence by ctivtion ofcertinlinege specific progrm t the cost of n lterntive progrm [64]. Figure 2.6 provides sketch illustrting the typicl cross-ntgonism between two generic trnscription fctors. As prominent exmple, it hs been shown on the level of common myeloid progenitors (CMP) tht the overexpression of trnscription fctor GATA-1 cn induce differentition towrds erythroid/megkryocyte development s opposed to myeloid lineges [102]. A similr mechnism is know for trnscription fctor PU.1 lthough in the opposite direction [103]. Such fte switch between two lterntive linege-specific progrms cn be chieved if the key regultor for one linege progrm hs direct negtive feedbck on the competing linege progrms. In the cse of trnscription fctors PU.1 nd GATA-1 it could be shown tht besides promoting their own progrm (utoregultion) the trnscription fctors 22

33 2.3. Linege specifiction of hemtopoietic stem cells promotor gene A A B gene B promotor Figure 2.6.: Key regultors. The sketch illustrtes the cross-ntgonism between two generic trnscription fctors, termed A nd B, tht re key regultors for the development of the blue nd green linege, respectively. Such switch like behvior is fcilitted by the bility of A to suppress trnscription of B, nd vice vers. negtively regulte their mutul expression [104, 105, 106, 107],thussuppressing the competition counterprt. For the prticulr cse of the PU.1-GATA-1 interction, but lso in the more generl cse, it hd been demonstrted by number of theoreticl pproches tht such n ntgonistic ction is sufficient to induce switch-like behvior [92, 108, 109, 110, 111] Reversibility of linege decisions Within the clssicl prdigm of hierrchicl development fromstemcelltowrds differentited cell types, linege specifiction is commonly perceivedsseriesof irreversible fte decisions. This implies tht once decision is mde, cell is committed to the prticulr linege nd cnnot lter its fte [112]. However, this restrictive view on linege specifiction hs been seriously chllenged by number of experimentl [22, 41, 42] s well s conceptul works [113, 114]. For the exmple of differentited B cells it hs been reported tht enforcedexpression of C/EBPα nd C/EBPβ leds to their rpid nd efficient reprogrmming into mcrophges [115]. Similrly, there is evidence tht conversion between erly committed erythroid nd myeloid cells is possible if the culture conditions re chnged respectively [116]. Also on the conceptul level is hs been rgued tht mechnismoflinegespecifiction,whichincludesthepotentil for reversible ctions, is much more flexible in response to different environmentl signls [113]. With respect to linege decisions the term reversibility is commonly used in 23

34 2. Biologicl bckground: Stem cells nd linege specifiction stem cells differentited cells Figure 2.7.: Reversibility. In contrst to the solid rrows indicting mjor developmentl pthwys, the concept of reversibility llows for the existence of lterntive pthwys. The dshed rrows illustrte the concept of fte reversibility. Such reversion from one linege into nother might by rre event under physiologicl conditions but cn be chieved by trgeted overexpression of certin genes. The sme pplies to the dsh-dotted rrow indicting developmentl reversibility in which the cell is shifted to less committed stte. two, slightly different menings: First, reversibility describes the reversion of cell ftes s it is outlined for the bove exmples: cells cn be mnipulted to revert their fte to different cell type s the one they re originlly committed to. This phenomen is sometimes lso referred to s trns-differentition. In reltedcontextthetermplsticity hs been introduced to chrcterize the potentil of (e.g. hemtopoietic) stem cell to revert its fte towrdsnother(e.g. non-hemtopoietic) linege. In its second, more conceptul mening,reversibility refers to the developmentl (nd moleculr) reversion of decisionprocessby moving the cell bckwrds to n erlier developmentl stge. This reversion might include the recquisition of stem cell properties such sself-renewlbility nd multi-linege potentil. Prominent exmple of such behvior re found in Drosophil melnogster [117, 118] nd re lso proposed for thehemtopoietic system [46, 119]. Such behvior is sometimes referred to s de-differentition. The different spects of reversible linege decisions re visulized in Figure 2.7. However, it remins illusive whether cler distinction between these two spects is necessry nd instructive. Both, trns- nd de-differentition chrcterize behvior tht is contrry to the mjor developmentl pthwys. The physiologicl nd functionl importnce of such reversible developments remins subject to 24

35 2.4. Anlysis of single cell developments further experimentl nd theoreticl reserch Heterogeneity nd linege bis There is incresing evidence tht HSCs re n intrinsiclly heterogeneous popultion, not only with respect to their repopultion bility [45, 120, 121, 122], their cell cycle ctivity [66, 67] or their expression of certin surfce mrkers [123], but lso with respect to their linege contribution. Using single cell trnsplnttion experiments Dykstr nd collegues demonstrted tht individul HSCs showed different contributions to the popultions of B-, T- nd myeloid cells fter reestblishment of hemtopoiesis in irrdited hosts [45]. In prticulr, the uthors defined four distinct types clssified ccording to their contribution to either myeloid or lymphoid cells. Two of these cell types with significntly highercontribution to the myeloid lineges showed incresed repopultion potentil. Upon trnsplnttion of bone mrrow from the corresponding primry recipients in secondry nd tertiry hosts the pttern of linege contribution ws lrgely reproduced, suggesting tht the so clled linege bis is stbilized by epigenetic mechnisms. These results re in generl greement with erlier reports bout the stble inheritnce of the linege bis nd higher repopultion efficiency for the myeloid-bised stem cells [44]. Figure 2.8 illustrtes the ide of linege bised, heterogenous stem cell popultion. However, Dykstr nd collegues [45] lso report tht in the course of trnsplnttions slow conversion of the subpopultions towrds highercontribution of lymphoid cells nd decresing repopultion potentil hs beenobserved. Inthis context, it is less obvious whether clssifiction of defined number of subsets is helpful for the understnding of the popultion inherent heterogeneity or whether continuousspectrumdoesbetterreflecttheunderlyingregultion Anlysis of single cell developments The direct experimentl chrcteriztion of linege specifiction in HSCs poses numberoftechnicldifficulties. Mostchllengingisthenlysis of the development of individul stem cell in vivo. Only in the cse of clonl repopultion ssys or by the use of retrovirl mrkers, the linege contribution of single cells is ccessible over time. However, the loction of the cells in the bone mrrow nd their ctivtion ptterns re subject to extensive reserch [71]. Alterntively, mny experiments chrcterizing the nture of the linege specifiction process in HSCs hve been performed in culture systems. As outlined in the previous section, these experiments re mostly designed tocpturetheoverll linege contribution of certin initil cell popultion without pying much ttention to the temporl evolution nd chronology of cellulr development s it occurs within single cell. However, it is precisely the development of ech individul 25

36 2. Biologicl bckground: Stem cells nd linege specifiction linege bis stem cells differentited cells Figure 2.8.: Heterogeneous linege contributions. Stem cell popultions (shown on top) contin mixture of cells with vrying potentil to contribute to one or the other mture cell types. Such linege bised cells primrily give rise to one prticulr cell type (solid rrows) nd yield only minor contributions to other cell types (dshed rrows). Whether there is slow flux between these linege bised sttes (dotted rrows) is still controversil. cell nd its progeny tht represents possible reliztion of the developmentl sequence nd retins much of the necessry informtion: on the correltions between differentition nd cell cycle regultion, on the timing of linege specifiction processes nd cell deth events s well s on the role of symmetric developments [124, 125]. In this respect, it is the informtion bout ech cell s identity tht llows to put the vilble dt in its divisionl context. Figure 2.9 outlines the dilemm. It is here tht the digitl revolution in microscopy s well s theincresing memory cpcity of computer systems opens new dimension for theppliction of time lpse video microscopy for the nlysis of cell cultures. Such high resolution technologies fcilitte the trcing of single cell, comprising ll its progeny over extended time periods up to severl dys. This includes the temporl nlysis of cell specific prmeters like morphology, cell cycle time, motility or the occurrence of cell deth within the popultion context. Time lpse video monitoring with single cell trcking hs been pplied to cultures of hemtopoietic [124, 126, 127] s well s neurl [128], muscle [129], nd embryonic stem cells [130]. In recent study it could be shown tht the identifiction of ptterns in the in vitro cell cycle time distribution proved useful for the enrichment of cells with higher repopultion potentil in vivo [126]. Continuing these ides, the fluo- 26

37 2.4. Anlysis of single cell developments A time t B C Figure 2.9.: Single cell development. (A). Lyout of clssicl cell culture experiment for cell fte nlysis in which popultion of undifferentited cells (grey) develops into popultions of cells with contributions of different lineges (blue nd green). However, there is n infinite number of possibilities giving rise to this outcome. Two potentil reliztions re shown in (B) nd (C) with different levels of division, cell deth nd linege potentil of the originlly undifferentited cells. rescence lbeling of mrker genes for differentition nd linege specifiction will soon llow better identifiction nd temporl determintion of centrl decision events in the developmentl sequence [131, 132]. All these different informtion on cellulr development, divisionl history, nd differentition cn be comprised into pedigree-like structure in which the founder cell represents the root nd the progeny is rrnged in the brnches. These pedigrees represent specil clss of nnotted trees nd re referred to s cellulr genelogies [125]. Anlyzing the time lpse video of cell culture llows the trcking of multitude of root cells. The resulting cellulr genelogies represent uniqueexmplesofthe developmentl sequence s they occur under the prticulr ssy conditions. Sttisticl nlysis of these cellulr genelogies cn revel typicl ptterns of cellulr development s they re imprinted in the topology. Although this novel technique is pushed by number of groups, there re no estblished mesures for nlyzing nd compring this prticulr type of dt. However, forml chrcteriztion of the topologies together with set of newly developed mesures is sufficient to extrct the footprints of potentil mechnisms of linege specifiction tht re imprinted in the cellulr genelogies. A more detiled ccount is provided in Chpters 6 nd 7. 27

38 2. Biologicl bckground: Stem cells nd linege specifiction 2.5. Experimentl techniques nd mesures Hemtopoietic stem cells re mong the best studied stem cell systems for which lrgebodyofexperimentlresultshsbeenccumultedover the lst decdes. There exists huge number of vilble ssys nd isoltion techniques to study the functionlity of these cells. Some of the techniques re briefly explined s they support the motivtion nd understnding of this thesis. Hemtopoietic stem cell ssys. As outlined in Section 2.1 the bility of stemcellpopultiontorepopultedepletednimlisstill the mjor functionl criteri of stem cell function. This is tested using the long-term repopulting bility (LTRA) ssy which evlutes the contribution ofdonorcellstoll hemtopoietic lineges fter 6 or more months [133]. Using this ssy it is possible to distinguish long-term repopulting stem cells from cells thtonlycontribute to hemtopoiesis for shorter time spn (short-term repopulting cells) which do not gurntee the extended survivl of the niml. Moreover, the ssy lso ccesses the contribution to the individul lineges nd is suited to detect linege bises induced by the donor cells [45]. Alterntive to the LTRA ssy number of in vitro ssys hve been developed to mesure the frequency of progenitors (colony-forming unit in culture; CFU-C), stem cells (long-term culture-inititing cell; LTC-IC), or both(cobblestonereforming cell ssy; CAFC) [134, 135]. Generlly, these ssys relesssuitedto determine the linege potentil of the cell types in question. Hemtopoietic stem cell mrkers. Especilly in the hemtopoietic system, in which prospective isoltion of stem cells bsed on their morphology or locliztion is not possible, lterntive methods for the purifiction re required. Most such techniques re bsed on flow-cytometry which llows to select cells bsed on the expression (or bsence) of set of cell surfce proteins. In order to quntify these expression levels, fluorescence tgged ntibodies re usedwhichbindtothe corresponding ntigens on the trget cells. The most common strtegy to enrich for HSCs is the selection of subpopultion of cells tht show no or very low expression for ny mrkers of mture cell types such s TER-119 (erythroid), B220 (B cells), Mc-1 (monocytes),gr-1 (grnulocytes), or CD3, CD4 nd CD8 (T cells) but high or very high expression of Sc-1 nd c-kit [136, 70]. Such cells re termed LSK (lin, Sc 1 high, c Kit high ) cells. However, the purity of long-term repopulting HSCs cn be enhnced using dditionl signls of the SLAM 1 mrker fmily [82]. HSCs with high repopultion potentil were reported to be positive for the SLAM mrkers CD150 but negtive 1 Signling Lymphocyte Activtion Molecule 28

39 2.5. Experimentl techniques nd mesures for CD48, CD244, nd CD41. Combining these mrkers together with the LSK mrkers up to 50 % of the isolted cells qulified for single cell repopultion[82]. Alterntively, dye efflux properties re regulrly used to select for cell popultions contining incresed frctions of HSCs. For exmple, the exclusion of efflux of DNA binding dye Hoechst (commonly referred to s side popultion) proved useful to further enhnce the purity of LSK popultions [137, 70]. In the humn sitution, HSCs hve been purified on the bsis of the expression of cell surfce mrkers such s CD34 nd CD133 nd the bsence of glycoprotein CD38 [138]. However, in the cse of CD34 expression it could be demonstrted tht the expression levels depend on the cell s ctivtion stte nd re subject to reversible chnges [22, 23, 139]. Although the outlined purifiction protocols re indispensble tool to enrich for HSCs there re lso number of structurl deficits connected to these methods. First, for mny of the used mrkers it is not yet cler how their expression is functionlly correlted to the stem cell function [60, 61]. Second, there is considerble level of heterogeneity inherent to the hemtopoietic system [140]. It might even be the cse tht fluctutions in the expression of certin mrkers re ultimtely required for the function of HSCs nd might be reestblished fter purifiction procedure [61, 123]. Differentition ssys. Hemtopoietic stem nd progenitor cells re generlly cultured in either of two conditions: self-renewing or differentiting. In the first cse the culture conditions re optimized (using pproprite stroml cell lines, serum nd/or combintions of cytokines) to keep the cells in rtherundifferentited stte, possibly incresing their numbers without mjor contributions of differentiting cells. In the second cse, the culture conditions re tuned to yield potentillypureoutputofdifferentitedcellsofspecilcelltype. Typiclly, such conditions re supplemented with pproprite growth fctors nd cytokines (e.g. erythropoietin nd stem cell fctor for erythroid differentition [141, 142] or grnulocyte colony-stimulting fctor (G-CSF) nd grnulocyte-mcrophge colony-stimulting fctor (GM-CSF) for myeloid differentitions [143]). The differentition sttus of the cells is generlly ssessed usingmorphologicl chrcteristics (supported by the use of specific stining methods), or the detection of cell type specific surfce mrkers s there re TER-119 for erythroid cells, B220 for B cells, Mc-1 for monocytes, Gr-1 for grnulocytes, or CD3, CD4 nd CD8 for T cells. Single cell development. The development of single cells nd their contribution to different lineges is most commonly studied in single cell ssys [26]. After plting individul cells the composition of the resulting colonies is studied using bove mentioned methods. 29

40 2. Biologicl bckground: Stem cells nd linege specifiction The vilbility of stble trnsgene insertion into host genome llows for the irrevocble nd unique mrking of individul cells s the rndom integrtion of the trnsgene llows the detection of ll its descendnts. Bsed on this method the retrovirl gene mrking hs become n importnt tool for investigting the in vivo fte of different cell types, both in niml models nd in clinicl pplictions [144, 145, 146]. After trnsplnttion of n ppropritely treted HSC popultion the contribution of multiple cell clones to the different hemtopoietic cell lineges cn be studied over extended time periods. Alterntively, clonl informtion bout the development of individul cells cn be provided from continuous time-lpse monitoring of in vitro cell cultures [147]. In contrst to the clonl trcking using trnsgene integrtion, this method llows for the derivtion of complete pedigrees subtending from one initil cell. In combintion with the fluorescence lbeling of certin relevnt mrker genes for differentition these methods hold gret potentil to study the linege specifiction in its divisionl nd developmentl context. Moleculr methods in stem cell biology. Modern stem cell reserch benefits from the vilbility of biotechnologicl methods to study moleculr processes on mny different scles. Especilly the estblishment of the polymersechin rection (PCR) s stndrd technique to mplify single or few copies of piece of DNA or RNA cross severl orders of mgnitude hs gretly supported this development. Furthermore, the development of different typesofmicrorrys llows for thelrge scle interrogtion of moleculr content in cell popultions (e.g. for the detection of mrna trnscripts (DNA microrrys), the presence or bsence of proteins (protein microrry), or protein specific DNA binding sites (Chromtin immunoprecipittion on Chip; ChIP-on-chip)). Appliction of DNA microrry techniques in time structured experiments cn elucidted temporl chnges in the genetic expression profile nd relte it to phenotypicl nd functionl ltertions [40, 92, 98]. The vilbility of even more dvnced methods for the sequencing of pieces of mrna nd their simultneous quntifiction using high-throughput sequencing (lso termed pyrosequencing ) will drmticlly influence biologicl reserch in generl nd stem cell reserch in prticulr. However, mong the gretest chllenges with these high-throughput techniques is the sttisticl nlysis of the resulting dt, nd in prticulr their integrtion into n biologiclly meningful context. It is often the cse thtmongsetof identified components nd interctions just for minority of themtheirrolein relevntbiologiclprocessesislredyresolved. Forthereminingfindings comprehensive understnding of the underlying regultory principles is missing nd cn hrdly be predicted bsed on the vilble dt lone. 30

41 2.6. Technicl chllenges nd ethicl considertions 2.6. Technicl chllenges nd ethicl considertions Primry interest in stem cell reserch derived from the expecttion to gin insight into the orgniztionl principles of higher orgnisms. Beyond this cdemic interest it soon becme cler tht tissue resident stem cells hold gret promise for medicl pplictions s these cells re in principle ble to regenerte or replce disesed or ml-functioning tissue. As lredy illustrted in the introduction, direct trnsltion into medicl pplictions is still limited s mny types of tissue stem cells re rther difficult to isolte nd to expnd in vitro, remoreorless restricted to prticulr tissue type nd, in mny cses, hve limited cpcity to regenerte mjor prts of tissue or even whole orgn. In contrst, these limittions do not pply to embryonic stem cells.thesecells re derived from inner cell mss of the blstocyst nd re defined s cells tht cn beculturedin vitro for mny pssges nd retin the principle bility to contribute to ll three germ lyers. However, even the vilbility of embryonic stem cell cultures did not overcome fundmentl problem in regenertive therpies which is the immune-incomptibility between the llogenic donor tissue nd the host system, often resulting in trnsplnt rejection. In remrkble experiment in 1996, In Wilmut nd collegues demonstrted tht the trnsfer of the nucleus of n dult endothelil cell of sheep into enucleted oocyte (generlly referred to s somtic cell nucler trnsfer) wsin principle sufficient to derive developing blstocyst [148]. After implnttion of the resulting blstocyst in surrogte mother cloned niml (which in the first reported cse becme known s Dolly, the Sheep) ws estblished tht ws geneticlly identicl to the donor niml of the originl nucleus. This experiment proved tht, first, ll relevnt genetic informtion is retined even in differentited cell nd tht, second, there exist possibility to derive geneticlly identicl ( cloned ) embryonic tissues with the full developmentl potentil to generte cloned niml. Although the dption of the experimentl protocols to the humn sitution nd the derivtion of ptient specific humn embryonic stem cell lines is in principle possible these protocols involve number of steps tht re ethiclly controversil s there re the dontion nd utiliztion of humn oocytes, nd the mnipultion of cloned humn blstocysts. These techniques strongly interfere with severl spects touching the dignity of humn life, nd the public discussion within this re illustrtes tht there exists no generl consensus on whether such cells should be mnipulted in order to use them for the tretment of severe ndpotentilly lethl humn diseses. However, the efforts to derive humn ESC lines from cloned blstocysts declined rpidly s n lterntive method for the derivtion of geneticlly-customized stem cell lines becme vilble. In 2006 Kzutoshi Tkhshi nd ShinyYmnk proposed the reprogrmming of norml body cells into pluripotent, embryonic-like 31

42 2. Biologicl bckground: Stem cells nd linege specifiction stem cells by the use of retroviruses to trnsfect the cells with set of four criticl trnscription fctors [6]. These methods becme soon vilble for the humn sitution [7, 149] nd re now further refined to void the permnent integrtion of virl fctors nd to ensure long-term sfety of the reprogrmmed cells [150]. The vilbility of protocols for the derivtion of ptient specificinduced pluripotent stem (ips) cells overcomes two fundmentl problems in regenertive stem cell therpy: first, these protocols do not rely on the ethiclly questionble usge of oocytes nd the trnsient genertion of humn blstocytes nd,second,the resulting cells re geneticlly identicl to the somtic cell donor, thus voiding complictions from immune system rejection of the generted trnsplnt. Although these protocols do not yet exist for clinicl pplictions there is strong reserch interest in this field nd first results cn be expected in foreseeble future. It is the chllenge of the next decde to identify experimentl techniques to not only chieve the reprogrmming from the somtic to the pluripotent stte but to direct the differentition from the pluripotent stte towrds the desired tissue type tht is necessry for trnsplnttion. At this point it is not even cler whether complete reprogrmming to the pluripotent stte is ultimtelyneces- sry or whether somtic cell cn be directly reprogrmmed nd expnded into nother, desired type of tissue cell. A fundmentl understnding of the underlying processes on ll orgniztionl levels certinly requires the joint efforts of experimentl biologist, clinicins nd theoreticl scientists like. 32

43 3. Theoreticl bckground: Conceptul nd mthemticl models 3.1. Generl spects Models in the nturl sciences Models re generlly chrcterized s representtions of nturl object or process in which not ll ttributes of the originl re necessrily considered (reduction nd bstrction). Focusing on the im of model construction nd the benefit of its ppliction, certin spect re intentionlly neglected in order to pronounce the prticulrly relevnt fetures of the originl nd to llow the genertion of cceptbly ccurte solutions (prgmtism) [151]. In nturl sciences, theoreticl model is construct with set of vribles nd setoflogiclndquntittivereltionshipsbetweenthemtoenbleresoning bout theunderlyingprocesses within n idelized logiclfrmework. Such models re n importnt component of scientific theories nd cn either be qulittive (i.e. descriptive nd logicl representtions) or quntittive (i.e. mthemticl representtions). In contrst to qulittive models, quntittive models llow for n nlytic, numeric, or simultion nlysis [152]. Quntittive model pproches hve plyed n importnt role inmostnturl sciences with prticulr success in the field of physics. However, even there it took bout 300 yers from the erliest works of Glilei nd Kepler until revolutionry works by Mxwell, Plnck nd Einstein t the end of the 19th nd beginningof the 20th century tht finlly chnged the perception on theoreticl sciences. Since this time theoreticl physics hs estblished s n indispensble brnch of reserch tht ctively guides experimentl pproches in ll fields of physics. Asimilrinfluenceoftheoreticlreserchisstilllckingin biologicl sciences. This is lrgely due to the nture of the studied objects which re living entities. Such objects re difficult to define since they re themselves subject to multitude of extrinsic influences [153]. Moreover, the limited ccessibility nd the complexity of the constituting prts hve long hmpered rigorous chrcteriztion which is prerequisite for ny quntittive model construction. Due to the incresing vilbility of pproprite experimentl techniques on one hnd nd the computtionl resources on the other hnd, quntittive pproches renowginingmore nd more impct in the biologicl sciences. By reduction nd bstrction, such theoreticl models re indispensble tools to elucidte regulting principles nd therefore to design experimentl strtegies nd to verify results [154]. 33

44 3. Theoreticl bckground: Conceptul nd mthemticl models Quntittive models in stem cell biology Although the first demonstrtion of self-renewing popultion of hemtopoietic progenitors by Till nd McCulloch in the 1960s [48] ws ccompnied by mthemticl description of the dt [155], theoreticl pproches plyed minor role in stem cell biology for long time. However, there re number ofoutstnding modeling contributions with significnt impct on the reserch field s there re the works of Mckey nd Glss on the dynmicl behvior of hemtopoietic diseses [156, 157], the works of Wichmnn, Loeffler nd collegues on the regultion of grnulopoiesis nd erythropoiesis [158, 159, 160, 161, 162, 163] s well s on the orgniztion of intestinl nd epiderml stem cells [164, 165, 166], the works of Ogw nd coworkers on the stochsticity of cell fte decisions [167], the works of Abkowitz nd collegues on hemtopoietic stem cell regultion nd mlignncies [168, 169, 170, 171], the conceptul works on stem cell identity by Potten nd Loeffler [1] s well s their trnsformtion in comprehensive single-cellbsed modeling frmework for hemtopoietic stem cells by Roeder nd Loeffler [33]. The bove list is neither complete nor does it estblish vlution. However it demonstrtes tht theoreticl models in stem cell biology ddressdifferentbiologicl phenomen which re lso pproched on different levels of description. Wheres some models re bsed on verge responses of cell popultion rther thn on individul cells, others explicitly ccount for the vribility between individul cells by modeling cellulr interctions on the single-cell level. Inspired by the incresing knowledge on the moleculr orgniztion of stem cells,there is novel clss of models emerging tht ims on the understnding of moleculr regultion nd cell-intrinsic responses to externl stimuli within individul cells. However, these cell-intrinsic models hve to be coupled to the cellulr level to chieve n understnding of the tissue orgniztion. The different spects of modeling pproches in stem cell biology re subject of the subsequent Sections 3.2 nd 3.3. As outlined in the previous chpter, much of the common perception of stem cell orgniztion derives from the ide tht stem nd progenitor cells cn be clerly distinguished on the bsis of their functionl potentil, their surfce mrker expression or even their morphology. This view is internlized inthehierrchicl structuring of stem cell orgniztion s it is shown in Figure 2.2ndisfundmentlly bsed on the concept of distinct (stem) cell comprtments. This reflects the ide tht differentition of primitive stem cells is sequentil trnsition through sequence of developmentl sttes tht cn by chrcterized by comprtments with certinsetoffetures(e.g. expressionofcellsurfcemrkers, linege potentil) nd well-defined boundries. As the stem cells pss through these subsequent comprtments they progressively lose stem cell potentil, restrict their linege choices nd cquire linege specific fetures. 34

45 3.2. Models of stem cell self-renewl nd differentition However, functionl test, like the determintion of single cell slinegepo- tentil within certin ssy is inherently incomplete since it cnnot be exclude tht under different ssy conditions nother linege contribution would be observed. Experiments on the independent development of pired dughter cells showed tht cells immeditely seprted fter division do not necessrily undergo the sme developmentl processes nd contribute to identicl lineges [35, 28]. This imposes structurl dilemm, since the mesurement of certinfunction of cell does ultimtely lter the cell itself. This phenomen hs been described s the uncertinty principle of stem cell biology [46] nd cn equllybeppliedto experiments tht im to simultneously mesure self-renewl nd differentition cpbilities or the differentition potentil long multiple lineges. The comprtmentliztion of the hemtopoietic system is closely interrelted (but not identicl) to the ide tht the trnsition through the prticulr comprtments is lwys unidirectionl from the most primitive cell stges down to the committed progeny. However, it hs been shown tht the repopultion potentil nd the linege contribution of stem cells is correlted tothecellcycle[172], nd tht the expression of surfce mrkers like CD34 nd Sc-1 resubjectto reversible chnges [22, 123]. Such findings on reversibility swellstheinbility to prospectively isolte pure stem cell popultions [173] seriously chllenge this concept of strictly comprtmentlized stem cell hierrchy. This controversy led to the proposition of concept of stem cell orgniztion on the bsis of flexible nd self-orgnizing cellulr units (gents) which re not by definition restricted to unidirectionl flow through sequence of comprtments (see for exmple [1, 34, 46, 60, 113, 174, 175, 176]). Although such dptive systems proofed very robust in other fields of science (e.g. swrm intelligence, nt lgorithms, distributed computing), there is still level of reluctnce ginst such novel nd lterntive pproches in stem cell biology Models of stem cell self-renewl nd differentition It is long-stnding set of question on how the blnce between self-renewl nd differentition is mintined in the hemtopoietic but lso in other stem cells systems, how the stem cells mintin the bility to respond to chngingdemnds nd how mlignncies lter these orgniztionl properties. In simple words, it is sked which mechnisms ccount for the mintennce of stem cell popultion on one side nd on the other side provide enough mture cells for the support nd regenertion of the prticulr tissue. An overview over the min clsses of quntittive models in hemtopoiesis is provided below. 35

