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A simple mass-action model for the eukaryotic heat shock response and its mathematical validation

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Abstract

The heat shock response is a primordial defense mechanism against cell stress and protein misfolding. It proceeds with the minimum number of mechanisms that any regulatory network must include, a stress-induced activation and a feedback regulation, and can thus be regarded as the archetype for a cellular regulatory process. We propose here a simple mechanistic model for the eukaryotic heat shock response, including its mathematical validation. Based on numerical predictions of the model and on its sensitivity analysis, we minimize the model by identifying the reactions with marginal contribution to the heat shock response. As the heat shock response is a very basic and conserved regulatory network, our analysis of the network provides a useful foundation for modeling strategies of more complex cellular processes.

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References

  • Abravaya K, Philips B, Morimoto RI (1991) Attenuation of the heat-shock response in Hela-cells is mediated by the release of bound heat-shock transcription factor and is modulated by changes in growth and in heat-shock temperatures. Genes Dev 5(11):2117–2127

    Article  Google Scholar 

  • Abravaya K, Myers M, Murphy S, Morimoto RI (1992) Human heat shock protein HSP70 interacts with HSF, the transcription factor that regulates heat shock gene expression. Genes Dev 6:1153–1164

    Article  Google Scholar 

  • Balch WE, Morimoto RI, Dillin A, Kelly JW (2008) Adapting proteostasis for disease intervention. Science 319:916–919

    Article  Google Scholar 

  • Ballew RM, Sabelko J, Gruebele M (1996) Direct observation of fast protein folding: the initial collapse of apomyoglobin. Proc Natl Acad Sci USA 93:5759-64

    Article  Google Scholar 

  • Chen Y, Voegli TS, Liu PP, Noble EG, Currie RW (2007) Heat shock paradox and a new role of heat shock proteins and their receptors as anti-inflammation targets. Inflamm Allergy Drug Targets 6(2):91–100

    Article  Google Scholar 

  • Chen WW, Schorberl B, Jasper PJ, Niepel M, Nielsen UB, Lauffenburger DA, Sorger PK (2009) Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol Syst Biol 5:1–19

    Google Scholar 

  • Ciocca DR, Calderwood SK (2005) Heat shock proteins in cancer: diagnostic, prognostic, predictive, and treatment implications. Cell Stress Chaperones 10(2):86–103

    Article  Google Scholar 

  • Donati YRA, Slosman DO, Polla BS (1990) Oxidative injury and the heat shock response. Biochem Pharmacol 40:2571–2577

    Article  Google Scholar 

  • El Samad H, Kurata H, Doyle JC, Gross CA, Khammash M (2005) Surviving heat shock: control strategies for robustness and performance. Proc Natl Acad Sci USA 102(8):2736–2741

    Article  Google Scholar 

  • Guldberg CM, Waage P (1864) Studies concerning affinity. C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 35

  • Guldberg CM, Waage P (1879) Concerning chemical affinity. Erdmann’s Journal fr Practische Chemie 127:69–114

    Article  Google Scholar 

  • Helton JC, Davis FJ (2002) Illustration of sampling-based methods for uncertainty and sensitivity analysis. Risk Anal 22(3):591–622

    Article  Google Scholar 

  • Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81:23–69

    Article  Google Scholar 

  • Holmberg CI, Tran SE, Eriksson JE, Sistonen L (2002) Multisite phosphorylation provides sophisticated regulation of transcription factors. Trends Biochem Sci 27(12):619–627

    Article  Google Scholar 

  • Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI—a COmplex PAthway SImulator. Bioinformatics 22:3067–3074

    Article  Google Scholar 

  • Jones CM, Henry ER, Hu Y, Chan C, Luck SD, Bhuyan A, Roder H, Hofrichter J, Eaton WA, et al. (1993) Fast events in protein folding initiated by nanosecond laser photolysis. Proc Natl Acad Sci USA 90:11860–64

    Article  Google Scholar 

  • Kline MP, Morimoto RI (1997) Repression of the heat shock factor 1 transcriptional activation domain is modulated by constitutive phosphorylation. Mol Cell Biol 17(4):2107–2115

    Google Scholar 

  • Lepock JR, Frey HE, Ritchie KP (1993) Protein denaturation in intact hepatocytes and isolated cellular organelles during heat shock. J Cell Biol 122(6):1267–1276

    Article  Google Scholar 

  • Lipan O, Navenot J-M, Wang Z, Huang L, Peiper SC (2007) Heat shock response in CHO mammalian cells is controlled by a nonlinear stochastic process. PLoS Comput Biol 3(10):1859–1870

