Cells perform the core processes of life via physical interactions between biomolecules like DNA and proteins. Understanding the nature of these interactions is crucial, given that changes to them can cause serious disruption to cellular behaviour. Drug perturbation experiments are commonly used to infer interactions; cells are exposed to chemical perturbations and changes in average biomolecular levels are observed. Linear response theory is used to analyze these experiments; however mathematical formulations rely use deterministic approximations that ignore the influence of stochastic fluctuations in molecular levels on the observed responses.

We use deterministic linear response theory to analyze a high-throughput drug perturbation experiment to infer interactions between signalling pathways in cancer cells. We extend deterministic theory to the case of random perturbations on gene expression systems with feedback. However, we show that stochastic fluctuations in the components can lead to incorrect inferences about the feedback dynamics. In simple example stochastic systems, we identify conditions under which deterministic approximations of responses are valid. Finally, we demonstrate how stochastic fluctuations and perturbation responses can constrain dynamics in biological systems.