METABOLIC PETRI NETS. MONIKA HEINER, BTU Cottbus REINHARDT HEINRICH, HU BERLIN SOFTWARE ENGINEERING & PETRI NETS
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1 Petri Nets & Metabolic Networks October 000 Petri Nets & Metabolic Networks October 000 BTU COTTBUS COMPUTER SCIENCE INSTITUTE SOFTWARE ENGINEERING & PETRI NETS METABOLIC PETRI NETS software Problem Petrinetz Petri net MONIKA HEINER, BTU Cottbus REINHARDT HEINRICH, HU BERLIN properties properties metabolic networks 1 / 30 mh@informatik.tu-cottbus.de / 30
2 Petri Nets & Metabolic Networks October 000 Petri Nets & Metabolic Networks October 000 TOOL OVERVIEW informal specification press hierarchy browser PED hierarchical Petri Net Editor with output filters Production Cell: deposit belt (belt ) arm travelling crane robot arm 1 feed belt (belt 1) elevating rotary table functional testing protocols qualitative analysis protocols quantitative analysis protocols (distributed) animation tool (rapid prototyping) functional requirements INA PROD qualitative Petri net analyzers INA (non-stochastic) PEDVisor PEP performance requirements safety requirements SMV TimeNet (stochastic) quantitative Petri net analyzers execution protocols FUNLite motion lib execution tool mh@informatik.tu-cottbus.de 3 / 30 mh@informatik.tu-cottbus.de 4 / 30
3 Petri Nets & Metabolic Networks October 000 Petri Nets & Metabolic Networks October 000 NAD + + P i EXAMPLE PENTOSE PHOSPHATE CYCLE 15 1,3-BPG glucose 6-phosphate 4 Xu5P Ru5P EXAMPLE [REDDY 96] E4P 8 S7P R5P GSSG NH 1 3 N + 4 GSH 11 1 FBP 10 G6P 9 Gluc DHAP NAD Pyr PEP PG 3PG [Reddy 96] Reddy, V. N.; Liebman, M. N.; Mavrovouniotis, M. L.: Qualitative Analysis of Biochemical Reaction Systems; Computers in Biology and Medicine 6(96), 9-4. dihydroxyacetone phosphate dihydroxyacetone phosphate fructose 6-phosphate fructose 1,6-bisphosphate glucose 6-phosphate fructose 6-phosphate fructose 1,6-bisphosphate glycerinaldehyde 3-phosphate 1. possibility N + NH 3. possibility CO glycerinaldehyde 3-phosphate Stryer, L.: Biochemistry; Freeman, New York, NY, 1995, p ribose 5-phosphate ribulose 5-phosphate ribose 5-phosphate dihydroxyacetone phosphate glucose 6-phosphate glucose 6-phosphate fructose 6-phosphate fructose 1,6-biphosphate N + NH CO. possibility N + NH CO glycerinaldehyde 3-phosphate pyruvate 4. possibility ribulose 5-phosphate ribose 5-phosphate ribulose 5-phosphate ribose 5-phosphate mh@informatik.tu-cottbus.de 5 / 30 mh@informatik.tu-cottbus.de 6 / 30
4 Petri Nets & Metabolic Networks October 000 PETRI NETS, BASICS 1 Petri Nets & Metabolic Networks October 000 PETRI NETS, BASICS (1) NODES places transitions (3) TOKENS (moving objects, vehicles, work pieces, dates, control flow pointer,..., units of substances (e. g. Mol),...) passive elements conditions states chem. compounds () ARCS preconditions active elements events actions chem. reactions postconditions 5 (4) MARKING condition is not fulfilled condition is (one times) fulfilled n condition is n times fulfilled (system state, substance distribution) 3 event How many tokens are on each place? -> initial marking mh@informatik.tu-cottbus.de 7 / 30 mh@informatik.tu-cottbus.de 8 / 30
5 Petri Nets & Metabolic Networks October 000 PETRI NETS, BASICS 3 Petri Nets & Metabolic Networks October 000 EXAMPLES, REACTION EQUATIONS (5) FLOW OF TOKENS an event may happen, if -> all preconditions are fulfilled (corresponding to the arc weights); if an event 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); FOR LIGHT-INDUCED PHOSPHORYLATION NAD + + H O -> + H + + O NAD + r1 H O H + O FROM THE PHOTOSYNTHESIS CO + H S + H O -> (CH O) + H SO 4 an event happens (firing of a transition) -> atomic -> time-less CO H S H O r CH O H SO 4 mh@informatik.tu-cottbus.de 9 / 30 mh@informatik.tu-cottbus.de 10 / 30
