Stochastic Control Analysis for Biochemical Reaction Systems

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances and the control distribution of the flux variances is shown to depend on the size of the measurement time window (ǫ) within which reaction events are counted for measuring a single flux. It is found that the degree of the ǫ-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time scale separation. This ǫ-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks. We also propose a systematic way to control fluctuations of reactant concentrations while minimizing changes in mean concentration levels by applying the stochastic sensitivities.