ISMB, J ULY 2008 PN & Systems Biology A S TRUCTURED A PPROACH . . . T UTORIAL , P ART II F ROM P ETRI N ETS TO D IFFERENTIAL E QUATIONS Monika Heiner Brandenburg University of Technology Cottbus, Dept. of CS monika.heiner@tu-cottbus.de July 2008
F RAMEWORK : S YSTEMS B IOLOGY PN & Systems Biology MODELLING = FORMAL KNOWLEDGE REPRESENTATION formalizing wetlab experiments understanding observed behaviour natural model model biosystem validation predicted behaviour wetlab model-based experiments experiment design MODEL VALIDATION = CONFIDENCE INCREASE monika.heiner@tu-cottbus.de July 2008
PN & Systems Biology W HAT KIND OF MODEL SHOULD BE USED ? monika.heiner@tu-cottbus.de July 2008
N ETWORK R EPRESENTATIONS , E X 1 PN & Systems Biology ? Receptor Receptor e.g. 7-TMR e.g. 7-TMR cell m cell m em em brane brane SEMANTICS γ γ γ γ γ γ γ α α α α tyrosine tyrosine Ras Ras Ras α α α β β β β β β β β β shc shc shc AdC AdC AdC AdC yc yc yc yc SO SO SO S S S kinase kinase R R R as as as Akt Akt Akt cAM cAM cAM P P P heterotrim heterotrim eric eric grb2 grb2 grb2 R R R ac ac ac Rap1 Rap1 Rap1 G G -protein -protein G G G EF EF EF A A A A TP TP TP cA TP cA cA cA cA M M M M M P P P P P PI-3 PI-3 PI-3 Raf-1 Raf-1 Raf-1 cA cA cA M M M P P P cA cA cA cA M M M M P P P P K K K PKA PKA PKA PKA cA cA cA cA M M M M P P P P PAK PAK PAK B-R B-R B-R af af af cA cA cA cA cA M M M M M P A P A P P A P A M M M M P P P P PKA PKA PKA PKA M M M EK EK EK PD PD PD PD E E E E M M M EK1,2 EK1,2 EK1,2 ER ER ER K1,2 K1,2 K1,2 FORMAL ERK1,2 ERK1,2 ERK1,2 cytosol cytosol M M M KP KP KP transcription transcription transcription factors factors factors > - nucleus nucleus monika.heiner@tu-cottbus.de July 2008
N ETWORK R EPRESENTATIONS , E X 2 PN & Systems Biology ? Y T I L I B A D A E R > - monika.heiner@tu-cottbus.de July 2008
N ETWORK R EPRESENTATIONS PN & Systems Biology informal cartoon-like representations � -> readability -> fault avoidance formal = mathematical representations � -> analysability WHY NOT BOTH ? & EXECUTABILITY monika.heiner@tu-cottbus.de July 2008
PN & Systems Biology P ETRI NETS - AN INFORMAL CRASH COURSE monika.heiner@tu-cottbus.de July 2008
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@tu-cottbus.de July 2008
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@tu-cottbus.de July 2008
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@tu-cottbus.de July 2008
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/signal flow) 2 2 2 H + r1 2 H 2 O STATE SPACE O 2 monika.heiner@tu-cottbus.de July 2008
T YPICAL B ASIC S TRUCTURES I PN & Systems Biology A B A --> B + C A + B --> C A C r1 r2 B C A r3 B r5 A --> C, A --> B, A C B --> C A --> C C B r4 r6 monika.heiner@tu-cottbus.de July 2008
T YPICAL B ASIC S TRUCTURES II PN & Systems Biology A <--> B A --> B r1 r1 A A B B B A r1, r2 r2 E E A <--> B A --> B E E E r1 B B A r1 B A A r1, r2 r2 monika.heiner@tu-cottbus.de July 2008
T YPICAL B ASIC S TRUCTURES III PN & Systems Biology E enzymatic reaction, A <--> A|E --> B mass-action approach 1 E r1 A A|E B r3 r2 E E A r1, r2 A|E r3 B A B MA1 monika.heiner@tu-cottbus.de July 2008
T YPICAL B ASIC S TRUCTURES IV PN & Systems Biology metabolic networks � e1 e2 e3 -> substance flows r1 r2 r3 signal transduction � networks -> signal flows r1 r2 r3 monika.heiner@tu-cottbus.de July 2008
T YPICAL B ASIC S TRUCTURES IV PN & Systems Biology metabolic networks � e1 e2 e3 -> substance flows r1 r2 r3 INPUT OUTPUT COMPOUND COMPOUND signal transduction � networks INPUT -> signal flows SIGNAL r1 r2 OUTPUT SIGNAL r3 -> OPEN / CLOSED SYSTEMS monika.heiner@tu-cottbus.de July 2008
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-catalysed conversions of metabolites, proteins, . . . -> complexations / decomplexations, de- / phosphorylations, . . . places � -> (primary, secondary) chemical compounds, -> (various states of) proteins, protein complex, genes, . . . tokens � -> molecules, moles, -> concentration levels, gene expression levels, . . . (e.g., high / low = present / not present, or any finite number) monika.heiner@tu-cottbus.de July 2008
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@tu-cottbus.de July 2008
PN & Systems Biology B IO P ETRI NETS - S OME E XAMPLES monika.heiner@tu-cottbus.de July 2008
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 3 2 1 2 NADP + 4 GSH 9 10 11 12 Gluc G6P F6P FBP GAP 13 14 ATP ADP ATP ADP NAD + DHAP + Pi 15 NAD + NADH NADH ATP ADP ATP ADP 20 19 18 17 16 Lac Pyr 2PG 3PG PEP 1,3-BPG monika.heiner@tu-cottbus.de July 2008
E X 1 - Glycolysis and Pentose Phosphate Pathway PN & Systems Biology Xu5P [Reddy 1993] 4 E4P S7P Ru5P 6 7 8 ATP GSSG NADPH GAP F6P 5 R5P 2 2 1 3 ADP 2 2 2 NADP+ GSH 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@tu-cottbus.de July 2008
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 PP PGI F6P UGPase 29 28 28 29 ADP Pi Glyc(b) ATP 29 ATP G6P ATPcons(b) 29 NDPkin G1P ADP 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@tu-cottbus.de July 2008
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 s10 s6 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 [H EINER ; K OCH ; WI LL 2004] [GON 2003] monika.heiner@tu-cottbus.de July 2008
E X 4 - S WITCH C YCLE H ALOBACTERIUM S ALINARUM PN & Systems Biology [Marwan; Oesterhelt 1999] monika.heiner@tu-cottbus.de July 2008
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