6 Petri Nets & Metabolic Networks October 000 TYPICAL BASIC STRUCTURES Petri Nets & Metabolic Networks October 000 METABOLIC PETRI NETS CHAIN OF REACTIONS (1) PLACES -> involved substances / chem. compounds MB1 r1 MB r MB3 substrates (boundary places), (FREE-CHOICE) BRANCHING r1 MB InSub r1 input substrat r OutSub output substrat MB1 MB3 r BRANCHING WITH SIDE CONDITION MB r1 MB1 e. g. glucose, lactate; metabolites, e. g. glucose 6-phosphate side conditions for reactions, e. g. electron carrier, phosphate carrier; enzymes, if any r MB3 mh@informatik.tu-cottbus.de 11 / 30 mh@informatik.tu-cottbus.de 1 / 30
7 Petri Nets & Metabolic Networks October 000 METABOLIC PETRI NETS Petri Nets & Metabolic Networks October 000 METABOLIC PETRI NETS 3 () TRANSITIONS spontaneous reactions enzyme-catalyzed reactions, two ways of modelling: without the enzyme concentration MB1 Enzym MB (3) ARC INSCRIPTIONS -> amount of the units of substances involved in the reaction (4) AMOUNT OF TOKENS -> amount of available units of substances with the enzyme concentration x (5) INITIAL MARKING x enzyme x -> initial substance distribution MB1 enzym-catalyzed reaction MB x - amount of units of substances required by the reaction transport steps, if any -> inhomogeneous substance distribution; Σ METABOLIC PETRI NET (MPN): set of all paths from the input to the output substrates taking into consideration the stoichiometric relations; mh@informatik.tu-cottbus.de 13 / 30 mh@informatik.tu-cottbus.de 14 / 30
8 Petri Nets & Metabolic Networks October 000 EXAMPLE [REDDY 96] AS PETRI NET, VERSION 1 Petri Nets & Metabolic Networks October 000 EXAMPLE [REDDY 96] AS PETRI NET, VERSION Gluc Ru5P Xu5P S7P E4P G6P N+ NH Ru5P GSSG NH R5P GSSG GSH R5P Xu5P S7P GSH N+ FBP E4P DHAP DHAP Pi 1,3-BPG Gluc G6P FBP 3PG Pi PG PEP Pyr PEP PG 3PG 1,3-BPG Pyr glukose1.ped glukose.ped mh@informatik.tu-cottbus.de 15 / 30 mh@informatik.tu-cottbus.de 16 / 30
9 Petri Nets & Metabolic Networks October 000 EXAMPLE [REDDY 96] AS PETRI NET, VERSION 3 Petri Nets & Metabolic Networks October 000 EXAMPLE [REDDY 96] AS PETRI NET, VERSION 4 Gluc Gluc G6P Ru5P G6P Ru5P N+ NH N+ NH GSSG GSH R5P Xu5P GSSG GSH R5P Xu5P FBP S7P FBP S7P DHAP 1,3-BPG Pi E4P 1,3-BPG DHAP 1,3-BPG Pi E4P 1,3-BPG two-layered representation 3PG PG reduced to 3PG PG PEP PEP Pyr Pyr glukose3.ped glukose4.ped mh@informatik.tu-cottbus.de 17 / 30 mh@informatik.tu-cottbus.de 18 / 30
10 Petri Nets & Metabolic Networks October 000 TYPICAL PETRI NET QUESTIONS Petri Nets & Metabolic Networks October 000 EXAMPLE [REDDY 96] AS PETRI NET, VERSION 5 Gluc (1) How many tokens may reside at most in a given place? b b1 Ru5P (0, 1, k, oo) -> BOUNDEDNESS G6P 3 3 b1 b N+ GSSG NH GSH R5P a1 a a a1 Xu5P () How often may a transition fire? FBP S7P (0-times, n-times, oo-times) -> LIVENESS DHAP E4P Pi (3) Is a given system state 1,3-BPG always reachable again? -> PROGRESS PROPERTIES 7 start Gluc never reachable? -> SAFETY PROPERTIES Pi glukose4_zyk.ped mh@informatik.tu-cottbus.de 19 / 30 mh@informatik.tu-cottbus.de 0 / 30
11 Petri Nets & Metabolic Networks October 000 ASSUMPTIONS IN VERSION 5 Petri Nets & Metabolic Networks October 000 TYPICAL ANALYSIS TECHNIQUES 1 (1) TOKEN GAME (?) the two appearances of can be separated (no logical / fusion nodes) the branching probabilities at the conflicts of G6P and Ru5P are known and may be characterized by the relations G6P - 3 : 1 Ru5P - : 1 -> STEADY STATE: all intermediates have to be balanced with respect to inputs and outputs () REACHABILITY GRAPH nodes: system states arcs: the firing transition z t4 t1 z1 t z3 z4 (3) REDUCED REACHABILITY GRAPH t3 (4) STRUCTURAL ANALYSES e. g.: conservative -> bounded mh@informatik.tu-cottbus.de 1 / 30 mh@informatik.tu-cottbus.de / 30
