Using random perturbations to infer the structure of feedback control in gene expression

Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities between cellular modules. However, in large-scale drug perturbation studies the effect of any given drug may not be known and may not only affect one module at a time. Here, we analyze the response of gene expression models to random perturbations that affect multiple modules simultaneously. In the deterministic regime we analytically show how cellular responses to infinitesimal random perturbations can be used to infer the nature of feedback regulation in gene expression, as long as the effects of perturbations are statistically independent between modules. We numerically extend this deterministic analysis to the response of average abundances of stochastic gene expression models to finite perturbations. By sampling simple models of stochastic gene expression, we identify example systems that violate the bounds predicted within a deterministic framework. We show these violations persist even in the limit of infinitesimal perturbations and are due to the inherently stochastic dynamics of biochemical feedback circuits. These discrepancies demonstrate how deterministic analyses can fail to correctly describe the response of cellular averages to perturbations even in the linear response regime.