Delay-induced anomalous fluctuations in intracellular regulation

Direct negative feedback decreases fluctuations and is a ubiquitous mechanism for homoeostatic control. However, intracellular regulation frequently operates indirectly, resulting in delayed responses. Here we derive an analytical expression that quantifies the consequences from delayed negative feedback resulting from typical multistep synthesis pathways, for example, transcription or translation. We find that indirect feedback leads to more fluctuations than without feedback for intermediate delays, but surprisingly not for long delays. The anomalous fluctuations at intermediate delays emerge from positive correlations between the delayed regulatory events, and are shown to be equivalent to an increased stoichiometry in the synthesis of new molecules. The results primarily give us insight about the design principles of delayed stochastic control systems and why a fixed feedback delay gives more fluctuations than a broadly distributed feedback delay. It is also shown that the feedback delay of auto-repressed regulators can result in more sensitive regulation of downstream processes through stochastic focusing.