  Environmental stress, such as oxidative or heat stress, induces the
activation of the Heat Shock Response (HSR) which leads to an increase in the
heat shock proteins (HSPs) level. These HSPs act as molecular chaperones to
maintain proteostasis. Even if the main heat shock response partners are well
known, a detailed description of the dynamical properties of the HSR network is
still missing. In this study, we derive a minimal mathematical model of
cellular response to heat shock that reproduces available experimental data
sets both on transcription factor activity and cell viability. This simplistic
model highlights the key mechanistic processes that rule the HSR network and
reveals (i) the titration of Heat Shock Factor 1 (HSF1) by chaperones as the
guiding line of the network, (ii) that protein triage governs the fate of
damaged proteins and (iii) three different temperature regimes describing
normal, acute or chronic stress.
