Propagation of fluctuations in biochemical systems, II: Nonlinear chains

We consider biochemical reaction chains and investigate how random external fluctuations, as characterised by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of molecules is high enough so that the behaviour of the concentrations of the system is well approximated by differential equations. We conclude that the variances and coefficients of variation of the fluxes will decrease as one moves down the chain and, through an example, show that there is no corresponding result for the variances of the concentrations of the chemical species. We also prove that the fluctuations of the fluxes as characterised by their time averages decrease down reaction chains. The results presented give insight into how biochemical reaction systems are buffered against external perturbations solely by their underlying graphical structure and point out the benefits of studying the out-of-equilibrium dynamics of systems.