Modeling Reveal Bitability and Low-Pa Filtering in the Network Module Determining Blood Stem Cell Fate Jatin Narula, Aileen M. Smith 2, Berthold Gottgen 2, Oleg A. Igohin * Department of Bioengineering, Rice Univerity, Houton, Texa, United State of America, 2 Cambridge Intitute for Medical Reearch, Univerity of Cambridge, Cambridge, United Kingdom Abtract Combinatorial regulation of gene expreion i ubiquitou in eukaryote with multiple input converging on regulatory control element. The dynamic propertie of thee element determine the functionality of genetic network regulating differentiation and development. Here we propoe a method to quantitatively characterize the regulatory output of ditant enhancer with a biophyical approach that recurively determine free energie of protein-protein and protein-dna interaction from experimental analyi of trancriptional reporter librarie. We apply thi method to model the -- Fli triad a network module important for cell fate pecification of hematopoietic tem cell. We how that thi triad module i inherently bitable with irreverible tranition in repone to phyiologically relevant ignal uch a Notch, Bmp4 and Gata and we ue the model to predict the enitivity of the network to mutation. We alo how that the triad act a a low-pa filter by witching between teady tate only in repone to ignal that perit for longer than a minimum duration threhold. We have found that the auto-regulation loop connecting the low-degrading to and Fli are crucial for thi low-pa filtering property. Taken together our analyi not only reveal new inight into hematopoietic tem cell regulatory network functionality but alo provide a novel and widely applicable trategy to incorporate experimental meaurement into dynamical network model. Citation: Narula J, Smith AM, Gottgen B, Igohin OA (200) Modeling Reveal Bitability and Low-Pa Filtering in the Network Module Determining Blood Stem Cell Fate. PLoS Comput Biol 6(5): e00077. doi:0.37/journal.pcbi.00077 Editor: Anand R. Athagiri, California Intitute of Technology, United State of America Received December 3, 2009; Accepted March 30, 200; Publihed May 6, 200 Copyright: ß 200 Narula et al. Thi i an open-acce article ditributed under the term of the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original author and ource are credited. Funding: JN and OAI are upported by Rice Univerity tartup fund and NSF award MCB-084599. OAI i grateful to International Collaboration Travel Fund at Rice Univerity that allowed ite-viit to Cambridge, UK. AMS and BG are upported by Leukemia Reearch Fund. The funder had no role in tudy deign, data collection and analyi, deciion to publih, or preparation of the manucript. Competing Interet: The author have declared that no competing interet exit. * E-mail: igohin@rice.edu Introduction Appropriate patiotemporal control of gene expreion i central to metazoan development. []. Combinatorial interaction of regulatory protein with regulatory region of DNA and the baal trancriptional machinery form the building block of complex gene regulatory network (GRN). The availability of whole genome equence a well a advanced bioinformatic and highthroughput experimental technique have vatly accelerated the identification of candidate regulatory equence. However, experiment that can uncover and/or validate the underlying connectivity of GRN remain both cotly and time conuming. Conequently, our undertanding of the functionality of GRN even for the mot tudied model organim remain uperficial. Moreover, imply cataloguing ever increaing number of interaction between GRN component i not ufficient to deduce the underlying network architecture or function of individual module. Unraveling the dynamical propertie of GRN will be the key to undertanding their functionality. Throughout development, cell progre through a ucceion of differentiation tep from tem cell via immature progenitor to fully differentiated mature cell, and each of thee ubtype i aociated with a unique regulatory tate of the GRN []. It i therefore eential to undertand dynamical propertie of the variou regulatory tate of GRN, tranition between them and their interplay with intercellular ignaling. It i unlikely that thi goal can be achieved olely uing experimental approache. However, the development of dynamical model of GRN offer great potential to interpret exiting experimental data in order to gain new mechanitic inight. Variou computational approache have been ued for regulatory network analyi in the pat. Boolean model provide qualitative information about network behavior uch a the exitence of teady tate and network robutne and are mot ueful for large network or when experimental information i carce [2,3]. However to examine dynamical apect, continuou ordinary differential equation (ODE) model are more appropriate. Thee model can be contructed with phenomenological decription of gene regulation in the form of Hill function or baed on more detailed biophyical mechanim and derived uing a tatitical thermodynamic approach. Phenomenological model are ueful for undertanding the general dynamic of network topology. They are mot effective for mall to medium ized network and can alo be predictive of cellular behavior [4]. Model baed on thermodynamic have the advantage of including an hypothei about the biophyic of the ytem [5,6,7]. Mot parameter in thee model have a direct biochemical interpretation. Unfortunately the lack of knowledge about pecific biochemical parameter uually make it difficult to relate reult from thee model to experimental information about gene expreion. Neverthele thi modeling approach ha been hown to be ueful in undertanding certain bacterial gene regulation PLoS Computational Biology www.plocompbiol.org May 200 Volume 6 Iue 5 e00077
