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

Abstract

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.

On Oscillations and Noise in Multicomponent Adsorption: The Nature of Multiple Stationary States

“…Stability is addressed firstly in a classical way, by analyzing the Jacobian of the Taylor expansion of the equation set (2), and then the procedure based on the Langevin approach is applied. Langevin forces and the relation between reaction flux and cross-correlation functions are modeled according to the procedures presented in [19][20][21]. Then stochastic analysis, based on the chemical master equation, is applied.…”

“…In order to gain a better insight into the adsorption process and how it behaves at very short times and high frequencies, we focus now on the correlation functions. We use the procedure in [19][20][21] and determine the correlation functions after the change of the basis by the use of the following matrix.…”

“…The stochastic treatment of the flux is even more insightful because it reveals statistics about species creation and depletion [18]. Works of Bianca and Lemarchand on the reaction fluxes of the steady state and the oscillating biological and chemical systems showed how the relation between the reaction flux and the cross-correlation functions of the concentration fluctuations may be utilized in the analysis of biological and chemical systems [19][20][21]. This approach has been so far the most appropriate for the analysis in this paper since it allows for addressing both oscillations and fluctuations at the same time.…”

Discrete flux and velocity fields of probability and their global maps in reaction systems

“…The flux J R (x, t) indeed satisfies the continuity equation, as we have: ∇ d · J r (x, t) = −∂p(x, t)/∂t from Eqs. (13), (22), and (23).…”

“…For example, determining the probability flux can help to infer the mechanism of dynamic switching among different attractors [20,21]. Quantifying the probability flux can also help to characterize the departure of non-equilibrium reaction systems from detailed balance [16,22,23], and can help to identify barriers and checkpoints between different stable cellular states [24]. Computing probability fluxes and velocity fields has found applications in studies of stem cell differentiation [25], cell cycle [24], and cancer development [26,27].Models of probability fluxes and velocities in well-mixed mesoscopic chemical reaction systems have been the focus of many studies [17,18,20,[22][23][24][28][29][30][31][32].…”