Modeling. FRANCK DELAPLACE IBISC GENOPOLE EVRY UNIVERSITY

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1 1 Modeling FRANCK DELAPLACE IBISC GENOPOLE EVRY UNIVERSITY

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3 R. Thom : «On essaye de dominer des situations à l aide de la modélisation, [..] en construisant un système [..] à travers une certaine analogie. [..] On formule une question sur la situation naturelle et, à travers l analogie, on la transfère sur le modèle [..] de manière à en obtenir une réponse.» Paraboles et Catastrophes, Analogy: An analogy is a comparison between two things that are quite different in nature. An analogy often explains a complex subject with one that is simpler or more familiar. William Harvey ( )

4 Modeling & causality What is responsible for? Find the causes Inverse problem Inference 4 What is the effect of? Find the consequences Direct Method Simulation

5 Modeling steps (for a computer scientist) 5 Describe Find a language Ability to express objects and notions Design of the analogy Assess: Expressivity of a theoretical framework Explain Find a (mechanistic) model Ability to represent the evolution Design of a model Assess: Capabilities of a theoretical framework Predict Find new insights/ elements Ability to compute effects or infer causes Validation of the predictions Assess: Performance of a theoretical framework (Theorems + methods)

6 Analogy in Genomic? 6 Information Interaction Network

7 Network Science 7 A framework to tackle with complexity systems becomes hopelessly complicated (Biology, Internet, Social network, ) Hard to derive collective behavior from a knowledge of the system s components. To get a comprehensive understanding of complex system behavior

8 Interactome 8 Whole set of molecular interactions in a cell Originally coined in 1999 by a group headed by Bernard Jacq Type of interactions Human PPI Name Nature of the interactions Type Protein-Protein Specific physical contact between protein steered by electrostatic forces reciprocal Signaling Signal transduction mechanism oriented Regulation mechanisms between genes regulating the production of specific gene product oriented

9 Definition of a Network 9 A network is a dynamical system nodes : Agents links: Interaction/dependence Each component as a internal dynamics parameterized by the state of its neighbors linked to the node. Network of gauges model

10 Graph Definition 10 Edge, Arc Node, Vertice ( ) Path Directed Undirected A Graph is a pair < V, E > V is a set of vertices/nodes E V V a set of edges A graph can be either directed or undirected Undirected means that x, y E, x, y = (y, x) Otherwise it is directed A path is a sequence v 1,, v n of vertices s.t. 1 i < n: v i, v i+1 E

11 Two modeling issues 11 Topological Analysis Dynamical Analysis Structure based network analysis find characteristic properties inducing/limiting the behavior? Evolution of the system Dynamical properties identification Asymptotic behavior

12 12 Topological analysis example Structural analysis of the consequences of diseases

13 Diseasome D1 G2 D4 13 Diseasome = Bipartite graph Gene Disease Disease G1 Gene A disorder and a gene are linked if mutations in that gene are implicated in that disorder. Two representations can be derived transitively: gene-gene association or disease-disease association D1 D2 Disease Disease D3 D3 Gene Gene G1 The latter reveals insights on comorbidity D2 D4 G2

14 Disease Disease Network 14 Kwang-Il Goh, and In-Geol Choi Briefings in Functional Genomics 2012;11: OMIM Mendelian disease data-base

15 Dynamical analysis 15

16 Boolean Network 16 Regulation of G by a Complex G1-G2 G1 G2 G = 0 = 1 G 1 G 2 = G

17 Fundamental operations 17 y = x 1 x 2 y = x 1 x 2 x 1 x 2 y x 1 x 2 y y = x 1 x 1 y = 0 = 1 Logical AND Logical OR Negation

18 Boolean network 18 Discrete Dynamical system on discrete states. Dynamical system on Booleans states. X= x 1,, x n is the set of variables of the Boolean network Boolean variable x i {0,1} F = x 1 = f 1 (x 1,, x n ) x i = f i (x 1,, x n ) x n = f n (x 1,, x n ) Boolean function x 1 = x 3 x 2 = x 1 x 3 x 3 = x 2 x 1

19 Interaction graph Abstraction of the dependence between variables x i x j x i Var(f j ) Extended to sign defining the nature of the interaction: Monotonous increasing Monotonous decreasing x 1 = x 3 x 2 = x 1 x 3 x 3 = x 2 x 1 Interaction graph x 1 x 2 19 x 3

20 Model of Dynamics 20 Model = Labelled transition system collecting all the trajectories M F = S,, M where, M 2 A is the updating mode such that: SYNCHRONOUS ASYNCHRONOUS all the states are updated during a transition ie. M = A 1 state is updated during a transition ie. M = a i a i A

21 Boolean Modeling 21 λ- phage Life cycle of -phage is controlled by two genes ci, Cro. The expression of ci promotes lysogeny. The expression of Cro promotes Lysis. Cro forbids the access to PRM promoter. ci forbids the access to promoter PR,PL

22 Lambda Phage Boolean model 22 Cro CI Lysogeny Cro Cro CI Cro = CI CI = Cro Lysis CI

23 Boolean Modeling Summary 23 Model designed from literature & Database Equilibrium corresponds to privileged states for the modeling A Boolean sub-profile at equilibrium is considered as a model of molecular signature of phenotype, assimilated to a bio-marking. Asynchronous update is often chosen to model dynamics of gene expression

24 24 Inference of Drug targets EXAMPLE

25 Causes of cellular phenotypes switches 25 Normal Cell Cancer Cell Dying Cell Mutations Anti-cancer drugs

26 Simulation screening efficiency? 26 Medium size network of 100 genes Multi-target therapy Target at most 10% of the molecules ( for toxicity condition ) Find the candidates for drug targets. Number of simulation trials?

