Biologically sound formal model of Hsp70 heat induction

A proper response to rapid environmental changes is essential for cell survival and requires efficient modifications in the pattern of gene expression. In this respect, a prominent example is Hsp70, a chaperone protein whose synthesis is dynamically regulated in stress conditions. In this paper, we expand a formal model of Hsp70 heat induction originally proposed in previous articles. To accurately capture various modes of heat shock effects, we not only introduce temperature dependencies in transcription to Hsp70 mRNA and in dissociation of transcriptional complexes, but we also derive a new formal expression for the temperature dependence in protein denaturation. We calibrate our model using comprehensive sets of both previously published experimental data and also biologically justified constraints. Interestingly, we obtain a biologically plausible temperature dependence of the transcriptional complex dissociation, despite the lack of biological constraints imposed in the calibration process. Finally, based on a sensitivity analysis of the model carried out in both deterministic and stochastic settings, we suggest that the regulation of the binding of transcriptional complexes plays a key role in Hsp70 induction upon heat shock. In conclusion, we provide a model that is able to capture the essential dynamics of the Hsp70 heat induction whilst being biologically sound in terms of temperature dependencies, description of protein denaturation and imposed calibration constraints.