Abstract
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker–Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
Highlights
The workhorse of much research on chemical kinetics has been macroscopic reaction-rate equations
We show that the derivatives of the autocorrelation function (ACF) of the concentration fluctuations are affected in opposite ways by burst b and confinement V{1, discriminating between the two noise source
Model As a representative model of non-linear reaction networks out of equilibrium we consider driven colloidal aggregation, for three reasons: First, it is a complete model since this reaction network comprises all three types of elementary reactions: bimolecular, source, and unimolecular [27], rendering the results obtained here valid for other reaction networks
Summary
The workhorse of much research on chemical kinetics has been macroscopic reaction-rate equations These are deterministic, mean-field descriptions that treat molecular populations as continuous and use macroscopically determined rate constants. They do not always provide an accurate description of reaction kinetics [1,2]. This lack of accuracy occurs for nonlinear reactions if the population (copy number) of the various chemical species is small enough such that standard errors are not negligible [3,4,5,6,7,8,9]. The noise due to molecular discreteness becomes apparent and acquires correlations to give a departure from the behaviour predicted by macroscopic reaction-rate equations [1,12,14,15,16]
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