G ATERSLEBEN 2004 PN & Systems Biology M ODEL C HECKING OF B IOCHEMICAL N ETWORKS U SING P ETRI N ETS Ina Koch Monika Heiner Technical University of Applied Sciences Brandenburg University of Technology Berlin Cottbus Dep. of Bioinformatics Dep. of CS monika.heiner@informatik.tu-cottbus.de August 2004
M ODEL - BASED S YSTEM A NALYSIS PN & Systems Biology system Problem system properties model Petrinetz model properties monika.heiner@informatik.tu-cottbus.de August 2004
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 August 2004
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 August 2004
T EMPORAL L OGICS , O VERVIEW PN & Systems Biology semantics interleaving partial order time traces runs (no conflict, no concurrency) (no conflict, but concurrency) linear (LTL) Manna & Pnueli, Kröger, jsp 2001 Reisig DSSZ/LTL tools: ? reachability graph prefix (conflict & concurrency (conflicts & concurrency) branching not distinguishable) (CTL) Emmerson, Clarke McMillan, Esparza, pd 2001 PROD/MARIA, INA, DSSZ/CTL PEP monika.heiner@informatik.tu-cottbus.de August 2004
T ECHNIQUES & T OOLS , O VERVIEW PN & Systems Biology technique CTL LTL reachability graph INA PROD, MARIA stubborn set reduced LoLA PROD (LTL\X) reachability graph symmetrically reduced LoLA ? reachability graph (symmetric formulas) BDD, NDD, ..., xDD DSSZ-CTL, SMART, DSSZ-CTL2 DSSZ-LTL Kronecker algebra [Kemper] ? prefix PEP (CTL 0 ) QQ (LTL\X) process automata [pd] ? monika.heiner@informatik.tu-cottbus.de August 2004
T EMPORAL L OGICS , B ASICS PN & Systems Biology extension of classical (propositional) logics by temporal operators ❑ atomic propositions ❑ -> elementary statements, having - in a given state - a well-defined truth value -> e. g. mutex, for 1-bounded pn -> e. g. buffer = 2, buffer > 2, else constants ❑ -> TRUE, FALSE classical Boolean operators ❑ negation ! conjunction * disjunction + implication -> temporal operators ❑ -> to refer to the sequence of states monika.heiner@informatik.tu-cottbus.de August 2004
CTL O PERATORS , I NTERLEAVING S EMANTICS PN & Systems Biology next f finally f f1 until f2 globally f AX AF AG AU on all branches EX EF EG EU f1 on some f1 branch f2 monika.heiner@informatik.tu-cottbus.de August 2004
M ODEL C HECKING PN & Systems Biology ... is a technique for verifying finite-state concurrent systems ❑ Clarke, E. M. Jr.; Grumberg, O.; Peled, D. A.: Model Checking; MIT Press 2001 finite state systems = steady state systems = bounded pn ❑ model checking of unbounded systems ❑ -> CTL undecidable -> LTL decidable, but no tools (not yet ?) -> unboundedness + inhibitors = undecidability how to get bounded bionetworks ? ❑ monika.heiner@informatik.tu-cottbus.de August 2004
TWO APPROACHES PN & Systems Biology approach 1: qualitative model ❑ -> model assumptions of environment behaviour: -> strong assumptions quantitative relations of input / output compounds -> control of conflicting alternative pathways approach 2: quantitative model = time-dependent model ❑ -> model assumptions of environment behaviour: -> weak assumptions infinite flow into/out the network -> relative transition firing rates -> control of conflicting alternative pathways claim ❑ -> transformation preserves all possible behaviour (= minimal T-invariants) monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1 PN & Systems Biology additional model component ❑ A D input output network B compounds compounds E C aA + bB +cC -> dD + eE network sum equation A a D d cycle input b output B compounds compounds e t c r t a a e t s p E C e r precondition ❑ -> equal sum equation for all pathways monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1 PN & Systems Biology additional model component, refinement ❑ A D input output network B compounds compounds E C pathway1, sum equation aA + bB -> dD pathway2, sum equation cC -> eE a A d D cycle input