Author Summary Hematopoiei blood cell development ha long erved a a model for tudy of cellular differentiation and it control by underlying gene regulatory network. The - -Fli triad i a network module eential for the development of hematopoietic tem cell but it mechanitic role i not well undertood. The trancription factor, and Fli act in combination to upregulate trancription of each other via dital enhancer ite binding. Similar network architecture are eential in other multipotent cell line. We propoe a method that ue experimental reult to circumvent the difficultie of mathematically modeling the combinatorial regulation of thi triad module. Uing thi dynamical model we how that the triad exhibit robut bitable behavior. Environmental ignal can irreveribly witch the triad between table tate in a manner that reflect the unidirectional witching in the formation and ubequent differentiation of hematopoietic tem cell. We alo how that the triad make reliable deciion in noiy environment by only witching in repone to tranient ignal that perit longer than the threhold duration. Thee reult ugget that the --Fli module poibly function a a control witch for hematopoietic tem cell development. The propoed method can be extended for quantitative characterization of other combinatorial gene regulatory module. module [8] and tudying the effect of nucleoome dynamic in eukaryotic gene regulation [9]. The hematopoietic ytem ha long erved a a powerful model to tudy the pecification and ubequent differentiation of tem cell [0]. Sophiticated cell purification protocol coupled with powerful functional aay have allowed a very detailed recontruction of the differentiation pathway leading from early meoderm via hemangioblat and hematopoietic tem cell (HSC) to the multiple mature hematopoietic lineage. Trancriptional regulator (TR) have long been recognized a key hematopoietic regulator but the wider network within which they operate remain ill defined []. Detailed molecular characterization of regulatory element (enhancer/promoter) active during the early tage of HSC development ha identified pecific connection between major regulator [2,3,4,5] and ha led to the definition of combinatorial regulatory code pecific for HSC enhancer [6,7,8]. Moreover, thee tudie identified a ubtantial degree of cro-talk and poitive feedback in the connectivity of major HSC TR [9]. In particular, a triad of HSC TR (, Fli, /Tal) form a regulatory module that appear to lie at the core of the HSC GRN [20]. Thi module conit of the three trancription factor protein a well a three regulatory element through which they are connected via cro-regulatory and autoregulatory interaction [2,20] (Figure A). The detail of regulatory interaction in thi triad are hown in Figure B; only ignificant binding ite in the enhancer are hown for implicity. -3 and Fli+2 enhancer contain multiple (GATA), Fli (ETS) and (E-BOX) binding motif. The +9 enhancer contain ETS and GATA binding motif., and Fli are all eential for normal hematopoiei in mice [2] uggeting that the triad i an important ub-circuit or kernel of the GRN that govern hematopoiei. The triad architecture (Figure A) i very dene in regulatory connection and poee multiple direct and indirect poitive feedback loop. Such network topologie are rare in prokaryote [2] but have been identified in other tem cell ytem uch a the Nanog-Oct4-Sox2 triad in the embryonic tem cell GRN [22,23]. Thee obervation ugget that the triad deign may be aociated with tem cell behavior. Thi idea prompted further invetigation of combinatorial control by the triad TR [20]. Generation of an enhancer library with wild type and mutant enhancer allowed the contruction of different combination of binding motif in each enhancer. Wild type and mutant enhancer were ub-cloned into a SV minimal promoter and lacz reporter vector and teted uing table tranfection of hematopoietic progenitor cell line [20]. Thi analyi produced reult uch a thoe chematically illutrated in Figure C. It ha been uggeted that the dene connectivity and poitive feedback loop within tem cell GRN module play important role in tabilizing the tem cell phenotype [20]. However, the dynamical nature a to how thi elf-enforcing circuit may be initiated or indeed exited remain unclear. In thi paper we contruct a mathematical model of the --Fli triad module and characterize it dynamical propertie uing continuou ODE modeling approache. We firt propoe a thermodynamic method of etimating free energie of different configuration of the enhancer region from the meaurement of the trancriptional reporter librarie. Thi method together with a propoed biochemical mechanim of ditant trancriptional enhancement ignificantly reduce dimenionality of the network parameter pace. Meaurement of protein lifetime provide experimentally informed timecale to model tranient behavior of the network. We analyze the network repone to phyiologically relevant ignal uch a Notch, Bmp4 and Gata and how that the network behave a an irreverible bitable witch in repone to thee ignal. Our model alo predict the reult of variou mutation in the enhancer equence and how that the triad module can ignore tranient differentiation ignal horter than threhold duration. The combination of a bitable witch with hort ignal filtering not only provide new mechanitic inight a to how the --Fli triad may function to control HSC pecification and differentiation but alo ugget a poibly more general role for thi network architecture in the development of other major organ ytem. Reult Thermodynamic model for enhancement of gene expreion Full quantitative characterization of the combinatorial nature of trancriptional regulation require meaurement of binding affinitie between the DNA and TR a well a interaction trength among TR. Moreover, the contribution of each individual TR and each poible combination to the trancriptional rate mut be aeed. Thi information i extremely tediou to meaure due to the combinatorial multiplicity of TR configuration and doe not exit for the majority of experimental ytem. Experimental data for ynthetic librarie of trancriptional reporter that contain the gene regulatory element i more readily available. We develop thermodynamic method to characterize the combinatorial trancriptional regulation by dital enhancer baed on thi type of data and apply it to model the --Fli triad - a core module of the GRN of hematopoietic tem cell. Recently thi ytem ha been experimentally characterized [20]. In thi tudy dital enhancer region regulating the trancriptional rate of network protein were identified and the relative contribution of each of the regulatory motif were thereafter aeed individually and in combination by the ue of a uitable trancriptional reporter (e.g., luciferae, lacz). The typical reult from thee experiment are illutrated in Figure ; ee Table S for the full data ued. We ue thi data to obtain the functional form PLoS Computational Biology www.plocompbiol.org 2 May 200 Volume 6 Iue 5 e00077
