M ODEL C HECKING OF B IOCHEMICAL N ETWORKS U SING P ETRI N ETS Ina - - PowerPoint PPT Presentation

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M ODEL C HECKING OF B IOCHEMICAL N ETWORKS U SING P ETRI N ETS Ina - - PowerPoint PPT Presentation

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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

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

GATERSLEBEN 2004

MODEL CHECKING OF BIOCHEMICAL NETWORKS USING PETRI NETS

Monika Heiner Brandenburg University of Technology Cottbus

  • Dep. of CS

Ina Koch Technical University of Applied Sciences Berlin

  • Dep. of Bioinformatics
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

MODEL- BASED SYSTEM ANALYSIS

Petrinetz model Problem system

system properties model properties

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

MODEL- BASED SYSTEM ANALYSIS

Petrinetz model Problem system

system properties model properties

technical system requirement specification verification

CONSTRUCTION

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

MODEL- BASED SYSTEM ANALYSIS

biological system known unknown properties properties validation behaviour prediction

UNDERSTANDING

Petrinetz model Problem system

system properties model properties

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

TEMPORAL LOGICS, OVERVIEW

semantics time interleaving partial order linear (LTL) traces (no conflict, no concurrency) Manna & Pnueli, Kröger, jsp 2001 DSSZ/LTL runs (no conflict, but concurrency) Reisig tools: ? branching (CTL) reachability graph (conflict & concurrency not distinguishable) Emmerson, Clarke PROD/MARIA, INA, DSSZ/CTL prefix (conflicts & concurrency) McMillan, Esparza, pd 2001 PEP

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

TECHNIQUES & TOOLS, OVERVIEW

technique CTL LTL reachability graph INA PROD, MARIA stubborn set reduced reachability graph LoLA PROD (LTL\X) symmetrically reduced reachability graph LoLA (symmetric formulas) ? BDD, NDD, ..., xDD DSSZ-CTL, SMART, DSSZ-CTL2 DSSZ-LTL Kronecker algebra [Kemper] ? prefix PEP (CTL0) QQ (LTL\X) process automata [pd] ?

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

TEMPORAL LOGICS, BASICS

❑ 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
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

CTL OPERATORS, INTERLEAVING SEMANTICS

  • n some
  • n all

next f finally f globally f f1 until f2

f1 f1 f2

EX EU AG EG AF EF AX AU branches branch

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

MODEL CHECKING

❑ ... 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 ?

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

TWO APPROACHES

❑ 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)
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1

❑ additional model component ❑ precondition

  • > equal sum equation for all pathways

input compounds

  • utput

compounds b a e d r e p e a t C B A E D

network sum equation

c s t a r t cycle

aA + bB +cC -> dD + eE

C B A E D

network

input compounds

  • utput

compounds

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1

❑ additional model component, refinement ❑ precondition

  • > controlled conflicts between pathways with unequal sum equations

input compounds

  • utput

compounds b a e d repeat C B A E D

pathway1, sum equation

c start cycle

aA + bB -> dD

C B A E D

network

input compounds

  • utput

compounds

pathway2, sum equation cC -> eE

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis

  • > Matsuno et al.

❑ signal-transduction pathway

http://www.genomicObject.net

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis

  • > Matsuno et al.

❑ signal-transduction pathway ❑ inhibitor arcs

http://www.genomicObject.net

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ network model ❑ inhibitor arcs ❑ three pathways = min. T-invariants

switch_off swich_on s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 CleavedDFF45_1 CleavedDFF45_2 CleavedDFF45_3 co_inhibitor DNA-Fragment DNA DFF40-Oligomer DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ network model ❑ environment, style 1

  • > three pathways

= min. T-invariants ❑ T-invariant 1

  • > Fas-induced
  • > ’death-receptor’

pathway

switch_off swich_on s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 CleavedDFF45_1 CleavedDFF45_2 CleavedDFF45_3 co_inhibitor DNA-Fragment DNA DFF40-Oligomer DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ network model ❑ environment, style 1

  • > three pathways

= min. T-invariants ❑ T-invariant 2

  • > apoptotic-stimuli-

induced

  • > ’mitochondrial’

pathway

switch_off swich_on s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 CleavedDFF45_1 CleavedDFF45_2 CleavedDFF45_3 co_inhibitor DNA-Fragment DNA DFF40-Oligomer DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand DFF40-Oligomer

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ network model ❑ environment, style 1

  • > three pathways

= min. T-invariants ❑ T-invariant 3

  • > ’cross-talk by Bid’

pathway

switch_off swich_on s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 CleavedDFF45_1 CleavedDFF45_2 CleavedDFF45_3 co_inhibitor DNA-Fragment DNA DFF40-Oligomer DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ environment model ❑ pathway 1 / 3

  • > overlap at the

beginning

  • > then branch
  • > controlled by places

choice1 / choice2 ❑ all pathways share the same ending

  • > only one

repeat transition

start1 repeat start2 start_crossTalk Procaspase-8 FADD Fas-Ligand Procaspase-3 DFF DNA init DNA-Fragment Apoptotic_Stimuli Apaf-1 Procaspase-9 dATP/ATP choice1 choice2 Bid CleavedDFF45_3 CleavedDFF45_2 CleavedDFF45_1

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 1, EX

❑ example - apoptosis ❑ network model, adapted ❑ system model

  • > network model
  • > environment model

❑ system model

  • > 1-bounded
  • > live

❑ ready for model checking

switch_off swich_on s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 CleavedDFF45_1 CleavedDFF45_2 CleavedDFF45_3 choice2 choice1 co_inhibitor DNA-Fragment DNA DFF40-Oligomer DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

