biological networks Claudine Chaouiya SBML Extention L3F meeting August

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1 Campus de Luminy - Marseille - France Petri nets and qualitative modelling of biological networks Claudine Chaouiya chaouiya@igc.gulbenkian.pt chaouiya@tagc.univ-mrs.fr SML Extention L3F meeting 1-13 ugust 008 1

2 a Firing of t 1 Firing of t b pre - condition matrix t 1 t t 3 p Pre = C = Post " Pre = post - condition matrix t 1 t t 3 p p Post = p p p p p incidence matrix t 1 t t 3 p p "1 0 1 p 3 4 "1 " p " initial marking " 1% $ ' M 0 = $ 1 ' $ 0' $ ' # 0& " 1% $ ' " 1% 0 M = $ ' $ ' = M $ 3' 0 + C. $ 1 ' $ ' # $ 0& ' # 1& state equation M'= M + C.", c R(M 0 ), the marking graph M 0 M 1 M SML Extention L3F meeting 1-13 ugust 008

3 Modelling of biochemical networks Qualitative PN modelling of metabolic networks transformation chemical reaction places: reactants, products, enzymes... transitions: reactions, catalysis... weighted arcs: stoichiometry Glucose hexokinase Glucose-6-phosphate TP DP hexokinase Glucose Glucose-6-phosphate TP DP SML Extention L3F meeting 1-13 ugust 008 3

4 Synthesis Decomposition Catalysed reaction Inhibited reaction Reversible reaction with stoichiometry SML Extention L3F meeting 1-13 ugust 008 4

5 Synthesis Decomposition Catalysed reaction Inhibited reaction New arcs: - Test/read - Inhibitory Reversible reaction with stoichiometry SML Extention L3F meeting 1-13 ugust 008 5

6 Modelling of biochemical networks Tools Snoopy (PN editor) + Charlie (PN analysis) + PIn (invariants, MCT sets, ) randenburg University of Technology Cottbus Genomic Object Net: Edition and simulation of biopathways by means of HFPNs. GON is now commercialised as Cell Illustrator. Matsuno & Miyano Hybrid Functional Petri Nets SML Extention L3F meeting 1-13 ugust 008 6

7 Tools Modelling of biochemical networks Name IN Prod Maria Features nalysis of standard (timed) PNs and CPNs, no graphical editor, includes a model-checker for CTL. Efficient reachability analysis tool for standard PNs. Extensive reachability analysis and model checking of CPNs. CPN Tools TimeNet Möbius Edition, simulation and analysis of (timed) CPNs, graphical editor, hierarchical modelling. Modelling, validation, and performance evaluation of distributed systems using Generalized SPNs and their colored extension. Edition, analysis, simulation of stochastic models SML Extention L3F meeting 1-13 ugust 008 7

8 Petri net extensions Time: deterministic delay, stochastic, intervals Marking: coloured, hybrid HFPNs: hybrid functional PNs Hybrid: mixing conituous/discrete places and transitions Functional: rules for consumption and production might be marking dependent SML Extention L3F meeting 1-13 ugust 008 8

9 Existing PN formats Elements for places - transitions - arcs PNML Petri Nets Markup Language extensions are described in specific documents PNN bstract Petri Net Notation many others Cell System Markup Language (CSML) used by Cell Illustrator (CSML SML) What extensions should be taken into account? SML Extention L3F meeting 1-13 ugust 008 9

10 Modelling of biological networks, Stochastic PNs SPN modelling of stochastic molecular interactions (Gillespie's algorithm) R. Srivastava,, MS Peterson and WE entley (001) iotechnol ioeng. Oct 5;75(1): Uncertainty attached to the data - Environmental noise Intrinsic noise (i.e. low molecular concentrations) Stochastic time-delay associated to each transition (exponential distribution, may depend on the marking) t1, θ1 Example : R R λ t monomérisation R R t + dimérisation λ + reaction involving a unique reactant: λ = k M(R ) constant monomerisation rate constant dimerisation rate, c + =k + /V.N reaction involving two reactants: λ + = c + M(R)(M(R)-1) SML Extention L3F meeting 1-13 ugust

11 Modelling of biological networks, Hybrid PNs HPN modelling of gene regulated metabolic networks M.Chen and R.Hofestädt (003), In Silico iology 3, 009 molecular concentration = continuous rather than discrete discrete places (with tokens) discrete transitions (with delays) continuous places (with marks IR + ) continuous transitions (with speeds SML Extention L3F meeting 1-13 ugust

12 Modelling of biological networks, Hybrid PNs HPN modelling of gene regulated metabolic networks Lambda phage genetic switch feedback mechanism. Doi, H. Matsuno, S. Miyano (000) Currents in Computational Molecular iology, Now Cell Illustrator SML Extention L3F meeting 1-13 ugust 008 1

13 PN modelling of logical regulatory networks Multi-valued Regulatory Petri Nets Genetic regulatory networks described in terms of logical models (multilevel discretisation) two complementary places for each gene two transitions for each logical parameter (effect of interactions on a given gene) Testing the exact amount of tokens in a place test (read) arc M(p) cste inhibitory arc M(p) cste SML Extention L3F meeting 1-13 ugust

14 PN modelling of logical regulatory networks Multi-valued Regulatory Petri Nets Genetic regulatory networks described in terms of logical models (multilevel discretisation) two complementary places for each gene two transitions for each logical parameter (effect of interactions on a given gene) Example max =1 max =3 K ()= K ( )=1 t t, M()+M(Ã)=1 M()+M()=3 + t + t, SML Extention L3F meeting 1-13 ugust

15 PN modelling of logical regulatory networks Multi-valued Regulatory Petri Nets Genetic regulatory networks described in terms of logical models (multilevel discretisation) two complementary places for each gene two transitions for each logical parameter (effect of interactions on a given gene) Example max =1 max =3 K ()= K ( )=1 t 3 t, M()+M(Ã)=1 M()+M()=3 + t + t, SML Extention L3F meeting 1-13 ugust

16 PN modelling of logical regulatory networks Multi-valued Regulatory Petri Nets Genetic regulatory networks described in terms of logical models (multilevel discretisation) two complementary places for each gene two transitions for each logical parameter (effect of interactions on a given gene) Example max =1 max =3 K ()= K ( )=1 t 3 t, M()+M(Ã)=1 M()+M()=3 + t 3 + t, SML Extention L3F meeting 1-13 ugust

17 max =1 max =3 M()+M(Ã)=1 M()+M()=3 K ()= K ( )=1 t 3 t, + t 3 + t, K ()=3 K ( )=0 "extremal" parameter values t SML Extention L3F meeting 1-13 ugust t,