A Gata +9 B Et Et -3 EBOX GATA Fli+2 GATA EBOX Et GATA Fli Et Et Et GATA Bmp4 Notch BINDING SITES : :: GATA :: EBOX Fli :: Et C Reporter Et Et GATA Reporter Et Et GATA 4 Reporter Et Et GATA 256 Reporter Et Et GATA 82 Expreion (normalized to enhancerle) Figure. Regulation of gene expreion in the --Fli triad. A., and Fli form a triad module of TR in the GRN of hematopoietic tem cell. The triad architecture conit of multiple poitive feedback loop. Signal activating or deactivating the network are hown in magenta. Notch activate the trancription of and Bmp4 activate the trancription of and Fli by acting at the promoter. Gata bind to the enhancer and downregulate expreion. B. The triad protein regulate each other trancription by acting at the +9, -3 and Fli+2 enhancer. Thee enhancer contain multiple binding ite that allow combinatorial control of gene expreion. Only ite ignificantly affecting expreion are hown C. Enhancer librarie imilar to the one hown for were contructed for all three protein and ubcloned with a uitable reporter in and in triad expreing cell to characterize the combinatorial control of gene expreion. Typical reult how the enhancement of gene expreion from TR binding ite individually and in combination relative to enhancerle expreion of the reporter. doi:0.37/journal.pcbi.00077.g00 decribing the trancriptional rate of the reporter-enhancer contruct and etimate the biochemical parameter characterizing thi function. Below we illutrate our approach for the +9 enhancer; the full model i derived in the method ection. We aume that the ditant enhancer increae the trancriptional rate via modulation of chromatin remodeling rather than through direct interaction with trancriptional machinery. Thi aumption i motivated by the obervation that activation of the +9 enhancer i only revealed upon integration of the enhancer-promoter contruct into chromatin and that the activity of the enhancer i independent of it poition (uptream or downtream) relative to the reporter gene [20,24]. Moreover, when integrated a ingle copy reporter into the genome of embryonic tem cell and aayed following 5 day of in vitro differentiation, the difference between wild type and mutant enhancer contruct lie in the number of cell that expre the trangene rather than the level at which it i expreed (cf. Figure S and Text S). Taken together, thee obervation ugget that chromatin dynamic play a ignificant role in the action of TR at the enhancer. In the abence of enhancer binding, the gene can be in either open or a relatively table cloed chromatin tate. In the cloed chromatin tate the binding region for the TR and the trancriptional machinery are wrapped in nucleoome and are inacceible; thu no gene expreion i poible from thi tate. The cloed chromatin tate can pontaneouly unwrap to an open tate where the binding ite become acceible to allow polymerae to bind to the promoter and initiate trancription. Since mot promoter bind RNA polymerae weakly, the probability of RNA polymerae binding and ubequently trancription rate I i proportional to the probability of the chromatin being in the open tate (I~I o p o ;ee Method Eq (5) (7)). Thi probability depend on the equilibrium between open and cloed chromatin tate. Binding of the TR at the enhancer tabilize the open conformation thu hifting the equilibrium toward the open tate (cf. Figure S2). Thi way the probability of open conformation increae with increae in TR concentration or increae in binding affinity. The rate of gene expreion i till given by I o p o but p o i now defined by a more complicated thermodynamic expreion accounting for all the poible configuration of TR binding. Mutation in the enhancer ite eliminate the configuration of TR binding thereby affecting p o but not I o. Below we illutrate thi formalim for the +9 enhancer. The +9 enhancer contain binding ite for and a Fli dimer and therefore can exit in cloed and four different open tate (enhancer empty, bound, Fli dimer bound, both and Fli bound).the cumulative probability of all open PLoS Computational Biology www.plocompbiol.org 3 May 200 Volume 6 Iue 5 e00077
tate configuration i then given by p o ~{p cloed, where p cloed i the probability of the cloed tate given by p cloed ~e {bgc =Z where ubcript denote the the +9 enhancer: G C i the effective cloed tate energy, and Z i the partition function given by the um of exponentiated free energie G a of each tate a: Z ~ P a e{bga. b~=kt i an invere temperature and hereafter all free energie are in it unit. For TR-bound tate, free energie are concentration dependent due to the lo of entropic degree of freedom, e.g. for the -bound tate G a~g {logð½gatšþ, where ½GATŠ denote concentration of. (Similarly ½SCLŠ and ½FLIŠ denote concentration of and Fli repectively). Since the free energie are only defined up-to a contant we can chooe the free energy of the open tate to be zero and thu obtain the following expreion for the partition function: Z ~ze {GC z½gat z½fli Š 2 ½GAT Še {G z½fliš 2 e {GFli Še {GFli ~e {GC zz E where G Fli and G Fli repreent the free energie of Fli dimer and -Fli multimer binding and Z E i the partition function for all open chromatin tate. We ue the ubcript in all thee term to pecify that they are aociated with the +9 enhancer and the upercript to pecify the binding configuration (cf. Table S2 for notation). Direct meaurement of the binding free energie in thi expreion may be tediou but thee can be traightforwardly computed from the ratio of the trancription rate from ynthetic reporter librarie with full or mutated enhancer ite. Ratio of the reporter expreion level of cell line with wild-type (wt) and mutated (mut) enhancer can be ued a contraint on the value of the binding free energie. I wt I mut ~ pwt o p mut o ~ {e{gc =Z wt {e {GC =Z mut Equation imilar to (3) can be contructed for all reporterenhancer librarie and ued to recurively compute the binding free energie (cf. Eq (22) (27) in Method and Eq (S.) (S.) in Text S3). Mathematical model for the --Fli Network triad module, and Fli form an interconnected triad of poitive interaction and play an important role in hematopoietic differentiation [2,20]. To undertand the role of the unique architecture of the triad module we contruct a dynamical model of the ytem. Auming firt-order degradation kinetic, determinitic rate equation for the change in TR concentration take the form d½sclš ~VS z dt {ks d ½SCLŠ; d½gatš ~VG z dt {kg d ½GATŠ; d½fliš ~VF z dt {kf d ½FLIŠ ðþ ð2þ ð3þ ð4þ where the function VS z, V G z and VF z decribe the rate production wherea kd S, kg d and kd F denote degradation rate contant for, and Fli repectively. Rate contant for protein degradation are etimated from known half-live of the protein. Since protein are long-lived relative to mrna, we can aume that production rate are directly proportional to the repective trancription rate I i ~I o p i o (cf. Eq (28)). In addition to ditant enhancer, Notch and Bmp4 are known to erve a activator of the promoter of and Fli, repectively [25,26]. Thee activator increae the rate of trancription by increaing the recruitment of RNA polymerae to the repective promoter. In particular, Notch and Bmp4 increae expreion by 3.5 fold [26] and 4 fold [27] repectively. In thi cae, to compute VG z one need thermodynamic expreion of the probabilitie of multiple open conformation correponding to binding of Notch or Bmp4. Thee probabilitie depend upon Notch and Bmp4 concentration ( ½NŠ and ½BŠrepectively) and their binding energie G N and G B via the full partition function Z g (ubcript g tand for -3 enhancer): Z g ~K g z(z½nše {GN z½bše {GB )Zg E, where Z E g ~z ½ GAT z½fli Š 2 ½GAT Še{G g Še {GFli g z½fliš 2 e {GFli g z½sclš½gat ð5þ Š½FLIŠ 2 e {GFli g Here K g ~e {GC g i the equilibrium contant for chromatin tranition between open and cloed tate for enhancer (imilarly K ~e {GC and K f ~e {GC f for +9 and Fli+2 enhancer repectively). Thee equilibrium contant are dimenionle quantitie characterizing the maximum poible fold enhancement of gene expreion by the repective enhancer. The partition function are ued to compute ynthei rate VG z (cf. Eq (20)). The ame procedure i ued to decribe the rate of expreion of Fli, although in thi cae only Bmp4 act at the promoter (cf. Eq (2)). Converion to dimenionle form can greatly implify the model allowing eay interpretation of imulation reult. We normalize the pecie concentration of, and Fli a ½clŠ~ ½SCLŠ= ½SCLŠ, ½gat ½fliŠ~ ½FLIŠ= ½FLIŠ. ½SCLŠ, ½GATŠ and ½FLI Š~ ½GAT Š= ½GATŠ and Š repreent the mean oberved concentration of, and Fli in wildtype HSC where the triad i actively expreed. In addition, ½nŠ and ½bŠ are Notch and Bmp4 concentration normalized with repect to their promoter diociation contant. With thee normalization, wildtype HSC in the abence of ignal would have ½clŠ~ ½gatŠ~ ½fliŠ~ and ½nŠ~ ½bŠ~0. We chooe thi tate a a reference tate for the etimation of free-energie (cf. Method Section for detail). The dimenionle form of equation (4) i then given by dcl ½ Š ~ p o ( ½gat Š, ½ fli Š) dt p o (,) { ½clŠ k S d k G d d½gatš ~ pg o ( ½cl Š, ½ gatš, ½ fli Š; ½nŠ, ½bŠ) dt p g { ½gatŠ o(,,; 0,0) k F d dfli ½ Š dt ~ pf o ( ½cl Š, ½ gatš, ½ fli Š; ½bŠ) p f { ½fliŠ o(,,; 0) Where p i o are dimenionle ynthei rate (cf. Eq 25). Note that in the final form of our model equation the wild-type tate of HSC ð6þ PLoS Computational Biology www.plocompbiol.org 4 May 200 Volume 6 Iue 5 e00077
½clŠ~ ½gatŠ~ ½fliŠ~; i alway a teady tate in the abence of ignal ½nŠ~ ½bŠ~0. By uing the parameter etimation method decribed in the previou ection and reduction of the ytem to dimenionle form, we have reduced the dimenion of the parameter pace and the only free parameter are the equilibrium contant for chromatin opening-cloing K,K g and K f. In the following ection we ue thi ODE model to analyze teady tate and dynamical propertie of thi triad module. Steady tate repone of the triad module We ue the model developed in the preceding ection to analyze the teady tate repone of the triad to Notch and Bmp4. By varying K,K g and K f and calculating free energie that conform to the experimental prediction of mutant enhancer expreion rate we can explore all region of the relevant parameter pace. Bifurcation analyi of the teady tate repone how that the triad module ha two table teady tate (ee Figure 2). For certain value of the chromatin equilibrium contant Notch and Bmp4 can witch the triad between a low expreion OFF tate and a high expreion ON tate (Figure 2A). Thi witch in expreion level i irreverible and utained even without Notch and Bmp4 ignal. Therefore tranient Notch/ Bmp4 ignal may lock the triad into the ON tate. Thi irreverible progreion witch behavior i expected from the triad module which ha been reported to play a ignificant role in the pecification of HSC in the hemogenic endothelium. We ue the above-decribed approache to etimate the parameter for our model. Equation (25) (27) relate the gene expreion reult from the +9 enhancer to the chromatin equilibrium contant K. When we ue thee equation to etimate the free energie G,G Fli and G Fli the model reult match the experimental reult exactly. The matching i only poible for the value of equilibrium contant above a threhold: K w89:5. Thi lower bound i imple a conequence of the fact that in the propoed thermodynamic framework the maximal poible enhancement i given by K z and the experimentally meaurable enhancement i 820.5. Similarly the free energie for the -3 and Fli+2 enhancer are etimated baed on the experimental reult and K g and K f repectively (cf. Method ection and Text S3 for detail). The value of thee contant are alo limited from below by the repective maximal meaured enhancer factor. In addition qualitative information about ytem behavior, namely it witchability a a repone to phyiologically relevant Notch and Bmp4 ignal, place an upper bound on chromatin equilibrium contant value. For a different et of K value the computed free energie are uch that Notch and/or Bmp4 [gat] 0 A 0. 0.0 2 0 0 0.4 [gat] 0 0. 0.0 B [gat] 0.0 0. 0 00 Bmp4 [b], Notch [n] 0 C 0. 0.0 [gat] 0.0 0. 0 00 Bmp4 [b], Notch [n] D 0.0 0.6 0.2 0.5 0.0 0. 