F ROM P ETRI N ETS TO D IFFERENTIAL E QUATIONS AN I NTEGRATIVE A - PowerPoint PPT Presentation

MSBF, M AY 2005 PN & Systems Biology F ROM P ETRI N ETS TO D IFFERENTIAL E QUATIONS AN I NTEGRATIVE A PPROACH FOR B IOCHEMICAL N ETWORK A NALYSIS Monika Heiner Brandenburg University of Technology Cottbus Dept. of CS monika.heiner@informatik.tu-cottbus.de May 2005

M ODEL - BASED S YSTEM A NALYSIS PN & Systems Biology system Problem system properties model Petrinetz model properties monika.heiner@informatik.tu-cottbus.de May 2005

M ODEL - BASED S YSTEM A NALYSIS PN & Systems Biology system Problem system properties verification technical requirement CONSTRUCTION system specification model Petrinetz model properties monika.heiner@informatik.tu-cottbus.de May 2005

M ODEL - BASED S YSTEM A NALYSIS PN & Systems Biology system Problem system properties known validation properties biological UNDERSTANDING system unknown behaviour properties prediction model Petrinetz model properties monika.heiner@informatik.tu-cottbus.de May 2005

PN & Systems Biology W HAT KIND OF MODEL SHOULD BE USED ? monika.heiner@informatik.tu-cottbus.de May 2005

N ETWORK R EPRESENTATIONS , E X 1 PN & Systems Biology monika.heiner@informatik.tu-cottbus.de May 2005

N ETWORK R EPRESENTATIONS , E X 1 PN & Systems Biology ? SEMANTICS FORMAL > - monika.heiner@informatik.tu-cottbus.de May 2005

N ETWORK R EPRESENTATIONS , E X 2 PN & Systems Biology monika.heiner@informatik.tu-cottbus.de May 2005

N ETWORK R EPRESENTATIONS , E X 2 PN & Systems Biology -> READABILITY ? monika.heiner@informatik.tu-cottbus.de May 2005

B IONETWORKS , SOME P ROBLEMS PN & Systems Biology various, mostly ambiguous representations ❑ -> PROBLEM 1 -> verbose descriptions -> diverse graphical representations -> contradictory and / or fuzzy statements knowledge ❑ -> PROBLEM 2 -> uncertain -> growing, changing -> distributed over various data bases, papers, journals, . . . network structures ❑ -> PROBLEM 3 -> tend to grow fast -> dense, apparently unstructured -> hard to read - - >> models are full of ASSUMPTIONS << - - monika.heiner@informatik.tu-cottbus.de May 2005

F RAMEWORK PN & Systems Biology bionetworks knowledge quantitative modelling understanding animation / quantitative model validation analysis /simulation models ODEs quantitative behaviour prediction monika.heiner@informatik.tu-cottbus.de May 2005

F RAMEWORK PN & Systems Biology bionetworks knowledge qualitative modelling understanding Petri net theory (invariants) animation / qualitative model validation analysis models model qualitative checking behaviour prediction quantitative quantitative parameters modelling understanding animation / quantitative model validation analysis /simulation models ODEs quantitative behaviour prediction monika.heiner@informatik.tu-cottbus.de May 2005

F RAMEWORK PN & Systems Biology bionetworks knowledge qualitative modelling understanding Petri net theory (invariants) animation / qualitative model validation analysis models model qualitative checking behaviour prediction quantitative quantitative parameters modelling understanding RG SLI animation / quantitative model validation LP analysis /simulation models ODEs quantitative behaviour prediction monika.heiner@informatik.tu-cottbus.de May 2005

PN & Systems Biology P ETRI NETS - AN INFORMAL CRASH COURSE monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 hyperarcs 2 NAD + 2 NADH 2 H + 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O pre-conditions post-conditions O 2 local conditions -> Petri net places -> chemical compounds ❑ monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 local conditions -> Petri net places -> chemical compounds ❑ multiplicities -> Petri net arc weights -> stoichiometric relations ❑ monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 local conditions -> Petri net places -> chemical compounds ❑ multiplicities -> Petri net arc weights -> stoichiometric relations ❑ condition’s state -> token(s) in its place -> available amount (e.g. mol) ❑ system state -> marking -> compounds distribution ❑ monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 local conditions -> Petri net places -> chemical compounds ❑ multiplicities -> Petri net arc weights -> stoichiometric relations ❑ condition’s state -> token(s) in its place -> available amount (e.g. mol) ❑ system state -> marking -> compounds distribution ❑ PN = (P, T, F, m 0 ), F: (P x T) U (T x P) -> N 0 , m 0 : P -> N 0 ❑ monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE B EHAVIOUR PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE B EHAVIOUR PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 FIRING NADH NAD + 2 2 2 H + r1 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de May 2005

P ETRI N ETS , B ASICS - THE B EHAVIOUR PN & Systems Biology atomic actions -> Petri net transitions -> chemical reactions ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 input output 2 H + r1 compounds compounds 2 H 2 O O 2 TOKEN GAME FIRING NADH NAD + 2 2 DYNAMIC BEHAVIOUR 2 H + r1 (substance flow) 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de May 2005

T YPICAL B ASIC S TRUCTURES PN & Systems Biology metabolic networks ❑ e1 e2 e3 -> substance flows r1 r2 r3 signal transduction networks ❑ -> signal flows r1 r2 r3 monika.heiner@informatik.tu-cottbus.de May 2005

T HE R UNNING E XAMPLE - T HE RKIP P ATHWAY PN & Systems Biology [Cho et al., CMSB 2003] monika.heiner@informatik.tu-cottbus.de May 2005

T HE RKIP P ATHWAY , P ETRI N ET PN & Systems Biology Raf-1Star RKIP m1 m2 k2 k1 ERK-PP m9 m3 Raf-1Star_RKIP k4 k3 k8 k11 m11 m8 m4 RKIP-P_RP MEK-PP_ERK Raf-1Star_RKIP_ERK-PP k7 k5 k6 k10 k9 m7 m5 m6 m10 ERK RP RKIP-P MEK-PP monika.heiner@informatik.tu-cottbus.de May 2005

T HE RKIP P ATHWAY , H IERARCHICAL P ETRI N ET PN & Systems Biology Raf-1Star RKIP m1 m2 k1_k2 ERK-PP m9 Raf-1Star_RKIP m3 k3_k4 k8 k11 m8 m11 m4 RKIP-P_RP MEK-PP_ERK Raf-1Star_RKIP_ERK-PP k9_k10 k5 k6_k7 m7 m6 m5 m10 MEK-PP ERK RP RKIP-P monika.heiner@informatik.tu-cottbus.de May 2005

T HE RKIP P ATHWAY , H IERARCHICAL P ETRI N ET PN & Systems Biology Raf-1Star RKIP initial marking m1 m2 k1_k2 ERK-PP m9 Raf-1Star_RKIP m3 k3_k4 k8 k11 m8 m11 m4 RKIP-P_RP MEK-PP_ERK Raf-1Star_RKIP_ERK-PP k9_k10 k5 k6_k7 m7 m6 m5 m10 MEK-PP ERK RP RKIP-P monika.heiner@informatik.tu-cottbus.de May 2005