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

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

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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 &

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

BIOPATHWAYS & PETRI NETS

MONIKA HEINER

BTU COTTBUS COMPUTER SCIENCE

INA KOCH

TFH BERLIN COMPUTATIONAL BIOLOGY

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 2 / 52

OUTLINE

  • 1. MOTIVATION
  • 2. INTRODUCTION INTO

(QUALITATIVE) PETRI NETS

  • 3. APPLICATION TO APOPTOTIC PATHWAYS
  • > MODELLING & ANIMATION
  • 4. MODEL ANALYSIS
  • > QUALITATIVE & QUANTITATIV
  • 5. SUMMARY
  • 6. OUTLOOK
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 3 / 52

1. MOTIVATION

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 4 / 52

MODEL- BASED SYSTEM ENGINEERING

Petrinetz model properties properties Problem bio - system pathways Petri net

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 5 / 52

BIOPATHWAYS

EXAMPLES

❑ metabolic pathways ❑ signal transduction cascades ❑ gene regulation ❑ . . .

BASIC PROPERTIES

❑ very complex structures ❑ causal interplay of basic actions (sequence, branching, concurrency)

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 6 / 52

REPRESENTATIONS, OBJECTIVES ❑ readability

  • > understanding

❑ animation

  • > experience

❑ validation

  • > consistency checks

❑ analysis

  • > behaviour prediction

(qualitative / quantitative)

=>> How many representations do we really need?

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 7 / 52

2. INTRODUCTION INTO (QUALITATIVE) PETRI NETS

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 8 / 52

[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.

Ru5P 4 5 Xu5P R5P 6 S7P GAP 7 E4P F6P 8 GAP 15 NAD+ + Pi NADH G6P F6P 10 ATP ADP FBP 11 12 DHAP 13 14 ATP ADP 9 Gluc 1,3-BPG ATP ADP 16 ATP ADP 19 NAD+ NADH 20 3PG 17 2PG PEP 18 Pyr Lac 2 NADP+ 2 NADPH 4 GSH 2 3 1 2 GSSG

EXAMPLE [REDDY 96]

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 9 / 52

EXAMPLE PENTOSE PHOSPHATE CYCLE

glucose 6-phosphate ribulose 5-phosphate ribose 5-phosphate

  • 2. possibility

2 NADP+ 2 NADPH CO2 glucose 6-phosphate fructose 6-phosphate fructose 1,6-bisphosphate dihydroxyacetone phosphate glycerinaldehyde 3-phosphate

  • 1. possibility

ribose 5-phosphate ribulose 5-phosphate ribose 5-phosphate 2 NADP+ 2 NADPH CO2 glucose 6-phosphate fructose 6-phosphate fructose 1,6-bisphosphate dihydroxyacetone phosphate glycerinaldehyde 3-phosphate

  • 3. possibility

ribulose 5-phosphate ribose 5-phosphate 2 NADP+ 2 NADPH CO2 glucose 6-phosphate fructose 6-phosphate fructose 1,6-biphosphate dihydroxyacetone phosphate glycerinaldehyde 3-phosphate

  • 4. possibility

2 ATP pyruvate Stryer, L.: Biochemistry; Freeman, New York, NY, 1995, p. 450.

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 10 / 52

PETRI NETS, BASICS 1 (1) NODES places transitions “passive elements” “active elements” conditions events states actions “chem. compounds” “chem. reactions” (2) ARCS preconditions postconditions action 3 5

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 11 / 52

PETRI NETS, BASICS 2 (3) TOKENS (moving objects, vehicles, work pieces, control flow pointer, dates,..., units of substances (e. g. Mol), ...) (4) MARKING (system state, substance distribution) How many tokens are on each place?

  • > initial marking

condition is not fulfilled condition is (one times) fulfilled condition is n times fulfilled n

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 12 / 52

PETRI NETS, BASICS 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
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 13 / 52

EXAMPLES, REACTION EQUATIONS ❑

FOR LIGHT-INDUCED PHOSPHORYLATION

❑

FROM THE PHOTOSYNTHESIS

2 2 2 2 2 2 2 r1 r2 H2SO4 CH2O H2O H2S CO2 O2 H+ NADH H2O NAD+

2 CO2 + H2S + 2 H2O -> 2 (CH2O) + H2SO4 2 NAD+ + 2 H2O -> 2 NADH + 2 H+ + O2

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 14 / 52

TYPICAL BASIC STRUCTURES 1

r2 r1 MB1 MB2 MB3 MB3 MB2 MB1 r1 r2 r2 r1 MB3 MB2 MB1

❑

CHAIN OF REACTIONS

❑ (FREE-CHOICE)

