Quel type de modlisation pour des interactions entre composants - PowerPoint PPT Presentation

Quel type de modélisation pour des interactions entre composants biologiques ? Andrei Doncescu LAAS-UPR8001/Université Paul Sabatier Pierre Siegel LIF Marseille

Why a biological system is complex ? • • Contains many interacting parts • Interactions are nonlinear • Contains feedback loops (+/-) • Cause and effect intermingled • Driven out of equilibrium • Evolves in time (not static) • Usually chaotic • Can self-organize and adapt Emergent behavior is what's left after everything else has been explained.”

Biological Reaction or Regulation by Enzymes

The Analytic Equation of the Tree of Life • Living Organisms are open systems O.S. that maintein their particulary form of organization by utilizing large quantities of energy and metter from the environment • Prigogine demonstrated that OS driven far from equilibrium display self-ordering tendancies as they receive an input energy

Biological Reaction Catabolisme Microorganisme Substrate Chemical Pounds Microorganism Heat Anabolisme Substrate

EQUATION BILAN Flux d’accumulation = Flux net de conversion + Flux net d’échange Formulation : dE    E   E e . dV Flux d'accumulation avec dt V     r . dV Flux net de conversion = E E V Soit :   convective   diffuse  d e . dV storage element transport   transport   V      r . dV . dV E E dt local change in the reaction local local = - volume inflow-outflow inflow-outflow V V

Metabolic Dynamic Modelling C i = the concentration of • Mass Balance : metabolite i,  = is the specific growth rate, dC     i v . r . C  ij = is the stoichiometric ij j i dt j coefficient for this metabolite in reaction j, which occurs at the • The flux is : rate r j . Since masses were balanced, the equation for extracellular r  max r . f ( C , P ) glucose needs to include a j j j j j conversion factor for the difference between the max Flux maximum r intracellular volume and the j culture volume.

Dynamic Equilibrum • A reaction rate determines how fast a reaction proceeds, and is mathematically defined as the change in concentration of a species over the change in time. • At dynamic equilibrium, reactants are converted to products and products are converted to reactants at an equal and constant rate. • Reactions do not necessarily—and most often do not—end up with equal concentrations. Equilibrium is the state of equal, opposite rates, not equal concentrations.

  Glycolise d X       GLC , ACE X ex ex dt   d GLC ex     v X dt PTS   d G 6 P        v v v G 6 P dt PTS PFK G 6 PDH   d FDP       v v FDP dt PFK ALDO   d GAP       2 v v GAP dt ALDO GAPDH    d ACP       v v ACP dt PTA ACK   d ACE       v v ACE dt ACK ACS Glycolysis is a series of reactions that and extract energy from glucose by splitting it into two three-carbon molecules called pyruvates. Glycolysis is an ancient metabolic pathway, meaning that it evolved long ago, and it is found in the great majority of organisms alive today

Biological Networks Pathways (KEGG) Graph: G=(V,E)

Analytical     d X     GLC ex , ACE ex X Solution ? dt   ex d GLC     v X PTS dt   d G 6 P        v v v G 6 P PTS PFK G 6 PDH dt   d FDP       v v FDP PFK ALDO dt   d GAP       2 v v GAP ALDO GAPDH dt   d PEP   Glycolysis Pathway        v v v v v PEP GAPDH PCK PTS PYK PPC dt   d PYR         v v v v PYR PYK MEZ PDH PPS dt   d AcCoA   Time Scalling Transformation      v v v AcCoA PDH CS PTA dt   d ICIT    v  v  v   ICIT CS ICDH ICL dt   d 2 KG       v v 2 KG ICDH 2 KGDH dt   d SUC        v v v SUC 2 KGDH ICL SDH dt   d FUM    v  v  v   FUM PTS PFK G 6 PDH dt   d MAL         v v v v MAL FUM MS MDH MEZ dt   d OAA         v v v v OAA MDH PPC CS PCK dt   d GOX    v  v   GOX ICL MS dt   d ACP       v v ACP PTA ACK dt   d ACE       v v ACE ACK ACS dt E. Montseny, A. Doncescu: Operatorial Parametrizing of Dynamic Systems. 17th IFAC World Congress, July 6-11, 2008, Seoul, Korea.