46 3. Theoreticl bckground: Conceptul nd mthemticl models stem cells differentiting cells division p differentition q Figure 3.1.: Comprtment model of hemtopoietic self-mintennce. A simple comprtment model ws proposed by Till nd McCulloch [155]. Cells in the stem cell comprtment (drk grey) re either trnsferred into the comprtment of differentiting cells (grey circles) with rte q or they undergo division with rte p producing two dughter stem cells. In the stble sitution the rtes for differentition nd division re equl p = q Comprtment models with fixed stem cell chrcteristics Entity-bsed models. Entity-bsed models of stem cell orgniztion emerged from the clssicl perception of stem cells s well-defined nd clerly distinguishble objects. These entities re defined by set of fixed developmentl options chrcterizing the trnsition between the comprtments. Such comprtments re commonly envisioned to contin certin cell popultions like stem cells, progenitors, or more mture cell types. The trnsition rules cn potentilly be influenced by extrinsic signls like feedbck regultion from mture cell stges using growth fctors or micro-environmentl regultions. A typicl exmple of this model clss is the mthemticl model tht ccompnied the first experimentl demonstrtion of the self-renewing bility of hemtopoietic progenitor cells by Till nd McCulloch in the 1960s [155]. This model ssumes tht within stem cell comprtment ech cell cn either divide symmetriclly (giving rise to two stem cells which corresponds to self-mintennce of the popultion) or differentite (Figure 3.1). These options re relized with fixed probbilities denoted s p nd q, respectively.evenwithoutthessumption of feedbck regultion or micro-environment interction, the uthors could explin the frequency distribution of spleen colonies (CFU-S colonies) in secondry recipients. Picking up on this ide of stochstic trnsitions between rther distinct cell popultions, in which probbility is ssigned to ech developmentl option, the mthemticl concept ws extended for the hemtopoietic system [177] nd for other tissues [166]. In simple, lbeit elegnt pproch, Abkowitz nd collegues used such n extended model to ccess the frequency nd repliction kinetics 36

47 3.2. Models of stem cell self-renewl nd differentition of hemtopoietic stem cells in vivo s well s the evolution of myeloprolifertive disorders [169, 170, 171]. Besides the developmentl options of symmetric division nd differentition the uthors lso ccounted for the process of poptosis. Popultion-bsed models. Assuming homogeneous stem cell popultions of sufficient size, entity-bsed systems cn be described eqully well by chnging to popultion-bsed pproches in which the individul stochstic decision is replced by verged, deterministic rte constnts. Feedbck regultionscnbe introduced in both scenrios by dynmic dption of the either the trnsition probbilities tht blnce self-renewl nd differentition in the stochstic (single-cell bsed) pproches or by the corresponding rte constntsinthedeterministic (popultion-bsed) pproches. Additionlly to the evlution of the stedy-stte sitution, such feedbck regultions llow the nlysis of the system response to vrious perturbtions, s they occur fter dmge or injury. Sophisticted exmples for these kind of models hven been developed by Mckey nd coworkers. Under the ssumptions of delyed feedbcks from lter cell stges on the hemtopoietic stem cell comprtment the uthors explined typicl oscilltion ptterns occurring in number of specific mlignncies of the hemtopoietic system [156, 157, 178, 179, 180]. Even more extensive re the multi-comprtment models of lter stges of hemtopoiesis by Loeffler nd collegues, s there re models on grnulopoiesis [159, 160, 181] nd erythropoiesis [161]. Symmetric nd symmetric divisions. Till nd collegues lredy recognized in 1964 tht the possibility of n symmetric division (one stem cell giving rise to on stem nd one differentited cell) cn be well integrted in their concept of seprting division nd differentition by ssuming tht symmetricdivision event is followed by the differentition of just one dughter cell (Figure 3.2). This view ws lso supported by single cell experiments using bcl-2 trnsfected FDCPmix cells [182] s well s by the conceptul works of Loeffler ndroeder[1,46,183]. In contrst, nd driven by the observtion of functionlly symmetric divisions in other stem cell system (e.g. in invertebrtes [184] or in other tissues like the nervous system [185] or the epidermis [186]), the concept of symmetric cell divisions is still strongly promoted in hemtopoiesis nd is present in mnydebtesbout orgniztionl principles [94, 46, 114]. On simplified level it is often ssumed tht only by mens of symmetric divisions the blnce between self-mintennce nd differentition cn be estblished. However, this blnce needstobemin- tined on the popultion level nd t the present stge there is no convincing evidence for functionlly symmetric division event in hemtopoiesis t the single cell level. Moreover, the ssumption of strictly symmetric divisions of HSCs re not sufficient to explin the observed dynmic response of the hemtopoietic system to injury or dmge s loss in stem cell number cnnot be compensted. 37

48 3. Theoreticl bckground: Conceptul nd mthemticl models A popultion level B cellulr level C cellulr level symmetric division symmetric division differentition Figure 3.2.: Symmetric nd symmetric divisions. (A). On the popultion level, the number of stem cells (drk grey) is mintined while t the sme time frction of differentiting cells (colored circles) is generted. (B). On the cellulr level this results cn be obtined by ssuming functionlly symmetric divisions of the stem cells in which one dughter cell remins stem cell wheres the other dughter cell enters into differentition. (C). Alterntively, the findings on the popultion level cn be obtined if the processes of division nd differentition re decoupled. Thus, ech stem cell division leds to the genertion of two closely similr dughter cells (symmetric division) of which some might undergo further differentition (colored rrows) Models of dptive nd self-orgnizing stem cell systems It hs become incresingly evident tht n entity-bsed view onstemcellsisnot pproprite to ccount for ll fcets of stemness including the degree of heterogeneity within stem cell popultions, the reversibility of cellulr developments nd the dptiveness to chnging demnds. Motivted by, but lso stimultingthese discussions, number of stem cell models hve been estblished tht represent stem cells s individul objects with inheritble nd dynmiclly regulted properties which only exhibit stem cell functionlity in the popultion context. Cellulr properties re continuously chnging under the influence of environmentl signls 38

49 3.2. Models of stem cell self-renewl nd differentition nd re not restricted by the boundries of n bstrct comprtmentliztion. For exmple, within such concept the repopultion bility of cell does not vnish t once when the cell trnsits from the stem cell comprtment to progenitor stge, but the the loss of function is grdul. This includes, thtinscenrio with mny competitor cells, prticulr cell might not contribute to long term repopultion, wheres in different sitution with few competitors it could do so. Stemness s continuum prmeter. The explicit conditioning on the micro-environment (either by locl interction rules or by globl informtion nd feedbck loops) llows n dptive control of the blnce between self-mintennce nd differentition, generlly referred to s self-orgniztion. Thefuturedevelopment of ech cell depends on its current stte nd on the stte of the surrounding environment nd cn only be predicted in probbilistic sense. These single cell bsed models re prticulrly suited to ccount for the heterogeneity in clonl development s it occurs in chimerism studies nd clonl trcking experiments (e.g. using retrovirl mrkers). Moreover, the single cell-bsed structure llows to study the consequences on the tissue level tht result from ofechcellnd cn lso evlute the impct of chnges of the locl interction rules on the tissue level. Building on the erly conceptul works by Potten nd Loeffler [1, 62] which plced stem cell properties in the popultion context, the ide of stemness s continuous property ws formlized by Loeffler nd Roeder [46]. Inspired by the specil role of the hemtopoietic niche for the mintennce of HSCs the model concept ssumes tht stem cell development is directly influenced by ech cell s locl micro-environment, or more generlly speking, by the signling context to which cellispresentlyexposedto.thissimplessumptionisoutlined in Figure 3.3 in which two bstrct cell properties (A nd B) re modulted in contrryfshion within two distinct signling contexts. Subsequently, mthemticl formliztion of this concept hs been developed by Roeder nd Loeffler [33] to construct singlecell-bsedmodelofhemtopoieticstemcellorgniztion in which the cellulr development is directly regulted by the cell s micro-environment. The ssumptions of reversible binding nd detchment from niche-like environment plce the cells under the governnce of two ntgonistic regimes which is sufficient to explin self-mintennce nd differentition of HSCs s self-orgnizing process. Since this model is used to ccommodte the linege specifiction dynmic developed within this thesis it is presented in more detil in Section3.4ttheend of this chpter. Another elegnt pproch to model stem cells s self-orgnizing, dptive systems hs been presented by Kirklnd [34]. This work demonstrtes tht stem cell orgniztion cn be sufficiently described in continuum spce explicitly excluding ny kind of comprtmentliztion in discrete subpopultions. In this concept 39

50 3. Theoreticl bckground: Conceptul nd mthemticl models Signl context I Property A Signl context II Property A Property B Property B Figure 3.3.: Influence of the signling context on cellulr development. Two bstrct cellulr properties (nmed A nd B) re under the governnce of two distinct signling contexts (nmed I nd II). The signling contexts, between which the cells cn ctively chnge, modulte the properties A nd B in contrry fshion. cells re defined by continuous vribles tht describe functionl nd phenotypic properties (such s repopultion potentil or multipotency). Bsed on this ide, cells cn hrdly be clssified s stem cells or non-stem cells but cn lso cquire possible sttes in-between. The vribles chnge ccording to set of probbility density functions which themselves depend on the current stte of the cell: cells with higher stemness cycle slower nd hve smller probbility for differentition s compred to cells with reduced stemness (comprefigure3.4). In this concept, self-renewl is no longer cellulr fetures but necessrily refers to cell popultion. These works hve recently been complemented by n pproch of Hoffmnn, Glle nd Loeffler to described popultion of stem nd progenitor cells s probbilistic process tht rises from cell prolifertion nd smll fluctutions in the stte of differentition [187]. These fluctutions re ssumed to reflect rndom trnsitions between different ctivtion ptterns of the underlyingregultory network nd the fluctution mplitudes re stte-dependent nd governed by the cells micro-environment. The uthors demonstrted tht such s system reproduces the blnce between mintennce of the stem cell stte nd terminl differentition. 40

51 3.2. Models of stem cell self-renewl nd differentition Figure 3.4.: Phse spce model of hemtopoiesis. Cells t the periphery (in the light ornge to yellow re e.g. cell ()) hve high probbility of moving out further towrds more mture stges (white) but low probbility for de-differentition towrds the center. In contrst, cells close to the center (red re, e.g. cell (c)) hve mximl stemness with slow cycling nd reduced probbility of moving towrds the terminl cell stges t the periphery. Cell (b) hs intermedite chrcteristics. Picture tken from [34] with kind permission from Mrk Kirklnd. Stem cells s dptive gents. Aformlfoundtionfortheconceptofperceiving cells s rective gents, which underlies ll the bove mentioned models, ws recently provided by Theise nd d Inverno [174]. The uthors rgue tht criticl phenomen of the system only emerge if sufficient number of rective gents re present. Moreover, self-orgniztion of complex dptive system requires interctions between the gents s well s certin degree of non-determinism. The uthors demonstrte tht the perception of stem cells s rective gents is possible tool to relte the phenomen on the single cell level totheresultingpopultion dynmics of stem cells. In this sense the chrcteristics defining stemness on the popultion level cn possibly be trnslted to set of rules on the single cell level. 41

52 3. Theoreticl bckground: Conceptul nd mthemticl models 3.3. Conceptul pproches on linege specifiction The mechnisms tht regulte the mintennce of multipotency re closely relted to the more generl spects of self-mintennce of stem cell popultion s outlined bove. However, lso in historicl context, the conceptul pproches towrds linege specifiction hve been discussed rther isolted from the question of stem cell mintennce. Therefore, the following generl overview bout concepts of linege specifiction nd their mthemticl implementtions is completed by brief discussion on how these models integrte with the conceptul ides bout stem cell self-mintennce. On rther simplistic level it is pprent tht the trnsition from multipotent cell stge towrds functionlly fixed cell type is ultimtely coupled to decision process which fvors one linege t the expense of the others. Thequestionremins how this process of linege specifiction is orgnized on the moleculr level nd how it cn be influenced by externl queues. Furthermore, it is lsonotclerhow much flexibility is ssocited with the processes of linege decisions. This in turn, refers bck to the discussion bout reversibility of generl stemcellchrcteristics in Section 2.1 s well s in the bove sections The concept of developmentl lndscpes Due to the complexity of intrcellulr regultion in linege specifictionthenumber of nlyticl pproches is limited. However, it is long recognized tht processes of linege specifiction in dult stem cell systems hve close counterprt in embryology where zygote gives rise to complete orgnisms composed of multitude of different tissues. In 1956, Conrd Wddington pictured this decision sequence by bll rolling down n incline with different brnching ridges nd vlleys [188, 189] (Figure 3.5). Wheres the vlleys correspond to the different developmentl options the ridges represent the distinctions between the tissue types. This net visuliztion of the process of linege specifiction in development received comebck in the lst yers [190] nd is now commonly used especilly in the discussions bout reprogrmming nd induced pluripotency [191, 192, 193]. Although the building principles of linege specifiction process re lredy well cptured by this erly visuliztion of developmentl lndscpe,the picture deserves criticl interprettion nd discussion. Strting from the principle ssumption tht the phenotype of cell is the direct result of the ctivity of the cell s genes nd gene products it follows tht linege specifiction (i.e. thechngein the cell s phenotype) is ultimtely linked to chnge in the underlying moleculr expression pttern. The question remins, which moleculr components interct with ech other, how these interctions re chrcterized nd how robust nd self-stbilizing expression pttern of these components ppers. Alrgernumberoftheoreticlworksonthedynmicsofsuchlrge intercting 42

53 3.3. Conceptul pproches on linege specifiction multipotent (stem) cell differentited cell linege A linege B linege C linege D Figure 3.5.: Linege specifiction in the concept of stte spce. The developmentl lndscpe s suggested by Wddington [188, 189] provides the bckground to understnd linege specifiction s decision process in high dimensionl lndscpe tht rises s the consequence of complex intrcellulr interction network. A possible development is shown by the red rrows, lterntive options re indicted by the dshed rrows. Figure modified from [189]. systems re in the focus of current reserch for the conceptul understnding of linege specifiction. It is lredy evident tht the vlleys ndridgesproposedby Wddington [188] (compre Figure 3.5) do not correspond to physicl structures or potentil energy lndscpes s they re known from physics but rther represent unstble nd stble sttes of the cell s underlying complex interction network [190, 194]. Such lndscpes describing the probbility for finding cell in certin stte cn lredy be computed for smller systems [92, 195] nd provide very helpful nd intuitive interprettions of the underlying network dynmics The concept of stte spce It should be pointed out explicitly tht the network dynmics (i.e. chngesingene expression nd the existence of stedy sttes) re determined by the prticulr rrngement nd strength of the network interctions. Assume for exmple tht 43

54 3. Theoreticl bckground: Conceptul nd mthemticl models gene A represses gene B nd tht genes C nd D re mutul ctivtors. Given tht these interctions re fixed bsed on the promoter structure of the genes, only certin expression ptterns re possible while others re not. For exmple, A nd Bcnnotbothbectivtedsimultneouslyifoneinhibitstheother;conversely, CndDmustbothturnoniftheyremutulctivtors.Interctions like these limit the number of self-dpting expression sttes nd determine how they evolve over time. Given certin stimulus the internl stte of cell might trnsiently shift through vrious intermedite stges before it finlly stbilizes in one of the self-dpting expression sttes [196]. In more forml description, every cellulr component (gene trnscripts,proteins, soluble fctors, etc.) within certin cell cn be represented s dimension in high-dimensionl stte spce. Insuchsttespceechcellcnbeidentified by vector S = {S 1,S 2,...,S n } in which ech component S i represents the concentrtion of prticulr moleculr component X i. Given the generl consensus tht the phenotypic ppernce of cell is the result of the moleculr interctions between ll the genes, their trnscripts, proteins, signling pthwys nd other intrcellulr components, this lso implies tht the dimensions of the stte spce re not independent of ech other. Such complex, high-dimensionl system of interctions is most conveniently represented by complex network in which the nodes correspond to the different moleculr components X i wheres the edges chrcterize their mutul interctions x ij.itisnowthesupportivendrepressive nture of these mutul interctions x ij leding to the emergence of ptterns in which certin components X i re expressed while others re silenced. The bility to mintin such n internl equilibrium is termed homeostsis wheres the stbilized, self-dpting ptterns re referred to s ttrctors of the network. On the phenotypic level such stble ttrctor cn be ssocited with certin cell type (e.g. stem cells, mture cell types) being chrcterized by certinchrcteristic expression of moleculr components nd fulfilling prticulr functionl tsks [197, 198]. In the bove interprettion, the picture by Wddington is representtion of the intrcellulr ttrctor lndscpe nd the developmentl options between them. However, there is centrl, lthough fundmentl question which is not cptured by the sketch: Is this ttrctor lndscpe fixed or is it chnging in the course of differentition? In terms of the stte spce formultion the cell s intrinsic stte is chrcterized by the vector of concentrtions S i for ech of the intrcellulr components. However, it is the the mtrix of ll potentil interctions x ij tht ctully shpes the ttrctor lndscpe nd tht determines howthecellsttes i develops within the stte spce. As the concept of the developmentl lndscpe is simplifiction of highly complex process, there is no unique nswer on whether this lndscpe is constnt in time or not. In fct, the nswerdependson the ssumptions nd interprettions mde for the underlying moleculrnetwork. Two contrsting perspectives re outlined below: 44

55 3.3. Conceptul pproches on linege specifiction The locl view. In the locl view the network contins only limited number of importnt moleculr components for which the dynmic behvior is subject to quntittive nlysis. The concentrtions ofothercomponents tht re constnt over time or tht only chnge on long time scles re not explicitly described s nodes of the network but re represented s (constnt) prmeters. However, such prmeters chrcterize the nture nd intensity of the interction between two or more network components. As n exmple one might think of trnscription rtes tht cn be described s functions of DNA methyltion ptterns. If such ptterns chnge on long time scleslso the depending trnscription rtes chnge slowly over time. As consequence of this interprettion quntittive (nd qulittive) chnges of the network interction ultimtely lter the network dynmics nd potentilly modify the ttrctor lndscpe. As for the exmple of bistble switches, which is illustrted in more detil below, it is the modifiction of bifurction prmeter, commonly generlized trnscription rte, which moves the system from stte with just one ttrctor towrds stte with multiple such ttrctors [110, 108]. Furthermore, it could be shown by studying boolen dynmics on lrger networks tht modifictions of the interction rules cn (lthough they do not necessrily hve to) led to drmtic effects on the ttrctor lndscpe [199]. On the bsis of these findings, the processes of differentition nd linege specifiction, which re evidently coupled to specific epigenetic chnges nd re closely regulted from externl signls, cn be interpreted s ltertions of the developmentl lndscpe. The globl view. In contrst to the locl view the globl view represents the concentrtions of ech nd every relevnt moleculr component (chromosomes nd genes, trnscripts, proteins, receptors etc.) within the underlying network structure. In this frmework ll the prmeters tht influencethe system behvior in the locl view re internlized s dditionl nodes of the network grph. In principle this pproch cn be pplied to ll externl influences s well (like concentrtions of externl cytokines nd nutrition, temperture etc.) leding to significntly incresed dimension of the stte spce vector S. It is the ide of the globl view tht interctions between ny ofthenetwork components re solely chrcterized by physicl nd chemicl properties nd do not involve ny temporl dependence. As ll externl influences nd chnges tht occur even on slow time scles (e.g. epigenetic remodeling) re lredy internlized within the network structure, theinterction rtes represent bsolute nd conserved properties. This, in turn,ledsto fixed developmentl lndscpe in which ll possible ttrctors re lredy 45

56 3. Theoreticl bckground: Conceptul nd mthemticl models A developmentl lndscpe B locl view C globl view Figure 3.6.: Interprettions of the developmentl lndscpe. The developmentl lndscpe in (A) re interpreted in the locl view (B) nd in the globl view (C). For three different time points possible, two-dimensionl lndscpe model for the stte spce is provided. The ctul cell stte is represented by the red dot. represented. However, s the number of intercting components is lrge, the resulting lndscpe is diverse nd the ttrctors re possibly scttered over the whole stte spce. This view closely resembles the rigorous definition of the cellulr stte spce first formulted by Kuffmn [197, 200]. Coming bck to the developmentl lndscpe s it hs been proposed by Wddington, this picture cn be interpreted in two different wys, outlined in Figure 3.6. In the locl view the ttrctor lndscpe chnges s the interction prmeters re functions of the time of differentition (depicted s sequence of pictures in Figure 3.6(B)). However, it is modultion of the lndscpe which drives the cell stte (depicted in red) into nother (evolving) ttrctor while previous options vnish. In this interprettion, the developmentl lndscpe shown in Figure 3.6(A) hs to be interpreted s time-ordered sequence of snpshots rther thn fixedlndscpe. In contrst, in the globl view the lndscpe remins fixed (Figure 3.6(C)) nd only the trjectory of the cell in the simplified, two-dimensionl stte spce is functionoftime. Inthissense,thereiscoexistenceofmultiple ttrctors corresponding to the multipotent nd the subsequently restricted developmentl 46

57 3.3. Conceptul pproches on linege specifiction sttes, nd differentition is illustrted s trnsition from one ttrctor towrds the next ttrctor potentilly involving the decision between more thn one option. It should be clerly stted tht the low-dimensionl representtion in Figure 3.6(C) is insufficient to cptures the complex, high-dimensionl stte spce in the globl view but it illustrtes the coexistence of severl locl ttrctors in sttic lndscpe. Tking together it needs to be emphsized tht the two different views on developmentl lndscpes re not mutully exclusive. In fct, the loclviewpperss low-dimensionlprojectionofthegloblview. Thereinsome dimensions of the globl view (i.e. concentrtions of certin moleculr components) re collpsed into interction prmeters of the network such s trnscription nd inhibition rtes. The preference for one or the other view should depend on the prticulr problem in question Fluctutions nd robustness Even within stble ttrctor of the stte spce the concentrtions of the intrcellulr components S i might fluctute round the optiml stte. Such fluctutions occur nturlly nd re the results of smll copy numbers, degrdtion nd diffusion processes within the cells (intrinsic noise) or sptil rrngements nd influences of the locl micro-environment (extrinsic noise) [201, 202, 203]. Noise effects cn be further enhnced in non-liner systems [204]. However one needs to distinguish whether the shpe of the ttrctor nd the noise mplitude re suited to induce chnge of the ttrctor stte or not. Generlly, smll fluctutions do in most cses not led to chnge of vilble ttrctors nd thus do not significntly chnge the overll expression pttern nd the cells phenotype [205]. This feture is commonly referred tosrobustness nd is illustrted by the width of the ttrctors in Figure 3.6. In contrst, nd most likely induced by extrinsic effects, fluctutions of sufficient mplitude cn lso contribute to phenotypic vribility. In fctnoiseinduced fluctutions re possible stimulus to induce chnges of the cell stte nd to shift the cell into different ttrctor (i.e. into nother phenotype) [206, 207, 208, 209]. In the concept of developmentl lndscpes s it is illustrted in Figure 3.5, the fluctutions do in principle enble the cells to move from one vlley (i.e. ttrctor) into seprte vlley. The probbility for such stte chnges depends predominntly on the noise mplitude nd on the loction of thelterntive ttrctor. As outlined bove, in the globl view the picture of low-dimensionl developmentl lndscpe is oversimplifying s the lterntive ttrctors might be distnt nd seprted through rugged developmentl lndscpe. In the locl view this trnsltes into the question of whether certin lterntive ttrctor coexists for given prmeter configurtion or whether it needs to be recreted by chnging prmeter configurtion e.g. encoding epigenetic remodeling. 47

58 3. Theoreticl bckground: Conceptul nd mthemticl models Reduction of complexity The complexity of the stte spce representtion of cell including the chrcteriztion of ll the mutul interctions between the cellulr components mkes comprehensivepprochtothecellintrinsicdynmicintheglobl view numericlly very chllenging, in fct not fesible t the moment. However, it is not just the fesibility, but lso the vilbility of the prticulr dt which limits globl pproch. Although the vilbility of high-throughput mesures like mrna-microrrys llow to simultneously determine the expression of thousnds of genes in cell popultion, these methods re rrely dequte to chrcterize the complex interctions between them. In the context of the cell s stte spce, the current stte S i cn be roughly determined by these methods but the interctions x ij remin unknown. Consequently dynmic picture of the cells behvior in globl stte spce cn not be obtined. In order to reduce this level of complexity for descriptive pproches, the whole phenomen of intrcellulr regultion nd linege specifiction is more successfully ddressed in the locl view. Here, one my roughly distinguish between two principle pproches: phenomenologicl pproch nd functionl pproch. Figure 3.7 outlines these principle perspectives. Wheres the cell ontopisdepictedwith different sets of competing nd potentilly intercting genes nd gene products s well s their mutul interctions (globl view), the snpshots below refer to the low-dimensionl projections (locl view). The phenomenologicl pproch summrizes the complex regultions within coregulted gene sets into different mjor components nd studies the interctions between them. Although this pproch misses the moleculr detils of the interctions within the components, it is sufficient to ddress the generl principles of developmentl phenomen like linege specifiction nd the temporl ordering of events. In contrst, the functionl pproch focuses on the interctions between certin key regultors, for which detils of the moleculr regultion re vilble. Although this process cn elucidte the role of moleculr switches for certin intrcellulr decisions, it cptures just brief sequence out of the complex nd temporlly extended differentition dynmic nd fils to embed these ctions into greter context. For both the phenomenologicl nd the functionl pproch brief overview bout selected models is provided below Phenomenologicl models of linege specifiction Driven by the experimentl findings on the seprte differentition of pired progenitors using HSC [35, 27] Ogw nd Mosmnn developed n erly, mechnistic pproch to describe linege specifiction [167]. From the observtion tht the dughter cells gve rise to different colonies with vrying contributions of hemtopoietic lineges, the uthors concluded tht the linege potentil is pro- 48

59 3.3. Conceptul pproches on linege specifiction globl view locl view phenomenologicl pproch functionl pproch Figure 3.7.: Levels of description. The cell on top reflects the entire stte spce of cell in the globl view (grey shded re) with multitude of intercting moleculr components (e.g. genes, trnscripts, proteins, receptors etc.). The representtions below illustrte different vrints of the locl view. The left rm outlines the phenomenologicl pproch in which complex regultions within coregulted gene sets (mrked with identicl colors) re summrized into different mjor components. In contrst, the functionl pproches (shown for the right cell) focus on interctions between certin key regultors for which detils of the moleculr interctions re known. gressively lost during differentition. In prticulr, the uthors ssumed tht multipotent progenitor cell undergoes multiple cell divisions in which the dughter cells pss on subset of the prents linege potentil. The decision of whether the linege potentil hd been restricted to single linege, certin number of lineges or the full potentil of the prent, is chrcterized s stochstic (see Figure 3.8). Although the model could conceptully ccount for the experimentl observtions, it does not ddress the question how the stochsticity of the decision process is intrinsiclly represented within the cell. Moreover, it is not convincingly demonstrted why the process of linege restriction is stringently coupled to the decision process itself. It could well be the cse tht linege restriction occurs during the subsequent development of the dughter cells. It is the prticulr merit of Sturt Kuffmn [197, 200] who estblished the 49

