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.