Mathematical modeling and analysis of the heat shock protein response during thermal stress in fish and HeLa cells.

The climate change has the potential to dramatically affect species' thermal physiology and may change the ecology and evolution of species' lineages. In this work, we investigated the transition of dynamics in the heat shock response when the thermal stress approaches the upper thermal limits of species to understand how the climate change may affect the heat shock responses in ectotherms and endotherms. The heat shock protein 70, HSP70, prevents protein denaturation or misfolding under thermal stresses. When thermal stress increases, the number of misfolded proteins increases, which leads to high levels of HSP70 protein. However, when temperatures approach limits of thermal tolerance (i.e., the critical thermal maximum, CTmax, for ectotherms and the superior critical temperature, SCT, for endotherms), levels of HSP70 protein synthesis start to decrease. Thus, we hypothesized that the temperature at the first reduction of HSP abundance indicates the thermal limits of the species. In this work, we provide a mathematical model to investigate the behavior of the heat shock responses related to HSP70 protein. This model captures the dynamics of HSP70 protein and Hsp70 mRNA, in HeLa cells (i.e., representative for endotherms) and multiple species of fishes (i.e., representative for ectotherms) with different acclimation histories. Based on our hypothesis of the relationship between the HSP70 protein level and CTmax/SCT, our model provides three methods to predict the CTmax of fishes with varying acclimation temperature and the SCT of HeLa cells. The CTmax increases as the acclimation temperature increases in fishes, however the CTmax plateaus when the acclimation temperature is higher than 20°C in brook trout, a representative cool water salmonid. Our model also captures the situation that the heat shock reaction in fish is more sensitive to the heat shock temperature than HeLa cells, when the heat shock temperature is lower than the upper thermal tolerance. However, both fish and HeLa cells are sensitive to the heat shock temperature when the temperature reaches the thermal tolerance limits. Additionally, our sensitive analysis result indicates that the status of some components in the heat shock reaction changes when the temperature reaches the thermal tolerance resulting in failure in protein refolding in fish and speeding up the refolding process in HeLa cells. Mathematical analysis is also applied on a simplified mathematical model to investigate the detailed dynamics of the model, such as the steady states of the substrate, Hsp70 mRNA, and HSP70 protein, at different thermal stresses. The comparison between the original model and simplified model shows that the inhibition on HSP70 protein transcription by thermal stresses leads to the reduction in HSP70 protein at extreme temperatures.