Computational Biomodelling Lab. Department of Information Technologies, Åbo Akademi University, Turku, Finland Heat shock response & Petri-net

2 The molecular model (Ion Petre et. al) Transcription 1. HSF+HSF HSF 2 2. HSF+HSF 2 HSF 3 3. HSF 3 +HSE HSF 3 :HSE 4. HSF 3 :HSE->HSF 3 :HSE+HSP Backregulation 5. HSP+HSF HSP:HSF 6. HSP+HSF 2 ->HSP:HSF+HSF 7. HSP+HSF 3 ->HSP:HSF+2HSF 8. HSP+HSF 3 :HSE->HSP:HSF+2HSF+HSE Response to stress 9. PROT->MFP 10. HSP+MFP HSP:MFP 11. HSP:MFP->HSP+PROT Protein degradation 12. HSP  0

3 Petri-net Gene-net place transition Reactions tokens metabolites HSF HSF2 HSF:HSF2 HSF+HSF2->HSF3 # of o o o o o o

4 Types of reactions into Petri-net 2HSF -> HSF 2 HSF 3 +HSE ->HSF 3 :HSE HSP+HSF 2 ->HSP:HSF+HSF HSF 3 :HSE->HSF 3 :HSE+HSP PROT->MFP (rewriting) HSP  0 (degradation) HSF+HSF 2 HSF 3 (reverse) 2 k

5 transition Reaction HSF:HSF2 transition HSF+HSF2->HSF3->HSF+HSF2 o o o o o o

6 translation

7 A Petri-net for the HSR model 37C42C

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