Dynamics and bifurcation analysis of the heat-shock response in eukaryotic cells

The heat-shock response mechanism in eukaryotic cells is one of the most important survival features of living organisms and comprises a genetic network coordinating the cellular response to protein damage. The importance and function of the heat-shock transcription factor-1 (HSF-1), which is central to the
heat-shock response mechanism, has been studied extensively, as documented in numerous publications. Detailed network representations and dynamic mathematical models have been derived and tested in order to analyze quantitatively all species and their concentrations in the heat-shock response cycle. Furthermore, parameter estimation and sensitivity analysis have provided additional insight regarding the relative importance of a large number of kinetic parameters within the respective expression networks. This paper focuses on analyzing the importance of an uncertain, temperature-dependent parameter (βm,k). A bifurcation analysis is conducted in order to identify and analyze multiple steady states of the system.