ipetre@abo.fi

1. Ion PETRE Computational Biomodelling Laboratory Turku Centre for Computer Science (TUCS) http://combio.abo.fi/ ipetre@abo.fi Mathematical models for the heat shock response in eukaryotes Joint work with • C.Seceleanu (TUCS) • D.Preoteasa (Math) • A.Pada (TUCS) • S.Saxen (TUCS) • K.Nylund (TUCS) • H. Ogoe (TUCS) • R.Back (TUCS) • J.Eriksson (BTK) • L.Sistonen (BTK) • A.Mikhailov (BTK) • C. Hyder (BTK)

2. Starting point • Rieger, Morimoto, Hatzimanikatis – Mathematical modeling of the eukaryotic heat shock response: Dynamics of the hsp70 promoter, Biophys J BioFAST, 2004 • Key elements in the model • HSP • HSF • HSE • Stress kinase (switched on by a stimulus signal) • Model • the stimulus signal switches the stress kinase S from inactive to active (S*)  the stress is thus proportional to the relative catalytic activity of the kinase that activates S over the phosphatase that inactivates S • HSF trimers bind to HSE and is then phosphorylated by S*  elevated transcription of the hsp mRNAs • Backregulation 1: HSP binds to HSF:HSE, HSF is then dephosphorylated and then unbinds from the DNA • Backregulation 2: HSP binds and sequesters free HSF  they are unable to trimerize and bind to DNA • Regulation 3: stability of hsp mRNAs is increased because of the stress • Conserved quantities: HSFtot, HSEtot, Stot, Itot (stress phosphatase) Heat shock response in Eukaryotes

3. Our model • Central elements • Heat shock proteins (HSP) – function as molecular chaperones • Heat shock transcription factor (HSF) – regulates the transcription of the HSP species, binds to a promoter site (HSE) of the HSP-encoding genes • Heat shock element (HSE) – the promoter site where HSF binds • Misfolded proteins (MFP) – induced through exposure to stress • We do not consider the stress stimulus and the stress kinase • The stress for us is the elevated temperature that contributes to elevated levels of MFP • What is the typical misfolding rate depending on temperature? Heat shock response in Eukaryotes

4. Heat shock response - model • Transcription mechanism for HSP • HSF trimerizes • HSF trimers binds to HSE (HSF:HSE), become phosphorylated (not modeled explicitly) and induces the transcription of the HSP-encoding genes • Transcription regulation • HSP binds to free HSF  trimerization of HSF shut down because of lack of free HSF • HSP binds to HSF:HSE unbinding HSF from HSE • Response to stress • Proteins misfolded: MFPs created • HSP as a chaperone to MFP • HSF becomes free and available for trimerization • More HSP mRNAs translated Heat shock response in Eukaryotes

5. Transcription HSF+HSFHSF2 (rev) HSF+HSF2HSF3 (rev) HSF3+HSEHSF3:HSE HSF3:HSEHSF3:HSE+HSP Backregulation HSP+HSFHSP:HSF (rev) HSP+HSF2HSP:HSF+HSF HSP+HSF3HSP:HSF+2HSF HSP+HSF3:HSEHSP:HSF+2HSF+HSE Response to stress PROT+TempMFP HSP+MFPHSP:MFP HSP:HSF+MFPHSP:MFP+HSF HSP:MFPHSP+PROT Protein degradation HSP0 HSP:HSFHSF MFP0 Our model – see the reactions drawn in CellDesigner Heat shock response in Eukaryotes

6. Model dynamics • No stress • No (or very little) HSP mRNA transcription takes place • HSP and HSF are in an equilibrium so that very few HSF trimers exist in the system  most HSFs are sequestered by HSPs • Stress • Early stages • The MFP level starts to build up • The free HSP starts binding to MFP • The HSPs in the complexes HSP:HSF start unbinding from HSF and bind to MFP • Induction of HSP • Free HSF accumulates and is able to trimerize • HSF trimers bind to HSE and induce HSP mRNA transcription • HSP level starts to build up, MFP level continues to build up • If the stress is not too severe, the HSP level catches up with the MFP level • Backregulation • Once the HSP level is high enough, available HSPs start binding to HSF (both free and bound to DNA) and shut down the HSP mRNAs transcription • There are not enough free HSFs to trimerize • Exposure to prolonged stress • After a while, the HSP molecules start being naturally degraded, while the level of MFPs is continuously increased • HSFs again find themselves free, induce the transcription of more HSPs • Some oscillations appear, with shorter amplitude as time goes Heat shock response in Eukaryotes