60 3. Theoreticl bckground: Conceptul nd mthemticl models Figure 3.8.: Progressive restriction of linege potentil. The sketch (dpted from [210]) illustrtes the model first proposed by Ogw nd Mosmnn to describe linege potentil s progressive loss of linege potentil [167]. Strting from multipotent stem cell shown on the left side, upon ech division the number of possible developmentl options (indicted by the letters within ech cell) is rndomly reduced until the dughter cell is finlly committed to certin linege (shown on the right side). The developmentl options re encoded s follows: n, neutrophil; m, mcrophge; e, eosinophil; b, bsophil; E, erythrocyte; M, megkryocyte. theory of dynmiclly nd self-regulting networks in the relm of modern moleculr biology. Using simplified, boolen network dynmics he nd others [196, 199] showed, tht even highly complex networks finlly converge towrds finite number of possible ttrctors. Typicl phenomenologicl fetures of differentiting cells could be recptured by studying the number of possible ttrctors, their bsins of ttrction nd the robustness of the ttrctor sttes ginst perturbtions. Attributing different cellulr phenotypes (e.g. undifferentited or linege specific cell sttes) to the different ttrctors, the trnsition between them corresponds to the process of differentition. As Hung pointed out [205], the trnsition to nother ttrctor requires perturbtion possibly involving multiple genes. Such perturbtion might be initited vi externl regultory stimuli tht trigger receptor medited signls nd often trget set of key regultors. The set of ffected genes nd proteins tht finlly chnge their expression is defined by the interction network nd might be the evolutionry result of the cell s response to pproprite environmentl signls [205]. 50

61 3.3. Conceptul pproches on linege specifiction In sequence of ppers Kneko nd coworkers studied the prllel existence of multiple stble ttrctors using medium sized networks described in terms of ordinry differentil equtions [211, 212, 213, 214]. Their modeling pproches re bsed on the ide tht ech cell is chrcterized by the concentrtions of setofchemiclswhichprticipteinnetworkofutoctlytic biochemicl rections. Furthermore the internl chemicl concentrtions re influenced by the grdient of chemicl concentrtion within the cell, its surrounding medium s well s neighboring cells. Kneko et l. showed by temporl evolution of the internl cell sttes tht the finl ttrctors for ech cell re highly depending on the initil conditions nd on the nture of the cell-environment interction. It needs to be mentioned tht non of the bove outlined pproches could successfully integrte direct biologicl prmeters into the prticulr quntittive models. In spite of this, the prticulr clss of models gives resontossume tht stble ttrctors re common feture of lrge dynmicl networks s they re observed for gene nd protein interctions within cell nd tht they re pproprite representtions of cell s internl stte. In this respect the models provide phenomenologicl understnding bout the connection between the existence of stble expression ptterns in complex networks nd their trnsltion into cellulr phenotypes. The nlyticl studies on the bsins of ttrction nd on the robustness of the ttrctors provide insight into the building principles of phenotypic heterogeneity nd the stbility of the phenotypes ginst minor nd mjor perturbtions Functionl models of linege specifiction In contrst to the phenomenologicl pproches there is nother clss of models focusing on the functionl understnding of the mutul interctions between key regultors. Such interctions re typiclly studied for smll networks with focus on rther well chrcterized components nd their interction dynmics. It ws not until the 1990s tht the dvnces in the chrcteriztion of moleculr interctions led to the identifiction of certin key regultory elements which in turn opened the gte for mthemticl modeling pproches of specificbiologicl systems nd estblished the concept of moleculr switches relted to differentition nd linege specifiction. It hs been shown tht simple regultory genetic networks (intrinsiclly coupled by positive or negtive interctions) cn exhibit different, seprble stble ttrctors which re closely linked to different developmentl options. The bility to chnge between these different stble sttes is the defining criteri of moleculr switch. As demonstrtive exmple,grdner nd collegues presented synthetic genetic toggle-switch in E. Coli [110] (Figure 3.9). The switch, which is constructed from two repressible promoters in mutullyinhibitorynetworkndforwhichtheuthorslsoprovide simple mthemticl model, could be flipped by trnsient chemicl or thermlinduction. 51

62 3. Theoreticl bckground: Conceptul nd mthemticl models A b B repressor A promotor promotor repressor B Figure 3.9.: Network with two mutul repressors. The sketch illustrtes simple genetic network of two mutully repressive genes, similr to the model for the toggle switch proposed by Grdner et l. [110]. Depending on the coopertivity of the interction nd strength of the interction prmeters nd b the system cn chnge from monostble to bistble regime. The uthors proofed the existence of prmeter configurtions in which just one stble ttrctor exists (monostbility) or, for chnging prmeters, in which two such ttrctors exist (bistbility). With prticulr focus on hemtopoiesis, the decisions of myeloid progenitors to differentite either into erythroid/megkryocytic cells or into myeloid cells (reviewed in [99, 215]) hs been subject to different modeling pproches. It is the mutul regultion between zinc finger fctor GATA-1 nd the Ets-fmily trnscription fctor PU.1 tht supports the ide of moleculr switch. A representtive exmple hs been proposed by Roeder nd Gluche [108] nd is briefly illustrted in Figure A detiled nlysis of the possible moleculr interctions between the two trnscription fctors reveled rich mnifold of possible dynmicl phenomen. Wheres in the cse of low trnscriptionl ctivity the system is chrcterized by stble stte in which both trnscription fctors re eqully expressed, incresing the trnscriptionl ctivity of the utoregultion of GATA-1 nd PU.1 leds to the emergence of different stbles sttes tht re chrcterized by the dominnce of either one of the two fctors, thus reveling the typicl properties of moleculr switch. A sequence of corresponding ttrctor lndscpes is shown in Figure 3.11 illustrting this qulittive chnge in the number of ttrctors. In the bistble regime, the system is fixed in either of the two ttrctors nd switch between these ttrctors requires nexternlperturbtion. In this interprettion, the bistble switch cn be mpped onto the developmentl lndscpe outlined in Figure 3.5 in which the different ttrctors re seprted by the ridges in-between. Supported by experimentl results this PU.1-GATA-1 switch hs beenfurther studied by Lslo et l. [109] nd Soneji et l. [140]. Relted switch dynmics hve been suggested for the differentition of T-lymphocytes bsed on the interction of trnscription fctors GATA-3 nd T-bet [216, 217]. In ddition to the works on 52

63 3.3. Conceptul pproches on linege specifiction s GATA 1 u u PU.1 s k k GATA 1 PU.1 Figure 3.10.: Interction network for trnscription fctors GATA-1 nd PU.1. The sketch shows possible configurtion of the interction network between GATA-1 nd PU.1 s discussed in [108] for completely symmetric system with following prmeters: s - trnscription rte of the utoregultion, k - inhibition of trnscription by the heterodimer, u - mutul ctivtion (this process is most likely indirect). Crosses indicte decy. As shown in [108] this interction network cn be trnslted in set of dimensionless ordinry differentil equtions. bistble switches, Cinquin nd Demongeot [218] nd Foster nd collegues [219] proposed more generlized, higher dimensionl switches tht fcilittes decision events between more thn just two options. Although the moleculr description of intrcellulr interctions is most likely the best wy to finlly chieve globl view on linege specifiction in which ll intercting components re represented, the limited knowledge bout the nture of interctions but lso the technicl chllenges to describe such highly complex systems in n ppropritely mthemticl frmework mke this vision not yet fesible. Even for the smll-scle networks discussed bove, mny of the interction prmeters re not ccessible. However, tking the locl view is not necessrily disdvntgebutoffersthebilitytostudycomplexsystemsinbottom-up pproch, thus getting notion bout the functionl role of different network motifs. For the exmple of the discussed moleculr switches it is demonstrted tht externl influences or chnges in the generl ccessibility of the genes re not encoded s dditionl network components but re ttributed totheinterction prmeters (e.g. the trnscription nd inhibition rtes s, u, k in Figure 3.10). In this sense, the chnges of these secondry prmeters modify the ttrctor lndscpe nd induce switches between different stbility regimes (e.g. mono- vs. bistbility). Such behvior is typicl consequences of the locl view. 53

64 3. Theoreticl bckground: Conceptul nd mthemticl models A B C GATA 1 GATA 1 GATA 1 PU.1 PU.1 PU.1 s = 2 s = 5 s = 8 Figure 3.11.: Attrctor lndscpe. (A - C) show sequence of ttrctor lndscpes for different prmeters of the trnscription rtes s for the PU.1 - GATA-1 model introduced by Roeder nd Gluche [108]. The z-xis corresponds to the negtive logrithm of the probbility for finding cell t certin position in the stte spce of PU.1 nd GATA-1 concentrtions. Thus, the ttrctor regions re indicted by the ornge color Integrtion of linege specifiction nd self-mintennce Although the phenomenologicl models of linege specifiction fil to substntite the network topologies by experimentl dt, nd the moleculr networks re limited to rther specific components, the whole body of evidence provides n insight in how the process of linege specifiction is potentilly represented t the moleculr level. However, it is defining feture of stem cell popultions to remin in n uncommitted stte from which the linege specifiction towrds different cell ftes is still possible. This stte of mintennce of multipotency is closely correlted with the mintennce of the stem cell popultion itself. This interreltion between multipotency nd stem cell self-mintennce is not reflected by ny of the bove model pproches. In this context the question rises, how the ttributes of stem cell popultion s being dptive to chnging demnds nd the options of flexibility nd reversibility extend on the process of linege specifiction. Furthermore, it is uncler how the mintennce of the experimentlly observed priming behvior (to low-level coexpression of linege specific, potentilly ntgonistic genes) is efficiently coupled to the mintennce of the stem cell popultion nd the corresponding environmentl cues. Bsed on the ide tht linege specifiction is competitive interction between different linege specific progrms comprehensive concept is developed in the next chpter integrting the bility for linege specifiction nd the selfmintennce of stem cell popultion into common conceptul frmework. 54

65 3.4. Roeder nd Loeffler model of hemtopoietic stem cell orgniztion 3.4. Roeder nd Loeffler model of hemtopoietic stem cell orgniztion The single cell bsed model by Roeder nd Loeffler [33] develops fromtheide, tht stem cells hve the bility to independently respond to multitudeofenvironmentl signls. The coopertion of mny such cells results in the overll ppernce of the tissue specific stem cell system. The specil role of the hemtopoietic niche for the mintennce of HSCs hs lredy been outlined in Section 2.2. Building up on the ide tht different configurtions of the cell s locl micro-environment propgte differentsignlsnd developmentl ftes (see Figure 3.3) quntittive model for the HSC system hs been developed. In this model the cells re in principle exposed to two contrry signling contexts. The first signling context, termed A,iscommonlyssocited with the hemtopoietic niche nd supports cellulr quiescence nd the mintennce of the repopultion potentil. In contrst, the second signlingcontext, termed Ω, is ssocited with the decoupling from the niche nd supportsprolifertion nd loss of repopultion bility which finlly leds to differentition. The model by Roeder nd Loeffler [33, 220] describes ech cell s nindividul object with discrete set of chrcteristic vribles which reupdtedforllcells t discrete time steps typiclly mesuring one hour. The ctul sttus of stem cell (i.e. its position in the stte spce of the defining vribles) is chrcterized by its current signling context (A or Ω ), its position in the cell cycle c (indicting the cell is in either G1, S, G2, M or G0 phse) nd its ffinity which quntifies the propensity of prticulr cell to reside in signling context A. It is this ffinity which is itself modulted by the ction of the two signling contexts nd which directly influences the trnsition probbilities. Wheres the non-prolifertive cells in A re mintining or even regining their ffinity up to n upper limit mx = 1, the prolifertive cells in signling context Ω grdully lose their ffinity. It cn be shown tht the ffinity is good indictor for the stem cell qulity s it pproximtes the cell s bility to relize long-term system repopultion. An overview of the model setup is provided in Figure Accounting for the presumed underlying complexity, trnsitions between the two signling contexts re described by stochstic process. The probbility of switching depends on the ctul vlue of s well s on the number of cells in the trget signling context. The trnsition probbilities redescribedbythe following sigmoid functions: trnsition from A to Ω : ω(, N Ω )= min f ω(n Ω ) (3.1) 55

66 3. Theoreticl bckground: Conceptul nd mthemticl models Ω Α mx 1 / d stem cells ω... α r... min differentiting cells with prolifertion w/o prolifertion Figure 3.12.: Model of HSC orgniztion. The model proposed by Roeder nd Loeffler [33] is chrcterized bytwodifferent signl contexts (A nd Ω ). Cells cn reversibly chnge between A nd Ω with probbilities α nd ω which depend on the cell numbers nd the cell specific ffinity (font sizes indicte the vlue of for ech cell). Wheres ctivted cells in Ω undergo divisions nd exponentilly degrde their cell specific ffinity with rte d, cellsina re quiescent nd preserve/regin their ffinity with rte r. Cells with ffinity < min cnnot chnge into A gin nd undergo finl differentition (with nd without prolifertion). nd trnsition from Ω to A : α(, N A )= mx f α (N A ) (3.2) Within these equtions N Ω nd N A refer to the cell numbers in signling context ΩndA,respectively. Theprmeter min is n rbitrry, but numericlly necessry boundry to ccount for the fct tht cells with < min hve significntly reduced probbility for trnsition into A but high probbility for trnsition into Ω. In other words, cells with < min do hrdly ccount for the mintennce of repopultion bility within A nd re thus referred to s differentiting cells. The functions f ω (N Ω )ndf α (N A )resigmoidfunctionsofthetype: f(n) = 1 ν 1 + ν 2 exp ( ν 3 N ) + ν 4. (3.3) Ñ Wheres the prmeters ν 1,ν 2,ν 3,ndν 4 determine the shpe of f, theprmeter Ñ is scling fctor for N. Itispossibletotrnsformtheshpefctors 56

67 3.4. Roeder nd Loeffler model of hemtopoietic stem cell orgniztion ν 1,ν 2,ν 3,ndν 4 into the more intuitive vlues f(0), f(ñ ), f(ñ), nd f( ) := 2 lim N f(n). Detils re provided in [47]. If cell does not trnsit between the signling contexts (with probbilities (1 ω) nd (1 α), respectively) the cell s ffinity s well s the internl cell cycle clock c re modified ccording to the following rules. For cells in A the ffinity increses by fctor r, termedregenertionfctor(r 1), in ech time step until n upper limit mx is reched. Since cells in A re ssumed to be quiescent (G0 phse), the cell cycle clock c is not updted. In contrst, cells in Ω decrese their ffinity prmeter by fctor 1/d in which d is the differentition constnt (d >1). The cell cycle clock c is incresed by one. If the cell cycle clock c equls the length of the cell cycle τ c,divisionisperformed,inwhichtheprentlcellisreplced by two identicl copies of it. Only the cell cycle clock hs been reset to c =0. The phses of the cell cycle re defined in terms of the cell cycle clock c. For cells in Ω G1 phse of time τ G1 is followed by S phse of time τ S nd G2/M phse of time τ G2/M. Generlly it holds τ c = τ G1 + τ S + τ G2/M. Trnsition from Ωto A is restricted to cells in G1 phse. However, chnging bck into Ωthe cell cycle clock c is set to the beginning of S phse. The differentiting cells with < min remin in Ω, nd continue to divide throughout prolifertive phse with chrcteristic cell cycletime,followedby precludingmturtionphsewithoutfurthermplifiction. Finlly, mture cells re removed from the system to reflect their limited life spn. Further detils bout the numericl implementtion re provided in [47] s well s in the Appendix B. The Roeder nd Loeffler model is successful exmple of how n flexible nd rective view on cellulr development cn be put into mthemticl context nd provide insight into potentil regultions on the cellulr s well s on the tissue level. The model hs been successfully pplied to phenomen of clonl competition [221], symmetric stem cell ftes [183] nd chronic myeloid leukemi [220]. From conceptul perspective there re two limittions of the model. First, the trnsition functions for ech cell re bsed on globl informtion (the bsolute cell number within ech signling context) rther thn on locl density informtion. However, it could be shown by d Inverno nd Sunders (publiction in revision) tht within sptil structure the globl informtion cn be exchnged by locl one (bsed on the locl concentrtion of niche-derived mrker substnce) without ny generl impct on the system dynmics. Second, lthough the model ccounts for the output of differentiting cells the mechnisms of linege specifiction remin illusive. Within the next chpter mthemticl model for the description of linege specifiction is presented which lso puts the processes of mintennce of repopultion bility nd multipotency into common context. 57

68

69 4. Methods I: Modeling the linege specifiction of HSCs Within this chpter ctlog of experimentlly nd conceptul criteri is formulted which is subsequently used to motivte new model of linege specifiction. Generlly the model should describe linege specifiction s dynmiclly regulted, temporlly extended nd potentilly reversible process tht integrtes in the concept of self-orgnizing stem cell system. extend the existing model of hemtopoietic stem cell self-renewl nd differentition to incorporte the spects of linege specifiction. consistently explin vriety of experimentlly observed phenomen. be s simple s possible. After specifiction of the model ssumptions, forml description of the mthemticl representtion is provided. A sensitivity nlysis of the model nd comprison to experimentl results is provided in Chpter Ctlog of criticl phenomen Bsed on the phenomenology of linege specifiction introduced in Chpter 1 s well s the biologicl nd conceptul bckground outlined in Chpters 2 nd 3, the centrl spects of the biologicl process cn be summrized into the following ctlog of criteri tht need to be covered by the proposed model: Linege commitment (C1). Strting from multipotent stem or progenitor cell, linege specifiction is chrcterized s progressive restriction in linege potentil, finlly giving rise to functionlly restricted, mture cells (cf. Section 2.3.1). Experimentl results bout the linege contribution of single hemtopoietic progenitor cells [26, 222] serve s quntittive mesure for this criterion. 59

70 4. Methods I: Modeling the linege specifiction of HSCs Genertion of diversity (C2). Different mture cell types re generted through the process oflinege specifiction. Cndidte mechnisms for the genertion of this phenotypic diversity re cell intrinsic fluctutions cused by different sourcesofnoise (cf. Sections nd 3.3.3). Phenotypic diversity is estimted using experimentl results bout the linege contribution of pired hemtopoietic progenitor cells [27,222]. Temporl extension nd reversibility (C3). The process of linege specifiction is not n ll-or-none decision but is chrcterized s progressive restriction of linege potentil with temporl extension. This includes spects of reversibility which, depending on the stte of commitment nd the prticulr environmentl conditions, my be more or less likely (cf. Sections nd 2.3.3). Time course dt on the in vitro differentition of prticulr mouse cell line is used to study these temporl effects. Regultion of linege specifiction (C4). Linege specifiction is regulted on the level of individul commitment decisions (instructive) orbymensofselectivesurvivlofpreferredlineges (selective). Such n dptive regultion is required on the popultion level for both scenrios even though individul linege decisions might not be predictble on the single cell level (cf. Section 2.3.2). The spects re discussed using dt on the in vitro differentition of mouse cell line. Priming (C5). On the moleculr level, the uncommitted stte is chrcterized by coexpression of mny, potentilly ntgonistic genes nd trnscription fctors (cf. Section 2.3.2). In contrst, differentited cell types show certin typicl gene expression pttern supporting their functionl requirements. In this sense, linege specifiction is perceived s process tht shifts gene expression from the undifferentited coexpression stte towrds the dominnce of certinpttern. Due to the phenotypic perspective of the model these spects re only verified in qulittive mnner. 60

71 4.2. The intrcellulr linege specifiction model 4.2. The intrcellulr linege specifiction model The mintennce of HSCs is lrgely governed by the ction of hemtopoietic niches. It hs been illustrted in Section 2.2 tht the protective ction of prticulr sptil micro-environment preserves frction of cells in n uncommitted, mostly quiescent stte with exceptionlly high repopultion potentil. In contrst, cells tht re not under the tight regultion of the hemtopoietic niches progressively lose their repopultion potentil nd undergo terminl differentition. On conceptul level it hs been shown by Roeder nd Loeffler tht the interply of two, rther ntgonistic environments is sufficient to explintheblnceof stem cell mintennce nd differentition in the context of self-orgnizing system (cf. Section 3.4). Wheres one such environment promotes stem cell mintennce the other one promotes differentition nd the loss of stem cell function. It is the dptive bility of the cells to chnge between the two environments tht finlly leds to the estblishment of dynmiclly stbilized stem cell pool which lso gives rise to popultion of differentiting cells. Coming bck to the observtion tht stem cells re defined s uncommitted, multipotent cells with high regenertive potentil (cf. Section 2.1) it is lso commonly perceived tht the linege commitment of HSCs is closely correlted with the loss of regenertive potentil. Although this correltion does by no wy imply functionlidentitybetweenlinegecommitmentndlossofregenertivepotentil, it suggests tht the two distinct processes re t lest regultedbycorrelted mechnisms. Following this line of rgument it is resonble tossumethtnot only the process of stem cell self-mintennce but lso the process of mintennce of multipotency cn be explined in the context of two ntgonistic environments. For the prticulr sitution this mens tht the two micro-environmentl configurtions impose different control regimes on the process of linege specifiction: wheres regressive control regime mintins multipotency it is the role of dissiptive control regime to fcilitte linege commitment. The ntgonistic ction of regressive nd dissiptive control regime is illustrted in Figure 4.1, in which the complex interction of potentilly relevnt genes nd gene products re depicted by simple, intrcellulr network grph. Assuming tht the uncommitted stte is chrcterized by the low-level coexpression of mny, potentilly ntgonistic genes, linege commitment is chrcterized by the up-regultion of certin linege specific subset of genes while others re down-regulted. In this sense, the coexpression is mintined in the regressive control regime, wheresthedominnceofonesubsetofgenesisestblishedin the dissiptive control regime. Chngesbetweenthecontrolregimesrerequired in order to llow for n dptive nd dynmiclly stbilized system. However, such chnges do lso imply tht reversible developments in the process of linege specifiction re generlly possible. Anumberofsimplifictionsrenecessrytoreducethecomplexity of the un- 61

72 4. Methods I: Modeling the linege specifiction of HSCs regressive control regime dissiptive control regime Figure 4.1.: Network dynmics under two control regimes. Simplified representtions of the stte spce S re depicted for prticulr cell (illustrted by n intrcellulr interction network). Different, coregulted components (such s genes, trnscription fctors, receptors) tht re specific for one linege re depicted with the sme color (symbol size corresponds to the reltive expression). In the dissiptive control regime there is cler tendency for the upregultion of one (in this cse the blue ) coregulted cluster t the expense of the others (directed movement in the stte spce). In contrst, the regressive control regime supports leveling of the expression sttes of the three clusters with moderte fluctutions nd reversible chnges (undirected movement in the stte spce). The cells obey the principle bility to chnge between the two control regimes (dshed rrows). derlying interction network governing the complex moleculr dynmics of linege specifiction nd trnslting it into mthemticlly fesible problem. Primrily, it is ssumed tht ll signls nd regultors tht re specific for one common linege fte re integrted in single generic mesure, clled linege propensity. This mens tht the ction of different control regimes is not described on the level of individul genes but summrized s the combined expression of coregulted, linege specific regultory components (i.e. genes, trnscriptionfctors, surfce fctors, receptors nd signling pthwys) tht re representtivefor certin cell fte. The level of the prticulr linege propensity represents the potentil of cell to develop into the corresponding linege. The scheme in Figure 4.1 trnsltes into simpler version s depicted in Figure

73 4.2. The intrcellulr linege specifiction model regressive control regime dissiptive control regime Figure 4.2.: Simplified network dynmics. Coregulted clusters of moleculr components re summrized in single, generic mesure termed linege propensity (indicted by the symbols). The overll dynmics within this low-dimensionl stte spce representtion remin the sme s in Figure 4.1. It is now possible to visulize the ction of the control regimes in simplified stte spce digrm (Figure 4.3). For the exmple of three competing lineges, which re ssigned to the xis of 3-dimensionl digrm, ech point in the stte spce refers to triplet of linege propensities. The temporl development is consequently depicted by trjectory s sequence of such points. Inthis stte spce, the regressive control regimes leds to trjectories close to the origin, chrcteristic for low nd blnced linege propensities, wheres the dissiptive control regime drives the trjectory long one of the xis, indicting dominting linege propensity while the others re suppressed. Although extensive effort hs been mde to revel the interction between certin competing linege specific genes nd gene products mny connections remin vguely chrcterized nd the resulting network dynmic cnonlybeperceivedon verycorsescle.thereforeitisproposedtopplysimpleinterctionprocess cting on the level of the linege propensities in order to understnd the phenotypic chnges in the course of cellulr differentition. In prticulr, it is ssumed tht the interction is governed by mutul competition process between ll such propensities in which every gin (or loss) in prticulr linege propensity will 63

74 4. Methods I: Modeling the linege specifiction of HSCs regressive control regime dissiptive control regime Figure 4.3.: Simplified network dynmics in stte spce digrm. In the stte spce digrm ech dimension corresponds to one linege propensity. A possible trjectory is indicted by the blck line. Wheresintheregressive control regime the propensities re kept t n lmost equl level, the dissiptive control regime supports the dominnce of one of them. This is n lterntive representtion to Figures 4.1 nd 4.2. led to the reduction (or increse) of the remining propensities. In order to ccount for the complexity of linege development the competition process involves stochsticelement. Thisimpliesthtthepreciseoutcomeof prticulr linege specifiction process is unpredictble. However, the overll frctions of cells committed to the cell ftes in questions cn still be mnipulted on the level of cell popultions. The mutul competition process cn ct in two distinct fcets to represent the different ctions ssocited with the control regimes outlined bove. In simple words, it is ssumed tht in the regressive control regime the competition process leds to the mintennce of the low-level coexpression (priming) by penlizing devitions from the men expression level, while in the dissiptive control regime the dominnce of one or the other linege propensity is promoted (commitment) by enhncing the occurring devitions. The bove rguments led to ctlog of forml ssumptions on which the mthemticl formliztion is bsed: Coregulted, linege specific components (e.g. genes, trnscription fctors, receptors) re summrized into linege propensities. Echlinegepropensity represents the potentil of cell to develop into the corresponding linege. Interctions between the linege propensities re represented by stochstic competition process with different configurtions for the regressive nd the dissiptive control regime. 64

75 4.3. Mthemticl representtion of the intrcellulr model The linege propensities re described s reltive vlues (normlized to unity). This mens tht the gin (or loss) in prticulr linege propensity will led to the reduction (or increse) of the remining propensities. The linege propensities represent cellulr fetures tht re inherited to the dughter cells. Inheritnce of the linege propensities is symmetric to both the dughter cells. The outcome of prticulr linege specifiction process cn only be predicted in probbilistic sense. The overll outcome on the cell popultion level cn be either regulted by modifying prmeters of the intrinsic competition process or by positive selection for cells with certin ptterns of their linege propensities Mthemticl representtion of the intrcellulr model Amthemticlformliztionisnecessryinordertostudythe quntittive model behvior under the set of stted ssumptions Linege specifiction s cellulr property The linege specifiction stte of model cell t ny given time point is chrcterized by the ctul levels of number N of different linege propensities denoted by vector x(t) =(x 1 (t),x 2 (t),...,x N (t)). N represents the number of different lineges in which the cell cn potentilly differentite. The propensitiesx i,which cn tke vlues between zero nd one, represent reltive propensity levels for the development into the N possible lineges. In other words, the linege propensity vector x(t) islwysnormlizedto1( i x i(t) =1) Dynmics of the competition process The stochstic competition process, which is modeled on discrete time scle (typiclly mesuring one hour), is orgnized s three step process. In the first step of the competition process, onelinegepropensityx i is rndomly chosen for the updte procedure. Herein, the probbility P for choosing prticulr linege i equls its propensity x i (t): P (i) =x i (t) (4.1) 65

