B IOPATHWAYS & P ETRI N ETS M ONIKA H EINER BTU C OTTBUS C - PDF document

Biopathways & Petri Nets September 2002 B IOPATHWAYS & P ETRI N ETS M ONIKA H EINER BTU C OTTBUS C OMPUTER S CIENCE I NA K OCH TFH B ERLIN C OMPUTATIONAL B IOLOGY mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 1 / 52

Biopathways & Petri Nets September 2002 O UTLINE 1. MOTIVATION 2. INTRODUCTION INTO (QUALITATIVE) PETRI NETS 3. APPLICATION TO APOPTOTIC PATHWAYS -> MODELLING & ANIMATION 4. MODEL ANALYSIS -> QUALITATIVE & QUANTITATIV 5. SUMMARY 6. OUTLOOK mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 2 / 52

Biopathways & Petri Nets September 2002 1. MOTIVATION mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 3 / 52

Biopathways & Petri Nets September 2002 M ODEL - BASED S YSTEM E NGINEERING Problem Petrinetz model system properties properties bio - Petri net pathways mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 4 / 52

Biopathways & Petri Nets September 2002 B IOPATHWAYS E XAMPLES ❑ metabolic pathways ❑ signal transduction cascades ❑ gene regulation ❑ . . . B ASIC P ROPERTIES ❑ very complex structures ❑ causal interplay of basic actions (sequence, branching, concurrency) mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 5 / 52

Biopathways & Petri Nets September 2002 R EPRESENTATIONS , O BJECTIVES ❑ readability -> understanding ❑ animation -> experience ❑ validation -> consistency checks ❑ analysis -> behaviour prediction (qualitative / quantitative) =>> How many representations do we really need? mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 6 / 52

Biopathways & Petri Nets September 2002 2. INTRODUCTION INTO (QUALITATIVE) PETRI NETS mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 7 / 52

mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de E XAMPLE 4 Ru5P Xu5P [R EDDY 96] 5 S7P E4P 6 7 8 2 NADPH 2 GSSG GAP F6P R5P 2 3 1 Biopathways & Petri Nets 2 NADP + 4 GSH 9 10 11 12 Gluc G6P F6P FBP GAP 13 14 ATP ADP ATP ADP NAD + DHAP + P i 15 NADH NAD + NADH ATP ADP ATP ADP 20 19 18 17 16 Lac Pyr PEP 2PG 3PG 1,3-BPG September 2002 [Reddy 96] Reddy, V. N.; Liebman, M. N.; Mavrovouniotis, M. L.: Qualitative Analysis of Biochemical Reaction Systems; Computers in Biology and Medicine 26(96), 9-24. 8 / 52

Biopathways & Petri Nets September 2002 E XAMPLE P ENTOSE P HOSPHATE C YCLE glucose 6-phosphate fructose ribose 6-phosphate 5-phosphate fructose 1,6-bisphosphate 2 NADP + 2 NADPH glucose ribulose 6-phosphate 5-phosphate dihydroxyacetone glycerinaldehyde CO 2 phosphate 3-phosphate ribose 5-phosphate 1. possibility 2. possibility 2 NADP + 2 NADPH glucose ribulose 6-phosphate 5-phosphate CO 2 ribose fructose 5-phosphate 6-phosphate 2 NADP + fructose 2 NADPH 1,6-bisphosphate glucose ribulose 6-phosphate 5-phosphate CO 2 dihydroxyacetone glycerinaldehyde ribose fructose phosphate 3-phosphate 5-phosphate 6-phosphate 3. possibility fructose 1,6-biphosphate dihydroxyacetone glycerinaldehyde phosphate 3-phosphate 2 ATP pyruvate Stryer, L.: Biochemistry; 4. possibility Freeman, New York, NY, 1995, p. 450. mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 9 / 52

Biopathways & Petri Nets September 2002 P ETRI N ETS , B ASICS 1 (1) NODES places transitions “passive elements” “active elements” conditions events states actions “ chem. compounds ” “ chem. reactions ” (2) ARCS postconditions preconditions 5 3 action mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 10 / 52

Biopathways & Petri Nets September 2002 P ETRI N ETS , B ASICS 2 (3) TOKENS (moving objects, vehicles, work pieces, control flow pointer, dates,..., units of substances (e. g. Mol) , ...) condition is not fulfilled condition is (one times) fulfilled n condition is n times fulfilled (4) MARKING (system state, substance distribution ) How many tokens are on each place? -> initial marking mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 11 / 52

Biopathways & Petri Nets September 2002 P ETRI N ETS , B ASICS 3 (5) FLOW OF TOKENS ❑ an action may happen, if -> all preconditions are fulfilled (corresponding to the arc weights); ❑ if an action happens, then -> tokens are removed from all preconditions (corresponding to the arc weights), and -> tokens are added to all postconditions (corresponding to the arc weights); ❑ an action happens (firing of a transition) -> atomic -> time-less mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 12 / 52

Biopathways & Petri Nets September 2002 E XAMPLES , R EACTION E QUATIONS ❑ FOR LIGHT - INDUCED PHOSPHORYLATION 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 ❑ FROM THE PHOTOSYNTHESIS 2 CO 2 + H 2 S + 2 H 2 O -> 2 (CH 2 O) + H 2 SO 4 CO 2 CH 2 O 2 2 H 2 S r2 2 H 2 SO 4 H 2 O mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 13 / 52