0 00 Bmp4 [b], Notch [n] 0.75 0.5 f([gata]) 0.25 0 Figure 2. Steady tate ignal-repone analyi of the triad module to Notch, Bmp4 and Gata ignal demontrate irreverible bitability. A. The action of Notch and Bmp4 at the promoter of witche the triad module from a low expreion (OFF) tate to a high expreion (ON) tate. Only concentration are hown for brevity. Solid line repreent table and dotted line repreent untable teady tate. (Notch and Bmp4 concentration are normalized by their repective binding affinitie). Once the triad i in the ON tate, the poitive feedback loop in the module architecture enure that it remain in that tate without ignal (inet: the ame plot in the linear cale). The witchability of the triad teady tate repone i enitive to the value of K and K g.inband C, we ue different value for thee chromatin equilibrium contant and recalculate all free energy value uing the analytical equation derived with experimental reult. For K g ~233:5 in B, only Bmp4 can witch the triad from OFF to ON. For K g ~235 (C) neither Notch nor Bmp4 can witch the triad to ON tate. D. Bitable repone of the triad module to Gata repreor ignal. Gata compete with for binding ite on the -3 enhancer and can witch the triad from ON tate to OFF by decreaing the recruitment of RNA polymerae to the promoter by a factor f ð½gatašþ. A a reult the ytem irreveribly witche from ON to OFF. (note that thi figure i hown in linear cale, the inet how the deactivation in log-log cale for comparion with A). To evaluate the teady tate doe repone of each ignal individually the concentration of other ignal were kept fixed at zero during imulation. doi:0.37/journal.pcbi.00077.g002 PLoS Computational Biology www.plocompbiol.org 5 May 200 Volume 6 Iue 5 e00077
cannot caue the witch between low and high teady tate (Figure 2B, C). A a reult the ytem remain witchable in the very narrow range of two equilibrium contant (89:5ƒK ƒ89:69, 233:38ƒK g ƒ233:47) where the full enhancer bring the trancriptional rate to a nearly aturated value. The reulting narrow range do not indicate lack of model robutne but rather are a conequence of trict contraint placed on free energy value by the exact matching to the experimental reporter data (cf. equation (S.) (S.) in Text S3). In fact without thee contraint the range of K and K g for witchable bitable repone extend over everal order of magnitude (cf. Figure S3 and below). If we tolerate ome deviation from the experimentally meaured trancriptional data we can relax thee contraint and ignificantly enhance the range of parameter value for which the ytem i bitable and witchable. For example, if we allowupto20%deviationfrom trancriptional reporter meaurement then the value of chromatin equilibrium contant can vary by 20% and till reult in witchable repone (data not hown). It i quite reaonable to tolerate uch level of deviation from the experimental reult becaue the experimental reult uually have a margin of error. Therefore wefindthatthequalitative prediction of the model (witchable bitable repone) are robut however the quantitative prediction (trancriptional data) are only a accurate a the experimental data one which the model i baed. We expect the triad to be witchable in repone to both Notch and Bmp4. Therefore we chooe the chromatin equilibrium contant from within the narrow range hown above and calculate the TR-enhancer binding free energie uing thee choen value. For thi choen et of parameter value the model how an irreverible bitable repone to Notch and Bmp4 (Figure 2A). Bmp4 concentration were et to zero for evaluating the Notch doe repone and vice vera. The preence of one ignal reduce the threhold concentration of the other ignal at which the triad witche from OFF to ON (data not hown). The calculated free energie are hown in Table S3 and ued through the remaining imulation. Once the free energie of TR binding are fixed at Table S value, the ytem become robut to variability of chromatin equilibrium contant (Figure S3). Such change may biologically correpond to hitone modification or other phyical perturbation. In repone to change over a large range the triad how witchable and irreverible bitable repone to Notch and Bmp4 (Figure S3). Therefore the witchable nature of triad bitability i robut to everal fold parameter change. Gata can diplace from it binding ite in the -3 enhancer. Through competition for binding ite and ubequent chromatin remodeling Gata can witch the triad from high expreion back to the low expreion tate. We repreent the chromatin remodeling effect of Gata by including a factor 0,f ð½gatašþ, in our expreion for the rate of gene trancription I g ~I o p g o f ð½gataš Þ. Becaue the exact biochemical mechanim of the Gata action i not etablihed we chooe a decreaing function of Gata and make no other aumption about the functional form of f ð½gatašþ. We therefore, plot Gata doe-repone curve with f ð½gatašþ a the x-axi where it value decreae left to right (Figure 2D). Thi phenomenological decription of the effect of Gata capture the effect it ha on RNA polymerae recruitment to the promoter by initiating chromatin remodeling. Incluion of Gata in our model (Figure 2D) allow the ytem to witch from ON to OFF tate. The witching i irreverible the ytem will remain OFF even after Gata ignal i gone (f ð½gatašþ~). Notch and Bmp4 concentration were fixed at zero for evaluating the Gata repone becaue the concurrence of Notch/Bmp4 and Gata ignal i phyiologically unlikely. Interetingly, Gata-deactivation i far more uceptible to noie than the activation by Notch/Bmp4. Thi can be concluded from the dotted line repreenting the untable teady tate that eparate the table ON and OFF tate (compare Figure 2A and D). Thi line characterize the magnitude of concentration fluctuation required for pontaneou tranition. For ub-threhold ignal, thi line i much cloer to the table teady tate in Gata doerepone curve (Figure 2D) a compared to Notch or Bmp4 curve (Figure 2A). A more rigorou invetigation of the magnitude of tochatic effect and their relation to eparatrix of determinitic model require a full tochatic model of the network and will be conducted elewhere. Mutation in the enhancer ite change the teady-tate repone of the triad We expect the teady tate repone of the --Fli module depend on the triad