Logical modelling of cellular decisions

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Logical modelling of cellular decisions Denis Thieffry (thieffry@ens.fr) Contents Introduction Logical modelling T-helper cell differentiation MAPK network Porquerolles, June 25th, 2013

Cell proliferation, differentiation or death... How are decisions taken?

Key biological questions How does a cell decide which differentiation pathway to follow? When and to what extend cells become committed? To what extend and how is it possible to force cell to change their differentiation states? => Investigations using dynamical modelling

Dynamical modelling Why? To gain rigourous, global, functional understanding of the (complex) underlying networks To predict the behaviour of the system in novel situations To design novel experiments How? Regulatory charts/maps/graphs (CellDesigner, Cytoscape) Qualitative modelling: Boolean / multilevel discrete networks Quantitative modelling: ODE, PDE, Stochastic equations

Boolean networks - Stuart Kauffman (1969) x t +1 = B(x t ) The Boolean vector x represents the state of the system Random connections, nodes with predefined degree Canalizing Boolean functions Focus on asymptotic behaviour Two types of attractors: stable states and (simple) cycles Deterministic behaviour (only one possible following state)

Kinetic logic - René Thomas (1973) X = B(x) Xi (image or logical function) specifies whether gene i is currently transcribed xi (logical variable) denotes the presence (above a threshold of the functional product of gene i Gene i switched ON Gene i switched OFF 1 Xi 0 1 xi 0 t Delay don Delay doff

Logical modelling of regulatory networks [1] B A [2] C A graph describes the interactions between genes or regulatory products Discrete levels of expression associated to each regulatory component and interaction Logical rules/parameters K A = 2 IFF (C=0) K A = 0 otherwise C K B = 1 IFF (A=1) K B = 0 otherwise A K C = 1 IFF (B=1) AND (C=0) K C = 0 otherwise B C=0 1 0 2 1 C C 2 0 0 1 0 Decision trees 0 0 1 0

Logical modelling of regulatory networks [1] B A [2] C A graph describes the interactions between genes or regulatory products Discrete levels of expression associated to each regulatory component and interaction Logical rules/parameters K A = 2 IFF (C=0) K A = 0 otherwise C C=0 1 K B = 1 IFF (A=1) K B = 0 otherwise A 0 2 1 K C = 1 IFF (B=1) AND (C=0) K C = 0 otherwise B C 2 0 1 0 Decision diagrams 1 0

Logical state transition graphs [1] B A [2] C Regulatory graph + Logical rules => simulations / dynamical analysis Asynchronous updating (R Thomas) ABC C C A State transition graph B B Stable state

Logical state transition graphs A [1] [2] C Synchronous updating (S Kauffman) B + Logical rules ABC A C State transition graph B C Cycle Cycle C A Stable state

Logical state transition graphs [1] A [2] C Mixed a/synchronous updating: 2 priority classes: (1) synchronous fast decays (2) synchronous slow syntheses B + Logical rules ABC A C State transition graph B B C A B B A Stable state Fauré et al (2006) Bioinformatics 22: e124-31

GINsim (Gene Interaction Networks simulation) Aurélien NALDI Fabrice LOPEZ Duncan BERENGIER Claudine CHAOUIYA analysis toolbox core simulator State transition graph GINML parser Regulatory graph graph editor user interface graph analysis simulation Available at http://ginsim.org Naldi et al (2009) BioSystems 97: 134-9 Chaouiya et al (2013) Meth Mol Biol 804: 463-79

Development of dynamical analysis tools Decision diagrams Identification of attractors State transition graph compression Analysis of regulatory circuits Model reduction Priority classes Mixed a/synchronous simulations Petri nets Standard Petri nets Coloured Petri nets Model checking Verification of dynamical properties (temporal logic) Logical programming Attractor identification and reachability analysis

Efficient identification of stable states C => 2 stable states : 001 et 110 A B KA= 1 IFF A KB =1 IFF A &!C KC =1 IFF!A A A A 0 1 C 1 0 1 0

Efficient identification of stable states C => 2 stable states : 001 et 110 A B KA A KB A KC A A 1 1 * B B * B B stable 1 C C C C C 0 C stable 0 1 0 0 1 0 0 1 0 unstable Stability condition Naldi, Chaouiya & Thieffry (2007) LNCS 4695: 233-47.

