Long delay times in reaction rates increase intrinsic fluctuations

TL;DR

This paper investigates how long delay times in reaction rates affect intrinsic fluctuations in stochastic spatially distributed cellular systems, revealing that delays tend to increase noise and can induce limit cycles.

Contribution

It introduces a systematic approximation for stochastic delay reactions, showing how long delays influence fluctuations and enabling analysis of delay-induced oscillations.

Findings

Long delays increase intrinsic fluctuations.

Delayed reactions can induce limit cycles.

Method applies to nonlinear transition rates.

Abstract

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise, valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady-state. The method is general enough to accommodate nonlinear transition rates, allowing characterization of fluctuations around a delay-induced limit cycle.