Mathematical Modeling of the Heat-Shock Response in HeLa Cells

The heat-shock response is a key factor in diverse stress scenarios, ranging from hyperthermia to protein folding diseases. However, the complex dynamics of this physiological response have eluded mathematical modeling efforts. Although several computational models have attempted to characterize the heat-shock response, they were unable to model its dynamics across diverse experimental datasets. To address this limitation, we mined the literature to obtain a compendium of in vitro hyperthermia experiments investigating the heat-shock response in HeLa cells. We identified mechanisms previously discussed in the experimental literature, such as temperature-dependent transcription, translation, and heat-shock factor (HSF) oligomerization, as well as the role of heat-shock protein mRNA, and constructed an expanded mathematical model to explain the temperature-varying DNA-binding dynamics, the presence of free HSF during homeostasis and the initial phase of the heat-shock response, and heat-shock protein dynamics in the long-term heat-shock response. In addition, our model was able to consistently predict the extent of damage produced by different combinations of exposure temperatures and durations, which were validated against known cellular-response patterns. Our model was also in agreement with experiments showing that the number of HSF molecules in a HeLa cell is roughly 100 times greater than the number of stress-activated heat-shock element sites, further confirming the model’s ability to reproduce experimental results not used in model calibration. Finally, a sensitivity analysis revealed that altering the homeostatic concentration of HSF can lead to large changes in the stress response without significantly impacting the homeostatic levels of other model components, making it an attractive target for intervention. Overall, this model represents a step forward in the quantitative understanding of the dynamics of the heat-shock response.