A New Mathematical Model for the Heat Shock Response

The phosphorylation of the heat shock factor as a modulator for the heat shock response

The heat shock response is a well-conserved defence mechanism against the accumulation of misfolded proteins due to prolonged elevated heat. The cell responds to heat shock by raising the levels of heat shock proteins (hsp), which are responsible for chaperoning protein refolding. The synthesis of hsp is highly regulated at the transcription level by specific heat shock (transcription) factors (hsf). One of the regulation mechanisms is the phosphorylation of hsf's. Experimental evidence shows a connection between the hyper-phosphorylation of hsfs and the transactivation of the hsp-encoding genes. In this paper, we incorporate several (de)phosphorylation pathways into an existing well-validated computational model of the heat shock response. We analyze the quantitative control of each of these pathways over the entire process. For each of these pathways we create detailed computational models which we subject to parameter estimation in order to fit them to existing experimental data. In particular, we find conclusive evidence supporting only one of the analyzed pathways. Also, we corroborate our results with a set of computational models of a more reduced size.

Stochastic modelling of the eukaryotic heat shock response

The heat shock response (HSR) is a highly evolutionarily conserved defence mechanism allowing the cell to promptly react to elevated temperature conditions and other forms of stress. It has been subject to intense research for at least two main reasons. First, it is considered a promising candidate for deciphering the engineering principles underlying regulatory networks. Second, heat shock proteins (main actors of the HSR) play crucial role in many fundamental cellular processes. Therefore, profound understanding of the heat shock response would have far-reaching ramifications for the cell biology. Recently, a new deterministic model of the eukaryotic heat shock response has been proposed in the literature. It is very attractive since it consists of only the minimum number of components required by any functional regulatory network, while yet being capable of biological validation. However, it admits small molecule populations of some of the considered metabolites. In this paper a stochastic model corresponding to the deterministic one is constructed and the outcomes of these two models are confronted. The aim with this comparison is to show that, in the case of the heat shock response, the approximation of a discrete system with a continuous model is a reasonable approach. This is not always the truth, especially when the numbers of molecules of the considered species are small. By making the effort of performing and analysing 1000 stochastic simulations, we investigate the range of behaviour the stochastic model is likely to exhibit. We demonstrate that the obtained results agree well with the dynamics displayed by the continuous model, which strengthens the trust in the deterministic description. A proof of the existence and uniqueness of the stationary distribution of the Markov chain underlying the stochastic model is given. Moreover, the obtained view of the stochastic dynamics and the performed comparison to the outcome of the continuous formulation provide more insight into the dynamics of the heat shock response mechanism.