Evaluation of reaction fluxes in stationary and oscillating far-from-equilibrium biological systems

•We design a protocol for determining a reaction flux in far-from-equilibrium systems.•Time asymmetry of the correlation functions reveal departure from equilibrium.•The fluctuations of the concentrations depend on the nonlinearities of dynamics.•Time correlation functions are derived for bistable and oscillating systems.

The complex spatio-temporal structures that appear in chemical and biological systems require far-from-equilibrium conditions which may lead to the circulation of reaction fluxes. We investigate how time asymmetry of cross-correlation functions of concentration fluctuations may be exploited to determine reaction fluxes at the cellular level. Using simulations of the master equation as a reference, we show that, far from a bifurcation, the Langevin approach provides a reliable tool to compute analytical expressions for time correlation functions. Biochemical mechanisms associated with bistability and oscillations issued from a Hopf bifurcation or a saddle–node infinite period bifurcation are considered. We show that the blind use of the simple relation obtained when assuming a linear deterministic dynamics often leads to a poor estimation of the value of the reaction flux and even of its sign.