architecture and deign of enhancer. The model preented above allow u to verify thi claim by introducing change in the triad deign correponding to mutation of enhancer equence and gene knockout and examining the effect on the teady tate repone. To thi end, we ytematically deleted TR-binding ite from each enhancer in ilico and analyzed the teady tate repone of the ytem. We alo analyze the teady tate repone of, and Fli deletion mutant. Mutation in the triad enhancer equence can produce many module with impler architecture a hown in Figure 3. Notably, ince ome TR-enhancer configuration do not make a ignificant contribution to the enhancer activity, removal of a ingle enhancer binding ite might effectively eliminate multiple TR-enhancer interaction. For example, the effect of on the and Fli enhancer i only ignificant when both and Fli are bound to the enhancer. Therefore the probability of bound enhancer configuration for thee enhancer i negligible for any motif where the or Fli ite on thee enhancer are deleted. Keeping thi in mind we analyze 0 different triad module deign that can be obtained by elective ingle and double mutation of enhancer binding ite. The model decribed above i uitably altered to predict the teady tate repone of thee alternate deign. All relevant parameter value are taken from the full triad model. Of the 0 mutant deign, all 6 module where the +9 or -3 enhancer are mutated how only a ingle teady tate with the expreion of, and Fli comparable to the low expreion tate of the full triad (cf. Figure 3A). On the other hand, high level of expreion can till be oberved in 4 module with mutation in the Fli+2 enhancer (ee Figure 3B and 3C). However, in contrat to wild-type (Figure 2A), thi high level of expreion cannot be maintained in the abence of Notch and Bmp4. Even when the E-BOX biding ite for i eliminated from the Fli+2 enhancer the ytem remain bitable for a range of ignal. For the deign in which the GATA ite in the Fli+2 enhancer i eliminated (Figure 3C) Fli expreion i uncoupled from and and i monotable while the repone of and are till bitable. Thi i expected becaue Fli autoregulation i not trong enough to produce bitability. Complementarily, we can alo ae the effect from alteration of TR rather than their binding ite. Simulation how that 2/2, 2/2 and Fli 2/2 knockout mutant cannot upport the high expreion tate of the triad. Thee mutant produce a phenotype imilar to the enhancer mutation in Figure 3A. Comprehenive analyi of knockout mice ha hown that hematopoiei i everely PLoS Computational Biology www.plocompbiol.org 6 May 200 Volume 6 Iue 5 e00077
A Fli Fli -3-3 Fli -3 Fli +9 [gat] 0 0. 0.0 0.0 0. 0 00 Bmp4 [b], Notch [n] Fli Fli Single Low Expreion State +9-3 Fli+2 B Fli+2 Fli+2 Fli Fli Fli [fli] 0.05 0.03 0.0 0.0 0. 0 Bmp4 [b], Notch [n] [gat] 0. 0.0 0.00 0.0 0. 0 Bmp4 [b], Notch [n], and Fli: Reverible Bitability to Notch and Bmp4 0 C 0.086 0 Fli+2 Fli+2 Fli Fli Fli [fli] 0.072 0.0 0. 0 00 Bmp4 [b], Notch [n] Fli: monotable [gat] 0. 0.0 0.00 0. 0 00 Bmp4 [b], Notch [n], : Reverible Bitability to Notch and Bmp4 BINDING SITES : :: :: Fli :: Figure 3. Selective deletion of enhancer binding ite can change the teady tate repone characteritic. A. Deletion of any of the enhancer binding ite from the +9 or -3 enhancer eliminate the high expreion tate of, and Fli een in the wildtype HSC. Black croe mark the deleted ite, red croe mark the interaction that are no longer ignificant a a reult of the deletion. B. Mutation in the PLoS Computational Biology www.plocompbiol.org 7 May 200 Volume 6 Iue 5 e00077
or Fli binding ite in the Fli+2 enhancer allow triad activation but lead to reverible bitability-the ON tate witche back to OFF in the abence of Notch and Bmp4. C. Deletion of the primary binding ite from the Fli+2 enhancer make the interaction with the enhancer inignificant. Thi effectively make Fli independent of external regulator and. Fli expreion i low for thee mutant and monotable. Notch ha no effect on Fli concentration. and how reverible bitability in repone to Notch and Bmp4 in thee mutant. doi:0.37/journal.pcbi.00077.g003 impaired in all three deletion mutant [28,29,30,3]. Our model ugget that the knockout of any of the triad protein prevent the witch to ON tate which i likely to affect the pecification of HSC during early embryonic development and therefore compromie the development of all mature blood cell type a een experimentally. On the other hand, the irreverible bitability of triad repone i preervedifwedeleteonechromoomalcopyofanyoneofthe three triad gene; however the heterozygotic mutant are expected to be more prone to differentiation (cf. Figure S4 and Text S2). Thi could explain why thee mutant have reduced repopulation capacity [32,33]. Dynamical repone of the triad module architecture The dynamic of the repone of the bitable triad module to a pule of Notch i illutrated in Figure 4A. The tep increae in Notch concentration almot immediately increae concentration lightly. However Fli concentration remain tagnant becaue level rie very lowly. The low peed of repone i governed by it low degradation rate (half life,8 hr). Once enough ha accumulated, the probability of being preent on the and Fli enhancer become ignificant. Thi reult in a rapid increae of expreion rate and the triad witche to the high expreion tate. The rate limiting tep for witching ON the triad expreion level i therefore the low accumulation of. To further invetigate the dynamic of triad witching in repone to tranient timuli we have computed the minimal pule duration that can caue irreverible witching a a function of ignal amplitude (Figure 4 B, C; black line). The reult indicate that the ytem can be witched ON by ignal pule longer than a certain threhold level (,42 hr for a Notch pule and,2 hr for a Bmp4 pule). Thi threhold i a few fold larger than -lifetime, the longet timecale for the ytem. Our imulation therefore indicate that the triad module i capable of filtering tranient ignal that are horter than the threhold imulation. We refer to thi property a low-pa filtering a term accepted for imilar phenomena in engineering literature [34]. Thi filtering appear to be related to the low turnover of and the feedback loop connecting with and