Determination of reaction flux from concentration fluctuations near a Hopf bifurcation

Small open chemical systems, typically associated with far-from-equilibrium, nonlinear stochastic dynamics, offer the appropriate framework to elucidate biological phenomena at the cellular scale. Stochastic differential equations of Langevin-type are employed to establish the relation between the departure from equilibrium and the time cross-correlation functions of concentration fluctuations for chemical species susceptible to oscillate. Except in the immediate vicinity of the Hopf bifurcation, the results are in agreement with simulations of the chemical master equation but always differ from the prediction obtained for linear deterministic dynamics. In general, the magnitude of the asymmetry of time correlation functions definitely depends on the reaction flux circulating in an open system but also on the details of the nonlinearities of deterministic dynamics.