The cellular environment modifies cellular phenotypes, in particular, the stress response phenotype, which easily exhibits high phenotypic heterogeneity due to the common characteristics of its regulatory networks. The aim of this work is to quantify and interpret the impact of collagen type I, a major component of the cellular environment, on the phenotypic heterogeneity of the cellular response. Our approach combines in an original way the monitoring of the response of a single cell and the mathematical modeling of the network. After a detailed statistical description of the phenotypic heterogeneity of the cellular response, the mathematical modeling explains how the observed changes can be explained by an induced increase in the average expression of a central protein of the regulatory network. The predictions of the data-driven model are fully consistent with the biochemical measurements performed. The framework presented here is also a new general methodology to study phenotypic heterogeneity, although we focus here on the response to proteotoxic stress in HeLa cells.