Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Declarative Modeling of Regulatory Genetic Networks with Non Monotonic Logical Programming A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France 22-06-2017 A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Personal view. AI AI : what, not how. e.g. p(x, y) instead of y = f(x). What for ? To get a panel of functionalities. e.g. from p(1, 2) to p(x, y). A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Motivations To show the interest of a declarative approach based on non monotonic logical programming ( Answer Set Programming , ASP) for modeling Thomas’ logical discrete Genetic Regulatory Networks (GRNs) for inducing all GRNs a priori consistent with actual biological knowledge ( reverse engineering ). for taking into account both automatic inconsistency repairing and gene interaction properties which are only generally true , by using default rules provided by ASP. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Declarative approach for GRNs. Personal view Four steps methodology. Formalization (network structure, behaviors, ...) with constraints. Consistency test (see below). Learning common properties of consistent GRNs (theorems). Choice of experiments / Knowledge addition (non monotony helps) Return to step1. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Content 1 Basics: ASP and logical modeling of Thomas GRNs 2 Applications 3 Generally true Additivity Constraints and automatic consistency repairing 4 On going works A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Belief revision with ASP (Answer Set Programming). ASP is a logic programming technology based on a non monotonic logic with models said stable which are minimal. Rules are: a 0 : − a 1 , . . . , a m , not a m + 1 , . . . , not a n The typical example for introducing to non monotonic logics: From the axioms in ordinary (monotonic) logic: flies ( X ) ⇐ bird ( X ) bird ( tweety ) one deduces flies ( tweety ) . The problem is with penguins. Taking them into account demands: completing the 1st axiom by ¬ penguin ( X ) as a premise, qualifying by hand every bird (is it or not a penguin ?). A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Advantages of ASP. Belief revision(cont.) With ASP, these manual revisions may be avoided by using defaults . Unless the contrary is proved , a bird is not a penguin. From: flies(X) :- bird(X), not penguin(X). bird(tweety). one deduces flies(tweety) . If by addition of new knowledge (e.g. result of experimentation), penguin(tweety) can been proved then flies(tweety) is no more deducible (non monotony). Additivity constraints on gene interactions (see later) are typical candidates for being modeled by such defaults. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Thomas GRNs. Interaction graph + , 2 + , 1 a b − , 1 Focal equations: � if x b < θ 1 K a b X a = K b if x b ≥ θ 1 a b if x a < θ 1 a and x b < θ 2 K b b K a if x a ≥ θ 1 a and x b < θ 2 b b X b = if x a < θ 1 a and x b ≥ θ 2 K b b b K ab if x a ≥ θ 1 a and x b ≥ θ 2 b b x a : (discrete) concentration of protein a . θ 1 a : threshold of a . A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Thomas GRNs. Dynamics Focal equations relate a state [ x a , x b ] and its focal state [ X a , X b ] indicating in which direction are its neighboring successors (one or no concentration changing), thanks to parameters K . Semantics of signs, in terms of the parameters: + , 1 Observability constraint ( always true) for a → b : ( K b < K a b ) ∨ ( K b b < K ab b ) i.e activation in at least on case. + , 1 Additivity constraint ( generally true) for a → b : ( K b ≤ K a b ) ∧ ( K b b ≤ K ab b ) i.e. no inhibition. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Transition graph steady state max y max y max y θ 2 θ 2 θ 2 y y y G 1 : G 2 : G 3 : θ 1 θ 1 θ 1 y y y 0 0 0 θ 1 θ 1 θ 1 max x max x max x x x x max y max y max y θ 2 θ 2 θ 2 y y y G 4 : G 5 : G 6 : θ 1 θ 1 θ 1 y y y 0 0 0 Transition graphs satisfying observability and additivity constraints. One equilibrium for G 1 , G 3 , G 5 . Mutistationarity for G 2 , G 4 , G 6 . There are 2 2 ∗ 3 4 = 332 possible set of parameters. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Experiments (behaviors) represented as paths Examples: Enforcing the existence of a path of two successive identical states (steady state) gives all transition graphs except G 3 . Enforcing the existence of a path beginning with the state [ 0 , 0 ] and reaching the state w [ 0 , 2 ] leads to the models G 4 and G 6 . A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Other facilities Include automatic inconsistency repairing. mutant specification. minimization (interactions and thresholds values): the ASP software provides para-logical operators like #minimize{f_1,...,f_n} that produces only models with the lowest number of literals f_i true. deduction of properties on domains specified by biologists (e.g. clauses of chosen size on chosen literals). For example : ( K b < K a b ) ∨ ¬ ( K b < K ab b ) true in all models. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Content 1 Basics: ASP and logical modeling of Thomas GRNs 2 Applications 3 Generally true Additivity Constraints and automatic consistency repairing 4 On going works A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
Basics: ASP and logical modeling of Thomas GRNs Applications Generally true Additivity Constraints and automatic consistency repairing On going works Carbon Starvation in E.Coli [Ropers et al., Biosyst., 2006] -,2 +,1 +,1 -,1 gyrAB signal -,1 -,4 +,1 -,2 crp +,1 +,2 fis -,1 -,2 +,1 -,1 +,3 -,3 cya topA +,1 +,4 -,1 rrn -,3 -,1 Two steady states : 1) with a high concentration of Fis and a high supercoiling (e.g. high ratio GyrAB / TopA), 2) after carbon deprivation, with a high concentration of Crp and a weaker supercoiling. Two response paths to the two stresses: carbon deprivation, carbon-source availability. A. Rocca 1 , E.Fanchon 1 , L. Trilling 1 1 Lab. TIMC-IMAG, U. de Grenoble, France BIOSS-IA.Gif.06-2017
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