Cell-to-cell variability in stress response is a bottleneck for the construction of accurate and predictive models which could guide clinical diagnosis and treatment of certain diseases, for example, cancer. Indeed, such phenotypic heterogeneity can lead to fractional killing and persistence of a subpopulation of cells which are resistant to a given treatment. The heat shock response network plays a major role in protecting the proteome against several types of injuries. Here, we combine high-throughput measurements and mathematical modeling to unveil the molecular origin of the phenotypic variability in the heat shock response network. Although the mean response coincides with known biochemical measurements, we found a surprisingly broad diversity in single-cell dynamics with a continuum of response amplitudes and temporal shapes for several stimulus strengths. We theoretically predict that the broad phenotypic heterogeneity is due to network ultrasensitivity together with variations in the expression level of chaperones controlled by the transcription factor heat shock factor 1. Furthermore, we experimentally confirm this prediction by mapping the response amplitude to chaperone and heat shock factor 1 expression levels.

Introduction: Models of dose-effect relationships seek systematic and predictive descriptions of how cell survival depends on the level and duration of the stressor. The CEM43 thermal dose model has been empirically derived more than thirty years ago and still serves as a benchmark for hyperthermia protocols despitethe advent of regulatory network models. Objective: In this paper, we propose and realize a simple experimental test to assess whether mechanistic models can prove more reliable indicators for some protocols. We define two time-asymmetric hyperthermia profiles, faster rise than decay or slower rise than decay, for which the CEM43 model predicts the same survival while a regulatory network model predicts significant differences. Materials: Experimental data (both control 37 C and hyperthermia assays) were collected from duplicate HeLa cell cultures. Cells were imaged before and 24, 48 and 72 h after the hyperthermia assay double-stained with fluorescein-5-isothiocyanate (FITC)-labeled annexin V and propidium iodide for detecting cell death. Results: Survival experiments of HeLa cells show that a fast temperature rise followed by a slow decay can be twice more lethal than the opposite, consistently with the prediction of the network model. Conclusions: Using a model reduction approach, we obtained a simple nonlinear dynamic equation that identifies the limited repair capacity as the main factor underlying the dose-asymmetry effect and that could be useful for refining thermal doses for dynamic protocols.

13Cell-to-cell variability in stress response is a bottleneck for the construction of accurate and 14 predictive models that could guide clinical diagnosis and treatment of diseases as for instance 15 cancers. Indeed such phenotypic heterogeneity can lead to fractional killing and persistence 16 of a subpopulation of cells resistant to a given treatment. The heat shock response network 17 plays a major role in protecting the proteome against several types of injuries. We combine 18 high-throughput measurements and mathematical modeling to unveil the molecular origin of 19 the phenotypic variability in the heat shock response network. Although the mean response 20 coincides with known biochemical measurements, we found a surprisingly broad diversity in 21 single cell dynamics with a continuum of response amplitudes and temporal shapes for several 22 stimuli strengths. We theoretically predict that the broad phenotypic heterogeneity is due to 23 network ultrasensitivity together with variations in the expression level of chaperons controlled 24 by heat shock factor 1. We experimentally confirm this prediction by mapping the response 25 amplitude to concentrations chaperons and heat shock factor 1 expression level. 26