76 4. Methods I: Modeling the linege specifiction of HSCs In the subsequent, second step of the competition process the chosen linege propensity x i (t) isupdtedccordingto x i (t +1)=x i (t)(1 + m i ) (4.2) wheres the other propensities remin unchnged in the first step. The generl ide of this updte procedure is inspired by so clled Póly urn model (see Appendix A.1). The linege specific rewrd for the rndomly chosen linege i is defined s function m i = f m (x i (t)). For ll other lineges j the rewrd is set to m j =0. The prmeteriztion of the prticulr rewrd functions for ech individul linege is the primry trget to mnipulte the overll system dynmics. For the updte, two different control regimes re ssumed depending on the micro-environmentl context the cell is ctully exposed to ndwhichre chrcterized by qulittively different rewrd functions: Regressive control regime: Devitions between the chosen linege propensities x i nd common men propensity level re modulted by positive or negtive rewrds m i,respectively. Therewrdfunctioncneither be described by liner function of the type m i = f m (x i (t)) = b i x i + n i (4.3) with negtive slope (b i < 0) nd root t x R = n i /b i or, lterntively, by sigmoid function of type m i = f m (x i (t)) = σ is i (x i x R ) 1+(si (x i x R )) 2. (4.4) This sigmoid function is defined by the root x R,thesteepnessprmeter s i nd the sturtion prmeter σ i.theroottx R should in both cses be chosen such tht x R x =1/N in order to get convergence to the men propensity level x =1/N.Inthissettingtherewrdm i is positive for x i <x R nd negtive for x i >x R.Exmplesoftherewrdfunctions re shown in Figure 4.4(A). The liner rewrd function in eqution (4.3) is suitble in mny cses. However, for lrge devitions of the chosen linege propensity x i from the men propensity level x =1/N the rewrd could potentilly fll below m i = 1. This, in turn, leds to negtive linege propensities in the updte function in eqution (4.2) which re not defined. In orderto prevent this cse lower limit for the liner rewrd hs been introduced t m i =

77 4.3. Mthemticl representtion of the intrcellulr model A regressive control regime linege specific rewrd m i 0.15 liner rewrd function x R = men(x) = 1/3 0 σ i = σ i = 0.05 σ i = linege propensity x i B dissiptive control regime linege specific rewrd m i n i prog = prog n i = 0.05 n i prog = linege propensity x i Figure 4.4.: Rewrd functions m i = f m (x i (t)) for the two control regimes. (A). For the regressive control regime liner rewrd function (given in eqution (4.3)) with slope b i = 1 nd three exmples of sigmoid rewrd functions (given in eqution (4.4)) re shown with prmeters x R =1/3, s i =1/σ i nd σ i = 0.1, 0.05, (B). Three exmples of liner rewrd functions (eqution (4.5)) re shown for the dissiptive control regime. Prmeters re n i =0.1, 0.05, Alterntively, n pproprite sigmoid function cn be used s given in (4.4). Prticulr exmples re shown in Figure 4.4(A). Tking the second derivtive of eqution (4.4), it cn be shown tht the mximum slope (occurring t the root point x R )isgivensb i = σ i s i. For the three exmples illustrted in Figures 4.4 the steepness is set to s i =1/σ i.itfollowsthttheslopeforllthreeexmplesisb i = 1 t the root point x R.Thereforethefunctionsdifferonlyintheirsturtion level σ i. Dissiptive control regime: The chosen linege propensity x i is lwys enhnced by linege specific, positive rewrds m i.inthesimplestcse constntrewrdischosen,resultinginlinerrewrdfunctions of the type m i = f m (x i (t)) = n i (4.5) These functions hve zero slope nd re restricted to the positive plne (n i > 0). This wy m i n i is independent of x i (Figure 4.4(B)). This leds to incresing divergence from the men propensity level x =1/N. The preferentil updte of lineges with high propensities (due to the coupling of updte probbility nd ctul linege propensity in the first updte step), ultimtely leds to the dominnce of one linege over the others. In the finl, third step of the competition process, thelinegepropensity vector x(t) isnormlizedtounity.thisnormliztionccountsforthe 67

78 4. Methods I: Modeling the linege specifiction of HSCs concept of ntgonistic interction between different lineges: if one propensity is up-regulted, the other ones re (reltively) down-regulted nd vice vers. It cn be shown mthemticlly tht this renormliztion cn be interpreted s generl decy term cting on ll linege propensities. For further detils the reder is referred to Appendix A.2. Tken together, the complete updte procedure reds s: x(t +1)= 1 x(t)(1 + m(t)) (4.6) Cn in which m(t)correspondstothevectoroflinegespecificrewrdswhichis reclculted t every time step t. Theindividulvluesregenerllysettom j =0except for the updted linege i which hs been chosen with probbility P (i) =x i (t). For the updted linege m i = f m (x i (t)) is clculted ccording to the corresponding control regime s described in equtions (4.3) to (4.5). The normliztion constnt C n ccounts for the subsequent normliztion of the linege propensity vector x to unity. In prticulr, C n is given s C n = x j (t)(1 + m j )=1+m i (4.7) j {1...N} in which m i corresponds to the individul rewrd of the updted linege i. Correltions between lineges. As outlined in Section certin linege ftes re more closely relted thn others. For exmple, it hs been observed tht the development of grnulocytes nd mcrophges is often closely correlted, wheres similr effects re less frequent mong other cell types. Since this phenomenon is cused by common developmentl pthwys, such correltion in the modeling pproch is reflected by functionl coupling of the prticulrlinege propensities. Techniclly this is implemented s follows: Given there is correltion between ny two lineges propensities, sy i nd j, theupdteprocedure is extended. If linege i is chosen for the updte process, x i is updted ccording to the updte function in eqution (4.2). However, t the sme instnce lso the correlted linege j undergoes modified updte procedure: the propensity x j is simultneously updted ccording to x j (t+1) = x j (t)(1+γ ij m j ). The prmeters γ ij chrcterize the correltion nd re considered between 1 <γ ij < 1(prmeter vlues γ ij < 0ccountfornegtivecorreltions). Aprticulrppliction is provided in Section Phenotypic mpping In the model one needs to decide how chnges of the intrcellulr stte correspond to chnges in the phenotype of the cells. Such mpping is necessry to compre 68

79 4.3. Mthemticl representtion of the intrcellulr model Figure 4.5.: Phenotypic mpping. The br indictes the linege propensity x i of the dominting linege. According to this vlue nd the threshold vlues x com1/2 the cell is clssified s uncommitted, erly or finlly committed cell. the results of the modeling pproch to experimentl dt which typiclly detect phenotypic chnges during the course of differentition. For the prticulr mpping, it is ssumed tht the phenotype of n individul cell is chrcterized by its highest ctul linege propensity x mx =mx i x i. The linege i for which holds x i (t) = x mx is termed the dominnt linege. Subsequently this propensity is denoted s x i (t). For dominnt linege with x i (t) < 0.5 thessignmentshouldbehndledwithcresincepotentilly more thn one linege propensity cn hve closely similr vlues. According to the linege propensity of the dominnt linege x i (t) thecells re clssified in comprison to threshold vlue x com1 s undifferentited cells (x i (t) <x com1 )orscellscommittedtolinegei(x i (t) >x com1 ). If further sttes of commitment cn be defined phenotypiclly it might be useful tointroduce further clss of cells with second threshold vlue x com2. The simple sketch in Figure 4.5 illustrtes such n exmple with secondry distinction in erly nd lte committed cells. It should be clerly stted tht the specifiction of the threshold vlues x com1/2 is used solely for the phenotypic mpping of model results to experimentl dt nd does not imply the irreversibility of the commitment decision. However, the probbility for chnge of the dominnt linege decreses with incresing vlues of the propensity x i (see nlysis in Section 5.1.2) Regultion of linege specifiction Conceptully there re two different mechnisms for the regultion of the outcome of linege specifiction process. Wheres the biologicl bckground hs been discussed in Section 2.3.2, conceptul plcement is provided below. 69

80 4. Methods I: Modeling the linege specifiction of HSCs Linege specifiction s n instructive process. The shpe of the rewrd functions f m defined in equtions (4.3) to (4.5) is suitble prmeter for the regultion of the linege specifiction process. In prticulr, the constnt rewrd in the dissiptive regime f m (x i (t)) = m i = n i is especilly sensitive to influence the finl linege commitment s the choice of different vlues n i for different lineges i skews the probbility for their occurrence. A detiled sensitivity nlysis is provided in Section 5.1 of the next chpter. Although, cell deth might occur in this scenrio, it generlly does not hve regultingfunctionndffectsllcellsinsimilrfshion (i.e. bckground cell deth with equl intensity). Therefore, the regultion of linege specifiction is solely ttributed to the mnipultion of the rewrdfunctions f m. As this is considered to be n instructive process, medited e.g. by the ction of linege specific cytokines, the whole process is referredtos instructive linege specifiction. Linege specifiction s selective process. In the cse tht the linege specifiction process outlined in Section hs no intrinsic skewing (i.e. the rewrd functions f m re identicl for ll lineges i)lln possible lineges re generted with the equl probbilities. Therefore regultion of the frction of cells in ech linege cn only be chieved by the process of selective cell deth. Depending on the ction of supportive or permissive environment (e.g. linege specific cytokines, feedbck regultions) the survivlofcertin lineges is propgted while other lineges re not supported nd undergo cell deth. As the regultion of the frction of cells in ech individul linege is solely regulted by selective survivl signls nd trgeted cell deth, the process is referred to s selective linege specifiction. This conceptul pproch ssumes cell deth occurrence in two principle menings, nmely s generl effect occurring in ll cells (bckground cell deth) ors n effect tht is coupled to certin cellulr properties (selective cell deth). The trnsltion into the model concept of linege specifiction is outlined below: Bckground cell deth. Bckground cell deth is defined s unspecific cell deth process cting on ll cell types irrespective of their current stte. Techniclly, the occurrence of cell deth is modeled s stochstic process. The probbility for cell to undergo cell deth in ny given updte step, referred to s Φ B,isgivens: Φ B = φ (4.8) 70

81 4.3. Mthemticl representtion of the intrcellulr model Figure 4.6.: Cell deth intensities Φ. The probbility for cell deth during one updte step Φ is shown s function of the dominting linege propensity x i (t). (A). For the bckground cell deth ΦB remins constnt. (B). For the selective cell deth Φ S is defined by linege specific step functions (indicted by the colors). Without loss of generlity x deth/high i =1 for ll i. Here, φ is generl nd constnt cell deth intensity which does not depend on the linege propensities x(t) (see lso Figure 4.6(A)). Selective cell deth. In contrst, the selective cell deth does not ct eqully on ll cells but cells with certin dominnt lineges re primry trgets wheres cells with other dominnt lineges re spred. In this sense, theoccurrence of cell deth for prticulr cell depends explicitly on its ctul linege propensities x(t). Agin, the occurrence of cell deth is modeled s stochstic process. However, the probbility Φ S (t) thtcellundergoescelldethingiventime step t is now described s function of the dominting linege propensity x i (t). In the most simple pproch Φ S (t) isdefinedsstepfunctionofthe form 71

82 4. Methods I: Modeling the linege specifiction of HSCs Φ S (t) = { φ i 0 else for (x deth/low i <x i (t) <x deth/high i ) (4.9) In this cse, the probbilities φ i s well s the boundries x deth/low i nd re individul prmeters for ech linege i. Choosing higher x deth/high i vlue of φ i >φ j leds to n incresed cell deth probbility for cells with the dominting linege i s compred to cells with dominting linege j. Inthis sense, it is the propensity of the dominting linege x i tht further specifies eqution (4.9). Typicl curves for the cell deth intensities Φ S re provided in Figure 4.6(B). Prcticlly, the lower bound for the ction of the selective cell deth is chosen such tht x deth/low i > 0.5. Only in this cse the definition of dominnt linege is robust ginst smll perturbtions 1.Similrrestrictionspplyfor the upper bound x deth/high i. As it is unlikely tht n initilly unsupported linege hs better survivl chnces lter in development, the upper bound for the ction of the selective cell deth is generlly set to x deth/high i =1. Integrting the concepts of cell deth in the mthemticl nd numericl formultion of the linege specifiction model, the three-prt updte procedure introduced in Section is complemented by one of the bove scenrios for the occurrence of cell deth. Consequently the scenrios of instructive nd selective linege specifiction re summrized s follows: Instructive linege specifiction. linege specific rewrd functions f m (x i )skewtheintrinsiclinege decision nd bckground cell deth with intensity Φ B cts on ll cells without regultion of the linege contribution 1 For ny linege propensity x i < 0.5 twoormorelinegescnhvecloselysimilrvlues,even fluctuting round certin common men vlue. In this cse the dominnt linege would chnge frequently between subsequent updte steps. 72

83 4.4. Integrtion of linege specifiction in the model of HSC self-mintennce Selective linege specifiction. identicl rewrd functions f m (x i )forllcellsledtoblncedlinege decisions nd selective cell deth with intensity Φ S regultes the finl linege contribution 4.4. Integrtion of linege specifiction in the model of HSC self-mintennce The intrcellulr linege specifiction dynmics described bove re defined under the control of two ntgonistic control regimes. Following the stted criteri tht reversible developments re generlly possible, trnsitions between the regressive nd the dissiptive control regime (nd vice vers) needtobeincludedin comprehensive model of HSC orgniztion. The previously proposed model of HSC orgniztion introduced by Roeder nd Loeffler (compre Section 3.4) describes dptive nd self-orgnizing HSC self-renewl in the context two, structurlly different nd ntgonistic microenvironmentl conditions: one promoting cellulr quiescence nd mintennce of the self-renewl bility (signling context A ), the other promoting prolifertion nd loss of self-renewl bility (signling context Ω ). It ppers s logicl consequence to extend this ide of micro-environmentlly directed development on the dynmics of linege specifiction. In prticulr, it is proposed tht the two signling contexts A nd Ω lso impose contrry effects on the intrcellulr linege specifiction dynmics of ech individul cell by Coupling the dissiptive control regime to signling context Ω. nd Coupling the regressive control regime to signling context A. Induced by this superposition of regulting mechnisms, cells in A preserve the uncommitted stte nd simultneously mintin their bility to ct s stem cells. Furthermore, the processes of linege commitment is correlted with the loss of self-renewl bility in signling context Ω. Techniclly, the cellulr properties defined in the originl model of HSC selfrenewl outlined in Section 3.4 (i.e. ttchment ffinity, positioninthecellcycle 73

84 4. Methods I: Modeling the linege specifiction of HSCs A stem cells differentiting cells with prolifertion w/o prolifertion Ω progressive control regime 1 / d ω... α r... Α regressive control regime mx min linege propensities B time C time D time E time Figure 4.7.: Extended model concept. (A). The generl model lyout nd the prmeters correspond to Figure Upon integrtion of the linege specifiction dynmics the cells now cquire prticulr linege during differentition in Ω (indicted by the chnge in shpe nd color). (B-E). Time courses of the linege propensities x for individul cells of interest. (B). The non-prolifertive, stem cell supporting signling context A hosts multipotent cells which re chrcterized by the blnced low level coexpression of the linege propensities. (C). Due to dissiptive control regime in signling context Ω the blnced coexpression is upset nd one linege propensity is expnded t the cost of the others. (D). Continution of the process in which the prticulr fctor mnifests the linege decision nd identifies the cell s committed (x i >x com). (E). Intrcellulr development of cell which hs been recptured into signling context A. Here, the regressive control regime countercts the differentition process nd reestblishes the typicl priming pttern. c nd the ffilition to either the signling context A or Ω ) re now extended to incorporte the vector of linege propensities x(t) =(x 1 (t),x 2 (t),...,x N (t)). During the sequentil processing of ech cell t the discrete timestepsofthe originl model, the cell s linege propensities x re dditionlly updted ccording to the dynmics of linege specifiction outlined in Section 4.3. Depending on the current signling context A or Ω, either the regressive or the dissiptive control regime is pplied for the updte procedure. The trnsitions between signling contexts A nd Ω (nd vice vers) re still 74

85 4.4. Integrtion of linege specifiction in the model of HSC self-mintennce governed by the functions defined in equtions (3.1) - (3.3). These functions depend only on the number of cells in the trget signling context nd on the cell s individul ffinity, buttheydonotexplicitlydependonthecell slinege propensity x(t). However, s the dynmics of linege specifiction re functionlly integrted in the model of HSC self-renewl s outlined bove, thereisclose correltion between cell s ffinity nd its linege propensity x. Acomprehensiveillustrtionoftheextendedmodelconceptis shown in Figure 4.7. As the intrinsic dynmics of linege specifiction re difficult to illustrte, typicl time courses of the linege propensities x for individul cells of interest re shown below the min grphic. Further detils of the necessry chnges to the numericl progrm structure of the Roeder nd Loeffler model re provided in Appendix B. For detils on the implementtion of the novel model of linege specifiction the reder is referred to Appendix C. 75

86

87 5. Results I: Dynmics of linege specifiction The first prt of this chpter provides generl overview of the dynmic behvior of the proposed model of linege specifiction including detiled description of the two control regimes nd the system s response to prmeter chnges. The second prt presents rnge of experimentl situtions to which the model hs been pplied Linege specifiction in the regressive nd the dissiptive control regime In order to understnd the rich dynmicl fetures of the linege specifiction model it is necessry to illustrte the behvior for the regressive nd for the dissiptive control regime seprtely. An integrted view of the extended stem cell model including both the spects of self-renewl nd linege specifiction is provided t the end of the section Dynmics in the regressive control regime Generl behvior In the regressive control regime the system is chrcterized by convergence of the linege propensities x i towrds their men propensity level x =1/N. This is fcilitted by the rewrd functions (given in equtions (4.3) nd (4.4)) which penlize devitions from the men propensity level. Given tht the root of the rewrd functions x R coincides with the men propensity level x =1/N,positiverewrd(m i > 0) is imposed in cse tht the propensity of the chosen linege is below the men level of the root x i <x R = x nd negtive rewrd (m i < 0) is imposed in the contrry cse (x i >x R = x). Following the updte procedure outlined in Section the individul propensities pproch the men propensity level x i x =1/N with incresing time. Typicl exmples of the resulting trjectories re shown in Figure 5.1 in which thedynmicsof convergence re shown for different independent reliztions. Strting from system in which one linege propensity domintes over the others, it ppers tht the convergence towrds the men coexpression level x is suitble mesure to chrcterize the dynmics of the linege propensities x in the regressive control regime. Techniclly, for ech individul trjectory the time point is recorded when linege propensity x i psses certin threshold x t.timevergesfordifferentindividulthresholdvluesreobtinedseprtely for ech linege i. Asoclledconvergence curve is obtined by connecting these 77

88 5. Results I: Dynmics of linege specifiction A linege 1 linege 2 linege 3 B linege 1 linege 2 linege 3 linege propensity linege propensity C time t in hours linege 1 linege 2 linege 3 D time t in hours linege 1 linege 2 linege 3 linege propensity linege propensity x time t in hours time to propensity in hours Figure 5.1.: Trjectories in the regressive control regime. (A - C). Typicl trjectories (linege propensity x i vs. time) for system of three intercting lineges with initil vlues x(t = 0) = {0.8, 0.11, 0.09}. Prmeters of the sigmoid rewrd function in eqution (4.4) re set to σ i =0.05, s i = 20, nd x R i =1/3 fori =1, 2, 3. (D). Chrcteristic convergence curves verged over independent trjectories for the dominting linege 1 (red) nd for the two competing lineges 2 (green) nd 3 (blue). Threshold vlues for the convergence curves (indicted by the squres) re set to x t = {0.75, 0.65, 0.55, 0.45, 0.35} for linege i = 1 nd x t = {0.12, 0.17, 0.22, 0.27, 0.32} for linege i =2, 3. Error brs indicte the interqurtile rnge. time verges for severl threshold vlues. These convergence curves chrcterize the verged temporl development of the convergence process for ech individul linege i nd re used throughout this section to illustrte the system behviorin the regressive control regime. Exmples re shown in Figure 5.1(D) in which the chrcteristic convergence curves re verged over independent simultion runs in which the initil vlues of the linege propensities re set to x(t =0)= {0.8, 0.11, 0.09}. Detils of the simultion procedure re provided in Appendix D.1. The speed of convergence criticlly depends on the shpe of the rewrd function, but lso on the number of competing linege propensities N. Inthesimplified 78

89 5.1. Linege specifiction in the regressive nd the dissiptive control regime cse, tht the men propensity level x =1/N nd the root x R of the rewrd function equl (x R = x), fluctutions round the men propensity level re grdully suppressed until the system reches stedy stte x i = x, i. Thisidelizedscenrio is subsequently used to outline the system behvior in the regressive control regime. However, the divergence of the root x R of the rewrd function from the men coexpression level x =1/N leds to fluctutions of the ground stte nd cn possibly introduce linege bis. The ltter cse is discussed in Section 5.3. Dependence on the rewrd function. The shpe of the rewrd function criticlly regultes the dynmics of convergence of the linege propensities x towrds the men level x. In prticulr, the clss of the rewrd function f m (sigmoid vs. liner), the slope b t the root point s well s the sturtion level σ (in the cse of sigmoid rewrd function) sensitively influence the chrcteristic convergence curves. The dependence on ech of these prmeters is discussed below: Clsses of rewrd functions. As outlined in Section two different types of rewrd functions f m hve been studied, nmely liner (eqution (4.3)) nd sigmoid one (eqution (4.4)). Figures 5.2(A) nd (C) show the chrcteristic convergence curves for different rewrd functions f m shown in the corresponding Figures 5.2(B) nd (D), respectively. For clerrepresenttion, only the convergence curves for the dominting linege strting t x i (t =0)=0.8 reshown. The sigmoid rewrd functions defined in eqution (4.4) cn be dpted such tht the mximl slope b i occurring t the root point x R equls the slope of corresponding liner rewrd function with the sme root point. As shown in Figures 5.2(B) nd (D) the sigmoid functions (indicted in redndgreen) diverge from their liner counterprt (indicted in blue) depending on their sturtion prmeter σ. Illustrted by the chrcteristic convergence curves in Figures 5.2(A) nd (C), the liner rewrd functions generlly led to fster convergence towrds the men propensity level x s compred to the sigmoid rewrd functions. This is cused by the fct tht for propensities x i x the negtive rewrd m i for the liner rewrd function is much lrger s compred to the rewrd for the sigmoid function. However, for linege propensities x i x the dynmics become more similr. It should be noted tht for lrge vlues of the sturtion prmeter σ the sigmoid functions nd the liner functions re identicl in the intervl of interest [0, 1]. As the sigmoid rewrd functions pper more robust (compre Section 4.3.2) the further discussion is bsed on this type of functionunless otherwise noted. 79

90 5. Results I: Dynmics of linege specifiction A linege propensity linege 1, sigmoid high linege 1, sigmoid low linege 1, liner B linege specific rewrd m i x C linege propensity x time to propensity in hours linege 1, sigmoid high linege 1, sigmoid low linege 1, liner D linege specific rewrd m i linege propensity x i x x time to propensity in hours linege propensity x i Figure 5.2.: Convergence curves for liner nd sigmoid rewrd functions. (A) nd (C) show the chrcteristic convergence curves (verged over reliztions initited with x(t = 0) = {0.8, 0.11, 0.09}) for the dominting linege propensity x i (t). The corresponding rewrd functions (identified by equl colors) re shown in (B) nd (D), respectively. Prmeters of the sigmoid rewrd function shown in (B) (nd thus relted to the convergence curves in (A)) re set to σ i =0.05 (green), σ i =0.166 (red), b i = 0.5, nd x R i =1/3 for ll i =1, 2, 3. Prmeters of the liner rewrd function (blue) re b i = 0.5, nd x R i =1/3 for ll i. Prmeters in (D) (relted to (C)) re set to σ i =0.1 (green), σ i =0.33 (red), b i = 1, nd x R i =1/3for ll i for the sigmoid rewrd function nd b i = 1, nd x R i =1/3 for ll i for the liner rewrd function (blue). Slope of the rewrd function. The slope b i of the sigmoid rewrd functions is crucil prmeter regulting how fst the system converges towrds the men propensity level x =1/N. As illustrted in Figures 5.3(A) nd (B) the convergence curves re directly correlted with the steepness of the rewrd function s lrger vlues of b i led to fster convergence. However, s the rewrd functions re more similr for vlues x i x the difference in the convergence curves only become obvious once the linege propensities x pproch their men vlue x. In this regime (x i x = x R )thedifferences between the rewrd functions re most pronounced. 80

91 5.1. Linege specifiction in the regressive nd the dissiptive control regime A linege propensity C linege propensity linege 1, slope=-10 linege 1, slope=-1 linege 1, slope=-0.5 x time to propensity in hours linege 1, height=0.1 linege 1, height=0.05 linege 1, height=0.025 x time to propensity in hours B linege specific rewrd m i D linege specific rewrd m i x linege propensity x i x linege propensity x i Figure 5.3.: Convergence curves depending on the slope nd the sturtion level of the sigmoid rewrd function. (A) nd (C) show chrcteristic convergence curves (verged over reliztions initited with x(t = 0) = {0.8, 0.11, 0.09}) for sigmoid rewrd functions with different shpe. The corresponding rewrd functions reshownin(b) nd (D), respectively. Prmeters of the sigmoid rewrd function with different steepness in (B) (thus relted to the color coded convergence curves in (A)) re set to σ i =0.1, x R i =1/3, nd b i = 0.5 (blue),b i = 1 (green), b i = 10 (red) for ll lineges i. For the scenrio with different sturtion levels σ in (D) (nd relted to the convergence curves in (C)), prmeters re set toσ i =0.025 (blue), σ i =0.05 (green), nd σ i =0.1 (red), nd x R i =1/3,b i = 1 for ll lineges i. Sturtion level of the rewrd function. The sturtion level σ of the sigmoid rewrd function turns out to be similrly sensitive prmeters the slope b i outlined bove. Keeping the slope b i constnt nd vrying the sturtion level σ i,thegrphsinfigures5.3(c)nd(d)illustrtethtthe convergence to the men expression level x is ccelerted for higher vlues of σ i. Within the scope of this thesis, both the slope b i nd the sturtion level σ i pper s sensitive prmeters regulting the dynmicl behvior of the linege propensities x in the regressive control regime. 81

92 5. Results I: Dynmics of linege specifiction A linege propensity x lineges 5 lineges 7 lineges B linege specific rewrd m i x 7 x 5 x x x time to propensity in hours linege propensity x i Figure 5.4.: Convergence curves depending on the number of lineges N. (A) shows the chrcteristic convergence curves for systems with different numbers of competing lineges: N = 3 (red) initilized with x(t = 0) = {0.8, 0.11, 0.09}; N = 5 (green), initilized with x(t = 0) = {0.8, 0.05, 0.05, 0.05, 0.05}; N = 7 (blue), initilized with x(t = 0) = {0.8, 0.033, 0.033, 0.033, 0.033, 0.033, 0.033}. For ech scenrio individul reliztions hve been performed to clculte the shown verge convergence curves. As the men expression level x scles with 1/N, the root x R is dpted for the sigmoid rewrd functions shown in (B) with x R =1/3 (red),x R =1/5 (green), x R =1/7 (blue), nd σ i =0.1, b i = 1 for ll lineges i. Dependence on the number of lineges. For vrying numbers of competing linege propensities N the sigmoid rewrd functions need to be modified. As the men propensity level x =1/N scles with the number of lineges N, theroot point x R = x of the rewrd functions is shifted long the x-xis. This dependency is illustrted in Figure 5.4(B) showing the sigmoid rewrd functions for the scenrios N = 3, 5, 7. However, s indicted by the chrcteristic convergence curves in Figure 5.4(A) this shift only hs minor effect on the dynmics of the convergence towrds the men propensity level x. Inthissensethesystemppers robust ginst vritions in the number of competing lineges Dynmics in the dissiptive control regime Generl behvior. In the dissiptive regime, the system initilly undergoes competitive phse chrcterized by moderte fluctutions of thelinegepropensity levels. These fluctutions occur, since ll propensities re generlly in the sme rnge (x i x =1/N )ndrethereforeequllylikelytobechosenforthe updte procedure. However, in the course of time one linege propensity tkes over, reducing the probbility for the updte procedure to ct on the competing lineges (see lso Section nd Appendix A.1). The increse of the dominting linege propensity leds to reduced fluctutions nd n ccelertion of the 82

