FMP B ERLIN , F EBRUARY 2007 PN & Systems Biology M ATHEMATICAL M ODELLING OF B IOCHEMICAL N ETWORKS WITH P ETRI N ETS Monika Heiner Brandenburg University of Technology Cottbus Dept. of CS monika.heiner@informatik.tu-cottbus.de February 2007 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 February 2007
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 February 2007 PN & Systems Biology W HAT KIND OF MODEL SHOULD BE USED ? monika.heiner@informatik.tu-cottbus.de February 2007
N ETWORK R EPRESENTATIONS , E X 1 PN & Systems Biology ? Receptor Receptor e.g e.g . 7-TM . 7-TM R R cell m cell m em em brane brane S γ γ γ γ γ γ γ C α α α α tyrosine tyrosine R R R as as as I α α α β β β β β β β β β AdC AdC AdC AdC yc yc yc yc kinase kinase shc shc shc SO SO SO S S S Ras Ras Ras T Akt Akt Akt cAM cAM cAM P P P heterotrim heterotrim eric eric grb2 grb2 grb2 Rac Rac Rac G G -protein -protein N R R R ap1 ap1 ap1 GEF GEF GEF ATP ATP cA ATP ATP cA cA cA cA M M M M M P P P P P cA cA cA M M M P P P R R R af-1 af-1 af-1 PI-3 PI-3 PI-3 cAM cAM cAM cAM P P P P A K K K PKA PKA PKA PKA cA cA cA cA M M M M P P P P M PAK PAK PAK B-Raf B-Raf B-Raf cAM cAM cAM cAM cAM P A P A P P A P A M M M M P P P P PKA PKA PKA PKA E M M M EK EK EK PDE PDE PDE PDE S M M M EK1,2 EK1,2 EK1,2 ERK1,2 ERK1,2 ERK1,2 L ERK1,2 ERK1,2 ERK1,2 A cytosol cytosol M M M M KP KP KP R O transcription transcription transcription F factors factors factors > - nucleus nucleus monika.heiner@informatik.tu-cottbus.de February 2007 N ETWORK R EPRESENTATIONS , E X 2 PN & Systems Biology -> READABILITY ? monika.heiner@informatik.tu-cottbus.de February 2007
- models are full of assumptions - B IO N ETWORKS , SOME P ROBLEMS PN & Systems Biology knowledge ❑ -> PROBLEM 1 -> uncertain -> growing, changing -> distributed over independent data bases, papers, journals, . . . various, mostly ambiguous representations ❑ -> PROBLEM 2 -> verbose descriptions -> diverse graphical representations -> contradictory and / or fuzzy statements network structure ❑ -> PROBLEM 3 -> tend to grow fast -> dense, apparently unstructured -> hard to read monika.heiner@informatik.tu-cottbus.de February 2007 B IO N ETWORKS , SOME P ROBLEMS PN & Systems Biology monika.heiner@informatik.tu-cottbus.de February 2007
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 Markov chains animation / quantitative model validation analysis /simulation models ODEs quantitative behaviour prediction monika.heiner@informatik.tu-cottbus.de February 2007 PN & Systems Biology P ETRI NETS - AN INFORMAL CRASH COURSE monika.heiner@informatik.tu-cottbus.de February 2007
P ETRI N ETS , B ASICS PN & Systems Biology ❑ 2 NAD + + 2 H 2 O -> 2 NADH + 2 H + + O 2 NADH NAD + 2 2 2 H + r1 2 H 2 O O 2 hyper-arcs 2 NAD + 2 NADH 2 H + 2 H 2 O O 2 monika.heiner@informatik.tu-cottbus.de February 2007 P ETRI N ETS , B ASICS - THE S TRUCTURE PN & Systems Biology atomic actions -> 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 -> places -> chemical compounds ❑ multiplicities -> arc weights -> stoichiometric relations ❑ condition’s state -> token(s) -> 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 February 2007