Coping with the exponential growth of logical state transition graphs Attractor identification Compaction of state transition graphs Model reduction Temporisation (e.g. priorities, delays, etc.) Model checking

Bacteriophage lambda: regulatory graph 2 3 1 2 1 2 2 3 Thieffry & Thomas (1995)

Phage lambda model : logical rules Node => target value CI => 2 CI => 0 Cro => 3 Cro => 2 Cro => 0 CII => 1 CII => 0 N => 1 N => 0 Logical Rule!Cro CII Otherwise!CI &!Cro!CI & Cro CI!CI &!Cro & N Otherwise!CI &!Cro Otherwise Thieffry & Thomas (1995)

Lambda phage model: state transition graph (STG) Lysogeny (only CI expressed) [CI, Cro, CII, N]

Lambda phage model: state transition graph (STG) coloration according to strongly connected components lysogeny only CI expressed cyclic attractor for lysis only CRO (homeostatically) expressed

Lambda phage model: graph of strongly connected components (SCCG) lysogeny lysis

Lambda phage model: hierarchical state transition graphs (HTG) transient pathways stable state CI CII N CI lysogeny only CI expressed Cro Cro Cro Cro CII N CI Cro CII N transient cycle CI cyclic attractor lysis only CRO (homeostatically) expressed HTG computation on the fly using Tarjan algorithm + decision diagrams

Content of HTG components (schemata) Component Type Number of states Schemata CI Cro CII N i-7 transient paths 7 0 0 0 * 0 0 1 1 1 0 * * i-3 transient paths 3 2 0 0 1 2 0 1 * ct-31 transient cycles 31 0 1 0 * 0 1 1 1 0 2-3 0 1 0 2-3 1 * 1 1 * * 1 2-3 0 1 1 2-3 1 * 2 1-3 * * ct-2 transient cycle 2 1 2-3 0 0 ss-2000 Stable state 1 2 0 0 0 ca-2 cyclic attractor 1 0 2-3 0 0

Regulatory circuits: dynamics in isolation Positive circuit Negative circuit A A D B D B C C attracting cycle stable states Remy et al (2003) Bioinformatics 10: ii172-8

Regulatory circuits & Thomas' rules A positive regulatory circuit is necessary to generate multiple stable states or attractors A negative regulatory circuit is necessary to generate sustained oscillatory behaviour Thomas R (1988). Springer Series in Synergics 9: 180-93. Mathematical theorems and demonstrations: In the differential framework: Thomas (+, 1994), Plathe et al. (±, 1995), Snoussi (±, 1998), Gouzé (±, 1998), Cinquin & Demongeot (+, 2002), Soulé (+, 2003). In the discrete framework: Aracena et al. (+, 2001), Remy et al. (±, 2005), Richard & Comet (+, 2005).

Regulatory circuit functionality A B C D Circuit properties depends on the effect of A on B If A alone is able to switch OFF B: In the presence of A: only one stable state with {A,B,C,D}= 1011 In the absence of A: two stable states 0100 and 0011 The positive cross-inhibitory circuit involving B and C is thus functional only in the absence of A Development of a computational algorithm enabling the analysis of the functionality of regulatory circuits in the discrete case => GINsim

CD4+ T-helper cell differentiation Multiple signalling pathways Various transcriptional factors Specific expression patterns (TFs and lymphokines)

Logical modelling of Th activation Klamt S et al (2006). BMC Bioinformatics 7: 56.

Logical modelling of Th1/Th2 cell differentiation Mendoza L (2006). BioSystems 84: 101-14.

Towards a comprehensive, modular logical model of the Th differentiation network $% $%& ' $%& (!"#!"#" Yamaoka et al. 2004 Yamoka et al (2004) ILR 1 if IL and ILR and ILR = 1 IFF IL AND ILR1 AND ILR2

Logical modelling of the Th network $%&' $%( ) $%( * $%( ILR = 1 IFF (IL OR IL_e) AND ILR1 AND ILR2 $%!"#"

Logical modelling of the Th network $%&' "6( $%*&' $%( ) $%( * $%*(9 $%*(2 $%( 78#" $%*(: $%*( $%!"#"!"#"5 IL = 1 IFF NFAT AND proliferation AND... +,-./01,23/-4

Logical modelling of the Th network!-./$%!"3$% Multiple uses of receptor chains!"#$%!-./&,!-./&#!"3&+!"#&'!"#&0!-./&!"3&!"#&(!"#& Converging signals Ternary variables )*+*, )*+*2 )*+*1

Current logical model of the Th network IFNB_e IFNG_e IL27_e IL6_e IL21_e IL23_e IL10_e TGFB_e IL12_e IL4_e IL15_e IL2_e APC CGC proliferation IFNGR2 IFNGR1 IL27RA IL6RA GP130 IL10RA IL10RB IL12RB1 IL12RB2 IL15RA IL4RA IL2RB IL2RA IFNBR IFNGR IL27R IL6R IL21R IL23R IL10R TGFBR IL12R IL4R IL15R IL2R CD28 TCR STAT1 STAT3 STAT4 STAT6 STAT5 NFAT IKB IFNG IL21 IL23 IL10 TGFB IL4 IL2 IL17 NFKB SMAD3 IRF1 RUNX3 TBET GATA3 RORGT FOXP3 13 input components, 52 internal components, 339 circuits => too large to perform simulations Naldi et al (2010) PLoS Comput Biol 6: e1000912.