93 5.1. Linege specifiction in the regressive nd the dissiptive control regime A linege 1 linege 2 linege 3 B linege 1 linege 2 linege 3 linege propensity linege propensity time t in hours time t in hours C linege 1 linege 2 linege 3 D linege 1 linege 2 linege 3 linege propensity linege propensity time t in hours time t in hours E linege 1 linege 2 linege 3 F linege 1 linege 2 linege 3 linege propensity linege propensity time t in hours time to propensity in hours Figure 5.5.: Trjectories in the dissiptive control regime. (A - E) show series of five possible reliztions of the linege specifiction process under the dissiptive control regime (linege propensity x vs. time for N = 3, n i =0.05, initilized with x(t = 0) = {0.33, 0.33, 0.33}). (F) illustrtes the chrcteristic divergence curve for the dominnt linege verged over independent simultion runs. Strting from x i (t = 0) = 0.33, threshold vlues (indicted by the squres) re set to x t = {0.45, 0.55, 0.7, 0.9, 0.98}. Error brs indicte the interqurtile rnge. Curves re slightly shifted within the figures to void superpositions. 83

94 5. Results I: Dynmics of linege specifiction linege specifiction process. Finlly, the normliztion procedure slows down the linege specifiction process nd the leding linege propensity x i (t) 1in the limit t. Figures 5.5(A-E) show exmples of five possible reliztions with slightly different behvior during the initil competition phse. These differences re cused by the intrinsic stochsticity of the underlying updte procedure. Further detils of the simultion procedure re provided in Appendix D.2. The set of reliztions in Figure 5.5(A-E) suggests tht the verge divergence from the men linege propensity level x =1/N is suitble mesure to chrcterize the dynmics in the dissiptive control regime (divergence curve). Techniclly, for ech individul trjectory the time point is recorded when the linege propensity of the dominting linege x i psses certin threshold x t.timevergesfor different individul threshold vlues re obtined seprtely for ech dominting linege i. The resulting divergence curves in Figure 5.5(F) connect the time verges for the individul threshold vlues x t = {0.45, 0.55, 0.7, 0.9, 0.98}, thus providing comprehensive picture of the temporl extension oflinegecommitment for ech individul linege i. Furthermore, the frction of cells tht finlly commit to echofthen possible lineges is n indictor of the intrinsic blnce of the linege specifiction process. The importnce of this mesure is illustrted below. Dependence on the rewrd. The criticl prmeter of the stochstic linege specifiction process in the dissiptive control regime is the intercept of the liner rewrd function f m,definedsn i in eqution (4.5), which is constnt nd independent of x i. As Figure 5.6(A) indictes, the process of linege specifiction slows down s the rewrd m i = n i declines with the intercept. However, s long s the intercepts re chosen to be identicl for ll lineges N lso the contribution to ech of the lineges is blnced. This is shown in Figure 5.6(B) outlining the frction of cells tht finlly commit to ech of the N =3possiblelinegesfor different vlues of n i. Incresing one of the individul intercepts n i results in higher likelihood for the promotion of the prticulr linege. Reclling tht the intercept n i directly determines the rewrd m i it follows tht the prticulr linege with the highest rewrd benefits most in the updte procedure. This unblnced contribution is illustrted in Figure 5.7 in which the intercepts n i re fixed for two of the three lineges (i =2, 3, green nd blue) wheres the other one is stepwise incresed (i = 1, red). Figures 5.7(A), (C), nd (E) illustrte the chrcteristic divergence curves. Given the incresed rewrd of the red linege the commitment process is ccelerted s compred to the blue nd green lineges. Furthermore, the linege contribution is skewed towrds thepreferredlinege. This behvior is illustrted by the br chrts in the corresponding Figures 5.7(B), (D), nd (F), respectively, in which the frction of cells in ech of the N =3 84

95 5.1. Linege specifiction in the regressive nd the dissiptive control regime A linege propensity n i = 0.2 n i = 0.1 n i = 0.05 n i = B linege contribution n i = n i = 0.05 n i = 0.1 n i = time to propensity in hours linege 1 linege 2 linege Figure 5.6.: Linege commitment for blnced rewrds. (A) illustrtes divergence curves (verged over individul reliztions with x(t = 0) = {0.33, 0.33, 0.33}) for different rewrds m i = n i =0.025, 0.05, 0.1, 0.2. For ech of the four scenrios, n i is identicl for ll N = 3 lineges ( blnced ). Br chrts in (B) show the frction of cells finlly committing to ech of the lineges (indicted by corresponding colors) for the different scenrios n i =0.025, 0.05, 0.1, 0.2. Error brs re negligible due to mny reliztions. possible lineges is shown. It is evident tht the skewing effect becomes more dominnt for incresed intercept levels n i of the preferred linege. In Figure 5.8 similr scenrio is shown in which only the intercept n i of the blue linege (i =3)iskeptfixed. Theinterceptsofthe red ndthe green lineges (i =1, 2, respectively) re both incresed (in Figures 5.8(A-D): n 1 > n 2 >n 3,inFigures5.8(E),(F):n 1 = n 2 >n 3 ). As indicted in the corresponding br chrts these scenrios led to different skewed linege contributions with n incresing disdvntge of the blue linege (i =3). Dependence on number of lineges. Unlike the regressive control regime in which the number of competing lineges hs little impct on dynmics of convergence towrds the men coexpression level x, thiseffectismorepronouncedinthe dissiptive regime. Upon initition of the competition process in the dissiptive regime there re in generl N different lineges with similr probbilities to be chosen in the updte process. As the individul updte probbility of prticulr linege decreses with the number of competitors it is evident tht the time point until one of the lineges domintes over the others is delyed. This effect is illustrted in Figure 5.9(A) in which the divergence curves recompredfor the scenrios N =3, 5, 7. Figures 5.9(B), (C), (D) provide smple trjectories for the cses N =3(B),N =5(C),ndN =7(D).Theseindividulreliztions support the notion tht n increse in the number of lineges leds to prolonged competition phse in which most of the lineges hve similr propensitylevels. 85

96 5. Results I: Dynmics of linege specifiction A linege propensity linege 1 linege 2 linege 3 B linege contribution C linege 1 linege 2 linege 3 time to propensity in hours D linege propensity linege contribution E linege 1 linege 2 linege 3 time to propensity in hours F linege propensity linege contribution time to propensity in hours Figure 5.7.: Linege commitment for unblnced rewrds (1). (A), (C), (E) illustrte chnges in the divergence curves for different unblnced rewrds. Intercepts of the lineges i = 2 (green) nd i = 3 (blue) re kept fixed (n 2 = n 3 =0.05) nd the intercept of linege i =1(red)issubsequently incresed (n 1 =0.055 in (A), n 1 =0.06 in (C), n 1 =0.07 in (E)). Averges for ech scenrio re bsed on individul reliztions initilized with x(t = 0) = {0.33, 0.33, 0.33}. The br chrts in (B), (D), (F) show the corresponding frctions of cells finlly committing to ech of the 3 lineges (linege contribution, indicted by the color coding). 86

97 5.1. Linege specifiction in the regressive nd the dissiptive control regime A linege 1 linege 2 linege 3 B linege propensity linege contribution C linege 1 linege 2 linege 3 time to propensity in hours D linege propensity linege contribution E linege 1 linege 2 linege 3 time to propensity in hours F linege propensity linege contribution time to propensity in hours Figure 5.8.: Linege commitment for unblnced rewrds (2). (A), (C), (E) illustrte chnges of the divergence curves for different unblnced rewrds. The intercepts of linege i = 3 (blue) is kept fixed t n 3 =0.05 for ll scenrios. However, the intercepts of lineges i = 1 (red) nd i = 2 (green) re subsequently incresed (n 1 =0.06, n 2 =0.055 in (A), n 1 =0.07, n 2 =0.055 in (C), n 1 =0.07, n 2 =0.07 in (E)). Ech scenrio represents n verge over individul reliztions initilized with x(t = 0) = {0.33, 0.33, 0.33}. The br chrts in (B), (D), (F) show the corresponding frction of cells finlly committing to ech of the 3 lineges (linege contribution). 87

98 5. Results I: Dynmics of linege specifiction A time to propensity in hours N = 3 N = 5 N = 7 B time to propensity in hours N = 3 C N = 5 linege propensity D linege propensity 1 N = time to propensity in hours time to propensity in hours linege propensity linege propensity Figure 5.9.: Linege commitment depending on the number of lineges. (A) shows the divergence curves for systems with N = 3, 5, 7 competing lineges. Averges re tken over individul reliztions, ech initited with identicl propensities t time t = 0, i.e. x i =1/N for ll i. The intercept of the liner rewrd functions hs been set to n i = 0.05, i. (B - D) illustrte typicl, individul reliztions for the three scenrios N = 3, 5, 7, respectively. Reversibility. Within the dissiptive control regime it is centrl question until which point of development the process of linege commitment isstillreversible. This issue is best ddressed by nlyzing the propensities of thelinegestht re not dominting t the end of the commitment process (referred to s inferior lineges of prticulr reliztion). The mximum vlue of the linege propensity (mx x j )fornyinferiorlinegej is n indictor for how fr the dissiptive process cn continue while it is still possible to revert to nother dominting linege i which is finlly up-regulted (x i 1). Figure 5.10 provides n estimte of this mesure for different vluesofthe rewrd m i = n i. For higher vlues of m i there re few cses for which the linege propensity for n inferior linege ws lredy up to x j 0.7buttheprocess still reverted to nother dominting linege. As for smller vlues of the rewrd m i = n i more nd more simultion steps re necessry to ctully relize such reversion these mximl propensity for the inferior lineges decrese progressively. 88

99 5.2. Dynmics of the extended stem cell model reltive occurrence n i = 0.2 n i = 0.1 n i = 0.05 n i = mximl linege propensity of the inferior lineges Figure 5.10.: Reversibility of the commitment process. The figure shows the reltive frequency of observing mximl linege propensity of the inferior lineges before the process of linege commitment finlly reverts to n lterntive dominting linege. Inferior lineges re ll the lineges j N tht do not dominte prticulr reliztion of commitment process for t. Different colors correspond to different vlues of the rewrd m i = n i = 0.025, 0.05, 0.1, 0.2. The points indicte reltive frequencies of corresponding histogrm, connected by solid lines for better visuliztion. Histogrms re tken from 500,000 reliztions ech, initilized with x(t = 0) = {0.33, 0.33, 0.33} Dynmics of the extended stem cell model Modeling the in vivo sitution As proposed in Section 4.4 the individul dynmics of linege specifiction in the regressive nd the dissiptive control regime re embedded in the model of hemtopoietic stem cell orgniztion originlly proposed by Roeder nd Loeffler [33]. The overll dynmics of cell switches between signling contexts A nd Ω is not influenced by the dynmics of linege specifiction. However, the individul, cell-intrinsic linege propensity vectors x re modulted ccording to the rules of the regressive control regime for cells in A nd ccording to the rules of the dissiptive regime for cells in Ω. Although little informtion is vilble bout the vribility of trnscriptionl ctivity during the cell cycle,themodelssumes without loss of generlity tht the process of linege specifiction in signl context Ωonly tkes plce in G1 but not during S, G2 nd M phse. Following the process of linege specifiction within single cell nd its progeny over extended time periods, smple trjectories now pper s superposition of the two different control regimes. The bckground color for the four smple trjectories shown in Figure 5.11 encodes the signling context (nd thus the control 89

100 5. Results I: Dynmics of linege specifiction A linege 1 linege 2 linege 3 B linege 1 linege 2 linege 3 linege propensity linege propensity C linege 1 linege 2 linege 3 time t in hours D linege 1 linege 2 linege 3 time t in hours linege propensity linege propensity time t in hours time t in hours Figure 5.11.: Trjectories of the extended stem cell model. (A - D) Possible reliztion of the linege specifiction process within four smple cells chosen from one system (linege propensity x s function of time for N =3 lineges, indicted by the colors). Upon cell division (thin blck lines), linege propensities re only followed in one of the two dughter cells. Bckground colors indicte the current signling context of the cells (white bckground - A, grey bckground - Ω ). Prmeters re set to n i =0.1 for the rewrd function in the dissiptive regime, nd σ i =0.1, b i = 1, nd x R i =1/3 for i =1, 2, 3 for the sigmoid rewrd function in the regressive control regime. regime) to which the cell currently belongs. Wheres the white bckground indictes signling context A (with the regressive control regime), signling context Ω(with the dissiptive control regime) is encoded by the greybckground. The short intermedite plteus in Ω correspond to the S, G2 nd M phse of the cell cycle in which the process of linege specifiction is hlted. Techniclly,thetime courses in Figure 5.11 show the continution of the linege specifiction process over severl subsequent cell genertions, thus only following the linege propensities x in one of the two dughter cells fter ech cell division (blck horizontl lines). Initilizing the complete model with sufficient number of stem cells the system reches dynmiclly stbilized equilibrium with respect to the stem cell numbers 90

101 5.2. Dynmics of the extended stem cell model in A nd Ω s well s the numbers of differentiting cells 1 (see Figure 5.12(A)). Approprite prmeter configurtions re provided in Appendix D.3. Ontopof this cellulr dynmic the cell-intrinsic process of linege specifictionledstothe estblishment of stble frctions of cells committed to ech ofthen possible lineges. As for the exmple shown in Figure 5.12(B), N = 3differentlineges compete with identicl prmeters of the linege specifiction process (dissiptive regime n i =0.1, regressive regime with sigmoid rewrd function with sturtion level σ i =0.1, slope b i = 1). As the time courses indicte the three levels re fluctuting round the sme men level. The fluctutions re due to the limited life time of the cells, fter which lrge clones of cells re deleted t identicl times. Figure 5.12(C) shows the verge frction of cells committed toechofthethree lineges s well s the frction of uncommitted cells mesured from time step 1000 to As illustrted in the previous section, the intercept n i of the liner rewrd function f m = m i = n i in the dissiptive control regime is the criticl prmeter for the regultion of linege specifiction. Different representtive configurtions of rewrd prmeter m i = n i re discussed below: The sequence of grphs in Figure 5.12 compres two model systems with different rewrds m i = n i in the dissiptive control regime, nmely the rewrds for ll lineges i re incresed from m i = n i =0.1 (Figures 5.12(A- C)) to m i = n i =0.2 (Figures 5.12(D-E)). As expected, the overll cellulr dynmic (Figures 5.12(A) nd (D)) is left untouched s the prmeters of the underlying HSC model (compre Section 3.4) remin constnt. Similrly, the proportion of cells committing to ech of the three lineges remins blnced s the probbilities for commitment re still equl (Figures5.12(C)nd(F)). In contrst, the overll increse of the rewrds (m i = n i =0.1 m i = n i = 0.2) ccelertes the process of linege specifiction. This reduces the frction of uncommitted cells in which the dominnt linege propensity is below the threshold of commitment x i <x com (shown in grey in the Figures 5.12 (B), (C) nd (E), (F)). In the unblnced sitution, the individul rewrds m i = n i for the different lineges i differ. Figures 5.13(A-C) show simultion sequence, in which two of the rewrds re left untouched (m 1/2 = n 1/2 =0.1) nd one is slightly reduced (m 3 = n 3 =0.09). Agin, the overll cellulr dynmic is left untouched (Figure 5.13(A)). In contrst, the probbility of promoting the third linege (i =3,blue)isreduced. Thiseffectisvisibleinthetimecourses (Figure 5.13(B)) s well s in the verged frctions (Figure 5.13(C)). 1 Referring to Figure 4.7 the stem cell numbers in A comprise ll cells within signling context A, stem cell numbers in ΩreferstollcellsinsignlingcontextΩwith> min nd numbers of differentiting cells includes ll cells in signling context Ω with < min. 91

102 5. Results I: Dynmics of linege specifiction A B uncommitted cells linege 1 cells linege 2 cells linege 3 cells C cell numbers stem cells in A stem cells in Ω cells in Ω cell numbers stem cells in A 2000 stem cells in Ω cells in Ω time time D E F uncommitted cells linege 1 cells linege 2 cells linege 3 cells cell numbers time cell numbers time linege contribution linege contribution Figure 5.12.: Dynmics in system with blnced rewrds. (A), (D) show the number of stem cells in A (blck), stem cells (mgent) nd differentiting cells (ornge) in Ω s functions of time strting from sprsely populted initil system. (B), (E) show the corresponding time courses for the sme system with respect to linege commitment (grey - uncommitted cells; red, blue, green - cell numbers of the committed cells with x i >x com =0.75). Brchrts in (C), (F) indicte the frction of cells in ech of the four popultions, verged over the simultion run between time steps 1000 nd Prmeters of linege specifiction re chosen s n i =0.1 (A - C) nd n i =0.2 (D - F) for the rewrd function in the dissiptive regime, nd σ i =0.1, b i = 1, nd x R i =1/3 for i =1, 2, 3 for the sigmoid rewrd function in the regressive control regime. This effect is intensified if ll lineges re prmeterized with individul intercepts n i.thisisthecseinthesequenceofgrphsinfigures5.13(d-f) in which the intercepts re chosen s n 1 =0.12, n 2 =0.1, n 3 =0.08. Clerly, linege i =1(red)domintesthecommitmentprocess. Compred to the sequence of grphs in Figures 5.13(D-F), the simultions for Figures 5.13(E-J) re bsed on the doubling of the individul intercepts n i for the three lineges (n 1 =0.24, n 2 =0.2, n 3 =0.16) keeping their rtio constnt. Although the commitment process is generlly ccelerted the overll ppernce (one linege high, one intermedite, onelow)ismintined. 92

103 5.2. Dynmics of the extended stem cell model A cell numbers D cell numbers G stem cells in A stem cells in Ω cells in Ω time 10 stem cells in A stem cells in Ω cells in Ω time B cell numbers E cell numbers H uncommitted cells linege 1 cells linege 2 cells linege 3 cells time uncommitted cells linege 1 cells linege 2 cells linege 3 cells time uncommitted cells linege 1 cells linege 2 cells linege 3 cells linege contribution C linege contribution F J cell numbers stem cells in A stem cells in Ω cells in Ω time cell numbers time linege contribution Figure 5.13.: Dynmics in system with unblnced rewrds. Time courses of the cellulr composition nd the number of committed cells in ech linege s well s the verged proportions of cells re rrnged similr to Figure Prmeters of linege specifiction in the dissiptive regime re chosen s n 1 = n 2 =0.1 nd n 3 =0.09 (A-C); n 1 =0.12, n 2 =0.1 nd n 3 =0.08 (D-F); nd n 1 =0.24, n 2 =0.2 nd n 3 =0.16 (G-J).The sigmoid rewrd function in the regressive regime is given by σ i =0.1, b i = 1, nd x R i =1/3 for i =1, 2, 3. Cells re counted s committed if x i >x com =0.75. Tking these results together, it cn be demonstrted tht the bsolute rewrds m i = n i of the liner rewrd function in the dissiptive control regime determine the overll speed of linege commitment 2. However, it is the rtio between the 2 The speed of linege commitment is independent form the speed of differentition. The lter is defined by the differentition rte d tht hs been introduced in Section

104 5. Results I: Dynmics of linege specifiction individul linege specific vlues tht determine whether the commitment process is blnced or not. Interestingly, the model system is less sensitive to the defining prmeters of the regressive control regime. Even in the sitution tht the prmeters of the rewrd functions in the regressive control regime differ considerbly, there is lmost no visible effect on the cellulr level (dt not shown). Reclling tht the regressive regimes estblished the coexpression scenrio in which ll lineges propensities x re equlized, the corresponding prmeters only lter the speed of this process. Differences in the linege specific, individul prmeters do notccumultes long s the convergence to the men expression levels x is generlly shorter s the verge residence time in A. The individul trjectories in Figure 5.11 indicte tht cells chnging bck from signling context Ω into A re involved in process of fte reversion. As certin time in Ω promotes linege specifiction under the dissiptive control regime, the cell s linege propensity levels strt to diverge from the common coexpression level. However, s the model explicitly relies on dynmiclly stbilized equilibrium of cells in A nd Ω, the process of fte reversion under the regressive control regime ppers s nturl consequence. Assuming tht the process of linege specifiction is slow enough compred to the speed of differentition (loss of ffinity described by the model prmeter d) thisreversiononlyoccursforerlysteps of the linege commitment. However, in more extreme scenrios, s in the cse of trnsplnttion experiments in irrdited recipients, this effect might be more pronounced. Briefly summrizing, the model hs been constructed such tht thefinllydominting linege of prticulr reliztion cn only be predicted in probbilistic sense. In the cse of identicl rewrds n i in the dissiptive regime, the dominnce is eqully likely for ech linege i. However, the specifiction of rewrds n i with different vlues for ech linege skews the decision process towrds lineges with the higher rewrds. Moreover, self-renewing cell cn contribute to different cells types in vrying frctions Adpting the model to the in vitro sitution As shown in previous study [223], the experimentl in vitro sitution is sufficiently cptured by reducing the regenertion rte r nd mnipulting the min limit. These ssumptions generlly led to n exhustion of the popultion of self-renewing cells nd the initition of linege commitment processes within ll cells. However, the dynmics of the linege specifiction process remin lrgely untouched nd the phenomen of reduced self-renewl cpcity is merely ttributed to the originl cell-kinetic model. Since no stbilized dynmic equilibrium is estblished the composition of the cell culture is generlly ccessed in time-dependent mnner or by end point nlysis. 94

105 5.2. Dynmics of the extended stem cell model A cell numbers C cell numbers 1e totl cells uncommitted cells 10 linege 1 cells linege 2 cells linege 3 cells e time 100 totl cells uncommitted cells 10 linege 1 cells linege 2 cells linege 3 cells time frction of cells frction of cells B D time uncommitted cells linege 1 cells linege 2 cells linege 3 cells time uncommitted cells linege 1 cells linege 2 cells linege 3 cells Figure 5.14.: Dynmics of n in vitro system with blnced nd unblnced rewrds. Time courses of the cellulr composition re shown for simulted in vitro scenrio (regenertion rte r = 1, norm number of signling context A N A = 5, initited with 500 cells within [0.01, 1]). (A) Absolute cell numbers s function of time for scenrio with blnced contribution to ll lineges (blck - totl cells, grey - uncommitted cells, colored - lineges 1 to 3). (B) Frction of cells being uncommitted (grey) versus committed to lineges 1, 2 or 3 (red, green, blue) s function of time for the sme blnced rewrds (m = n =0.1). (C), (D) Corresponding grphs to (A) nd (B) for the sitution of unblnced rewrds (m 1 = n 1 =0.1, m 2 = n 2 =0.08, m 3 = n 3 =0.07). The sigmoid rewrd function in the regressive regime is set to σ i =0.1, b i = 1, nd x R i =1/3 for i =1, 2, 3 in ll scenrios. Cells re counted s committed if x i >x com =0.75. Figure 5.14 provides typicl time courses simulting n exponentilly expnding cell culture under in vitro conditions. As shown in Figure 5.14(A), the first cells pper s committed round time step t =50. Followingtheirexpnsions,the number of uncommitted cells (grey) diverges from the exponentilly incresing totl number of cells. Subsequently, the committed cells determine the overll system dynmics before the system finlly declines due to the limited lifetime of the differentiting cells. Figure 5.14(B) provides lmost identiclinformtion. 95

106 5. Results I: Dynmics of linege specifiction Here, the frction of cells within ech linege is shown insted of the totl cell numbers. This is conceptully closer to cell culture experiments in which the phenotypic composition is ccessed over time. Figures 5.14(C) nd (D) illustrte thesmebehvior for thesitution ofunblncedlinege contribution in which the development of the red linege is more likely s compred to theotherlineges. As for the modeling of the in vivo sitution, the skewed linege contribution results by djusting the intercepts in the dissiptive regime (for the shown sitution: n 1 >n 2 >n 3 ) Instructive versus selective linege specifiction As pointed out in Section of the previous chpter, there re in principle two scenrios to influence linege contribution, nmely the instructive nd the selective scenrio of linege specifiction. The previous nlysis in this section focused prticulrly on the question how linege contribution cn be intrinsicllyskewed by unblnced rewrds. This pproch directly corresponds to the instructive linege specifiction since subsequent cell deth does not hve regultingfunction on the linege contributions. In contrst, selective linege specifiction is bsed on the concept tht the initil linege decision is blnced (by using identicl rewrds m i for ll lineges) wheres the regultion of the linege contribution is fcilitted by subsequent,selective cell deth process. Detils of the selection process re described in Section In order to illustrte the dynmics of selective linege specifiction, system is studied in which the contributions to ech of N =3possiblelinegesisblnced on the level of the intrinsic linege decision by using identicl rewrds m i for ll lineges i. As reference system, the selective cell deth process Φ S is djusted such tht the linege specific intensities for cell deth (defined in eqution (4.9)) re set to φ i =0.01 for ll lineges i (lso, the boundries for the ction of the cell deth process x deth/low i =0.5 ndx deth/high i =1.0 resettoidenticlvluesforll i). In this cse, there is no selective effect s ll lineges re equllyffectedbythe cell deth process Φ S nd the frction of cells contributing to ech of the possible lineges is conserved (Figure 5.15(A), (B)). Additionl to the cellnumbersinech linege in Figure 5.15(A) lso the cumultive number of deth cells is shown (in yellow). As the cell deth intensity Φ S = φ i remins constnt once certin threshold for the dominting propensity is pssed (x i >x deth/low i )thecumultive number of deth cells follows the development of the trget cell popultion. In contrst, if the probbility for cell deth φ i is incresed for one linege s compred to the others, the reltive frction of cells committed to this linege decreses. This intuitive result is illustrted in Figures 5.15(C), (D). Going one step further nd ssigning different cell deth intensities φ i to ech individul linege, qulittively similr result is obtined s in the instructivescenrio (compre Figure 5.14(C), (D)): one linege is positively selected wheres the other 96

107 5.2. Dynmics of the extended stem cell model A cell numbers C cell numbers E cell numbers 1e totl vible cells uncommitted cells linege 1 cells 10 linege 2 cells linege 3 cells cumultive deth cells e time 100 totl vible cells uncommitted cells linege 1 cells 10 linege 2 cells linege 3 cells cumultive deth cells e time 100 totl vible cells uncommitted cells linege 1 cells 10 linege 2 cells linege 3 cells cumultive deth cells time frction of cells frction of cells frction of cells B D F time time uncommitted cells linege 1 cells linege 2 cells linege 3 cells time uncommitted cells linege 1 cells linege 2 cells linege 3 cells uncommitted cells linege 1 cells linege 2 cells linege 3 cells Figure 5.15.: Dynmics of n in vitro system with selective linege specifction. (A), (C), (F) Time courses of the cellulr composition including the cumultive number of deth cells nd (B), (D), (E) the frction of cells re shown s functions of time for simulted in vitro scenrio with selective linege specifiction (regenertion rte r = 1, norm number of signling context A N A = 5, initited with 500 cells within [0.01, 1]). Colors correspond to Figure Additionlly, the number of deth cells is shown in yellow. The scenrios differ in the linege specific cell deth intensity: (A), (B): φ i =0.01 for i =1, 2, 3; (C), (D): φ 1 = φ 2 = 0.0 nd φ 3 = 0.02; (E), (F): φ 1 = 0.0, φ 2 = 0.01 nd φ 3 =0.02. Boundries for the cell deth ction re set to x deth/low i = 0.5 nd x deth/high i = 1.0. Prmeters of the intrinsic linege specifiction re identicl for ll lineges: in the dissiptive regime m = n =0.1 nd for the sigmoid rewrd function in the regressive regime σ i =0.1, b i = 1, nd x R i =1/3. Cells re counted s committed if x i >x com =

