The heat-shock response network controls the adaptation and survival of the cell against environmental stress. This network is highly conserved and is connected with many other signaling pathways. A key element of the heat-shock network is the heat-shock transcription factor-1 (HSF), which is transiently activated by elevated temperatures. HSF translocates to the nucleus upon elevated temperatures, forming homotrimeric complexes. The HSF homotrimers bind to the heat shock element on the DNA and control the expression of the hsp70 gene. The Hsp70 proteins protect cells from thermal stress. Thermal stress causes the unfolding of proteins, perturbing thus the pathways under their control. By binding to these proteins, Hsp70 allows them to refold and prevents their aggregation. The modulation of the activity of the hsp70-promoter by the intensity of the input stress is thus critical for cell's survival. The promoter activity starts from a basal level and rapidly increases once the stress is applied, reaches a maximum level and attenuates slowely back to the basal level. This phenomenon is the hallmark of many experimental studies and of all computational network analysis.
The molecular construct used as a measure of the response to thermal stress is a Hsp70-GFP fusion gene transfected in Chinese hamster ovary (CHO) cells. The time profile of the GFP protein depends on the transient activity, Transient(t), of the heat shock system. The function Transient(t) depends on hsp70 promoter activity, transcriptional regulation and the translation initiation effects elicited by the heat stress. The GFP time profile is recorded using flow cytometry measurements, a technique that allows a quantitative measurement of the fluorescence of a large number of cells (104). The GFP responses to one and two heat shocks were measured for 261 conditions of different temperatures and durations. We found that: (i) the response of the cell to two consecutive shocks (i.e., no recovery time in between shocks) depends on the order of the input shocks, that is the shocks do not commute; (ii) the responses may be classified as mild or severe, depending on the temperature level and the duration of the heat shock and (iii) the response is highly sensitive to small variations in temperature.
We propose a mathematical model that maps temperature into the transient activity using experimental data that describes the time course of the response to input thermal stress. The model is built on thermotolerance without recovery time, sharp sensitivity to small variations in temperature and the existence of mild and severe classes of stress responses. The theoretical predictions are tested against experimental data using a series of double-shock inputs. The theoretical structure is represented by a sequence of three cascade processes that transform the input stress into the transient activity. The structure of the cascade is nonlinear-linear-nonlinear (NLN). The first nonlinear system (N) from the NLN structure represents the amplification of small changes in the environmental temperature; the linear system (L) represents the thermotolerance without recovery time, whereas the last system (N) represents the transition of the cell's response from a mild to a severe shock.