7. Differences with respect to Rieger et al • Hest shock simulated in Rieger et al through a stimulus signal that switches the stress kinase active • In our case, elevated temperature induces misfolding of proteins, which triggers a reaction from HSPs, freeing HSFs, which in turn induce more HSPs • Trimerization of HSF not modeled explicitly in Rieger et al • We model it explicitly through formation of dimers first and then trimers – simulations show that it is possible to have significant levels of trimers or monomers, while having low levels of dimers Heat shock response in Eukaryotes

8. Differences with respect to Rieger et al • Activation of HSF once bound to HSE is modeled in Rieger et al through binding of the active stress kinase, phosphorylating the HSF • Phosphorylation not modeled explicitly in our model; a certain (fixed in this version) percentage of all HSF3:HSE are assumed to be active • Possible to add modeling of the phosphorylation and variation in the level of phosphorylation depending on the heat stress • Consider the phosphatase and the kinase and how their relative activity is affected by stress • mRNA explicitly modeled in Rieger et al • Not modeled explicitly in our case • To simplify things we consider that HSF3:HSE yields HSPs directly (with a suitable delay/reaction speed) • Degradation of HSP not modeled explicitly in Rieger et al • Modeled in our case  allows us to run long simulations Heat shock response in Eukaryotes

9. Assumptions, constraints • Conserved quantities • Total HSF • Total HSE • HSP is long lived (half life of around 6 hours) • HSF is present in excess compared to HSE (1500 to 30) • At the peak of the heat shock response, most HSEs are occupied Heat shock response in Eukaryotes

10. Mathematical model • Model 1 • All reactions modeled through mass action kinetics • 15 reactions: 3 reversible reactions, 9 irreversible reactions , 3 degradation reactions • Model 2 • All reactions modeled through independent stochastic events Heat shock response in Eukaryotes

11. Experimental data • Quantitative data • GFP-encoding genes controlled by HSE promoter sites transfected in the cell culture • GFP used as a reporter for HSP • Measured the fluorescence intensity of GFP • Qualitative data • Very low level of HSF dimers even in the presence of high levels of HSF monomers and trimers • Phosphorylation curve: transiently goes up with stress Heat shock response in Eukaryotes

12. Comparing with the experimental data • Simulated HSF dimer level – as expected • Simulated level of GFP agrees qualitatively with the experimental data gated for fluorescence intensity over 300 • The predicted variation in the phosphorylation levels under constant stress seems to agree qualitatively with the experimental data (?) Heat shock response in Eukaryotes

13. Heat shock response in Eukaryotes

14. Additions to the model • Adding the GFP • Transcription of GFP-encoding genes controlled similarly as that of the HSP-encoding genes through HSF binding to HSE • GFP translated under stress as a misfolded protein, needs HSP to fold properly, after which it remains stable • Half-life of GFP shorter than that of HSP • Compared the simulated levels of GFP with the experimental data Heat shock response in Eukaryotes

15. Additions: phosphorylation • Phosphorylation controlled through kinases and phosphatases • Assumption: phosphatase (for HSF) more sensitive to heat than kinase (for HSF) • Under stress the balance between phosphatases and kinases changes towards kinases; this results in a high level of phosphorylation leading to activation of HSF • After a while, with HSPs being produced, phosphatases get refolded thus changing again the balance with respect to kinases and lowering the activation level of HSF • This suggest yet another control level for the stress-induced transcription of HSP-encoding genes, including variable transcription rate through the heat shock response • Low speed in the early phase, high with prolonged heat, lower speed later in the response, even if the heat is not changed • It then oscillates through long exposure to heat, with smaller and smaller amplitudes • Not yet implemented in the model Heat shock response in Eukaryotes