108 5. Results I: Dynmics of linege specifiction lineges ply only minor roles. A prticulr exmple for the selective scenrio is shown in Figures 5.15(E),(F). For resons of completeness, it is remrked tht selective linege specifiction cn lso be pplied for the simultions of the in vivo scenrios yielding stble popultions of committed cells over time. The qulittive result, tht some lineges cn be promoted t the expense of others, holds in this sitution, too. A comprtive study between the selective nd the instructive scenriosisprovided in Section Fluctutions of the ground stte nd linege bis As mentioned bove, divergence of the root of the rewrd functions x R from the men propensity level x =1/N induces the individul linege propensities to fluctute round their men expression level insted of converging to this level. In order to understnd this behvior one might follow brief experiment of thought: Given tht the root of the rewrd functions is higher thn the men propensity level (x R > x =1/N )ndssumingthtn lineges hve linege propensities x i 1/N,theupdteprocedurewouldchooseechlinegewithlmostidenticl probbility. This linege would receive positive rewrd (s x i 1/N < x R ), thus incresing its own propensity nd decresing the propensities of the others due to the normliztion routine. However, t certin point, n individul propensity x i might exceed the root of the rewrd functions x R,thusinthenextupdte,for which this linege hs been chosen, it receives negtive rewrd. This imposes n upper limittion nd keeps the whole updte process in the regressive regime in frustrted stte: the system cn neither diverge nor converge to fixed level. Asimilrexplntionholdsforthesitution,thttherootof the rewrd functions is smller thn the men propensity level (x R < x =1/N ). In this cse, the propensities preferentilly decrese until they re limited by lower boundry s soon s individul propensity levels decrese below x R.Thephenomenologicl behvior is illustrted in Figure 5.16 in which individul reliztions re shown for the cses x R < x =1/N (Figure 5.16(A), (B)), x R = x =1/N (Figure 5.16(C), this is the generl cse in which the propensities converge towrds x =1/N )nd x R > x =1/N (Figure 5.16(D), (E)). Figure 5.16(F) shows the corresponding sigmoid rewrd functions which re just shifted with respect to their root x R.Colors correspond to the individul reliztions in Figures 5.16(A-E). As long s the devitions between the root of the rewrd functions x R nd the men propensity level x =1/N re still moderte, ll propensities cn fluctute round their common men level. However, incresing the root of the rewrd functions such tht the x R 1/(N 1) the system cn rech qulittively different dynmicl equilibrium. As indicted for three exmple reliztions in Figure 5.17 with x R =0.47, 0.5, 0.55 the propensities in the cse N =3self- 98

109 5.3. Fluctutions of the ground stte nd linege bis A 0.6 B linege propensity linege propensity C time t in hours 0.6 D time t in hours linege propensity linege propensity E time t in hours 0.6 F time t in hours 0.15 linege propensity linege specific rewrd m i x time t in hours linege propensity x i Figure 5.16.: Fluctutions of the individul linege propensities for different vlues of the root x R. (A - E) Linege propensities x for system with N = 3 lineges re shown s functions of time for different vlues of the root of the sigmoid rewrd function x R =0.1 (A), 0.2 (B), 0.33 (C), 0.38 (D), 0.43 (E) in the regressive control regime. The sturtion level σ =0.1 nd the slope b = 1 of the rewrd function re identicl for ll reliztions. The shpe of the corresponding rewrd functions is shown in Subfigure (F). The coloring corresponds to the individul reliztions in (A - E). 99

110 5. Results I: Dynmics of linege specifiction orgnize such tht two of them re up-regulted while one is lredy suppressed. This phenomen is termed linege bis, suponswitchingtothedissiptiveregime the two up-regulted lineges re treted preferentilly. At this point brief remrk is in plce to clrify definitions. The process of shifting linege contributions from the blnced to the unblnced sitution (by tuning the rewrds m i = n i )sdiscussedinsection5.1.2isreferredtos skewing throughout this thesis. In these cses linege propensities convergeto x i = x =1/N in the regressive regime which corresponds to the prmeter choise for the root vlue x R.Incontrst,thepreferenceforcertinlinegesinducedby frustrtedsystemwithx R x =1/N s outlined bove is referred to s linege bis. For system with N =3linegesndx R 1/2 =1/(N 1) (Figure 5.17(A); red sigmoid rewrd function in Figure 5.17(D)) the higher propensities stbilize t level below 1/(N 1) = 1/2 resultinginnon-zerovlueforthethird, lower propensity. In contrst for the cse tht x R =1/(N 1) = 1/2 (Figure 5.17(B); green sigmoid rewrd function in Figure 5.17(D)) the system reches stblesttewithtwopropensitiestx i = 1/(N 1) = 1/2 ndthethird propensity pproching zero. This behvior is lso observed forthecsetht x R 1/(N 1) = 1/2 (Figure5.17(C);bluesigmoidrewrdfunctioninFigure 5.17(D)). However, s x R > 1/(N 1) the two up-regulted propensities fluctute round the level x i =1/(N 1) = 1/2. Considering lrge popultion of cells, the introduction of linegebisdoes not ultimtely result in shift in the linege contributions. If the rewrd functions in the regressive control regime hve identicl prmeters, thelinegepropensities, which re up- or down-regulted during the estblishment of the linege bis, re eqully distributed. Only in the cse, tht one linege i is lredy penlized in the regressive regime (e.g. by choosing smller sturtion levelσ i )itisless present mong the up-regulted linege propensities during theestblishmentof the linege bis. If the cells re then switched into the dissiptive regime, the prticulr linege does lredy hve n initil disdvntge leding to reduced linege contribution. This scenrio is exemplified in Figure After keeping cells in the regressive control for 1000 timesteps (with the root of the rewrd functions set to x R =0, 47, 0.5, 0.55, respectively), rndom linege bis estblishes within ech of these cells. Thus two propensities re up-regulted while one is downregulted. However, if this process is unbised (σ = 0.1), ll lineges re eqully likely to be mong the up-regulted ones. Chnging the system to the dissiptive regime, the linege contributions of the three individul lineges re still blnced s shown in Figure 5.18(A) for three different vlues of the root of the rewrd functions x R =0.47, 0.5, However, if one linege (in this cse the blue one) hs disdvntge during the estblishment of the linege bis in the regressive control regime (σ 1,2 =0.1, σ 3 =0.08), it is less present mong the up- 100

111 5.3. Fluctutions of the ground stte nd linege bis A 0.6 B linege propensity linege propensity C time t in hours 0.6 D time t in hours 0.15 linege propensity linege specific rewrd m i x time t in hours linege propensity x i Figure 5.17.: Linege bis for different vlues of the root x R. (A - C) Linege propensities x for system with N = 3 lineges re shown s functions of time for different vlues of the root of the sigmoid rewrd function x R =0.47 (A), 0.5 (B), 0.55 (C) in the regressive control regime. The sturtion level σ =0.1 nd the slope b = 1 of the rewrd function re identicl for ll reliztions. The shpe of the corresponding rewrd functions is shown in (D). The coloring corresponds to the individul reliztions in (A- C). regulted linege propensities. After switching the cells to the dissiptive control regime this effect becomes mnifest by the reduced contributions of the blue cells (Figure 5.18(B)). The nlysis shows tht the model is in principle ble to represent n intrinsic linege bis. A detiled comprison of this phenomenon to vilble dt is beyond the scope of this thesis nd will be subject to seprte scientific work. 101

112 5. Results I: Dynmics of linege specifiction A 0.5 linege 1, σ = 0.1 linege 2, σ = 0.1 linege 3, σ = 0.1 B linege 1, σ = 0.1 linege 2, σ = 0.1 linege 3, σ = 0.08 linege contribution x R = 0.38 x R = 0.47 x R = 0.55 linege contribution x R = 0.38 x R = 0.47 x R = Figure 5.18.: Linege contribution for the fluctuting ground stte. (A) cells re simulted in the regressive control regime with the root of the rewrd functions set to x R =0, 47, 0.5, Further prmeters re set to x (t = 0) = 0.333, sturtion level σ =0.1 nd slope b = 1. For the simultions in (B) only the sturtion level of the rewrd function of the third linege i =3isreducedtoσ 3 =0.08. After 1000 time steps ll cells re switched into the dissiptive control regime with prmeters n =0.05. The contribution to the individul lineges is shown by the br chrts depending on the position of the root point in the regressive regime x R Experimentl vlidtion In the following the estblished simultion model of linege specifictionispplied to number of lndmrk experiments tht chrcterize the developmentl potentil of hemtopoietic stem nd progenitor cells in vitro Linege contribution of single differentiting cells Erly experiments on the linege contribution of isolted hemtopoietic, spleenderived mouse cells reveled the existence of cells tht give risetomorethnone cell type [26, 27]. In prticulr protocol, Ogw nd coworkers used primry culture initition ssy to purify colony forming cells [26]. Within the popultion of colony forming cells, they found tht bout two thirds of the cells give rise to clonl colonies contining only one cell type, wheres the reminingthirdof the cells contributed to two or even more (up to six) different cell types. In recent study, Tkno et l. [222] used CD34- c-kit+ Sc-1+ lin- (CD34- KSL) cells tken from dult mouse bone mrrow for similr set of experiments. The linege composition of the progeny of these cells ws nlyzed in vitro using single cell differentition ssys. For the comprison of the prticulr dt with the proposed model, simple simultion protocol is dpted. A previously estblished reference prmeter 102

113 5.4. Experimentl vlidtion T S source ssy Ω 1 / d... ω α r... Α linege ssy Ω Α ω α Figure 5.19.: Simultion strtegies for single cell differentition experiments. Cells from defined region within the homeosttic source ssy (trnsfer pool) re trnsferred into linege ssy. The trnsfer pools re indicted by the boxes in the source ssy (pool S (red) - fit for the dt from Sud et l. [26, 27]; pool T (blue) - fit for the dt from Tkno et l. [222]). Within the linege ssy the cells undergo linege commitment nd the contribution of different linege types is evluted. set describing hemtopoietic stem cell orgniztion in unperturbed mice [221] is used for the representtion of the homeosttic sitution from which bone mrrow cells hd been isolted experimentlly (source ssy, comprefigure5.19). This prmeter set ws complemented by n pproprite representtion of the intrcellulr linege specifiction dynmics with equl rewrds m i for ll lineges, intentionlly neglecting ny correltions between the development of certin lineges. Prmeters re chosen such tht differentiting stem cellisconsidered committed (x i >x com )fterfourtotendysoflinegespecifictioninsignling context Ω. Cells used for trnsfer into the linege ssys re chosenrndomly mong well defined subpopultion of the source ssy (clled trnsfer pool), chrcterized by the rnge of the ffinity prmeter trns. The boundries of these trnsfer pools re the centrl prmeters to fit the simultion results to the experimentl dt by Sud et l. [26, 27] (pool S, shown in red in Figure 5.19) nd Tkno et l. [222] (pool T, shown in blue in Figure 5.19). The linege ssy is represented by n empty model system in which the development oftheprogenyis observed for 240 h. Finlly, the number nd the linege of cells produced in ech 103

114 5. Results I: Dynmics of linege specifiction A 50 experimentl results by Tkno et l. simultion results B 50 experimentl results by Tkno et l. simultion results (including linege correltion) percentge observed percentge observed linege contribution linege contribution Figure 5.20.: Linege contribution of single differentiting cells (A). Experimentl results for the differentition of single CD34- KSL cells [222] re indicted by the grey brs (men, CI not vilble). Results for the corresponding simulted cells re shown in blue (men of 50,000 simultion runs). The linege contribution is coded s follows: 1-neutrophil, 2-megkryocyte, 3- erythroblst, 4-mcrophge (B). Introduction of moderte correltion between lineges 1 nd 4 in the in silico model increses the prticulr linege contributions. Prmeters re provided in the text nd in Appendix D.4. linege ssy re evluted. Due to n expected deficiency of properlyfunctioning hemtopoietic niche environment in cell cultures it isssumedthtforll simulted in vitro ssys the signling context A simply mintins the self-renewl bility of cell (mesured by its ffinity ) butdoesnotpromoteitsregenertion (r =1,seelsoSection5.2.2). In their series of experiments, Ogw nd coworkers [26, 27] distinguished six different lineges, nmely neutrophils, mcrophges, eosinophils, mst cells, megkryocytes, nd erythrocytes. Therefore, the in silico intrcellulr linege specifiction dynmics re constructed with N =6differentlineges. Thetrnsfer pool S (cf. Figure 5.19) for the simultion of the single cell differentition dt [26] hs been djusted to S trns [ , 0.99]. Using this prmeteriztion the experimentl observtions re closely mtched: two third of the cells only contribute to single linege (model prediction: 65.5 %) wheres the remining third contributes to two or more lineges. The potentil development in six different lineges yields 57 possible combintions in which the coloniescontributeto two or more different cell types (multiple linege contribution). However, s the uthors report only bout 50 such colonies in totl, sttisticl evlution nd comprison with the simultion dt is not instructive. To dpt the model system to the experimentl setup presentedbytkno et l. [222], the number of possible lineges is reduced to N=4 (neutrophils, megkryocytes, erythroblsts, mcrophges). Due to the more sophisticted stem 104

115 5.4. Experimentl vlidtion cell sorting procedure used in this experiment, the source popultion of initil prent cells is expected to contin n incresed frction of uncommitted cells. This is reflected by the nrrower trnsfer pool T ( T trns [0.012, 0.99], cf. Figure 5.19) mrking the difference to the simultions of the previous experiments by Sud et l. [26]. In the single cell differentition studies of bone mrrow derived CD34- KSL cells [222], the mjority (43%) of plted cells contributed to ll four determined lineges while other combintions re observed with lower frequency. Applying the dpted trnsfer pool T it ppers tht in the mjority of cses (model result: 42.9%) the progeny contined ll four lineges wheres other combintionsre reduced (Figure 5.20(A)). It should be emphsized tht this qulittive pttern is chieved even under the simplifying ssumption of blnced rewrds m i = n i = m. However, the precise mtching of the results is incomplete. The experimentl dt suggests tht there is moderte correltion between neutrophil nd mcrophge differentition (see linege combintion 1:4 in Figure 5.20(A)). In order to study whether the rtificl introduction of moderte, positive correltion between two lineges results in this kind of behvior minor modifiction of the presented model hs been developed. The detils re provided Section For the prticulr cse of correltion between lineges 1 nd 4 (neutrophils nd mcrophges, respectively) positive correltion prmeter γ 14 = γ 41 =0.3 hs been pplied. For ll other pirs of cell types i, j, thesecorreltionsreneglected, thus γ i,j =0. As indicted in Figure 5.20(B), the in silico model leds to shift in the differentition pttern similr to the experimentl observtions. Progeny of single cells contining neutrophil nd mcrophge cells re now significntly enhnced compred to other developments. However, due to the complexity of these, potentilly wek correltions between certin lineges nd the limited mount of vilble dte, detiled quntifiction nd further study of this process hs not been performed. Specific prmeter settings for the simultions in this Section re provided in Appendix D Comprtive differentition of pired dughter cells Extending the experiments on the differentition of individul cells in vitro, Ogw nd coworkers exmined the developmentl fte of two dughter cells derived from one prent cell [27]. By compring the linege contribution within the colonies generted from ech of the dughters, the uthors concluded tht linege potentil is progressively restricted by sequence of stochstic commitment steps tking plce t ech cell division. However, s lredy discussed in Section 3.3.5, the coupling of the linege restriction to the cell divisions hs notbeendemonstrted convincingly. The proposed model of linege specifiction, which is intrinsiclly decoupled form the process of cell division, further chllenges this view. 105

116 5. Results I: Dynmics of linege specifiction ω α ω α ω α r... ω α linege ssy S T 1 / d... Α Ω Ω Α Ω Α Ω Α division ssy source ssy Figure 5.21.: Simultion strtegies for pired dughter cell differentition experiments. Cells from defined region within the homeosttic source ssy (trnsfer pool) re trnsferred into division ssy. The trnsfer pools re indicted by the boxes in the source ssy nd re identicl to the single cell differentition experiments outlined in Figure 5.19 (pool S (red) - fit for the dt from Sud et l. [27]; pool T (blue) - fit for the dt from Tkno et l. [222]). After the first division in the division ssy both dughter cells re seprted nd their linege contribution is evluted within linege ssy. To support the nlysis of this type of experiment in the context of the proposed model further dt set is tken into ccount. Tkno nd coworkers [222] repeted the erlier experiments by using more sophisticted selectionprotocolto identify progenitor hemtopoietic progenitor cells (CD34- KSL)tkenfromdult mouse bone mrrow. The vribility of the linege contribution of prentl cell 106

117 5.4. Experimentl vlidtion A percentge of pired dughter cells identicl single linege experimentl results by Sud et l. simultion results non-identicl multiple lineges identicl multiple lineges B percentge of pired dughter cells experimentl results by Tkno et l. simultion results linege contribution Figure 5.22.: Linege contribution of pired dughter cells. (A). Experimentl results for hemtopoietic spleen-derived mouse cells re shown in grey (men, 95% CI) [27]. Results for the simulted cells (defined by the trnsfer pool S of the source ssy) re shown in red (men of 50,000 simultion runs, CI negligible due to the high number of replictes). (B). Experimentl results (corresponding to prentl division of CD34- KSL cells in medi contining SCF + IL-3 13) re shown in grey (men, 95 % CI) [222]. Results for the simulted cells (trnsfer pool T) re shown in blue (men of 50,000 simultion runs). Only cells with complete linege potentil (contribution to ll four lineges) re shown. On the x-xis, the linege contribution of the first dughter is given on top, of the second dughter below (1-neutrophil, 2-megkryocyte, 3-erythroblst, 4- mcrophge). ws evluted by following the fte of its two dughter cells. The simultion setup is closely relted to the bove stted cse for the linege contribution of single cells. In order to ccount for the seprtion fter the prentl division, rndomly chosen cells from the respective pools T nd S of the source ssy re trnsferred in the intermedite division ssy. The division ssy is represented by n empty model system mimicking the culture conditions for the division of the prent cell. For simultion efficcy, ll trnsferred cells re under the governnce of signling context Ω. The cell cycle position, the ffinity, nd the linege propensities x re preserved during the trnsfer from the source ssy to the division ssy. After division, both dughter cells re finlly trnsferred into two seprte empty model systems in which the development of the progeny is observed for 240 h (linege ssy). Finlly, the number nd the linege of cells produced in ech linege ssy re evluted nd compred to their sibling. As in the cse of the single cell differentition ssys, Ogw nd coworkers [27] distinguished six different lineges within their series of experiments. For the spleen-derived mouse cells, the uthors observed tht the mjority (73%) of the pired dughter cells contributed to just one linege, identicl for both dughters, 107

118 5. Results I: Dynmics of linege specifiction suggesting tht the prentl cell hd lredy been committed tooneprticulr linege (identicl single linege contribution). In ddition, number of pired dughter cells were observed which contributed to more thn one linege. In 10% of the experiments, both dughter cells contributed to the sme combintion of lineges (identicl multiple lineges), wheres in 17 % the dughter cells contributed to different combintions of lineges (non-identicl multiple lineges). Under the outlined ssumptions, the experimentl results cn bereproducedusing exctly the sme trnsfer pool S s it hs been used for the single cell differentition experiments. The comprison of the dt is shown in Figure 5.22(A). In close correspondence to dditionl findings reported in [27], it is observed tht for one pir of cells one dughter cell might develop into up to five linegeswhilethe other dughter cell is restricted to just one or two. Furthermore, some simultions generted dughters tht contribute to the sme overll combintion of lineges with considerbly different proportions of the individul cell types mong their progeny. For the cse of the more sophisticted stem cell sorting procedure used by Tkno et l. [222] the nrrower trnsfer pool T is pplied. Chnging no other prmeters, the model reproduces the generl results of the experiments: Among the initil prentl cells with complete linege contribution (ll four lineges occur in t lest on of the dughter colonies) pired dughter cells withidenticllinege development dominte over pirs with symmetric development (Figure 5.22(B)). In the simultion results dditionl minor contributions ( %) to other combintions of lineges re observed (dt not shown). These re not described experimentlly, which is most likely due to the limited number of observtions. Prmeters for the simultions on pired dughter cells re provided in Appendix D Linege specifiction in differentiting cell cultures The bility of the simultion model to ccount for vrying frctions of committed cells is verified in the context of well chrcterized cell line, nmely the FDCPmix cell line. FDCP-mix cells re derived from murine, multipotent hemtopoietic progenitors nd retin the cpcity to self-renew in the presence of high concentrtions of IL-3 [39, 97]. When trnsferred to low concentrtions of IL-3 combined with other hemtopoietic growth fctors, or injected into experimentl nimls, FDCP-mix cells show n pprently norml progression of linege commitment nd differentition. FDCP-mix cells mintined in Iscove s Modified Dulbecco s Medium (IMDM) contining 20% horse serum nd 100u/ml Interleukin-3 (IL-3) were wshed nd trnsferred t density of 4 x 104 cells/ml to IMDM contining 20% fetl clf serum nd either myeloid (M) or erythroid (E) growth fctors s previously described [97]. The combintion of growth fctors support differentition either into mixture of grnulocytes nd mcrophges (M) or into 108

119 5.4. Experimentl vlidtion M differentition Ω m > m > m g m e Α ω α init E differentition Ω m e> m g> mm Α ω α init Figure 5.23.: Simultion strtegies for differentiting cell cultures. For the simultion 250 cells re initilized within well defined initil ffinity, uniformly distributed in the rnge init =[0.01, 0.1] in signl context Ω, indicted by the boxes mrked init. Simultion prmeters re individully dpted for the differentition in grnulocyte/mcrophge (M) or erythrocyte (E) stimulting conditions. predominntly erythroid (E) popultion. On consecutive dys up to dy 9, cells were hrvested from replicte cultures nd cytospun. Following My-Grunwld stining, differentil counts were performed blind on cells per time point. This wy, temporl pttern of the differentition process could be obtined. The experimentl dt ws kindly provided by Michel Cross. In order to reflect the usge of reltively homogenous cells from cell line in the simultion model, the differentition ssy is initilized with popultion of 250 cells with well defined initil ffinity, uniformly distributed in the rnge init = [0.01, 0.1], compre Figure The frction of undifferentited nd committed cells is evluted hourly for period of 9 dys. A blnced expression of the N =3 linege propensities x (t =0)=1/3 isssignedtothecells,suchthttheyre initilly identicl for the development in ech of the three experimentlly observed cell types: grnulocytes, mcrophges nd erythrocytes. Both, the instructive nd the selective scenrio of linege specifiction hve been pplied to nlyze the observed development of the cultures under grnulocyte/mcrophge (M) or erythrocyte (E) stimulting conditions. To simulte the differentition of FDCP-mix popultions in the presence of growth fctors in the instructive scenrio, the corresponding rewrds m i = n i of the dissiptive control regime re dpted in fvor of the relevnt ftes. The 109

120 5. Results I: Dynmics of linege specifiction simultion results re compred to the experimentl dt in Figure 5.24(A), (B) for both the differentition in M- nd E- medi. The linege specific vlues for the rewrds m i = n i in the dissiptive regime re the only difference ssumed for the different medi conditions. During erythroid development, erythrocytes mture from erythroblsts. Since it is possible to distinguish between these cell types morphologiclly, erythroid cells re subdivided for the phenotypic mpping (cf. Section 4.3.3), such tht the committed cell stge now comprises erly committed cells (erythroblsts) nd mture cells (erythrocytes). Figure 5.24 confirms tht the simultion model in the instructive scenrio is ble to quntittively ccount for the temporl development of the proportions of observed cell types in both, M- nd E-medi. Prmeter settings for the simultions re provided in Appendix D.6. Alterntively, the experimentl dt cn be described in the context of selective linege specifiction, demonstrted in Figures 5.24(C), (D). As discussed in Section 5.2 the linege specific rewrds in the dissiptive regime re identicl for ll three observed lineges (m 1 = m 2 = m 3 )suchthttheyrellpromotedwith equl likelihood. However, the simultions for the different culture conditions (M nd E) differ in the choice of the linege specific cell deth intensities φ i.wheres under M conditions the erythroid cells undergo cell deth, the sitution is different under E conditions in which the selection process leds to the preferentilremovl of cells committed towrds the grnulocyte nd mcrophge lineges. In both, the instructive nd the selective scenrio of linege specifiction, the regulting prmeters hve been dpted to meet the prticulr experimentl results. However, the greement of simultion nd experiment cnberegrded s proof of principle tht the proposed model is ble to dequtely ccount for differentition kinetics on the popultion level. The question remins whether the model could help to distinguish between instructive nd selective mechnisms governing the process of linege specifiction under prticulr conditions. As shown bove, this is hrdly possible on the popultion level. However, it will be demonstrted in the next chpters tht the developmentl process on the single cell level re more dequte to ddress this question Summry nd dditionl remrks The extensive nlysis of the system dynmic nd the ppliction to set of relevnt experimentl results illustrtes tht the model successfully ccounts for the criticl phenomen of linege specifiction stted in Section 4.1. In prticulr the model is suited to ccount for the centrl spects of restriction of linege potentil nd the genertion of diversity (criteri C1 nd C2). This is substntited by the ppliction of the model to results on the differentition of single cells nd pired progenitors in Sections nd As the model of linege specifiction is 110

121 5.5. Summry nd dditionl remrks A 100 M instructive B 100 E instructive % of differentiting cells % of differentiting cells C M selective time in hours D E selective time in hours % of differentiting cells % of differentiting cells time in hours time in hours Figure 5.24.: Linege contribution of FDCP-mix cells. Experimentl results for differentition in M-medium (A,C) nd E-medium (B,D) re illustrted by the brs (ssessed by morphology counts on dily bsis) s function of time. The simultion results re indicted by the corresponding lines (blue - grnulocytes; green - mcrophges; ornge - committed erythroblsts; red - mture erythrocytes; grey - undifferentited progenitors). (A,B) correspond to the instructive mode of linege specifiction, (C,D) to the selective mode. constructed s n ccelerted drift towrds rndom linege rther thn n immedite decision the spects of temporl extension nd reversibility re nturlly integrted s well (criterion C3). The pplicbility of n instructive nd selective mechnism of linege specifiction re strikingly demonstrted using the time course dt on the differentition of the FDCP-mix cell line under different culture conditions (criterion C4). However, the close concordnce of this two fundmentlly different mechnisms to explin the sme dt set hints towrds structurldeficiencyofmostpopultionbsedpproches. It is precisely the verging over multitude of cells tht erses minor differences on the single cell level. Therefore view is dvocted nlysing linege specifiction not only s popultion phenomen but on the bsis of individul cellulr developments. Using the proposed model the necessry methodology is presented in the subsequent chpters. 111