Knowledge Representation in System Biology • The causalities : 1.con(A,up,t i ) react(A,B) act(A,B) react(B,C) ¬act(B,C) → con(B,up,t i+1 ) 2.con(A,up,t j ) react(A,B) ¬act(A,B) react(B,C) act(B,C) → con(B,down,t j+1 ) 3.con(A,down,t k ) react(A,B) act(A,B) → con(B,down, t k+1 ) Where : • con(X, up/down,t x ): the concentration of A is increase/decreased at time t x . • act(A,B): metabolite A is consumed for the production of B • ¬act(A,B): A is not consumed during B production

Automated hypothesis-finding in Systems Biology (Doncescu ILP ‘09 ) discretization Pathway Model Background Knowledge (Qualitative / Kinetic) Pathway Data Observations (from lab + KEGG) Hypotheses Hypothesis Finder B H |= O SOLAR Hypothesis Evaluator BDD-EM 9.00E-01 Pathway 7.00E-01 5.00E-01 hypothesis ranking Best Hypotheses Analysis 3.00E-01 1.00E-01 135031 5459 114344 535847 2912 325535 30 9 561014 365160 1757 39 3 48 273441 1564 194525 203721 7 62 3365 1 2 4 5 6 8 161822 2324 262838 404246 4952 616366 -1.00E-01 Best Student Paper Award Certificate : International Conference on Bioinformatics Models, Methods and Algorithms, January 26-29, 2011 Rome Italy, pour le papier : « Kinetic Models and Qualitative Abstraction for Relational Learning in System Biology » G. Synnaeve, K.Inoue, A. Doncescu, T. Sato.

Causal Graphs Solution of Biological Systems Representation

Network motifs in Genetics Incoherent feed-forward Incoherent double path double loop 1 2 3 3-switch Negative regulon 4 Positive regulon 5 U. Alon Nature Rev. Genetics (2007)

Biological Networks • Gene regulatory network: two genes are connected if the expression of one gene modulates expression of another one by either activation or inhibition • Protein interaction network: proteins that are connected in physical interactions or metabolic and signaling pathways of the cell; • Metabolic network: metabolic products and substrates that participate in one reaction and/or metabolic pathway;

Machine Learning applications in Molecular Biology

Scientific Reasoning In Machine Learning 3 criteria have been traditionally used to compare And select hypothesis : consistency, completeness and simplicity Hypothesis Generation Evidential reasoning effect/cause Causal Reasoning cause/effect Deduction Abduction Simulation Prediction Observation Verification 18

Causal Reasoning Abduction reciprocal of Deduction Abduction is often viewed as inference to the “best explanation” The computation has the following basic form : extract from the given theory T a hypothesis and check this for consistency

Abduction : logical framework Input:  B : background theory  G : observations  Γ : possible causes (abducibles) B Abductive G Output: engine  H : hypothesis satisfying that H • B  H ╞ G • B  H is consistent • H is a set of instances of literals from Γ . Inverse Entailment (IE) Computing a hypothesis H can be done deductively by: B ￢ G ￢ H We use a consequence finding technique for IE computation.

Consequence finding Given an axiom set, the task of consequence finding is to find out some theorems of interest . • How to find only interesting conclusions? • Production field and characteristic clauses • Production field P = < L , Cond > – L : the set of literals to be collected – Cond : the condition to be satisfied (e.g. length) Th P ( Σ ) : the clauses entailed by Σ which belong to P . • Characteristic clause C of Σ (wrt P ): – C belongs to Th P ( Σ ) ; – no other clause in Th P ( Σ ) properly subsumes C . Carc( Σ, P ) : the characteristic clauses of Σ wrt P .

SOL-resolution (Siegel 1988) ■ Computing Carc ( Σ ， P ) where Σ is a given axiom set and P is a production field ■ Composed of three operations Skip , Reduction , Extension (An extension of SLD-resolution with Skip operation) ■ Preserving the soundness and completeness for finding characteristic clauses ． Suppose an axiom set Σ and a production field P as follows ． Σ = B ¬E = { g ← c 1 e 1 , c 2 ← c 1 , e 2 ← c 2 , c 3 ← c 2 e 2 , ¬g }, P = < { ¬c1 , ¬e1 , c3}, max_length =2 >.