MODEL CHECKING, EXAMPLES

❑ property 1 if inhibitor substance Bcl_2_Bcl_xL is present, then the progress of the cross-talk pathway is stopped at Mitochondrion AG ( Bcl_2_Bcl_xL * Mitochondrion -> AX (Mitochondrion) ); ❑ property 2 if inhibitor substance Bcl_2_Bcl_xL is present, then the progress of the cross-talk pathway is stopped at Mitochondrion until the inhibitor substance disappears AG ( Bcl_2_Bcl_xL * Mitochondrion -> A (Mitochondrion U ! Bcl_2_Bcl_xL) ); ❑ property 3 if inhibitor substance Bcl_2_Bcl_xL is not present, then the progress of the cross-talk pathway is not stopped at Mitochondrion AG ( !Bcl_2_Bcl_xL * Mitochondrion -> EX (CytochromeC) );

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 2, EX1

3 2 prod_B cons_D cons_C r1 prod_A B D C A

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N Y N Y Y N Y Y N N Y N Y Y Y CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N Y N N Y N ? N Y Y Y N

  • > properties as time-less net
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 2, EX1

3 2 prod_B cons_D cons_C r1 prod_A B D C A

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N Y N Y Y N Y Y N N Y N Y Y Y CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N Y N N Y N ? N Y Y Y N

  • > properties as time-less net

T-INVARIANTE

1 2 1 3 1

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 2, EX1

3 2 prod_B <3> cons_D <2> cons_C <6> r1 <6> prod_A <6> B D C A

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N Y N Y Y N Y Y N N Y N Y Y Y CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N Y Y N N N ? N Y Y Y N

  • > properties as duration net

size ( RG (d-net)) = 8 nodes

T-INVARIANTE

1 2 1 3 1

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

APPROACH 2, EX2

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N Y N Y Y N Y Y N N Y N Y Y Y CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N Y Y N N N ? N Y Y Y N

  • > properties as duration net

size ( RG (d-net)) = 11 nodes

2 3 cons_C <2> cons_B <3> r2 <6> r1 <6> prod_A <3> C B A

1 1 2

T-INVARIANTE1 T-INVARIANTE2

1 1 3

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

RG(EX2), PART 1

❑ transient state

S1 (0,0,0) S2 (A,0,0) S3 (A,0,0) S4 (A,0,3C) S5 (0,0,2C) S10 (A,0,0) S11 (A,2B,0)

t(r2) = 3 t(r2)=3 t(r1)=3 t(r1)=3 t(prod_A)=1 t(r1)=1 t(r2)=4 s6 s8 prod_A [3] prod_A, r2 prod_A, r1 [3] [3] [3] [3] [2] [1] [3] prod_A r1 start r2 end prod_A r1 end r2 start prod_A start r1 start cons_C prod_A r1 start r2 end prod_A end cons_C start cons_B

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

RG(EX2), PART 2

❑ steady state

S6 (A,2B,C) S7 (0,B,C) S8 (A,B,3C) S9 (0,0,2C)

t(r2)=3 t(cons_C)=1 t(prod_A)=2 t(r1)=5 t(r2)=2 t(cons_B)=2 t(r1)=3 t(prod_A)=1 t(r1)=1 t(r2)=4 t(cons_B)=1 s5 s11 [1] [2] [2] [1] prod_A start r1 start cons_B start, cons_C end prod_A end r2 end cons_B end, cons-C prod_A start r2 start cons_b start, cons_C prod_A end r1 end cons_B end cons-C start terminal SCC

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 200

EX2, TERMINAL SCC

❑ contains all transitions

  • > always running
  • > start / end

at different time points ❑ contains all minimal t-invariants ❑ relative transition firing rates prod_A : 1 + 1 r1 : 1 r2 : 1 cons_B : 2 cons_C : 3 ❑ timing diagram

s6 s7 s8 s9 s6 prod_A r1 r2 cons_B cons_C 6 time units

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 200

APPROACH 2, SUMMARY

❑ CTI, but not CPI ❑ transient state

  • >

initial behaviour to reach steady state

  • >

not REV

  • >

generally, not DCF ❑ steady state behaviour

  • >

terminal scc

  • >

BND

  • >

here, DCF

PN D/I NET

time not BND REV LIVE BND not REV LIVE

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

BIONETWORKS, VALIDATION

❑ validation criterion 1

  • > CTI
  • > no minimal T-invariant without biological interpretation
  • > no known biological behaviour without corresponding T-invariant

❑ validation criterion 2

  • > P-invariants - groups of compounds with conservation property
  • > no minimal P-invariant without biological interpretation

❑ validation criterion 3

  • > CPI
  • > all expected temporal-logic properties -> TRUE
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

CHALLENGES

❑ extensions

  • > read arcs
  • > inhibitor arcs !?

❑ efficient computation of minimal invariants

  • > exponential complexity
  • > compositional / step-wise refinement approach ?

❑ analysis of bounded, but not safe non-ordinary nets with inhibitor arcs

  • > huge state spaces, beyond exponential growth (?)
  • > smaller, bounded version of case study 2

1010 states (IDD-based mc tool) ❑ analysis of unbounded nets

  • > besides T-invariant analysis ?

❑ model checking

  • > relevant properties ?

≥

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

SUMMARY

❑ representation of bionetworks by Petri nets

  • > unifying view
  • > animation
  • > model validation against consistency criteria
  • > qualitative/quantitative behaviour prediction

❑ steady state behaviour

  • > qualitative model
  • > quantitative model

❑ many challenging questions for analysis techniques

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de August 2004

THANKS !