A mathematical model of heat shock response to study the competition between protein folding and aggregation

Abstract

Proteins, under conditions of cellular stress, typically tend to unfold and form lethal aggregates leading to neurological diseases like Parkinson’s and Alzheimer’s. A clear understanding of the conditions that favor dis-aggregation and restore the cell to its healthy state after they have been stressed is therefore important in dealing with these diseases. The heat shock response (HSR) mechanism is a signaling network that deals with these undue protein aggregates and aids in the maintenance of homeostasis within a cell. This framework, on its own, is a mathematically well studied mechanism. However, not much is known about how the various intermediate mis-folded protein states of the aggregation process interact with some of the key components of the HSR pathway such as the Heat Shock Protein (HSP), the Heat Shock transcription Factor (HSF) and the HSP-HSF complex. In this article, using kinetic parameters from the literature, we propose and analyze two mathematical models for HSR that also include explicit reactions for the formation of protein aggregates. Deterministic analysis and stochastic simulations of these models show that the folded proteins and the misfolded aggregates exhibit bistability in a certain region of the parameter space. Further, the models also highlight the role of HSF and the HSF-HSP complex in reducing the time lag of response to stress and in re-folding all the mis-folded proteins back to their native state. These models therefore call attention to the significance of studying related pathways such as the HSR and the protein aggregation and re-folding process in conjunction with each other.