    Article  MathSciNet  Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239-245

    Google Scholar 

  • Morimoto RI (1998) Regulation of the heat shock transcriptional response: cross talk between a family of heat shock factors, molecular chaperones, and negative regulators. Genes Dev 12:3788–3796

    Article  Google Scholar 

  • Morimoto RI (2008) Proteotoxic stress and inducible chaperone networks in neurodegenerative disease and aging. Genes Dev 22:1427–1438

    Article  Google Scholar 

  • Morimoto RI, Jurivich DA, Kroger PE, Mathur SK, Murphy SP, et al (1994) Regulation of heat shock gene transcription by a family of heat shock factors. In: Morimoto RI, Tissières A, Georgopoulos C (eds) The biology of the heat shock proteins and molecular chaperones. Cold Spring Harbor Laboratory, New York, pp. 417–455

  • Oberguggenberger M, King J, Schmelzer B (2009) Classical and imprecise probability methods for sensitivity analysis in engineering: a case study. Int J Approx Reason 50:680-693

    Article  Google Scholar 

  • Parsell DA, Lindquist S (1993) The function of heat-shock proteins in stress tolerance: degradation and reactivation of damaged proteins. Ann Rev Genetics 27:437–496

    Article  Google Scholar 

  • Peper A, Grimbergen CA, Spaan JAE, Souren JEM, van Wijk R (1997) A mathematical model of the hsp70 regulation in the cell. Int J Hyperth 14(1):97–124

    Article  Google Scholar 

  • Petre I, Mizera A, Hyder CL, Mikhailov A, Eriksson JE, Sistonen L, Back R-J (2009) A new mathematical model for the heat shock response. In: Condon A, Harel D, Kok J, Salomaa A (eds) Algorithmic bioprocesses. Springer, New York, pp. 411–428

  • Pockley AG (2003) Heat shock proteins as regulators of the immune response. The Lancet 362(9382):469–476

    Article  Google Scholar 

  • Powers MV, Workman P (2007) Inhibitors of the heat shock response: biology and pharmacology. FEBS Lett 581(19):3758–3769

    Article  Google Scholar 

  • Remondini D, Bernardini C, Forni M, Bersani F, Castellani GC, Bacci ML (2006) Induced metastable memory in heat shock response. J Biol Phys 32:49–59

    Article  Google Scholar 

  • Rieger TR, Morimoto RI, Hatzimanikatis V (2005) Mathematical modeling of the eukaryotic heat shock response: dynamics of the Hsp70 promoter. Biophys J 88:1646–1658

    Article  Google Scholar 

  • Shi Y, Mosser D, Morimoto RI (1998) Molecular chaperones as HSF1 specific transcriptional repressors. Genes Dev 12:654–666

    Article  Google Scholar 

  • Srivastava R, Peterson MS, Bentley WE (2001) Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32-trageted antisense. Biotechnol Bioeng 75(1):120–129

    Article  Google Scholar 

  • Szymańska Z, Zylicz M (2009) Mathematical modeling of heat shock protein synthesis in response to temperature change. J Theoret Biol 259:562–569

    Article  Google Scholar 

  • Turanyi T (1990) Sensitivity analysis of complex kinetic systems—tools and applications. J Math Chem 5(3):203–248

    Article  MathSciNet  Google Scholar 

  • Vastag B (2006) HSP-90 inhibitors promise to complement cancer therapies. Nat Biotechnol 24(11):1307

    Article  Google Scholar 

  • Voellmy R (1994) Transduction of the stress signal and mechanisms of transcriptional regulation of heat shock/stress protein gene expression in higher eukaryotes. Crit Rev Eukaryot Gene Expr 4:357–401

    Google Scholar 

  • Voellmy R, Boellmann F (2007) Chaperone regulation of the heat shock protein response. Adv Exp Med Biol 594:89–99

    Article  Google Scholar 

Download references

Acknowledgments

This work has been partially supported by the following grants from Academy of Finland: project 108421 (IP), project 203667 (A.Mizera), the Center of Excellence on Formal Methods in Programming (R-J.B.).

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Correspondence to Ion Petre.

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Petre, I., Mizera, A., Hyder, C.L. et al. A simple mass-action model for the eukaryotic heat shock response and its mathematical validation. Nat Comput 10, 595–612 (2011). https://doi.org/10.1007/s11047-010-9216-y

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