27 Targeting the functions of cancer cells 27 «Hallmarks of Cancer, the next generation», Hanahan & Weinberg, Cell (2011) Cancer = Disease of interactome

28 Mutations Network actions 28 Zhong et al Edgetic perturbation models of human inherited disorders. NonSense MissSense Val Glu STOP Glu Addition & Deletion of arcs and nodes

29 Generalisation: Genetic and epigenetic causes 29 (Maria Bargués i Ribera MSSB report) Arc/Node deletion Arc/Node addition

30 Dynamical systems reprogramming 30 F = x 1 = f 1 (x 1,, x n ) x i = f i (x 1,, x n ) x n = f n (x 1,, x n ) Structural actions F Act = x 1 = g 1 (x 1,, x n ) x i = g i (x 1,, x n ) x n = g n (x 1,, x n ) Knock-out x 1 x 2 x 3 Over-expression Break

31 31 Boolean network Reprogramming Theoretical Framework Reprogramming Specification Inference of actions

32 Boolean Control networks for reprogramming 32 U = {u 1, u m } : Control parameters F U = x 1 = f 1 (x 1,, x n, u 1,, u m ) x i = f i (x 1,, x n, u 1,, u m ) x n = f n (x 1,, x n, u 1,, u m ) Control input μ: U {0,1} A general framework for Boolean system reprogramming f Structural actions g F u = u f ( u g)

33 Structural control category 33 Convention : an control parameter freezing a variable is equal to 0 Knock-out x 1 x 2 Node Action: DEFINITION -freezing x i = f i x 1,, x n d i 0 x 3 Over-expression Break x i = f i x 1,, x n d i 1 Edge Action: USE -freezing x j = f j (x 1,, x i u 0 i,j,, x n x j = f j (x 1,, x i u 1 i,j,, x n

34 Boolean control network - Example 34 U = Set of control parameters U x 1 = (x 2 u 0 2,1 ) x 3,,,,,,,,,,,,,, 1 x 2 = x 3 u 3,2,,,,,,,,,,,,,,, x 3 = x 2 x 1 d 3 1 d 3 0 μ 1 = μ 2 = 0 u 2,1 1 1 u 3,2 1 d 3 1 d u 2,1 0 1 u 3,2 1 d 3 1 d

35 Reprogramming specification and Action inference 35

36 Possibility/Necessity of a property 36 Possibility (of p) Necessity (of p) s S STBL Fμ (s) p(s) Find a control input μ such that: s S STBL Fμ (s) p(s)

37 Causal inference = abduction problem 37 C Φ Θ CAUSE THEORY OBSERVATION μ Constraints of control parameters Possibility necessity of p on stable states A causal explanation of θ is an implicant C

38 Possibility and Necessity as abduction problems 38 THEOREM Finding μ such that: s S STBL Fμ (s) p(s) s S STBL Fμ (s) p(s) It is an abudction problem in propositional logic i.e. finding a cube C μ such that: C s C μ φ STBL FU p C μ φ STBL FU p where C s, C μ are the minterms of (respectively) s, μ and STBL FU i=1 (x i f i (x 1,, x n, u 1,, u m ))

39 39 Application to Synthetic lethality Inference of lethal partners

40 Synthetic lethality 40 VIABLE G1 VIABLE G1 G2 G1 LETHAL G2 G2 G1 VIABLE G2

41 in-silico Prediction Inference of drivers in Breast cancer (I) 41 Freeze to False PTEN P53 BRCA1 GSK3 Freeze to True Akt Bcl2 PI3K MDM2 Action on nodes Tumor supressors Oncogenes All nodes can be frozen to True or False Except Markers Loss of Apoptosis Necessary avoid the (apoptosis) marking Necessary avoid the biomarking CycD1=0, Bax=1 at equilibrium

42 in-silico Prediction Inference of targets for BRCA1 mutation (II) 42 FALSE PARP Freeze to False Freeze to True Synthetic lethal partner of BRCA1 Olaparib drug action Action on nodes All nodes can be frozen to True or False Except Markers and BRCA1 Gain of Apoptosis Possibly the (apoptosis) marking Possibly reach at equilibrium the marking CycD1=0, Bax=1

43 END 43 K. Popper : «Une théorie qui n est réfutable par aucun événement qui se puisse concevoir est dépourvue de caractère scientifique. Pour les théories, l irréfutabilité n est pas (comme on l imagine souvent) vertu mais défaut» F. Jacob : «il ne suffit pas de «voir» un objet jusque-là invisible pour le transformer en objet d analyse [..] il faut encore qu une théorie soit prête à l accueillir.»

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