Biopathways & Petri Nets September 2002 T YPICAL B ASIC S TRUCTURES 1 ❑ CHAIN OF REACTIONS r2 MB3 r1 MB1 MB2 ❑ ( FREE - CHOICE ) BRANCHING MB2 r1 MB1 MB3 r2 ❑ BRANCHING WITH SIDE CONDITION s1 s2 MB2 r1 MB1 MB3 r2 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 14 / 52

Biopathways & Petri Nets September 2002 T YPICAL B ASIC S TRUCTURES 2 ❑ CONCURRENCY t_fork t_join ❑ READ ARCS proCondition proCondition proCondition ❑ INHIBITOR ARCS BUT: CAUTION ! contraCondition mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 15 / 52

Biopathways & Petri Nets September 2002 M ETABOLIC P ETRI N ETS 1 (1) PLACES -> involved substances / chem. compounds ❑ substrates (boundary places), r2 OutSub r1 InSub input substrat output substrat e. g. glucose, lactate; ❑ metabolites, e. g. glucose 6-phosphate ❑ side conditions for reactions, e. g. electron carrier, phosphate carrier; ❑ enzymes, if any mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 16 / 52

Biopathways & Petri Nets September 2002 M ETABOLIC P ETRI N ETS 2 (2) TRANSITIONS ❑ spontaneous reactions ❑ enzyme-catalyzed reactions, two ways of modelling: without enzyme concentration MB1 MB2 Enzym with enzyme concentration x enzyme x x enzym-catalyzed MB1 MB2 reaction x - amount of enzyme units required by the reaction ❑ transport steps, if any -> inhomogeneous substance distribution; mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 17 / 52

Biopathways & Petri Nets September 2002 M ETABOLIC P ETRI N ETS 3 (3) ARC INSCRIPTIONS -> amount of units of the substances involved in the reaction (4) AMOUNT OF TOKENS -> amount of available units of substances (5) INITIAL MARKING -> initial substance distribution Σ M ETABOLIC P ETRI N ET ( M P N ): set of all paths from the input to the output substrates respecting the stoichiometric relations mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 18 / 52

Biopathways & Petri Nets September 2002 E XAMPLE [R EDDY 96] AS P ETRI N ET , V ERSION 1 Xu5P S7P E4P Ru5P NADPH GSSG GAP 2 F6P R5P 2 2 2 GSH NADP+ DHAP ATP ADP ATP ADP GAP G6P Gluc F6P FBP NAD+ Pi NAD+ NADH ATP ADP ATP ADP NADH 2PG 1,3-BPG Lac PEP Pyr 3PG glucose1.ped mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 19 / 52

Biopathways & Petri Nets September 2002 E XAMPLE [R EDDY 96] AS P ETRI N ET , V ERSION 3 Gluc ATP ADP Ru5P G6P NADP+ 2 2 NADPH Xu5P GSSG R5P F6P 2 GSH ATP 2 ADP GAP S7P FBP F6P E4P GAP NAD+ DHAP 1,3-BPG Pi ADP NADH 1,3-BPG ATP 3PG ADP ATP two-layered representation NADH 2PG NAD+ Lac PEP ADP ATP Pyr NADH NAD+ glucose3.ped Lac mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 20 / 52

Biopathways & Petri Nets September 2002 E XTENSIONS , S UMMARY S YNTACTIC S UGAR ❑ logical nodes -> connectors ❑ hierarchies -> different levels of abstraction ❑ read arcs -> pro-conditions MODELLING POWER ❑ inhibitor arcs -> contra-conditions mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 21 / 52

Biopathways & Petri Nets September 2002 3. APPLICATION TO APOPTOTIC PATHWAYS -> MODELLING & ANIMATION mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 22 / 52

Biopathways & Petri Nets September 2002 A POPTOSIS , TWO BASIC PATHWAYS http://www.genomicObject.net mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 23 / 52

Biopathways & Petri Nets September 2002 F AS 1 Apoptotic_Stimuli Fas-Ligand s7 FADD Procaspase-8 Apaf-1 Bax_Bad_Bim Bcl-2_Bcl-xL s8 dATP/ATP CytochromeC BidC-Terminal Bid s1 s9 s10 s6 s5 Mitochondrion Caspase-8 Procaspase-3 s2 (m20) Caspase-9 Caspase-3 s13 Procaspase-9 s11 DFF s3 s12 CleavedDFF45 (m22) DFF40-Oligomer s4 DNA DNA-Fragment mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 24 / 52

Biopathways & Petri Nets September 2002 F AS 2 = F AS 1 Fas-Ligand Apoptotic_Stimuli Procaspase-8 FADD s7 Bid s1 Bax_Bad_Bim s5 s8 Caspase-8 Mitochondrion Bcl-2_Bcl-xL s6 Procaspase-3 BidC-Terminal s9 s2 s12 Apaf-1 CytochromeC Caspase-3 s10 DFF (m20) dATP/ATP s11 s3 Procaspase-9 DFF40-Oligomer Caspase-9 CleavedDFF45 DNA s4 DNA-Fragment mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 25 / 52