122 5. Results I: Dynmics of linege specifiction It ppers s the logicl continution of the outlined reserch to couple the regultion of linege specifiction, this mens the regultion of the ctul linege contributions, to the presence nd concentrtion of progenitor nd mture cells. It hs been shown experimentlly s well s theoreticlly tht there exist multiple feedbck loops (mostly fcilitted by cytokine concentrtions) between more mture cell stges nd the stem cell comprtment [157, 224]. However, the current model lcks sufficient description of the development of ltercellstges. Therefore, the introduction of possible feedbcks would be rther specultive nd cn not go beyond generl sttement. An extension nd dption of the model pproch is scheduled to include spects of cell mturtion. Similr restrictions pply to the study of linege bis phenomen. It hs been shown in number of experiments tht hemtopoietic stem cells cn obviously inherit certin preference in their linege contribution [44, 45]. Addressing this dt in the concept of the presented model is subject to nother project which is currently underwy. The min results within Section 5.4 hve been published in [114]. The model simultions for this publiction re bsed on liner rewrd functionintheregressive control regime insted of the sigmoid rewrd function used throughout this thesis (compre Section 4.3.2). However, the results re bsiclly identicl s this is minor chnge under the pplied conditions. 112

123 6. Methods II: Chrcteristics of single cell development Clssicl cell culture pproches ddress cellulr prolifertion nd differentition potentil on the popultion level. However, the ppliction of time-lpse video monitoring combined with pproprite nlysis methods will soonllowtomp these observbles on the level of single cells. The resulting dtstructurerepresents the developmentl genelogy of ech individul cell, in which ll the popultion mesures re encoded. The following two chpters of this thesisredevoted to the sttisticl nlysis nd comprison of the resulting dt type in defined mthemticl frmework Records of single cell development The stem cell model presented in this thesis is bsed on the simultion of individul cells. Although the sme set of rules pply to ll these cells, ech nd every cell cn obey n individul position in the spce of their defining vribles, i.e. cell cycle position c, ttchmentffinity, signlingcontexta or Ω, nd linege propensities x. As outlined in Section 3.4 this individul position influences the tendency for certin future developments. The cell-bsed chrcter of the modeling pproch llows studying cell fte decisions on the level of single cells nd their progeny nd to record ll relevnt chnges in their defining vribles. For the exmple of the cell differentition ssys for the FDCP-mix cell cultures studied in Section 5.4.3, two such records re shown for rndomly chosen cellsinfigure6.1. These tree-like structures re more generlly referred to s cellulr genelogies. As discussed in Section 2.4 comprble type of dt cn be obtined by nlyzing time lpse videos tken from pproprite cell cultures. By keeping trck of the position nd the divisionl history of ech initil cell one obtins number of unique exmples of developmentl sequences s they occur under the prticulr ssy conditions. The suitbility of this pproch hs been shown recently in number of relevnt publictions [126, 128, 130, 225, 226]. The nture of the dt type, i.e. in situ records of single cell development, is closely similr between experimentl dt nd the proposed model frmework. On one hnd the experimentl dt will contribute to refinement ofthesimultion model (e.g. with respect to the distribution of cell cycle times) but on the other hnd the model nlysis llows bckwrd interprettion of the dt in the light of the model. The identifiction of similrities between experimentl nd simu- 113

124 6. Methods II: Chrcteristics of single cell development A B Figure 6.1.: Exmples of simulted cellulr genelogies. The two exmples shown in (A) nd (B) correspond to single cell records from the simulted popultion experiments shown in Figures 5.24(C), (D), respectively. The verticl lines represent division events nd the horizontl lines represent cells. The color coding corresponds to Figure 5.24, too. Further detils of cellulr genelogies re described in the min text below. lted dt could revel more insights bout generic principles tht govern cellulr development. However, due to technicl limittions the vilbility of experimentl dt is still limited, lthough it is expected to gin more importnceinthe next yers. In cell culture experiments the overll expnsions nd the differentition potentil cn be esily compred between different cell culture conditions. However comprisonofthenumerouscorrespondingcellulrgenelogies is more chllenging. In prticulr, the complexity of the prticulr type of trcking dt requires rigorous chrcteriztion nd set of well suited mesuresforsttisticl evlution. Moreover, lrge set of such cellulr genelogies cn revel typicl ptterns of cellulr development nd clonl heterogeneity which re hrdly visible by nlyzing single reliztions or observing the popultion verge. Bsed on this motivtion the following topics re ddressed: Estblishment of forml chrcteriztion of cellulr genelogies for the nlysis of the divisionl history (i.e. topology of the tree-like structure) nd for the storge of cell specific nd time dependent prmeters such s size, morphology, fluorescence ctivity etc. 114

125 6.2. Forml chrcteristics of cellulr genelogies Development of set of mesures for the comprison of different sets of cellulr genelogies with focus on: mesures of clonl expnsion mesures of symmetry within cellulr genelogies mesures of correltion between chrcteristic events Comprison of methods for representing cell fte decisions within cellulr genelogies. The introduction of the terminology nd the proposed mesures within this chpter is ccompnied by two exmples of their ppliction in the context of the simultion model in the next chpter Forml chrcteristics of cellulr genelogies Cellulr genelogies re derived from the trcking of single, specified cell object (generlly referred to s root cell) nditsentireclonloffspring. Techniclly, cellulr genelogy is n unordered tree grph G =(C, D) composedofsetof edges C = {c i,i=0...n} representing cells nd set of brnching points D = {d j,j=1...m} representing division events. Unordered trees re chrcterized s trees in which the prent-dughter reltionship is significnt, but the order mong the two dughter cells is not relevnt. Ech genelogy is uniquely identified by its root cell c 0 which is the cell tht hd been chosen s the initil cell of the trcking process. The root cell nd ll its descendents re ordered into subsets C g ccording to their genertion g, strting with the root cell c 0 C 0 nd followed by the dughter cells in the first to the gth genertion. Furthermore, cells re chrcterized by their future development, i.e. to ech cell c i belongs either subsequent division event d j,givingriseto two dughter cells (c i C div,withc div representing the subset of ll cells which undergo division), or the cell s existence termintes without further division either by cell deth (c i C deth,withc deth representing the subset of ll cells which die within the observtion period) or by termintion of the trcking process (c i C term,withc term representing the subset of ll cells with censored observtion, i.e. no informtion bout future cell fte is vilble). Finl cells re termed lef cells, i.e.c lef = C deth C term.thereltionr pq between ny two cells c p nd c q is defined s topologicl distnce which mesures the number of divisionsbetween these cells. Dughter cells tht shre the sme prentl cell retermedsiblings. A schemtic representtion of cellulr genelogy nd n illustrtion of the distnce mesure re provided in Figure 6.2. The temporl dimension of the trcking process is usully encoded in the length of the edges; however this is n ssocite informtion rther thngenuinetopo- 115

126 6. Methods II: Chrcteristics of single cell development root genertion root cell c 0 1st genertion c 1 d 1 c 2 2nd genertion c 3 d 2 c 4 c 5 d 3 c 6 * 3rd genertion * d c 7 4 c * 8 d c 9 5 c 10 d c 11 6 c 12 4th genertion d 7 c 13 * c 14 * * time * * Figure 6.2.: Schemtic sketch of cellulr genelogy. Within the given five genertion genelogy the thin horizontl lines represent the cells c i wheres the divisions d j re mrked by the thick verticl brs. Colors correspond to the cell s genertion g. The horizontl dimension is time t with the founding root cell c 0 indicted on the left side (grey, genertion g = 0). Thus, the length of the horizontl lines represents the durtion of the cell s existence nd is mesure of the cell cycle time τ c. Finl cells on the right side re clled lef cells (mrked with n sterisk). The degree of reltion r pq between ny two cells c p nd c q is given by the number of divisions between them. For exmple, cells c 6 nd c 8 hve degree of reltion r 6,8 = 4 (seprted by the divisions d 3, d 1, d 2, nd d 4 ). Using the sme mesure of reltion, the brnch length from the root c 0 to the lef cells is determined. For the prticulr exmple the longest brnch is r 0,14 = 4 nd the shortest brnch is r 0,6 = 2. logicl prmeter. Similrly, ny dditionl nd potentilly time-dependent informtion tht hs been recorded during the trcking process cn bettributedto the corresponding edges c i,suchsthesptilposition,thesizeofthecells,the expression of certin linege specific mrker genes, or the fluorescence ctivity of prticulr cell lbels. Specificlly, in the cse tht dt onthelinegecommitment is vilble, fte informtion χ i (t) isssignedtothecellc i. Different methods for this ssignment nd detiled exmples re presented in Section Topologicl mesures for cellulr genelogies The quntittive ssessment of cellulr genelogies is the bsis for their comprtive nlysis. Restricting the view to the prent-dughter reltionship one obtins n unordered tree structure tht cn be chrcterized by suitble topologicl mesures. This topologicl structure is the defining feture of ll cellulr genelogies nd is independent of ny experiment-specific, dditionl informtion (e.g. sptil informtion, fluorescence mesurements) ssigned to the trcked cell objects. 116

127 6.3. Topologicl mesures for cellulr genelogies One might recll tht the nlysis of tree like structures hs longtrdition in phylogenetics nd evolutionry biology (see the historicl overview in [227]). Compring different phylogenetic trees, the influence of externl pressure on the evolutionry development is chrcterized nd linked to ssocited ptterns in the tree shpe. Although some of the proposed mesures within this thesis pick up the ide of shpe mesures in phylogenetics the generl pproch in the nlysis of cellulr genelogies strts from different point: Wheres in sttisticl phylogenetics certin tree structure represents re rther unique set of events typicl for certin species, the nlysis of cellulr genelogies is bsed on the comprison of mny heterogeneous, lbeit similr pedigrees derivedunderidenticl culture conditions. Also the interprettion of the typicl events like cell deth/extinction nd division/brnching is different for cellulr genelogies s for phylogenetic trees, chnging the focus to other relevnt questions. The following list of suitble topologicl mesures for cellulr genelogies hs been derived fter extensive nlysis of multitude of potentil mesures using simulted cellulr genelogies. The presented mesures focus on distinction between cellulr genelogies tht hve been derived under different experimentl conditions with respect to expnsion, symmetry nd the occurrence of cell deth events. Furthermore, these mesures proofed useful to quntify the heterogeneity occurring within set of genelogies tht hs been derived under identicl conditions. The list is by no mens complete nd my require extension for different experimentl questions. Totl number of leves L nd the totl number of divisions D. The totl number of leves L is suitble mesure for the clonl expnsion of prticulr root cell. The index L counts ll cells c i of certin genelogy tht do not terminte with further division. The number of divisions D occurring in the sme genelogy is eqully well suited for estimtion of cellulr expnsion since D = L 1. The exmple of cellulr genelogy shown in Figure 6.3 hs L =11leves(mrkedbythesterisks)ndD =10 divisions (indicted by the thick verticl brs). Popultion verges of these vlues re closely relted to the overll expnsion of the cell culture. Beyond the verge vlues, the width of the distribution of the number of leves L (or divisions D, respectively) originting from different cells under the sme culture conditions is n indictor of popultion inherent heterogeneity in the clonl expnsion potentil tht cnnot bedetermined on the popultion level lone. Formlly, the totl number of leves L is given s: L = { 1 for c i C term I D, with I D = 0 else c i C (6.1) 117

128 6. Methods II: Chrcteristics of single cell development * B = 3 * * B = 4 B = 4 * B = 2 * B = 3 * * * * B = 4 * B = 4 B = 4 B = 4 B = 4 B = 4 Figure 6.3.: Leves nd brnch length. Exmple of cellulr genelogy with L = 11 leves (mrked by the sterisks) nd D = 10 divisions (indicted by the blck verticl brs). For ech lef cell the brnch length B is provided. Color coding of the cells corresponds to the genertion g (root - grey, g = 1 - mgent, g =2-blue,g = 3 - green, g =4- drk red). Brnch lengths B. The brnch length B = B k mesures the number of divisions between the root cell c 0 nd specific lef cell c k. The complete set of brnch lengths for ll lef cells of given genelogy is mesure of the prolifertive ctivity of the root cell, but, it lso ccounts for the heterogeneity within single expnding clone. Both these spects re briefly discussed. Due to the exponentil nture of cellulr expnsion, the verge brnch length B within prticulr genelogy is dominted by the mximl brnch lengths mx(b). To circumvent this inherent bis, chrcteristic brnch length of genelogy B chr is proposed for which the different brnch lengths B k re weighted by the genertion g in which the lef cell occurs. Intuitively speking, B chr is the expecttion vlue of the brnch length by rndomly following the genelogy from the root cell c 0 to the leves. Such normliztion process ensures tht longer nd more rmified brnches re weighted less compred to shorter brnches. The distribution of brnch lengths B k within prticulr genelogy chrcterizes the heterogeneity within the progeny of single expnding (root) cell. However, these distributions re lwys dominted by the longer brnches due to the exponentilly incresing number of lef cells. Therefore, it cn be rgued tht the reltion between the extreme vlues min(b) ndmx(b) is more instructive. Defining the rnge of brnch lengths B rnge s the dif- 118

129 6.3. Topologicl mesures for cellulr genelogies ference between the miniml nd the mximl brnch lengths provides simple mesure to quntify this heterogeneity. Formlly, the brnch length B k is defined s the topologicl distnce r 0,k between the root cell c 0 nd lef cell c k C term.thechrcteristicbrnch length of genelogy B chr is clculted s B chr = c k C term (B k /2 gk ) (6.2) in which g k refers to the genertion of lef cell c k. The rnge of brnch lengths B rnge for certin genelogy is given s B rnge = mx k (B k ) min k (B k ). For the exmple of the cellulr genelogy depicted in Figure 6.3 the brnch lengths B re provided for ech individul lef cell. For this genelogy, the chrcteristic brnch length evlutes to B chr = = nd the rnge of brnch lengths to B rnge =4 2=2. Symmetry index (weighted Colless index C w ). Tree shpe mesures with focus on symmetry hve long trdition in the nlysis of phylogenetic trees [227, 228, 229]. These mesures re commonly used to detect imblnces tht testify the regultion of diversity in ecologicl communities. Applied to the sitution of cellulr genelogies these mesures cn provide n understnding of the blnce between self-renewl nd differentition, s well s on the ction of cell deth processes. AprticulrusefulmesureistheColless indexofimblnce C [230]. This index compres the number of leves emerging from the two dughter cells c dughter;1 nd c dughter;2 resulting from the division of the prent cell c i.colless index C sums the difference in the number of leves subtended by the two dughter cells for ll divisions within the genelogy nd normlizes by dividing with the lrgest possible score. Colless index increses from C =0 for perfectly symmetric genelogies to C = 1 for completely symmetric genelogies. However, the clssicl Colless index puts the sme weight on symmetries tht occur lte in development compred to erlier events. This is contrry to the common biologicl perspective on the blnce between stem cell self-renewl nd differentition which ssumes tht symmetries re most pronounced in the erly divisions. Especilly in the cseoflrge, exponentilly expnding genelogies, such erly events re underestimted by the clssicl Colless index compred to vst mount of expnsion events in ltter stges of development. Therefore, weighted Colless index C w is proposed explicitly ccounting for the exponentil expnsion within cellulr 119

130 6. Methods II: Chrcteristics of single cell development L = 3 L = 4 1 (3 1) / 2 L = 1 0 (7 4) / 2 2 (2 1) / 2 L = 1 L = 2 L= 7 Figure 6.4.: Colless index. For three encircled divisions the contributions to the weighted Colless index C w re outlined below ech event. The color-coded pirs of prenthesis on the right side summrize the number of leves subtending from ech of the relevnt dughter cells. The exponent of the denomintor corresponds to the genertion g of the mother cell. The coloring scheme of the cells indictes their genertion g (compre Figure 6.3). genelogies. In contrst to the clssicl Colless index C, theweightedcolless index C w sums over the differences in the number of leves emerging from two dughter cells which re weighted ccording to the genertion in which the symmetry occurs. Formlly, the clssicl Colless index of imblnce is given s C = 2 (L 1)(L 2) c i C div L i;1 L i;2. (6.3) L i;1, L i;2 refer to the number of leves subtended by the two dughter cells of cell c i.incontrst,theweightedcolless indexc w is given s C w = N 1 C (1/2 gi ) L i;1 L i;2 (6.4) c i C div The genertion g i refers to the genertion of the prentl cell c i. C w is normlized with constnt N C which corresponds to the mximl possible vlue of the Colless index for completely symmetric tree with L leves. N C is defined s N C = (L 2 j) (6.5) 2 j j=0...(l 3) 120

131 6.3. Topologicl mesures for cellulr genelogies For the exmple of the cellulr genelogy in Figure 6.4 contributions to the weighted Colless index C w re outlined for the encircled division events. The denomintor results from the weighting with the genertion g of the mother cells. Cell deth index A. Progrmmed cell deth (lso referred to s poptosis) potentilly plys n importnt role in regultion of hemtopoiesis in vivo (compre Section 2.3.2) nd is lso regulrly observed in cell cultures. The cell deth index A mesures the observed frequency of cell deth events nd is, therefore, n estimte of the probbility of cell deth occurrence. To ccount for systemtic effects relted to cellulr development, it seems pproprite to consider the cell deth index A s function of the current cell stte nd/or the genertion g within the genelogy. Therefore, the cell deth index A g is clculted s the rtio of the number of cell deth events observed for cells in genertion g nd the number of ll cells existing in the sme genertion. In contrst to the cell deth index A g itself, generliztion to pirs of sibling cells llows to identify potentil correltions of cell deth events nd, therefore, to revel prticulr symmetries in cell ftes. The ide behind this pproch is tht in cse of sttisticlly independent events, the probbility of observing prticulr combintion of events in two siblings (i.e. cell deth in none, one or both siblings) equls the product of the probbilities of the corresponding events for individul cells. Thus, if cell deth events would occur independently of ech other, the ltter probbilitiescouldbeestimted by (1 A g ) 2,2A g (1 A g ), (A g ) 2, respectively. Using the differences in the observed nd the (under the independence ssumption) expected frequencies of these pir-wise events, it is possible to clculte the so clled mutul informtion (MI)ofllsiblingpirswithinprticulrgenertion. TheMI, which lwys hs vlues between 0 nd 1, is mesure of the informtion bout one of the two events tht is provided by the other one. In the prticulr cse, MI =0wouldimplythtonecnnotobtinnyinformtion bout the cell deth occurrence of one sibling cell from knowing the fte of the corresponding dughter cell, s expected under the pplied model ssumption of completely rndom cell deth. Formlly, the cell deth index A g is n estimtor of the probbility for cell deth event occurring in genertion g of certin genelogy. It is clculted s A g c = i C I D (6.6) in which the indictor function I D = c i C J D { 1 for c i {C deth C g } 0 else is used to 121

132 6. Methods II: Chrcteristics of single cell development count the number { of cell deth events in genertion g nd the indictor 1 for c i C g function J D = to determine the totl number of cells tht 0 else exist in the sme genertion g. The mutul informtion of two (discrete) rndom vribles X nd Y is defined s MI(X, Y )= ( ) p(x, y) p(x, y)log 2 (6.7) p(x)p(y) y Y x X in which p(x, y)isthejointprobbilitydistributionofx nd Y,ndp(x)nd p(y) rethemrginldistributionsofx nd Y,respectively. I.e.,theMI is the expected log-likelihood difference between the bivrite model nd the product of the mrginl models. In the prticulr cse of cell dethevents, one ssumes identicl probbility distributions for both sibling cells. Therefore, the expected probbilities for the three possible events (i.e. none (p 0 ), one (p 1 )ortwo(p 2 )celldetheventpersiblingpir)underthehypothesis of sttisticl independence of the two siblings cn be estimted by (1 A g ) 2, 2A g (1 A g ), (A g ) 2,respectively. Estimtingthebivriteprobbilitiesby the observed reltive frequencies (f i,i=0, 1, 2) of the forementioned events (p i,i=0, 1, 2), leds to the estimted mutul informtion per genertion g: MI g = f 0 log 2 ( f 0 (1 A g ) 2 ) + f 1 log 2 ( f 1 2A g (1 A g ) ) ( ) f2 + f 2 log 2 (A g ) 2 (6.8) For illustrtion of the MI mesure, two genelogies re shown in Figure 6.5. Although these genelogies hve identicl vlues for the number of leves L, the chrcteristic brnch length B chr nd the totl number of deth cells they differ significntly with respect to correltion of the cell deth events. Wheres in Figure 6.5(A) the cell deth events re rther isolted, they lwys pper mong sibling cells in Figure 6.5(B). This leds to incresed vlues of the mutul informtion mesure MI in the ltter scenrio. It should lso be noted tht this pproch cn be generlized to other events chrcterizing the fte of sibling cells. A relted but less nlyticl pproch to correlte fluorescence expression between closely relted cells, indicting synchronized epigenetic remodeling in embryonic stem cells, hs been published recently [130]. Miniml distnce between chrcteristic events R. Cellulr genelogies retin informtion bout the reltedness of certin chrcteristic cellulr events like the occurrence of cell deth, chnges in the cells morphology,or the expression of cell fte chrcteristic mrkers. Beyond the mutul informtion MI,thetopologicldistncer ij between such chrcteristic cellulr 122

133 6.3. Topologicl mesures for cellulr genelogies A B Figure 6.5.: Mutul reltion between cell deth events. The genelogies in (A) nd (B) hve similr topologiclly fetures (L = 14, B chr =3.75, B rnge = 1, C =0.05, A 3 =1/4, A 4 =1/3 for both genelogies). However they differ with respect to occurrence of cell deth events. Wheres in (A) the cell deth events re rther isolted, they lwys pper in sibling cells in (B), resulting in differences for the weighted Colless index (C w =0.068 in (A); C w =0.136 in (B)), the mutul informtion mesures MI g (MI 3 =0.036 nd MI 4 =0.076 in (A); MI 3 =0.244 nd MI 4 =0.276 in (B)) nd the miniml distnce R (R =3in(A);R = 1 in (B)). Coloring of the cells indictes their genertion g (compre Figure 6.3) events occurring in cells c i nd c j hs been identified s suitble mesure of their reltion. In prticulr, it is the miniml distnce (denoted s R i )between chrcteristic event of cell c i (e.g. cell deth) nd the closest similr event of nother cell c j tht proved useful for the identifiction of whether the events re rther isolted or pper closely relted. If t lest two chrcteristic events occur within given cellulr genelogy, minimldistnce R i cn be clculted for ech of them. To provide unique mesure forech cellulr genelogy, the verge R over these individul miniml distnces R i is clculted seprtely for ech genelogy. Lower miniml distnces R indicte closer reltion between the events, possibly due to similr developmentl stges of the cells in question, wheres tendency towrds higher miniml distnces is more likely cused by generl effects independent of the cell stte. Formlly, the individul miniml distnce R i for chrcteristic event occurring for cell c i is defined s R i = min (r ij ) (6.9) c j C chr in which C chr refers to the set of cells for which chrcteristic event hs 123

134 6. Methods II: Chrcteristics of single cell development been observed nd r ij is the topologicl distnce between them. The index R i (nd consequently the verge R) isnotdefinedforgenelogieswithless thn two such chrcteristic events in C chr. An illustrtive exmple for the detection of closely relted cell deth events is provided in Figure 6.5. Although the cellulr genelogies hve the sme number of cell deth events, the individul distnce to the next event is lwys R i > 1 for the cellulr genelogy in Figure 6.5(A) but R i =1forll cell deth events in Figure 6.5(B) Assignment of linege ftes The limittions in ccessing the commitment stte of cell in situ clerly effects the ssignment of the fte informtion χ i to the corresponding cell c i. Approching this phenomenon from the model perspective is good option to pprecite the two fundmentlly different views on linege ssignment nd their implictions for the interprettion of cell division events. Within the proposed simultion model, linege specifiction isrepresenteds continuousprocessprogressivelyrestrictingthenumberof vilble developmentl options. A simple phenotypic mpping, introduced in Section llows ttributing cells s uncommitted or committed to prticulr cell type lthough smllbutcontinuouslydecresingprobbilityforconversion remins. This informtion bout the commitment stte of cell is vilble throughoutthe whole trcking process for ech individul cell. Therefore, itcnberepresented in the cellulr genelogies in stright forwrd fshion, which is referred to s the prospective view: Applying the outlined mpping procedure, cell c i is mrked ccording to its current internl propensity levels x(t)sundifferentitedχ i (t) =0 (for x j(t) <x com )orcommittedtocertinlinegefteχ i (t) =1, 2,...,N (for x j(t) >x com )withn denoting the number of possible lineges. Figure 6.6(A) shows typicl cellulr genelogy in which linege informtion is ssigned in the prospective view. All divisions d j within this view re chrcterized by compring the linege specifiction stte of the prent cell (prior to division) to the stte of the dughter cells (immeditely fter division). This results in two clsses of division events: undifferentited symmetric divisions if n undifferentited prent gives rise to two undifferentited dughters (χ prent = χ dughter;1 = χ dughter;2 =0)ndsymmetric divisions if committed prent gives rise two dughters of the sme fte (χ prent = χ dughter;1 = χ dughter;2 > 0). Since cell divisions in the underlying model system do not involve ny differentition event nd re thus symmetric by definition, symmetric divisions do not occur in the prospective view. In contrst to the simultion model, linege ssignment is difficult tsk in the experimentl sitution, especilly if the cellulr genelogy needs to be min- 124

135 6.4. Assignment of linege ftes tined. Using clssicl time lpse microscopy of differentiting cell culture, the only, currently vilble, non-invsive method for this ssignment is the identifiction of cell type specific chnges in the cell s morphology. However, chnges in morphology re hrd to identify nd occur rther lte compred to chnges in the trnscriptionl ctivity of cell fte specific genes. Novel techniques tht re lredy developed for hemtopoietic stem nd progenitor cells [131], llow the trgeted plcement of genes coding for the expression of fluorescence proteins under the control of prticulr linege specific promoters ( reporter genes ). By use of these reporter genes it should be possible to obtin informtion bout the linege decisions during the trcking process. Currently, there re onlypreliminrystudies using this technique in the context of single cell trcking pproches; however it is the most promising strtegy for the prospective ssignment of linege ftes in cellulr genelogy. An lredy pplied technique for the identifiction of linege ftes in cellulr genelogies relies on stining methods. This pproch requires the conservtion of the finl, sptil configurtion of the trcking procedure in order to llow unique mpping into the genelogy. This is only fesible for dherent cell cultures s they re used e.g. for the trcking of neurl stem nd progenitor cells. However, this ssignment of linege ftes refers only to the finl configurtion nd erlier decision events hve to be estimted in retrospective view. Giventhtlinegefteχ i is ssigned to ech lef cell, the fte of ll cells within the genelogy is determined recursively s follows: If both dughter cells of prentl cell belong to the sme linege, then the sme linege is ttributed to the prent cell (χ prent = χ dughter;1 = χ dughter;2 ). The prticulr division is chrcterized s symmetric. In contrst, if the dughter cells re of different lineges or one is undifferentited (χ dughter;1 χ dughter;2 ), then the prent cell is mrked s undifferentited (χ prent =0)nd the prentl division is counted s symmetric. Two undifferentited dughter cells (χ dughter;1 = χ dughter;2 =0)derivefromnundifferentitedprent(χ prent = 0) due to n undifferentited symmetric division. Evluting the sme cellulr genelogy s Figure 6.6(A) in the retrospective view (i.e. only bsed on the linege fte of the lef cells) modified version of the genelogy is obtined s shown in Figure 6.6(B). There, the progeny of prentl cell tht only givesrisetoonecell linege is lwys shown in the sme color. 125

