Computational Heuristics for Simplifying a Biological Model

  • Ion Petre
  • Andrzej Mizera
  • Ralph-Johan Back
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5635)


Computational biomodelers adopt either of the following approaches: build rich, as complete as possible models in an effort to obtain very realistic models, or on the contrary, build as simple as possible models focusing only on the core aspects of the process, in an effort to obtain a model that is easier to analyze, fit, and validate. When the latter strategy is adopted, the aspects that are left outside the models are very often up to the subjective options of the modeler. We discuss in this paper a heuristic method to simplify an already fit model in such a way that the numerical fit to the experimental data is not lost. We focus in particular on eliminating some of the variables of the model and the reactions they take part in, while also modifying some of the remaining reactions. We illustrate the method on a computational model for the eukaryotic heat shock response. We also discuss the limitations of this method.


Model reduction heat shock response mathematical model 


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  1. 1.
    Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Essential Cell Biology, 2nd edn. Garland Science (2004)Google Scholar
  2. 2.
    Ciocca, D.R., Calderwood, S.K.: Heat shock proteins in cancer: diagnostic, prognostic, predictive, and treatment implications. Cell Stress and Chaperones 10(2), 86–103 (2005)CrossRefGoogle Scholar
  3. 3.
    El-Samad, H., Kurata, H., Doyle, J., Gross, C.A., Khamash, M.: Surviving heat shock: control strategies for robustness and performance. PNAS 102(8), 2736–2741 (2005)CrossRefGoogle Scholar
  4. 4.
    El-Samad, H., Prajna, S., Papachristodoulu, A., Khamash, M., Doyle, J.: Model validation and robust stability analysis of the bacterial heat shock response using sostools. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 3766–3741 (2003)Google Scholar
  5. 5.
    Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., Kummer, U.: Copasi – a COmplex PAthway SImulator. Bioinformatics 22(24), 3067–3074 (2006)CrossRefGoogle Scholar
  6. 6.
    Kampinga, H.K.: Thermotolerance in mammalian cells: protein denaturation and aggregation, and stress proteins. J. Cell Science 104, 11–17 (1993)Google Scholar
  7. 7.
    Kline, M.P., Morimoto, R.I.: Repression of the heat shock factor 1 transcriptional activation domain is modulated by constitutive phosphorylation. Molecular and Cellular Biology 17(4), 2107–2115 (1997)CrossRefGoogle Scholar
  8. 8.
    Kurata, H., El-Samad, H., Yi, T.M., Khamash, M., Doyle, J.: Feedback regulation of the heat shock response in e.coli. In: Proceedings of the 40th IEEE Conference on Decision and Control, pp. 837–842 (2001)Google Scholar
  9. 9.
    Liu, B., DeFilippo, A.M., Li, Z.: Overcomming immune toerance to cancer by heat shock protein vaccines. Molecular cancer therapeutics 1, 1147–1151 (2002)Google Scholar
  10. 10.
    Lukacs, K.V., Pardo, O.E., Colston, M.J., Geddes, D.M., Eric WFW Alton: Heat shock proteins in cancer therapy. In: Habib (ed.) Cancer Gene Therapy: Past Achievements and Future Challenges, pp. 363–368 (2000)Google Scholar
  11. 11.
    Peper, A., Grimbergent, C.A., Spaan, J.A.E., Souren, J.E.M., van Wijk, R.: A mathematical model of the hsp70 regulation in the cell. Int. J. Hyperthermia 14, 97–124 (1997)CrossRefGoogle Scholar
  12. 12.
    Lepock, J.R., Frey, H.E., Ritchie, K.P.: Protein denaturation in intact hepatocytes and isolated cellular organelles during heat shock. The Journal of Cell Biology 122(6), 1267–1276 (1993)CrossRefGoogle Scholar
  13. 13.
    Lepock, J.R., Frey, H.E., Rodahl, A.M., Kruuv, J.: Thermal analysis of chl v79 cells using differential scanning calorimetry: Implications for hyperthermic cell killing and the heat shock response. Journal of Cellular Physiology 137(1), 14–24 (1988)CrossRefGoogle Scholar
  14. 14.
    Petre, I., Mizera, A., Hyder, C.L., Mikhailov, A., Eriksson, J.E., Sistonen, L., Back, R.-J.: A new mathematical model for the heat shock response. In: Kok, J. (ed.) Algorithmic bioprocesses, Natural Computing. Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Petre, I., Hyder, C.L., Mizera, A., Mikhailov, A., Eriksson, J.E., Sistonen, L., Back, R.-J.: A simple mathematical model for the eukaryotic heat shock response (manuscript, 2009)Google Scholar
  16. 16.
    Graham Pockley, A.: Heat shock proteins as regulators of the immune response. The Lancet 362(9382), 469–476 (2003)CrossRefGoogle Scholar
  17. 17.
    Rieger, T.R., Morimoto, R.I., Hatzimanikatis, V.: Mathematical modeling of the eukaryotic heat shock response: Dynamics of the hsp70 promoter. Biophysical Journal 88(3), 1646–1658 (2005)CrossRefGoogle Scholar
  18. 18.
    Tomlin, C.J., Axelrod, J.D.: Understanding biology by reverse engineering the control. PNAS 102(12), 4219–4220 (2005)CrossRefGoogle Scholar
  19. 19.
    Workman, P., de Billy, E.: Putting the heat on cancer. Nature Medicine 13(12), 1415–1417 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ion Petre
    • 1
  • Andrzej Mizera
    • 1
  • Ralph-Johan Back
    • 1
  1. 1.Department of Information TechnologiesÅbo Akademi University, Computational Biomodeling Laboratory, Turku Centre for Computer ScienceTurkuFinland

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