Model Reduction Detailed model Comprehensive Difficult to analyse Reduced model Easier to analyse Loss of information - Biological (indirect effect) - Dynamical (delays)

Implementation of user defined model reductions R1 R3 X T R2 Keep the detailed model Reduction before analysis => New rules for targets of hidden nodes Choice of reduction Dynamical consistency R1 T R2 - No circuit deletion - Same stable states - Reachability may change R3 Naldi et al (2011) Theoretical Computer Science 412: 2207-18.

Reduced logical model IFNB_e IFNG_e IL27_e IL6_e IL21_e IL23_e IL10_e TGFB_e IL12_e IL4_e IL15_e IL2_e APC proliferation IL2RA IL2R STAT1 STAT3 STAT4 STAT6 STAT5 NFAT IFNG IL21 IL23 IL10 TGFB IL17 IL4 IL2 TBET GATA3 RORGT FOXP3 13 input components, 21 internal components

Selected environments for simulations APC IL2 IL4 IL6 IL10 IL12 IFNG TGFB No input APC Pro-Th1 Pro-Th1 Pro-Th2 Pro-Th17 Pro-Treg Pro-Treg

IL2R IL2RA IFNG IL2 Stable signatures IL4 IL10 IL21 IL23 TGFB TBET GATA3 FOXP3 NFAT STAT1 STAT3 STAT4 STAT5 STAT6 proliferation RORGT IL17 Support Th0 [7] Activated Th0 [7] Th1 [7] Activated Th1 [7] Anergic Th1 [78] Anergic Th1 ROR t+ predicted Th1 ROR t+ [44, 45, 70] Th1 Foxp3+ [12] Anergic Th17 Th2 [7] Activated Th2 [7] Anergic Th2 [78] Th2 ROR t+ [49] Activated Treg [79] Treg ROR t+ [46 48] Th1 Foxp3+ ROR t+ predicted Th2 Foxp3+ ROR t+ predicted

Simulations (Hierarchical Transition Graphs) APC + IL2 Pro Treg (TGFB) i#25 i#37 IL2+ Proliferation+ IFNG+ IL2- IL2- TGFb+ ss-1001000000000210100000000100020100 Activated Th0 ss-1001000000001210000001001100020100 Activated Th0 Pro Th1 (IFNG) i#79 ss-1011000000000211000000100110020100 Activated Th1 Pro TH2 (IL4, IL6) i#255 IL2- IL4+ IL10+ IL21+ IL23+ ss-1001110000000210011110010101021100 Activated Th2 Node order: APC, IFNB_e, IFNG_e, IL2_e, IL4_e, IL6_e, IL10_e, IL12_e, IL15_e, IL21_e, IL23_e, IL27_e, TGFB_e, IL2R, IL2RA, IFNG, IL2, IL4, IL10, IL21, IL23, TGFB, TBET, GATA3, FOXP3, NFAT, STAT1, STAT3, STAT4, STAT5, STAT6, Proliferation RORGT and IL17.

Simulations (HTG) Pro Th17 (TGFB, IL6) RORGT+ i#66 FOXP3+ i#39 i#91 IL2+ IL10+ IL21+ IL23+ RORGT+ TGFB+ RORGT+ IL2- IL10+ IL21+ IL23+ ss-1001010000001210101110000101020110 Activated Th17 FOXP3- ss-1001010000001210001111001101020110 Activated Th17 FOXP3+ Node order: APC, IFNB_e, IFNG_e, IL2_e, IL4_e, IL6_e, IL10_e, IL12_e, IL15_e, IL21_e, IL23_e, IL27_e, TGFB_e, IL2R, IL2RA, IFNG, IL2, IL4, IL10, IL21, IL23, TGFB, TBET, GATA3, FOXP3, NFAT, STAT1, STAT3, STAT4, STAT5, STAT6, Proliferation RORGT and IL17.