BRANCHING

❑

BRANCHING WITH SIDE CONDITION

s1 s2

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 15 / 52

TYPICAL BASIC STRUCTURES 2 ❑

CONCURRENCY

❑

READ ARCS

❑

INHIBITOR ARCS

contraCondition proCondition proCondition proCondition

BUT: CAUTION !

t_fork t_join

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 16 / 52

METABOLIC PETRI NETS 1 (1) PLACES

  • > involved substances / chem. compounds

❑ substrates (boundary places),

  • e. g. glucose, lactate;

❑ metabolites,

  • e. g. glucose 6-phosphate

❑ side conditions for reactions,

  • e. g. electron carrier,

phosphate carrier; ❑ enzymes, if any input substrat

  • utput substrat

r2 r1 OutSub InSub

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 17 / 52

METABOLIC PETRI NETS 2 (2) TRANSITIONS ❑ spontaneous reactions ❑ enzyme-catalyzed reactions, two ways of modelling: ❑ transport steps, if any

  • > inhomogeneous substance distribution;

Enzym MB2 MB1

without enzyme concentration with enzyme concentration x

x - amount of enzyme units required by the reaction enzyme MB2 MB1 enzym-catalyzed reaction x x

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 18 / 52

METABOLIC PETRI NETS 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 METABOLIC PETRI NET (MPN):

set of all paths from the input to the output substrates respecting the stoichiometric relations

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 19 / 52

EXAMPLE [REDDY 96]

AS PETRI NET,

VERSION 1

2 2 2 2 F6P GAP ATP ADP ADP ATP NADH NAD+ ATP ADP Lac Pyr PEP 2PG 3PG 1,3-BPG DHAP FBP G6P Gluc F6P E4P GAP S7P R5P Xu5P Ru5P GSH GSSG NADPH NADP+ NAD+ ADP ATP Pi

glucose1.ped

NADH

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 20 / 52

EXAMPLE [REDDY 96]

AS PETRI NET,

VERSION 3

2 2 2 2 F6P GAP ATP ADP ADP ATP NADH NAD+ ADP Lac 1,3-BPG DHAP FBP G6P Gluc F6P E4P GAP S7P R5P Xu5P Ru5P GSH GSSG NADPH NADP+ NADH NAD+ ATP Pi

glucose3.ped

Pyr PEP 2PG 3PG NADH NAD+ ADP ADP Lac 1,3-BPG ATP ATP

two-layered representation

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 21 / 52

EXTENSIONS, SUMMARY

SYNTACTIC SUGAR

❑ logical nodes

  • > connectors

❑ hierarchies

  • > different levels of abstraction

❑ read arcs

  • > pro-conditions

MODELLING POWER

❑ inhibitor arcs

  • > contra-conditions
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 22 / 52

3. APPLICATION TO APOPTOTIC PATHWAYS

  • > MODELLING

& ANIMATION

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 23 / 52

APOPTOSIS,

TWO BASIC PATHWAYS

http://www.genomicObject.net

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 24 / 52

FAS1

s6 s4 s3 s13 s12 s2 s11 s10 s5 s8 s9 s7 s1 Mitochondrion DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m22) (m20) Apaf-1 dATP/ATP CytochromeC Bcl-2_Bcl-xL Apoptotic_Stimuli Bax_Bad_Bim BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 25 / 52

FAS2 = FAS1

s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 26 / 52

FAS3

s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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

  • > animation
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 27 / 52

REFINEMENT: AUTOCATALYSIS ❑

REACTION

❑

CATALYSIS

❑

AUTOCATALYSIS

product substrate 2 product=enzyme proenzyme product=enzyme proenzyme proenzyme product=enzyme enzyme substrate product

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 28 / 52

FAS4A

2 2 2 2 s14 s13 s16 s15 s17 s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DISC DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 29 / 52

FAS4B ≈ FAS3

s8 s4 s3 s12 s10 s5 s6 s9 s7 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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

  • 3. s11
  • 2. s2
  • 1. s1
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 30 / 52

REFINEMENT:

INTERMEDIATE COMPLEXES

enzyme complex complex proenzyme

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 31 / 52

FAS5A

Complex Complex s7 s4 s3 s2 s17 s12 s16 s11 s10 s8 s9 s6 s5 s15 s14 s1 s13 Apoptotic_Stimuli Bcl-2_Bcl-xL Bax_Bad_Bim DNA-Fragment Complex DNA DFF40-Oligomer CleavedDFF45 DFF40 Complex DFF Complex Caspase-3 Procaspase-3 Complex Caspase-9 Complex Procaspase-9 Complex Complex dATP/ATP Apaf-1 CytochromeC Complex Mitochondrion BidC-Terminal Complex Bid Complex Complex Caspase-8 Complex DISC Procaspase-8 FADD Complex FasL-Trimer Fas-Ligand

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 32 / 52

FAS5B ≈ FAS4A

s13 s9 s7 DISC DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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

  • 14. s17
  • 13. s16
  • 12. s15
  • 11. s14
  • 10. s12
  • 9. s11
  • 8. s10
  • 7. s8
  • 6. s6
  • 5. s5
  • 4. s4
  • 3. s3
  • 2. s2
  • 1. s1
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 33 / 52

FAS5C ≈ FAS3

s9 s7 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 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

  • 10. s11
  • 9. s2
  • 8. s1
  • 7. s12
  • 6. s10
  • 5. s8
  • 4. s6
  • 3. s5
  • 2. s4
  • 1. s3
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 34 / 52

HIERARCHY TREE FAS5C

Top s3 1 s4 2 s5 3 s6 4 s8 5 s10 6 s12 7 s1 8 s2 9 s11 10 s1 8.1 s14 8.2 s15 8.3 s2 9.1 s16 9.2 s11 10.1 s17 10.2

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 35 / 52

MASTERING COMPLEXITY 1 ❑ STEP-WISE MODELLING

  • 1. literal scheme transformation

FAS1

  • 2. layout improvement

FAS2

  • > use of syntactic sugar
  • 3. adding environment behaviour

FAS3

  • > animation
  • 4. adding autocatalysis

FAS4A

  • > hierarchic Petri net

FAS4B

  • 5. adding intermediate complexes

FAS5A

  • > refined hierarchies

FAS5B FAS5C ❑ EXPLOIDING SYNTACTIC SUGAR

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 36 / 52

4. MODEL ANALYSIS

  • > QUALITATIVE

& QUANTITATIVE

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 37 / 52

TYPICAL ANALYSIS TECHNIQUE, EXAMPLE ❑ T - invariants

  • > set of transitions,

reproducing a given marking;

  • > metabolic Petri nets:

set of reactions, reproducing a substance distribution;

  • > bio Petri nets:

set of actions, reproducing a system state; ❑ minimal positive T - invariants

  • > basic behaviour
  • > any net behaviour =

linear combination of them ❑ computation:

  • (P x T) - incidence matrice
  • transition vector

C [ ] x ⋅ = C [ ] x

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 38 / 52

QUALITATIVE ANALYSIS, T - INVARIANT 1:

DEATH-RECEPTOR PATHWAY

g11 r4 g10 g3 r3 r2 r1 g9 g6 g5 g4 g8 g7 g2 g1 s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 39 / 52

QUALITATIVE ANALYSIS, T - INVARIANT 2: MITOCHONDRIAL PATHWAY

g11 r4 g10 g3 r3 r2 r1 g9 g6 g5 g4 g8 g7 g2 g1 s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 40 / 52

QUALITATIVE ANALYSIS, T - INVARIANT 3:

CROSS-TALK BY BID

g11 r4 g10 g3 r3 r2 r1 g9 g6 g5 g4 g8 g7 g2 g1 s8 s4 s3 s12 s2 s11 s10 s5 s6 s9 s7 s1 DNA-Fragment DNA DFF40-Oligomer CleavedDFF45 DFF Caspase-3 Procaspase-3 Caspase-9 Procaspase-9 (m20) Apaf-1 dATP/ATP CytochromeC Apoptotic_Stimuli Bax_Bad_Bim Mitochondrion BidC-Terminal Bid Caspase-8 Procaspase-8 FADD Fas-Ligand

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 41 / 52

Qualitative Analyses, Summary ❑ three minimal positive T - invariants

  • > three basic behaviours ,
  • > any net behaviour =

linear combination of them ❑ the net is covered by T - invariants

  • > no idle parts

❑ reproducible empty marking

  • > cyclic behaviour possible (reversability)