Fli. To undertand how low dynamic contribute to the filtering of tranient Notch and Bmp4 ignal we compare the dynamic of the triad module to that of a impler network module where the +9 enhancer ha been deleted. We call thi module the reduced module. In thi reduced module i aumed to be under an external regulator that control concentration. With thi reduction, concentration i contant and the dynamic of and Fli repone are not limited by the low accumulation of. For a controlled comparion of the dynamic [35] we aume that all relevant parameter have the ame value a they do in the full triad model. Thi leave the concentration a the only free parameter. The reduced module how irreverible bitable repone to Notch, Bmp4 and Gata for a range of value. We contrain the concentration uch that the threhold for OFF to ON tranition i the ame for the reduced module and the full triad (Figure 4D). Notably, the eparatrix between the two table tate (dotted line, Figure 4D) i much cloer to the ON tate for the reduced module. Thi ugget that the reduced module i more uceptible to fluctuation in TR level a compared to the full triad. We now ue the reduced module a decribed above for a controlled comparion of the dynamic of the OFF to ON and ON to OFF witching. Both bitable witche act a filter for tranient ignal above the threhold (Figure 4 B and C). We compared thi dynamic repone of the triad and reduced module to Notch and Bmp4 pule. The model for the two module have the ame Notch/Bmp4 threhold and cloe to the threhold the minimum pule duration for both module i high. However at higher concentration of Notch and Bmp4, the minimum pule duration i much higher for the triad module than for the reduced module (6 hr and 9.5 hr for Notch and Bmp4 pule repectively). Thee reult how how the low dynamic of allow the full triad module to act a a better low pa filter function for activation a compared to the reduced module. For a controlled comparion of the repone of the two module to Gata we fix the concentration of the reduced module uch that the threhold level of Gata i identical (Figure 4E). Thi fixed concentration of i 4 fold higher for deactivation than for activation. Gata act at the -3 enhancer to hut off trancription through chromatin remodeling. The low dynamic of do not affect the concentration during thi deactivation. A a reult the deactivation dynamic and the minimum pule duration for ON to OFF witching at high Gata concentration (,8 hr) of the reduced module and the full triad are identical. The triad and reduced module are equivalent low pa filter for deactivation ignal uch a Gata. Dicuion A new method for determining free energie of TR-DNA interaction Combinatorial gene regulation i ubiquitou in eukaryote with complex DNA regulatory region acting a integration point for multiple ignal and pathway involved in gene regulation. The characterization of thee regulatory region through mathematical model i an important tep toward undertanding the functionality of gene regulatory network. In order to fully characterize each regulatory element, one need to determine dynamical function that decribe the rate of trancription a a function of TR concentration. The mot biochemically and biophyically realitic method of characterizing trancriptional regulation i rooted in tatitical thermodynamic where each tate of the regulatory region i aigned a free-energy o that the probability of each tate can be computed from Boltzmann ditribution [5]. Thee method have been previouly applied to bacterial ytem [8] but rarely ued for eukaryotic gene regulatory network a a lack of reliable parameter meaurement prevent reearcher from undertaking detailed modeling approache. Here we have developed a method for the quantitative characterization of combinatorial gene regulation by multiple TR in eukaryotic ditant enhancer. Our propoed method extend the thermodynamic approach of [36] in order to relate it to experimental trancriptional reporter aay. We develop a recurive method to etimate relevant free energie from the meaurement of combinatorial librarie of trancriptional reporter. There are multiple benefit of computing freeenergie of TR-DNA configuration. Firt, thee parameter allow traightforward contruction of mathematical model for quantitative analyi of ytem behavior with no or jut a few free PLoS Computational Biology www.plocompbiol.org 8 May 200 Volume 6 Iue 5 e00077
A [cl] / [gat] / [fli] C Minimum Pule Duration E [gat] 3 2.5 2.5 0.5 0 2 0 0 0.2 0.8 0.6 0.4 0.2 0 0 0 0 2 Bmp4 [b] 0 Fli Notch 0.0 Notch 5 5 25 t acc 0 0 20 40 Time Full Triad No Feedback [cl] = 0.25 Triad ON Bmp4 pule.84 t0.5 0.75 0.5 f([gata]) 0.825 t0.5 0.25 5 2 9 6 3 0 Notch [n] 0 [gat] Minimum Pule Duration D 0.0 Minimum Pule Duration 0 0. 0 2 0 0 0 0 3 0 2 0 0 0 B 0 - Gata pule No Feedback [cl] = 0.25 Full Triad Triad ON Notch pule 3.68 t0.5 0 0 2 Notch [n] No Feedback [cl] = 0.98 Full Triad Triad OFF.37 t0.5 0.00 0.0 0. 0 00 F Notch [n] Full Triad Module Fli Fli Reduced Triad Module 0.70 t0.5 0-0 -2 f([gata]) PLoS Computational Biology www.plocompbiol.org 9 May 200 Volume 6 Iue 5 e00077
Figure 4. Comparion of dynamical repone of the triad and the reduced module to Notch, Bmp4 and Gata ignal. A. A time coure of the witching from low expreion to high expreion tate in repone to a pule of Notch. The inet how that there i an increae in concentration immediately after the introduction of Notch. tart accumulating lowly in repone to thi increae in concentration but Fli concentration i tagnant becaue enough i not preent to appreciably increae Fli expreion. Once ha reached the required concentration (t acc after tart of Notch pule) and Fli concentration increae rapidly to the ON tate level. Thu witching of the triad to the high expreion ON tate i rate-limited by the low accumulation of B. The minimum Notch pule-duration required for OFFRON witching a a function of pule amplitude. Black line i the full triad the red curve i the reduced module with contitutive (cf. text for detail). C. Same a (B) but for Bmp ignal. D. Steady-tate repone of the reduced module (red) with the concentration fixed at the value that enure that the witching threhold i identical to that of the wild-type triad (black). Note that the unteady