Simulations (HTG) APC + IL4 + IL6 + TGFB (pro Th2 + Th17 cytokines, in the absence of IL2) i#112(1) i#56 STAT5+ STAT5+ i#11 IL2- IL2R- IL2RA+ GATA3+ ss-1000110000001010000000010101011010 Anergic GATA3+ RORGT+ RORGT+ IL2R- IL2- STAT5+ STAT6+ RORGT+ RORGT+ i#24 RORGT+ i#112(2) IL10+ IL2R- IL4R+ IL21+ IL23+ STAT5+ RORGT+ i#143 ss-1000110000001010011110010101021110 Activated GATA3+ RORGT+ IL4+ IL10+ IL21+ IL23+ FOXP3+ FOXP3+ FOXP3+ FOXP3+ i#35 IL2R- IL2RA+ GATA3+ RORGT+ IL2R- IL2- STAT5+ STAT6+ IL2- IL2R- IL2- i#54 ss-1000110000001010000000011101011010 Anergic GATA3+ RORGT+ FOXP3+ STAT5+ i#595 IL2R- IL4- IL10+ IL21+ IL23+ TGFB+ GATA3+ RORGT+ ss-1000110000001010001111011101021110 Activated GATA3+ RORGT+ FOXP3+ IL10+ IL21+ IL23+ TGFB+ Node order: APC, IFNB_e, IFNG_e, IL2_e, IL4_e, IL6_e, IL10_e, IL12_e, IL15_e, IL21_e, IL23_e, IL27_e, TGFB_e, IL2R, IL2RA, IFNG, IL2, IL4, IL10, IL21, IL23, TGFB, TBET, GATA3, FOXP3, NFAT, STAT1, STAT3, STAT4, STAT5, STAT6, Proliferation RORGT and IL17.

Simulations in the absence of stimulation GATA3, Tbet, Foxp3 and RORγt

Pro Th2 environment (IL4 & IL6) GATA3, Tbet, Foxp3 and RORγt

Pro Treg environment (IL2 & TGFb IL10) GATA3, Tbet, Foxp3 and RORγt

Overview of the simulation results for micro-environments Absence of stimulation APC only Pro-Th1 IL2 & IFNg or IL12 Pro-Th2 IL4 & IL6 Pro-Treg IL2 & TGFb or IL10 Pro-Th17 IL6 & TGFb GATA3 Tbet Foxp3 RORγt Naldi et al (2010) PLoS Comput Biol 6: e1000912.

Use of model checking to assess cell plasticity Export of GINsim models into NuSMV format Specification of perturbation and stable patterns using temporal logic formula Graphical output Monteiro & Chaouiya (2012) Adv Intell Soft Comput 154: 259 67. Bérenguier et al (2013) Chaos, in press.

Regulatory circuit analysis Functional positive circuits Negative circuits

Conclusions Model reproducing the main reported Th subtypes (Th0, Th1, Th2, Treg, Th17) in terms of stable states Many more stable states depending on signalling environment, including hybrid subtypes Plasticity of Th subtypes depending on signalling environment Differentiation network rather than lineage tree

Prospects Simulations of mutants and other perturbations (e.g. different timing for combinations of external signals) Extension of cellular model (additional pathways, transcription factors, interactions) Incorporation of high-throughput datasets (transcriptomics, proteomics) in collaboration with Vassili Soumelis, Institut Curie Consideration of novel subtypes Quantification of alternative outcomes

ENS (Paris) Wassim Abou-Jaoudé Samuel Collombet Jérôme Feret Anna Niarakis Morgane Thomas-Chollier Institut Curie (Paris) Emmanuel Barillot Eric Bonnet Laurence Calzone Philippe Hupé Vassili Soumelis Maxime Touzot Andrei Zinovyev TAGC (Marseille) Luca Grieco Aurélien Naldi Brigitte Kahn-Perlès Jacques van Helden IML (Marseille) Duncan Berenguier Elisabeth Rémy IGC (Lisboa) Claudine Chaouiya Jorge Carneiro Pedro Monteiro Contributors & supports Belgian Inter-university Attraction Pole Bioinformatics and Modelling : from Genomes to Networks

Selected references Bérenguier D, Chaouiya C, Monteiro PT, Naldi A, Remy E, Thieffry D, Tichit L (2013).Dynamical modeling and analysis of large cellular regulatory networks. Chaos. In press. Monteiro PT, Chaouiya C (2012). Efficient verification for logical models of regulatory networks. Adv Intell Soft Comput 154: 259 67. Naldi A, Thieffry D, Chaouiya C (2007). Decision diagrams for the representation and analysis of logical models of genetic networks. Lecture Notes in Bioinformatics 4695: 233-47. Naldi A, Remy E, Thieffry D, Chaouiya C (2011). Dynamically consistent reduction of logical regulatory graphs. Theoretical Computer Science 412: 2207-18. Naldi A, Carneiro J, Chaouiya C, Thieffry D (2010). Diversity and plasticity of Th cell types predicted from regulatory network modelling. PLoS Computational Biology 6: e1000912.

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