P ETRI N ETS , B ASICS - THE F IRING R ULE PN & Systems Biology an action can happen, if -> prerequisite ❑ -> all preconditions are fulfilled (corresponding to the arc weights); if an action happens, then -> firing behaviour ❑ -> tokens are removed from all preconditions (corresponding to the arc weights), and -> tokens are added to all postconditions (corresponding to the arc weights); action happens (firing of a transition) -> model assumptions ❑ -> atomic -> time-less monika.heiner@informatik.tu-cottbus.de February 2007 P ETRI N ETS , B ASICS - THE B EHAVIOUR PN & Systems Biology atomic actions -> 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 DYNAMIC BEHAVIOUR NADH NAD + (substance flow) 2 2 2 H + r1 2 H 2 O STATE SPACE O 2 monika.heiner@informatik.tu-cottbus.de February 2007
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 February 2007 P ETRI N ET EL EMENTS , I NTERPRETATIONS PN & Systems Biology METABOLIC NETWORKS ❑ SIGNAL TRANSDUCTION NETWORKS GENE REGULATORY NETWORKS transitions ❑ -> (reversible, stoichiometric) chemical reactions, -> enzyme-catalyzed conversions of metabolites, proteins, . . . -> complexations/decomplexations, de-/phosphorylations, . . . places ❑ -> (primary, seocndary) chemical compounds, -> (various states of) proteins, protein complex, genes, . . . tokens ❑ -> molecules, moles, -> concentration levels, gene expression levels, . . . (e.g., high/low = present/not present) monika.heiner@informatik.tu-cottbus.de February 2007
B IOCHEMICAL P ETRI N ETS , S UMMARY PN & Systems Biology biochemical networks ❑ -> networks of (abstract) chemical reactions biochemically interpreted Petri net ❑ -> partial order sequences of chemical reactions (= elementary actions) transforming input into output compounds / signals [ respecting the given stoichiometric relations, if any ] -> set of all pathways from the input to the output compounds / signals [ respecting the stoichiometric relations, if any ] pathway ❑ -> self-contained partial order sequence of elementary (re-) actions monika.heiner@informatik.tu-cottbus.de February 2007 PN & Systems Biology B IO P ETRI NETS - S OME E XAMPLES monika.heiner@informatik.tu-cottbus.de February 2007
E X 1 - Glycolysis and Pentose Phosphate Pathway PN & Systems Biology [Reddy 1993] 4 Ru5P Xu5P 5 S7P E4P 6 7 8 2 NADPH 2 GSSG GAP F6P R5P 1 2 3 2 NADP + 4 GSH 9 10 11 12 Gluc G6P F6P FBP GAP 13 14 ATP ADP ATP ADP DHAP NAD + + Pi 15 NAD + NADH NADH ATP ADP ATP ADP 18 17 20 19 16 Lac Pyr PEP 2PG 3PG 1,3-BPG monika.heiner@informatik.tu-cottbus.de February 2007 E X 1 - Glycolysis and Pentose Phosphate Pathway PN & Systems Biology [Reddy 1993] Xu5P 4 E4P S7P Ru5P 6 7 8 ATP GSSG NADPH GAP F6P 5 R5P 2 1 2 3 ADP 2 2 2 GSH NADP+ Pi F6P Gluc FBP GAP 12 9 10 11 13 G6P 14 NAD ATP ATP ADP ADP DHAP Pi 15 NAD NAD+ NADH ATP ADP ATP ADP 20 19 18 17 16 1,3−BPG Lac Pyr 2PG PEP 3PG monika.heiner@informatik.tu-cottbus.de February 2007
E X 2 - Carbon Metabolism in Potato Tuber PN & Systems Biology geSuc eSuc SucTrans SPP Inv Suc SuSy 28 UDP Pi SPS Glc S6P UDPglc Frc ATP ATP HK FK UDP 29 ADP 29 ADP PGI PP F6P UGPase 29 28 28 29 ADP Pi Glyc(b) ATP 29 ATP G6P 29 ATPcons(b) NDPkin ADP G1P UTP [K OCH ; J UNKER ; H EINER 2005] PGM ATP StaSy(b) 28 Pi 29 ADP ATP 2 2 28 29 starch 2 AMP Pi AdK PP PPase ADP rstarch monika.heiner@informatik.tu-cottbus.de February 2007 E X 3: A POPTOSIS IN M AMMALIAN C ELLS PN & Systems Biology Fas−Ligand Apoptotic_Stimuli s7 Bax_Bad_Bim FADD Procaspase−8 Apaf−1 Bcl−2_Bcl−xL s8 CytochromeC BidC−Terminal s1 Bid dATP/ATP s9 s6 s10 Mitochondrion Caspase−8 s5 Procaspase−3 s2 (m20) Caspase−9 Caspase−3 s13 s11 Procaspase−9 s3 DFF CleavedDFF45 DFF40−Oligomer (m22) s12 s4 DNA DNA−Fragment [GON 2003] [H EINER ; K OCH ; WI LL 2004] monika.heiner@informatik.tu-cottbus.de February 2007
Recommend
More recommend