output B b compounds compounds e E c C repeat start precondition ❑ -> controlled conflicts between pathways with unequal sum equations monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology example - apoptosis ❑ -> Matsuno et al. signal-transduction ❑ pathway http://www.genomicObject.net monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology example - apoptosis ❑ -> Matsuno et al. signal-transduction ❑ pathway inhibitor arcs ❑ http://www.genomicObject.net monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology Fas-Ligand example - apoptosis ❑ Apoptotic_Stimuli FADD Procaspase-8 network model ❑ s7 s1 Bid Bax_Bad_Bim inhibitor arcs ❑ swich_on s5 s8 Caspase-8 Mitochondrion three pathways s6 ❑ Procaspase-3 Bcl-2_Bcl-xL co_inhibitor BidC-Terminal = min. T-invariants switch_off s9 s12 s2 CytochromeC Apaf-1 Caspase-3 s10 dATP/ATP (m20) DFF s11 Procaspase-9 CleavedDFF45_1 s3 CleavedDFF45_2 Caspase-9 DFF40-Oligomer CleavedDFF45_3 DNA s4 DNA-Fragment monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology Fas-Ligand example - apoptosis ❑ Apoptotic_Stimuli FADD Procaspase-8 network model ❑ s7 s1 Bid Bax_Bad_Bim environment, style 1 ❑ swich_on s5 s8 Caspase-8 -> three pathways Mitochondrion s6 Procaspase-3 = min. T-invariants Bcl-2_Bcl-xL co_inhibitor BidC-Terminal switch_off s9 s12 s2 T-invariant 1 ❑ CytochromeC Apaf-1 -> Fas-induced Caspase-3 s10 dATP/ATP -> ’death-receptor’ (m20) DFF pathway s11 Procaspase-9 CleavedDFF45_1 s3 CleavedDFF45_2 Caspase-9 DFF40-Oligomer CleavedDFF45_3 DNA s4 DNA-Fragment monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology Fas-Ligand example - apoptosis ❑ Apoptotic_Stimuli FADD Procaspase-8 network model ❑ s7 s1 Bid Bax_Bad_Bim environment, style 1 ❑ swich_on s5 s8 Caspase-8 -> three pathways Mitochondrion s6 Procaspase-3 = min. T-invariants Bcl-2_Bcl-xL co_inhibitor BidC-Terminal switch_off s9 s12 s2 T-invariant 2 ❑ CytochromeC Apaf-1 -> apoptotic-stimuli- Caspase-3 s10 dATP/ATP induced (m20) DFF -> ’mitochondrial’ s11 Procaspase-9 CleavedDFF45_1 pathway s3 CleavedDFF45_2 Caspase-9 DFF40-Oligomer DFF40-Oligomer CleavedDFF45_3 DNA s4 DNA-Fragment monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology Fas-Ligand example - apoptosis ❑ Apoptotic_Stimuli FADD Procaspase-8 network model ❑ s7 s1 Bid Bax_Bad_Bim environment, style 1 ❑ swich_on s5 s8 Caspase-8 -> three pathways Mitochondrion s6 Procaspase-3 = min. T-invariants Bcl-2_Bcl-xL co_inhibitor BidC-Terminal switch_off s9 s12 s2 T-invariant 3 ❑ CytochromeC Apaf-1 -> ’cross-talk by Bid’ Caspase-3 s10 dATP/ATP pathway (m20) DFF s11 Procaspase-9 CleavedDFF45_1 s3 CleavedDFF45_2 Caspase-9 DFF40-Oligomer CleavedDFF45_3 DNA s4 DNA-Fragment monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology example - apoptosis ❑ choice1 environment model ❑ Fas-Ligand FADD start1 pathway 1 / 3 ❑ Procaspase-8 Procaspase-3 -> overlap at the DFF beginning DNA DNA-Fragment -> then branch init CleavedDFF45_1 Apoptotic_Stimuli -> controlled by places CleavedDFF45_2 start2 repeat Apaf-1 choice1 / choice2 CleavedDFF45_3 dATP/ATP Procaspase-9 all pathways share ❑ the same ending choice2 start_crossTalk -> only one Bid repeat transition monika.heiner@informatik.tu-cottbus.de August 2004
A PPROACH 1, E X PN & Systems Biology Fas-Ligand example - apoptosis ❑ Apoptotic_Stimuli FADD Procaspase-8 network model, ❑ s7 adapted s1 Bid Bax_Bad_Bim swich_on s5 s8 Caspase-8 system model ❑ choice2 Mitochondrion s6 Procaspase-3 -> network model Bcl-2_Bcl-xL co_inhibitor BidC-Terminal switch_off s9 -> environment model choice1 s12 s2 CytochromeC Apaf-1 system model ❑ Caspase-3 s10 dATP/ATP -> 1-bounded (m20) DFF s11 -> live Procaspase-9 CleavedDFF45_1 s3 CleavedDFF45_2 ready for Caspase-9 ❑ DFF40-Oligomer CleavedDFF45_3 model checking DNA s4 DNA-Fragment monika.heiner@informatik.tu-cottbus.de August 2004
Recommend
More recommend