136 6. Methods II: Chrcteristics of single cell development A prospective view B retrospective view Figure 6.6.: Prospective versus retrospective view for the linege ssignment. (A). The sketch shows n exmple genelogy for which the linege fte is ssigned in the prospective view. Coloring of the cells indictes the stte of commitment s given by the phenotypic mpping, i.e. the color coding of cell might chnge during the cells existence from uncommitted (grey) to either the ornge or the green linege depending on the dominting linege propensity x i. In contrst, for the identicl genelogy in (B) the linege fte is ssigned recursively bsed on the linege fte of the dughter cells (i.e. bckwrds from the finl configurtion shown on the right). Colors for the divisions re ssigned s follows: undifferentited symmetric divisions - mgent, symmetric divisions of committed cells - light blue, symmetric divisions (only in the retrospective view )-red. 126

137 7. Results II: Quntittive nlysis of in silico cellulr genelogies Within this chpter, the sttisticl mesures for cellulr genelogies nd the different pproches for the linege ssignment re pplied to different sets of reference dt. Since prcticl problems with the genertion of sufficiently long nd qulittively nlyzble time lpse videos of suitble cell cultures s well s difficulties in the utomtic identifiction nd trcing of single cells in current imge-processing techniques limit the vilbility of experimentlly derived cellulr genelogies, the reference dt is tken from the single-cell bsed model introduced in the previous chpters. Bsed on this model, it cn be nlyzed how chnges in the prticulr (in silico) growthconditionsinfluencethetopologyofthecellulrgenelogies nd how the imprinted mechnisms of linege specifiction cn be reextrcted from the topology informtion Compring cellulr genelogies under different growth conditions Genertion of cellulr genelogies under different growth conditions In order to test the different mesures for the quntittive chrcteriztion of cellulr genelogies three different in silico conditions re studied which re inspired by typicl cell growth scenrios. First, n empty model system is initilized with one model stem cell which undergoes mssive expnsion. This is referred to s the growth scenrio. Therefter, the model system estblishes stble pool of self-renewing cells tht simultneously contribute to pool of differentiting cells. This is referred to s the homeosttic scenrio. Chnging the system prmeters such tht the self-renewl bility of the cells is lost, the whole popultion of cells undergoes finl differentition nd subsequent cell deth. This is referred to s the differentition scenrio which is inspired by in vitro cultures of stem nd progenitor cells lcking self-renewl promoting conditions. 127

138 7. Results II: Quntittive nlysis of in silico cellulr genelogies Linege specifiction is relized such tht ech of the N =3possiblelinege ftes occurs with the sme probbility (i.e. blnced rewrds m i = n i = m). For the derivtion of the cellulr genelogies in the growth scenrio 400 independent model reliztions re trcked for 300 hours (one hour corresponds to one time step of the simultion), ech initilized with one single stem cell. Only in this sitution with n empty model system, the strong initil expnsion is observed. In contrst, for the homeosttic scenrio nd for the differentition scenrio ll cells in the homeosttic stem cell comprtment of one prticulr model reliztion re uniquely mrked nd subsequently trcked for the next 300 hours. Typiclly round 400 cells re trcked in this process, similr to the 400 independent reliztions in the growth scenrio. Forthehomeosttic nd differentition scenrio, there is no sttisticl difference in choosing individul cells in different reliztions or within the sme reliztion s long s the systems re initillyinthe homeosttic sitution (i.e. stble numbers of stem cells in signling context A nd Ω). A schemtic representtion of the cell popultion dynmics for the different scenrios nd typicl chrcteristic cellulr genelogy for ech scenrio is shown in Figure 7.1. Further prmeter settings for these simultions re provided in Appendix D.7. For the explortion of the effects of cell deth on the cellulr genelogies, bckground cell deth is pplied with constnt intensity Φ B = φ for ll cells in G1-phse (cf. Section 4.3.4). Generlly, such n effect might lsooccurinother stges of the cell cycle. However, the focus of this nlysis is directedtowrdsthe (quntittive) chrcteriztion of the generl impct of cell deth events on cellulr genelogies rther thn on the detils of the biologicl process. The simplifying ssumption of restricting cell deth events to G1-phse does notqulittively chnge the results wherefore the nlysis is restricted to this scenrio without loss of generlity. A discussion of selective cell deth s regulting process in linege specifiction (selective linege specifiction, compresections4.3.4nd5.2.3)nd its effect on the resulting cellulr genelogies is provided Section Topologicl chrcteriztion nd comprison The topologicl mesures introduced in Section 6.3 re now pplied to the sets of cellulr genelogies resulting from the bove stted simultion scenrios. It is the centrl dvntge of this comprehensive set of mesures to llow for the quntittive comprison of the different cellulr genelogies which goes fr beyond the visul impression s it is provided in Figures 7.1(B-D). As some of the mesures re not invrint under chnges of the observtion period their scling behvior needs to be discussed seprtely. This is especilly necessry in the cse, in which genelogies from experiments withdifferentobservtion periods need to be compred. Alredy in the model sitution, sturtion effects (in the growth scenrio) orexhustion(inthedifferentition scenrio) re 128

139 7.1. Compring cellulr genelogies under different growth conditions A # of stem cells time in hours B C D Figure 7.1.: Simultion scenrios nd corresponding cellulr genelogies. (A). Numbers of stem cells in Ω (green) nd A (red). At time t=0, the system is initilized by single stem cell, tht subsequently undergoes expnsion. The corresponding growth scenrio is indicted by the first shded re (observtion period of 300 hours, trcking of 400 individul cellulr genelogies in independent reliztions). Around t=600 the system reches dynmiclly stbilized equilibrium. For the cellulr genelogies of the homeosttic scenrio, ll stem cells present t time point t=700 re uniquely mrked nd subsequently trcked for 300 hours (second shded re). Chnging differentition nd regenertion prmeters t time t=1500 (blue line), the self-renewl bility of the stem cells is lost nd they undergo terminl differentition (differentition scenrio). As in the homeosttic scenrio, cellulr genelogies re derived by mrking ll stem cells present t time point t=1500 prior to the chnge of prmeters nd their subsequent trcking for 300 hours (third shded re). (B - D). Chrcteristic genelogies for ech scenrio ((B) - growth scenrio, (C)-homeosttic scenrio, (D) - differentition scenrio). Colors indicte cell cycle sttus of the undifferentited cells nd commitment to three possible lineges for the differentiting cells: grey - undifferentited proliferting cell (Ω ); blck - undifferentited quiescent cell (A ); yellow/ornge - erly/finlly committed cell of the ornge linege; light/drk blue - erly/finlly committed cell of the blue linege; light/drk green - erly/finlly committed cell of the green linege. 129

140 7. Results II: Quntittive nlysis of in silico cellulr genelogies A Frequency Frequency Frequency 0 60 growth scenrio homeostsic scenrio differentition scenrio totl number of leves L B totl number of leves L growth homeostsis differentition observtion period in hours Figure 7.2.: Totl number of leves L. (A) shows histogrms of the distributions of the totl number of lef cells L for the three different scenrios growth, homeostsis nd differentition. (B) provides corresponding scling behvior, i.e. medin of the number of leves L (indicted by the dots nd supplemented by the first nd third qurtiles) s function of the observtion period (rnging from 100 h to 350 h, shown on x-xis). not negligible nd cn led to nonliner divergence from the nticiptedbehvior. It cn be expected tht the influence of such effects is even morepronounced in the experimentl sitution. Therefore, n dditionl discussion of the prticulr scling behvior for ech mesure is provided in the context of the model. Totl number of leves L. The totl number of leves L hs been introduced s mesure to quntify clonl expnsion. Histogrms of the distributions of the totl number of leves L for the three scenrios (growth, homeostsis nd differentition) re provided in Figure 7.2(A). Incresed vlues of L in the growth scenrio re plusible since the initil expnsion is chrcterized by high prolifertive ctivity nd shortening of the effective cell cycle time 1,whichledstonincresednumberofcelldivisionsduringthe observtion period for the cellulr genelogies. In contrst, the homeosttic nd the differentition scenrio show only moderte expnsion s the effective cell cycle time returns to norml vlues. For the vlidtion of the scling of the topologicl mesures, further sets of cellulr genelogies re obtined which use the sme set of root cells but for which the observtion time is vried, rnging from 100 hours to 350 hours. In 1 Due to low cell numbers in both signling contexts A nd Ω, cells in Ω re quickly ttrcted to chnge into A fter division. However, these cells re lso quickly rectivted into Ω to undergo the next round of divisions, thus leding to n effective shortening of the verge cell cycle times. For further detils the reder is referred to [47]. 130

141 7.1. Compring cellulr genelogies under different growth conditions the cse of unlimited growth, one would rgue the totl number oflevesl scles exponentilly with the observtion period. As shown by the log-lin plot in Figure 7.2(B) this scling behvior is verified for wide rnges of the observtionperiod. The different slopes indicte different overll expnsion rtes. A sturtion occurs for the differentition scenrio which is cused by the limited prolifertive ctivity of the differentiting cells within the model. The vrince in thenumberoflef cells L is indicted by the error brs (corresponding to the interqurtile rnge) for the different sets of cellulr genelogies. As this is lso trnsformed to the log-lin scle the vrince cn only be compred on reltive scle. Brnch lengths B. Similr to the totl number of leves L the chrcteristic brnch length B chr ddresses the expnsion of cell clone within given time intervl. Histogrms of the chrcteristic brnch length B chr for the cellulr genelogies derived under the three different culture scenrios re shown in Figure 7.3(A). It is evident tht the chrcteristic brnch length B chr is incresed in the growth scenrio s compred to the other scenrios. As illustrted bove, this effect is induced by the shortening of the effective cell cycle times s the system hs not reched its equilibrium stte, thus llowing more divisions within fixed time period. The dominnt pek t very short brnch lengths in thehomeosttic scenrio derives from popultion of cells minly residing in signling context Ωrrely undergoing cell division t ll. In comprison, lmost ll cells in the differentition scenrio re ctivted into cell cycle nd undergo regulr divisions. Therefore, the observed heterogeneity in the observed chrcteristic brnch length B chr is rther limited. As expected, Figure 7.3(B) supports the notion tht the chrcteristic brnch length B chr scles linerly s the observtion period vries. This scling behvior results from the direct coupling of the number of subsequent cell divisions to the durtion of the observtion. Possible sturtion effects thtreexpectedfor experimentl reliztions re most likely cused by limittions of spce, nutrition nd prolifertion cpcity of the cells. Both, the totl number of leves L nd the chrcteristic brnch length B chr re mesures for the expnsion of cell cultures under different conditions. Although the totl number of leves L scles exponentilly with time nd the chrcteristic brnch length B chr scles linerly with time, the resulting histogrms in Figures 7.2(A) nd 7.3(A) re qulittively relted. However, on top of this clssicl popultion mesure to quntify the expnsion of cell cultures, the individul cellulr genelogies give ccess to the heterogeneity within cell popultion. In this sense it is the vrince of the totl number of leves L nd of the chrcteristic brnch length B chr which indictes tht individul cells undergo expnsion t very different extent. 131

142 7. Results II: Quntittive nlysis of in silico cellulr genelogies A Frequency Frequency 0 60 Frequency growth scenrio homeosttic scenrio differentition scenrio chrcteristic brnch length B chr B chrcteristic brnch length B chr growth homeostsis differentition observtion period in hours Figure 7.3.: Chrcteristic brnch length B chr. (A) shows histogrms of the distributions of the chrcteristic brnch length B chr for the three rtificil culture scenrios. (B) provides medin vlues of the chrcteristic brnch length B chr (indicted by the dots nd supplemented by first nd third qurtiles) for different observtion periods (rnging from 100 h to 350 h). The rnge of brnch lengths B rnge is possible mesure to ddress this heterogeneity since it quntifies the difference between the shortest nd the longest brnch within one genelogy. Histogrms for the corresponding distributions re shown in Figure 7.4(A). The dominnce of high bsolute vlues in the growth nd in the differentition scenrio indictes tht uniform expnsion in ll brnches is rrely observed nd tht the genelogies re chrcterized by significnt differences in the brnch lengths B within individul genelogies. This effect is less pronounced in the homeosttic scenrio. However, the incresed occurrence of cellulr genelogies with low chrcteristic brnch length B chr 0(i.e. cellswith extended periods of cellulr quiescence, compre Figure 7.3(A)) mnipultes this perspective. The rnge of brnch lengths B rnge scles liner with the observtion period, see Figure 7.4(B). This scling results from the liner scling of the mximl brnch length mx(b) wherestheminimlbrnchlengthmin(b) rechesconstnt vlue for sufficiently long observtion periods due to the ction of bckground cell deth. Agin, the limittions in the prolifertive ctivity of the differentiting model cells led to sturtion effect in the differentition scenrio. Symmetry index (weighted Colless index C w ). Colless index C nd the weighted Colless index C w ddress the question of how prolifertion nd quiescence re blnced on the level of individul cells. However, ppliction of the clssicl Colless index C requires creful interprettion since ll symmetries re 132

143 7.1. Compring cellulr genelogies under different growth conditions A Frequency 0 60 Frequency Frequency growth scenrio homeosttic scenrio differentition scenrio rnge of brnch lengths B rnge B rnge of brnch lengths B rnge growth homeostsis differentition observtion period in hours Figure 7.4.: Rnge of brnch lengths B rnge. (A) shows histogrms of the distributions of the rnge of brnch lengths B rnge for the three rtificil culture scenrios. (B) provides the corresponding medin vlues (indicted by the dots nd supplemented by the first nd third qurtiles) for different observtion periods (rnging from 100 h to 350 h). weighted eqully, irrespective of whether they occur erly or lte in development. Therefore, weighted Colless index C w hs been introduced in Section 6.3 to ccount for the exponentil expnsion within the genelogy putting higher weight on erly symmetries. As visulized in Figure 7.5(A), there is tendency for higher vlues of the weighted Colless index C w in the homeosttic scenrio. It is here tht the blnced sitution between quiescence nd prolifertion leds tonumberofhighly symmetric genelogies (indicted by high vlues of C w ). However, t the sme time the width of the distribution indictes the pperence of number of lmost symmetric genelogies (i.e. low vlues of C w ). In these, the brnches re committed eqully to either continuous prolifertion or quiescence. Since cell prolifertion is more likely in the growth nd the differentition scenrio, verge vlues of the weighted Colless index C w re slightly reduced indicting higher numbers of more symmetric genelogies. Generlly, the width of distributions for the weighted Colless index C w indictes tht the there is significnt popultion inherent heterogeneity in ll simulted scenrios rnging from lmost symmetric genelogies to highly symmetric counterprts. Figure 7.5(B) illustrtes tht the weighted Colless index C w does not depend on the observtion period nd, thus, resembles n invrint mesure of imblnce in cellulr genelogies. In contrst, this scling invrince does not pply to the clssicl Colless index C (dt not shown). 133

144 7. Results II: Quntittive nlysis of in silico cellulr genelogies A Frequency 0 15 Frequency Frequency 0 10 growth scenrio homeosttic scenrio differentition scenrio weighted Colless index C w B weighted Colless index C w growth homeostsis differentition observtion period in hours Figure 7.5.: Weighted Colless index C w. (A) shows histogrms of the distributions of the weighted Colless index C w for the three different scenrios growth, homeostsis nd differentition. (B) provides the corresponding medin vlues (indicted by dots nd supplemented by first nd third qurtiles) for different observtion periods (rnging from 100 h to 350 h). Cell deth index A. The cell deth index A g is introduced to estimte the probbility for the occurrence of cell deth event conditioned on the prticulr genertion g. This mesure cn be used to ccount for chnges of the prticulr probbility during the course of differentition. Unlike in the experimentl sitution, in which the role of cell deth/ poptosis potentilly chnges in the course of differentition, the rndom occurrence of the bckground cell deth in the simultion model mkes distinction for different genertions g obsolete. For simplicity, generlized cell deth index A verges over ll genertion-depended vlues A g for ech genelogy (except the root cell genertion). Histogrms of the corresponding distributions reshowninfigure 7.6(A). Due to the incresed prolifertion ctivtion nd the resultingshortening of G1 phses in the growth scenrio, thecelldethindexa is reduced compred to the other scenrios. Within the simulted scenrios, cell deth occurs with intensity Φ B = φ =0.02 t ech time step in the simultion model. For typicl G1 phse of 12 hours (corresponding to 12 time steps), the cumultive probbility to encounter cell deth event within one cell cycle is clculted s Φ cum G1 =( )= This vlue is well pproximted by the generlized cell deth index A mesured from the simulted genelogies. As shown in Figure 7.6(B), the index vlues for the homeosttic nd for the differentition scenrio converge towrds this nlyticl estimte for sufficiently long observtion periods. Lower index vlues for the growth scenrio re plusible, since shortened cell-cycle times (by shortening of G1-phse, see [47]) reduce the probbility of induced cell deth. 134

145 7.1. Compring cellulr genelogies under different growth conditions A Frequency 0 30 Frequency 0 10 Frequency 0 15 growth scenrio homeosttic scenrio differentition scenrio cell deth index A B cell deth index A growth homeostsis differentition observtion period in hours Figure 7.6.: Cell deth index A. In (A) three histogrms re shown for the distributions of the cell deth index A in the growth, homeostsis nd differentition scenrio. (B) provides the corresponding medin vlues (indicted by the dots nd supplemented by the first nd third qurtiles) for different observtion periods (rnging from 100 h to 350 h). Miniml distnce between chrcteristic events R. The miniml topologicl distnce between chrcteristic events R is mesure to quntify whether such events pper correlted between closely relted cells orwhethertheyoccur isolted within the cellulr genelogy. Histogrms in Figure 7.7(A) show the distribution of the verge miniml distnces R in the three relevnt model scenrios. By definition, genelogies with less thn two cell deth events re excluded from the clcultion of the miniml distnce mesure R. Generlly,theminimldistncesR between cell deth events re rther similr for the three different model scenrios due totheunderlyingssumption of rndomly occurring cell deth events cting identiclly in ll three scenrios. However, since cell deth events re less likely in thegrowth scenrio (compre cell deth index A in Figure 7.6(A)), the medin of the verge miniml distnces R is slightly incresed compred to the other two scenrios. For the simulted culture scenrios, in which bckground cell deth occurs rndomly with intensity Φ B =0.02 during G1 phse, the miniml distnce R ppers to stbilize round R =2forsufficientlylongobservtionperiods. Thisbehvior is illustrted in Figure 7.7(B). Briefly summrizing, the ppliction of the proposed mesures to three generic model scenrios illustrtes their potentil for the ppliction to experimentl dt. In the first plce, verges over the single cell mesures (e.g. the number of leves L nd the chrcteristic brnch length B chr )sufficientlyreproduceoverll popultion dt (e.g. on cellulr expnsion). However, beyond these popultion 135

146 7. Results II: Quntittive nlysis of in silico cellulr genelogies A Frequency 0 30 Frequency Frequency growth scenrio homeosttic scenrio differentition scenrio miniml distnce of cell deth events R B miniml distnce between cell deth events R growth homeostsis differentition observtion period in hours Figure 7.7.: Miniml distnce between chrcteristic events R. In (A) histogrms re provided for the distributions of the miniml distnce between chrcteristic events R for the three rtificil culture scenrios. (B) provides the medin vlues of R (indicted by the dots nd supplemented by the first nd third qurtiles) for different observtion periods (rnging from 100 h to 350 h). verges, the distribution of the mesures for set of genelogies provide n essentilly novel ccess to estimte the popultion inherent heterogeneity. As second dvntge, the single cell nlysis llows to evlute certin chrcteristic events within the divisionl context (e.g. occurrence of cell deth, chnges in morphology, lineges decisions). As illustrted bove, the genertion nd the time point of the occurrence of chrcteristic cell deth events s well s the reltion to similr events occurring in other cells cn only be quntified on the single cell level. Although the proposed list of mesures might not be completend requires dption for certin experimentlly motivted questions it is bsis for the evlution nd sttisticl comprison of lrger numbers ofcellulrgenelogies Linege fte ssignment Two different modes of linege ssignment in cellulr genelogies, nmely the prospective nd the retrospective view, hve been introduced in Section 6.4. Compring the cellulr genelogies it ppers tht cells t certin positions re lredy mrked s committed in the retrospective view, while the prospective view indictes tht the linege specifiction process hs not reched detectblethreshold. This notion is supported by typicl cellulr genelogy of the differentition scenrio which is shown both in prospective nd the retrospective view in Figure 7.8(A) nd (B), respectively. In the context of the simulted culture scenrios it is now possible to quntify this effect. For sttisticl evlution, the occurrence of symmetric, symmetric or 136

147 7.1. Compring cellulr genelogies under different growth conditions A prospective linege ssignment B retrospective linege ssignment C D probbility of occurrence undiff. symmetric symmetric probbility of occurrence undiff. symmetric symmetric symmetric genertion g genertion g Figure 7.8.: Prospective versus retrospective view for the linege ssignment. (A). Linege fte is ssigned in situ for chosen cellulr genelogy of the differentition scenrio in the prospective view, e.g. the color coding of cell might chnge during the cells existence if certin criticl mrkers (linege propensities in the simultion model) exceed threshold level (i.e. x i >x com ). In contrst, in (B) linege fte is ssigned recursively bsed on the linege fte of the dughter cells for the sme genelogy s in (A). Color-coding of the cells is identicl to Figure 7.1 (neglecting the erly committed stges), colors for the divisions re ssigned s follows: undifferentited symmetric divisions - mgent, symmetric divisions of committed cells - light blue, symmetric divisions (only in the retrospective view) - red. In (C) nd (D) the probbility of occurrence of the prticulr division types for ech genertion g is given for the set of genelogies derived under the differentition scenrio. The color-coding is identicl to (A) nd (B). 137

148 7. Results II: Quntittive nlysis of in silico cellulr genelogies undifferentited symmetric division events, s defined in Section 6.4, is summrized in Figure 7.8(C) nd (D). Strting from popultion of rther uncommitted cells such histogrms re plotted ginst the genertion g in which the division event occurs. Although both fte ssignments re bsed on the sme set of underlying genelogies, in the prospective view (Figure 7.8(C)) symmetric expnsion of undifferentited cells in erly genertions (shown in mgent) is more pronounced compred to the retrospective view (Figure 7.8(D)). It is the prticulr construction of the linege ssignment in the retrospective view (bsed on subsequent cellulr development nd decoupled from the ctul intrcellulr differentition stte) suggesting n erlier onset of linege commitment compred to the prospective view. Although the propensity of cell for the development in one prticulr fte might lredy be skewed t such n erly time point, the prospective view indictes tht fixtion is not yet ccomplished. This bis is inherently present in ny retrospective ssignment of cellulr chrcteristics nd mrks centrl disdvntge to the prospective view in which criticl steps of the linege specifiction process re determined in their divisionl context. However, the retrospective view is helpful tool to identify cells tht give rise to more thn one linege fte (multipotent cells). Although the multipotency is not bsed on the trnscriptionl stte of the cell but on its future development, the retrospective linege ssignment is well suited to detect the occurrence nd timing of division events tht give rise to different (symmetric) cell ftes. In this respect the retrospective view illustrtes the difference between functionlly symmetric division, which does by construction not occur intheunderlyingmodel system, nd n symmetric cell fte, which is commonly detected in the resulting genelogies Compring cellulr genelogies under different modes of linege specifiction In Section 7.1 the question hs been ddressed how different scenrios for cellulr development influence the shpe of the resulting genelogies. Beyond refined nlysis of the popultion behvior the cellulr genelogies cn provide dditionl informtion bout the underlying mechnisms of developmentl process leding to the prticulr topologicl ptterns. The ide is similr to the nlysis of phylogenetic trees in which certin pprent fetures cn indicte periods of fierce competition nd extinction of species during evolution. In the following the prevlent debte bout the instructive versus selective modes of linege specifiction in hemtopoietic stem cells (see lso Section 2.3.2) is used s n exmple to illustrte the potentil of cellulr genelogies to revel underlying mechnisms of their genertion. Briefly summrizing, the question centers round whether linege specifiction is n instructive process in which 138

149 7.2. Compring cellulr genelogies under different modes of linege specifiction combintionofcytokinesndcellftespecificsignlsinfluences the undifferentited cells such tht certin lineges re promoted wheres others re not or whether linege specifiction is selective in the sense tht the intrinsic influence on the cells is negligible, but the regultion occurs on the level of differentil survivl signls. In the ltter setting, cytokines promote the survivl of certin lineges wheres cells determined towrds other lineges re not supported nd consequently undergo cell deth [94, 124, 231]. Experimentl pproches bsed on cell popultion verges re in most cses insufficient to nswer the outlined questions for two resons: first,stemcellpopultions hve certin, hrdly reducible degree of inherent heterogeneitywhich mkes it extremely difficult to initite cultures of identicl ndsynchronizedcells. Second, the popultion pproches do not cpture the temporl evolution nd chronology of cellulr development s it occurs within single cell. However, it is precisely the development of ech individul cell nd its progeny tht represents possible reliztion of the developmentl sequence nd retins much of the necessry informtion: on the correltions between differentition nd cell cycle regultion, on the timing of linege specifiction processes ndcelldethevents s well s on the role of symmetric developments. The comprehensive mthemticl model of HSC development introduced in the previous chpters forms the bckground to study instructive nd selective linege specifiction in n idelized nd well defined environment. The understnding of the principle effects of these different modes of linege specifiction on the popultion but lso on the single cell level re the prerequisite for the interprettion of dt tht hopefully becomes vilble in the next decde Genertion of cellulr genelogies under different modes of linege specifiction For the scope of this nlysis popultion of bipotent cells is considered, i.e. ech cell cn differentite in either of two possible lineges (i =1, 2; shown in blue nd green in Figure 7.9). Subsequently, two different modes of linegespecifiction re pplied, both fvoring (without loss of generlity) the development of the green linege (i =2). Brieflyrecllingtheformlintroductionin4.3.4,in the selective mode it is ssume tht the cell-intrinsic commitment process isblnced nd promotes the development of both possible lineges like( blnced rewrds m 1 = m 2 ). However, there is selective cell deth process (medited e.g. by the bstrct Pro green -cytokine) preferentilly ffecting cells tht initited development towrds the suppressed linege (i =1)wheresthepreferred linege (i =2)islrgelyunffected(φ 1 >φ 2 0). In contrst, in the instructive mode the cell-intrinsic commitment process is bised towrds the preferred linege ( unblnced rewrds m 1 <m 2 ), potentilly medited by the bstrct Pro green -cytokine. In this scenrio, cell deth occurs rndomly in ll cells (bck- 139

150 7. Results II: Quntittive nlysis of in silico cellulr genelogies Figure 7.9.: Instructive vs selective linege specifiction for bipotent cells. In generl cell culture scenrio (shown on top) the potentil ction of Pro- green cytokine results in the formtion of popultion of green cells. The mechnisms re only ccessible on the single cell level: in the cse of instructive linege specifiction the Pro- green cytokine intrinsiclly propgtes commitment to only the green linege while bckground cell deth cts rndomly on ll cells. In contrst, in the selective linege specifiction both the green nd blue lineges re promoted eqully, however selective cell deth primrily trgets the blue cells. ground cell deth Φ B ). The principle ide is outlined in the sketch in Figure 7.9. For the prticulr simultions two cell popultions of 500 uncommitted, bipotent cells (initil linege propensities x 1 = x 2 =0.5) with impired self-renewl bility (regenertion rte r =1.0) re initilized nd undergo linege specifiction in either the instructive or selective mode. The trcking process for ech of the genelogies extends over 200 hours, thus generting 500 representtive cellulr genelogies for ech scenrio. Further prmeters re provided in Appendix D.8. To nswer the question whether sttisticl nlysis of the cellulr genelogies revel ny dditionl informtion tht is not contined inthepopultion kinetics, the prmeter configurtion is chosen such tht the popultionkinetics (exponentil expnsion nd frction of linege committed cells) re indistinguishble for both scenrios. Figure 7.10 illustrtes comprison of the popultion chrcteristics. 140