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A minimal titration model of the mammalian dynamical heat shock response

Environmental stress, such as oxidative or heat stress, induces the activation of the heat shock response (HSR) and leads to an increase in the heat shock proteins (HSPs) level. These HSPs act as molecular chaperones to maintain cellular proteostasis. Controlled by highly intricate regulatory mechanisms, having stress-induced activation and feedback regulations with multiple partners, the HSR is still incompletely understood. In this context, we propose a minimal molecular model for the gene regulatory network of the HSR that reproduces quantitatively different heat shock experiments both on heat shock factor 1 (HSF1) and HSPs activities. This model, which is based on chemical kinetics laws, is kept with a low dimensionality without altering the biological interpretation of the model dynamics. This simplistic model highlights the titration of HSF1 by chaperones as the guiding line of the network. Moreover, by a steady states analysis of the network, three different temperature stress regimes appear: normal, acute, and chronic, where normal stress corresponds to pseudo thermal adaption. The protein triage that governs the fate of damaged proteins or the different stress regimes are consequences of the titration mechanism. The simplicity of the present model is of interest in order to study detailed modelling of cross regulation between the HSR and other major genetic networks like the cell cycle or the circadian clock.