tate (eparatrix-dotted curve) for the reduced module i much cloer to the ON tate. E. Controlled comparion for deactivation by Gata teady-tate repone with concentration fixed to enure that the deactivation threhold for both module are identical. F. Tranient filtering of Gata ignal i very imilar for the two deign ince doe not limit the rate of repone to Gata. doi:0.37/journal.pcbi.00077.g004 parameter. Second, free energie can be ued for model reduction by pecifically excluding thermodynamically unfavorable tate and ubequent model reduction. Third, the parameter provide important qualitative inight into gene regulatory mechanim uch a cooperativity of TR. We further reduce the number of parameter required to characterize the ditant trancriptional enhancer by propoing a detailed mechanim baed on the modulation of chromatin remodeling activity. Chromatin tructure i known to play an important role in eukaryotic gene regulation. The organization of DNA into nucleoome can prevent the trancriptional machinery and regulatory factor from acceing regulatory region. The detailed mechanim of action of ditant enhancer ite ha not been etablihed. It ha been uggeted however that it action may involve modulation of chromatin remodeling dynamic [37]. For intance, regulatory element of the - -Fli triad were hown to be critically dependent on integration into chromatin [2]. Here we propoe a ratchet mechanim of enhancer action (cf. Figure S2). We propoe that DNA can be in a dynamic equilibrium between open (promoter ite acceible) and cloed (promoter ite inacceible) conformation. Such a dynamic equilibrium between wrapped and unwrapped nucleoomal DNA ha alo been dicued elewhere [38]. In the abence of enhancer TR, the equilibrium i heavily hifted toward a cloed tate reulting in very low trancription probability. We hypotheize that binding of TR to the enhancer ite tabilize an open conformation and thereby hift the equilibrium toward it. Thi mechanim therefore allow the TR to ratchet the pontaneou unwrapping of nucleoomal DNA and trap it in a tate acceible to the trancriptional machinery. We apply thi thermodynamic framework to a regulatory module hypotheized to play a pivotal role in hematopoiei. Under thi aumption the binding of Fli, and to their enhancer ite activate gene trancription by increaing the probability of trancription rather than the rate of trancription. Thi hypothei i conitent with previouly reported reult of tudie focued on enhancer function in mammalian cell [37,39,40] and with our flow cytometry experiment with cell containing the +9 enhancer-reporter contruct (cf. Figure S2 and Text S). The propoed mechanim aume that the unwrapping of DNA from nucleoome i independent of all triad factor and thu effectively pontaneou. However chromatin modification and chromatin remodeling factor can affect thee nucleoome dynamic. In particular, factor uch a the repreor Gata may regulate the expreion by modulating free energie of DNA unwrapping through chromatin modification. By hifting the equilibrium further toward the cloed tate, Gata can uppre trancription to uch an extent that TR concentration are too low to ratchet the very hort-lived open tate. Steady tate characteritic of the --Fli triad The recently characterized -Fli- triad module include a large number of trancriptional interaction reulting in multiple poitive feedback loop. The complex enhancer tructure make it rather difficult to phenomenologically deduce dynamical expreion for, and Fli trancription. However, with our newly developed approach baed on trancriptional reporter data, contruction of a mathematical model of the triad become a traightforward tak. The reulting model of the triad exhibited bitability in repone to the action of Notch and Bmp4. We have choen the free energy value for DNA unwrapping to enure that the action of thee two activator at the promoter witche the triad from low expreion (OFF) tate to high expreion tate (ON). The model predict thi witching to be irreverible the triad will remain ON even after the ignal are gone (Fig 2A). The development of HSC in the hemogenic endothelium i known to be a Notch regulated event [4]. Notch i known to be expreed in endothelial cell and act a a regulator of expreion during the onet of hematopoiei [26]. Bmp4 expreion ha alo been oberved in the doral aorta region where HSC firt develop in the embryo [8,42]. Notch and Bmp4 are known to be mediator of HSC pecification during embryonic development [4]. Our model how how the action of Notch and Bmp4 i crucial for the OFF to ON witch of the --Fli triad. Since HSC pecification require, our model predict that in the abence of Notch and Bmp4, newly generated HSC are trapped in a low expreion tate and hematopoietic development i compromied. The network alo irreveribly witche from the ON to OFF tate when reaching a threhold value of repreion of trancription by Gata. The network will then remain in the OFF tate in the abence of other ignal. Interetingly, in ref. [22] the author ue a mathematical model to predict that a imilar triad module in embryonic tem cell i alo bitable. However their module i expected to be bitable only in the preence of activating or deactivating ignal unlike -- Fli triad that how irreverible bitability. Our analyi indicate eential role of all the enhancer ite included in the model in maintaining irreverible bitability in teady tate doe-repone curve of the triad. Elimination of any binding ite in or enhancer lead to complete elimination of bitability with only the OFF tate remaining. Mutation in the Fli enhancer may lead to a reverible bitability phenotype in which the triad i activated only in the preence of Notch and/or Bmp4 ignal above a certain threhold. We emphaize, however, that thee prediction do not indicate that impler triad network with le autoregulation are incapable of achieving irreverible bitable witching behavior. Our goal wa to predict the behavior of the triad to the mutation of the regulatory region. If one allow compenatory change in other model parameter one can retore the irreverible witching behavior and even et the witching threhold to be equal to that of wild-type PLoS Computational Biology www.plocompbiol.org 0 May 200 Volume 6 Iue 5 e00077