Real-time Control of Gene Expression

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1 Real-time Control of Gene Expression J. Uhlendorf 1,2 S. Bottani 2 F. Fages 1 P. Hersen 2 G. Batt 1 1 Contraintes Team - INRIA Paris-Rocquencourt 2 MSC Laboratory - Paris Diderot University Identification and Control of Biological Interaction Networks Workshop Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

2 Motivation Understanding dynamics of cellular processes Monitor the time-response to perturbations No experimental methods for applying tightly controlled intracellular time-varying perturbations Time varying perturbations more informative than static ones Goal: Experimental platform for the tight control of gene expression at the single cell level Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

3 A closed loop control platform Input flow controller Controller Microfluidic chamber Trash collector Image analysis Image acquisition (microscope) Main features: 1 real-time observation 2 real-time change of cellular stimulus 3 real-time control Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

4 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

5 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

6 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

7 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

8 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

9 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

10 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

11 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Outline 1 Experimental results on controling signal transduction 2 Computational results on controling Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

12 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? cell environment cytoplasm nucleus Osmotic stress P P gene activation phosphorylation Pprot Protein CFP Prot CFP Outline 1 Experimental results on controling signal transduction Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

13 Methods Which control algorithm? Proportional-integral-derivative (PID) controller define error e(t) as difference between desired and observed state u(t) = k1 e(t) + k 2 t 0 e(τ)dτ + k 3 d dt e(t) requires no structural knowledge about the controlled system but requires tuning of parameters How to quantify nuclear localization? Define colocalization with nuclear marker (Htb2) Relative colocalization: h(t) = <Pixel intensity> nuc <Pixel intensity> cyt Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

14 Experimental results: Sustained high activation Normalized nuclear localization Osmolarity [Sorb. M] time [min] time [min] PI-control works in principle Sustained high activation not possible due to cell adaptation Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

15 Experimental results: Repeated trapezoidal motifs Normalized nuclear localizatio Osmolarity [Sorb. M] time [min] time [min] Frequency encoding seems to work better than amplitude encoding (cells have time to relax) Still room for improvement (e.g. time-lag, reproducibility) Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

16 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? cell environment cytoplasm nucleus Osmotic stress P P gene activation phosphorylation Pprot Protein CFP Prot CFP Outline 1 Experimental results on controling signal transduction 2 Computational results on controling Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

17 The control problem Input: osmolarity Output: fluorescent measurements of Problem: what inputs to apply to achieve a desired behaviour? Osmotic stress cell environment phosphorylation cytoplasm P P nucleus gene activation Pprot Protein CFP Prot CFP Outline 2 Computational results on controling Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

18 A model based control approach Mathematical model (similar to Mettetal et al., 2008 and Muzzey et al., 2009) - if osm e osm i : (hyperosm. env.) osm i = κ ohog γ oosm i hog = κ g (osm e osm i ) γ g hog rna = κ mhog γ mrna ṗ = κ prna γ pp - if osm e < osm i : (hypoosm. env.) osm i = κ ohog (γ o + γ o )osm i hog = γ g hog rna = κ mhog γ mrna ṗ = κ prna γ pp Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

19 A model based control approach Mathematical model (similar to Mettetal et al., 2008 and Muzzey et al., 2009) - if osm e osm i : (hyperosm. env.) osm i = κ ohog γ oosm i hog = κ g (osm e osm i ) γ g hog rna = κ mhog γ mrna ṗ = κ prna γ pp - if osm e < osm i : (hypoosm. env.) osm i = κ ohog (γ o + γ o )osm i hog = γ g hog rna = κ mhog γ mrna ṗ = κ prna γ pp Parameters fitting signal transduction parameters fitted w.r.t our experimental data transduction response to osmotic shock of various durations or amplitude parameters set to arbitrary but realistic values Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

20 Control strategy Taking advantage of system structure: backstepping cascaded, fast/slow system (a) Input osm e (b) Applied Osmolarity Signal Transduction ST Controller nuc hog nuc Profile Gene Expression GE Controller Output p Target Profile Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

21 Control strategy Taking advantage of system structure: backstepping cascaded, fast/slow system (a) Input osm e (b) Applied Osmolarity Signal Transduction ST Controller nuc hog nuc Profile Gene Expression GE Controller Output p Target Profile Model predictive control approaches target protein O1 O2 O2 O1 tend don1 don2 don3 time drelax doff1 drelax doff2 drelax doff3 drelax doff4 Osm e u1 u2 u3 u4 dpulse u 0 u5 tp tend A B C D a b time GE controller using pulse modulation ST controller Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

22 Control strategy Taking advantage of system structure: backstepping cascaded, fast/slow system (a) Input osm e (b) Applied Osmolarity Signal Transduction ST Controller nuc hog nuc Profile Gene Expression GE Controller Output p Target Profile Model predictive control approaches target protein O1 O2 O2 O1 tend don1 don2 don3 time drelax doff1 drelax doff2 drelax doff3 drelax doff4 Osm e u1 u2 u3 u4 dpulse u 0 u5 tp tend A B C D a b time GE controller using pulse modulation ST controller Optimization-based implementation in Matlab/CMAES Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

23 In silico evaluation of control strategy Testing various control objectives with deterministic or stochastic models (and ignoring observation and state estimation problems) Protein conc. Protein conc. desired colocalization Osmolarity Time [min] Time [min] Time [min] Time [min] Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

24 In silico evaluation of control strategy Testing various control objectives with deterministic or stochastic models (and ignoring observation and state estimation problems) Protein conc. Protein conc. desired colocalization Osmolarity Time [min] Time [min] Time [min] Time [min] Proposed control strategy is feasible wrt real-time requirement and fairly robust wrt large biological variability Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

25 Discussion Summary first closed loop control of a signal transduction pathway adaptation to osmotic stress suggests pulse modulated strategy proposed control approach seems computationally tractable and fairly robust Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

26 Discussion Summary first closed loop control of a signal transduction pathway adaptation to osmotic stress suggests pulse modulated strategy proposed control approach seems computationally tractable and fairly robust Future work to actually control deal with observation and state estimation issues new strains to follow both signaling activity and new strains (partly) lacking adaptation response ( GPD1, GPD2) improve model of the pathway and develop MPC controller Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

27 Discussion Summary first closed loop control of a signal transduction pathway adaptation to osmotic stress suggests pulse modulated strategy proposed control approach seems computationally tractable and fairly robust Future work to actually control deal with observation and state estimation issues new strains to follow both signaling activity and new strains (partly) lacking adaptation response ( GPD1, GPD2) improve model of the pathway and develop MPC controller From I understand what I can build to I understand what I can control Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

28 Thank you for your attention Uhlendorf, Bottani, Fages, Hersen, Batt (2011). Towards Real-time Control of Gene Expression: controlling the Hog Signalling Cascade. PSB 11. Uhlendorf, Hersen, Batt (2011). Towards Real-time Control of Gene Expression: in silico Analysis. submitted. Muzzey, Gómez-Uribe, Mettetal, van Oudenaarden (2009). A Systems-Level Analysis of Perfect Adaptation in Yeast Osmoregulation. Cell. Mettetal, Muzzey, Gomez-Uribe, van Oudenaarden (2008). The frequency dependence of osmo-adaptation in Saccharomyces cerevisiae. Science Geifen, Gabay, Mumcouglu, Engel, Balaban (2008). Single-cell protein induction dynamics reveals a period of vulnerability to antibiotics in persister bacteria. PNAS Uhlendorf et al. (INRIA/MSC) Real-Time Control of Gene Expression February 8, / 13

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