12 (5) NET INVARIANTS Petri Nets & Metabolic Networks October 000 TYPICAL ANALYSIS TECHNIQUES Petri Nets & Metabolic Networks October 000 QUALITATIVE ANALYSIS TECHNIQUES NET REDUCTION P-INVARIANTS -> set of places with (weighted) constant token sum; mpn: meta substance preservation rules, all electron carriers Ex: P-Invariant (Pi,..., ); i.e. their can be produced only as much lactate as P i is provided; T-INVARIANTS -> set of transitions, reproducing a given marking; mpn: reaction chains, reproducing a substance distribution; BND, LIVE mpn: elementary modes [Schuster 9x] Ex: forward / backward reaction of the triose phosphate isomerase STRUCTURAL PROPERTIES LINEAR PROGRAMMING place / transition invariants state / trap equation REACHABILITY ANALYSIS (complete) reachability graph compressed state spaces OBDDs, ONDDS Kronecker products reduced state spaces coverability graph symmetry stubborn / sleep sets branching processes concurrent automaton static analysis dynamic analysis (model checking) mh@informatik.tu-cottbus.de 3 / 30 mh@informatik.tu-cottbus.de 4 / 30
13 Petri Nets & Metabolic Networks October 000 INTEGRATION OF QUALITATIVE AND QUANTITATIVE ANALYSES Petri Nets & Metabolic Networks October 000 MODEL CLASSES TIME CONSUMPTION time PETRI NETS PLACE/TRANSITION PETRI NET (COLOURED PN) TIME-DEPENDENT PN context checking by Petri net theory verification by temporal logics BRANCHING PROBABILITIES NON-STOCHASTIC PETRI NET worst-case evaluation p1 p p1 + p = 1 STOCHASTIC PETRI NET performance prediction reliability prediction mh@informatik.tu-cottbus.de 5 / 30 mh@informatik.tu-cottbus.de 6 / 30
14 Petri Nets & Metabolic Networks October 000 APPLICATIONS OF METABOLIC PETRI NETS Petri Nets & Metabolic Networks October 000 DERIVED BASIC QUESTIONS (1) step-wise construction of graphical (=visual) models for metabolic networks () graphical model animation (simulation) with / without disturbances relation between metabolic network properties Petri net properties (3) validation of metabolic models -> model integrity (4) qualitative analyses of biological / bio-technological questions relation between metabolic control theory (Heinrich) Petri net theory (Heiner) (5) quantitative analyses of biological / bio-technological questions -> pros / cons? -> strength / weaknesses? mh@informatik.tu-cottbus.de 7 / 30 mh@informatik.tu-cottbus.de 8 / 30
15 Petri Nets & Metabolic Networks October 000 WORK PACKAGES 1 Petri Nets & Metabolic Networks October 000 WORK PACKAGES (A) MAPPING THE TERMINOLOGIES A-1 selection of case studies A- initial comparison of modelling principles A-3 initial comparison concerning typical analysis questions (B) INVESTIGATION OF THE A-1 CASE STUDIES B-1 by means of control theory B- by means of Petri net theory (C) CASE STUDIES RESULT COMPARISON C-1 modelling power C- qualitative analysis -> power / efficiency C-3 quantitative analysis -> power /efficiency (D) INTEGRATION D-1 definition of selection criteria D- proposal of a combined methodology (E) PETRI NET BASED ANALYSES E-1 supplementing model validation E- realization with available pn techniques E-3 dedicated tool kit (F) CASE STUDIES -> more sophisticated case studies (G)TUTORIAL & DEMO VERSION (H) FINAL REPORT mh@informatik.tu-cottbus.de 9 / 30 mh@informatik.tu-cottbus.de 30 / 30
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