Computational Biomodelling Lab. Department of Information Technologies,Åbo Akademi University, 20520 Turku, Finland

Heat shock response & Petri-net

2

The molecular model (Ion Petre et. al)

Transcription

1. HSF+HSF<->HSF2

2. HSF+HSF2<->HSF3

3. HSF3+HSE<->HSF3:HSE

4. HSF3:HSE->HSF3:HSE+HSP

Backregulation

5. HSP+HSF<->HSP:HSF6. HSP+HSF2->HSP:HSF+HSF

7. HSP+HSF3->HSP:HSF+2HSF

8. HSP+HSF3:HSE->HSP:HSF+2HSF+HSE

Response to stress

9. PROT->MFP10.HSP+MFP<->HSP:MFP11.HSP:MFP->HSP+PROT

Protein degradation

12.HSP0

3

Petri-net <=> Gene-net

place transition

Reactions

tokens

metabolites

HSF

HSF2 HSF:HSF2

HSF+HSF2->HSF3

# of

o o o

o o

o

o

o o

4

Types of reactions into Petri-net

• 2HSF -> HSF2

• HSF3+HSE ->HSF3:HSE

• HSP+HSF2->HSP:HSF+HSF

• HSF3:HSE->HSF3:HSE+HSP

• PROT->MFP (rewriting)

• HSP0 (degradation)

• HSF+HSF2<-> HSF3 (reverse)

2

k

5

transition

Reaction

HSF:HSF2

transition

HSF+HSF2->HSF3 ->HSF+HSF2

o

o

o o

o o

o o o

6

translation

7

A Petri-net for the HSR model

37C 42C

8

Incidence matrice 10x17

9

Place invariant, Transition invariant

P-invariant: x is a non-zero vector of size n (n=10)

T-invariant: y is size of m (m=17)

10

P-invariant

*A P-invariant characterizes a token conservation rule for a set of places

*An inv. x is minimal, if any inv. z: supp(z) is not subset of supp(x)

- inv. 3 is minimal

Deadlock…

11

T-invariant

trivial

HS

A T-invariant represents a multiset of transitions, which have altogether a zero effect on the marking