❑ coverability graph (Karp - Miller)

  • > 8121 nodes
  • > no dead states

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

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 42 / 52

INTEGRATION OF QUANTITATIVE ANALYSES ❑

DISCRETE TIME

❑

CONTINEOUS TIME

m4 tCont p4Cont p1Cont p2Cont p3Cont tCont m1 m2 p1Cont p3Cont tCont m1 m2 m1 tCont p3Cont p2Cont p1Cont t p3 p2 p1 v = k * m1 v = k * m1 * m2 m3 v1 = k1 * m1 * m2 v2 = k2 * m3 d [p1Cont] / dt = d [p2Cont] / dt = - v1 d [p4Cont] / dt = v2 d [p3Cont] / dt = v1 - v2 duration, interval

  • > SELF-MODIFYING PETRI NETS

const [min, max]

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 43 / 52

MICHAELIS-MENTEN REACTION

[GENOMIC OBJECT NET]

50 100 150 200 t 0,03333 0,06667 0,1 m 1 50 100 150 200 t 0,03333 0,06667 0,1 m 2

m1 s m2 p m3 e T 0.005*m1/(0.1375+m1) Vmax = 0.005 (maximal reaction rate) Km = 0.1375 (Michaelis constant) d[s]/dt = d[p]/dt = Vmax*[s] / ( Km+[s] )

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 44 / 52

GENOMIC OBJECT NET [MATSUNO ET AL. 200X]

http://www.genomicObject.net

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 45 / 52

5. SUMMARY

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 46 / 52

MASTERING COMPLEXITY 2 ❑ step-wise model development for

  • > animation
  • > validation
  • > (qualitative) analysis
  • > (quantitative) simulation

❑ integration of

  • > model validation
  • > behaviour prediction

❑ one all-purpose model

  • > animation model
  • > “qualitative model = animation model”
  • > “quantitative model =

qualitative model + quantitative paramter”

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 47 / 52

APPLICATIONS

OF BIO PETRI NETS,

SUMMARY (1) step-wise construction

  • f graphical (=visual) models

(2) graphical model animation (3) validation of model integrity (4) qualitative analyses

  • f biological / bio-technological questions

(5) quantitative analyses

  • f biological / bio-technological questions
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 48 / 52

6. OUTLOOK

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 49 / 52

TYPICAL PETRI NET QUESTIONS ❑ How many tokens may reside at most in a given place ?

  • > (0, 1, k, oo)
  • > BOUNDEDNESS

❑ How often may a transition fire ?

  • > (0-times, n-times, oo-times)
  • > LIVENESS

❑ Is a given system state . . .

  • > always reachable again?
  • > PROGRESS PROPERTIES
  • > never reachable?
  • > SAFETY PROPERTIES

❑ Are there behavourally invariant structures?

  • > token conservation
  • > P - INVARIANTS
  • > token distribution reproduction
  • > T - INVARIANTS
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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 50 / 52

QUALITATIVE ANALYSIS TECHNIQUES

REACHABILITY ANALYSIS (complete) reachability graph reduced state spaces coverability graph symmetry stubborn / sleep sets NET REDUCTION STRUCTURAL PROPERTIES LINEAR PROGRAMMING place / transition invariants state / trap equation static dynamic analysis analysis compressed state spaces OBDDs, ONDDS Kronecker products branching processes (model checking) concurrent automaton

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Biopathways & Petri Nets September 2002 mh@informatik.tu-cottbus.de, ikoch@tfh-berlin.de 51 / 52

TOOL OVERVIEW

analysis protocols qualitative

PED

qualitative Petri net analyzers

PROD INA

quantitative Petri net analyzers

analysis protocols quantitative motion

execution tool

FUNLite

protocols execution lib

hierarchy browser

(distributed) animation tool

protocols functional testing informal specification safety requirements performance requirements

INA

(non-stochastic)

TimeNet

(stochastic)

hierarchical Petri Net Editor with output filters

PEP

functional requirements (rapid prototyping)

PEDVisor SMV

(UNCOMPLETE)

slide-52
SLIDE 52

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

MODEL CLASSES

context checking by Petri net theory verification by temporal logics worst-case evaluation performance prediction reliability prediction

PETRI NETS

PLACE/TRANSITION

(COLOURED PN)

TIME-DEPENDENT PN DISCRETE STOCHASTIC

PETRI NET PETRI NET PETRI NET

CONTINUOUS

PETRI NET