Mass Action Dynamics of Coupled Reactions using Fluctuation Theory

Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in scope and application by the fact that the determination of enzyme rate constants is laborious and low throughput. We present a statistical thermodynamic formulation of the law of mass action for coupled reactions at both steady states and non-stationary states. The formulation is based on a fluctuation theorem for coupled reactions and uses chemical potentials instead of rate constants. When used to model deterministic systems, the theory corresponds to a rescaling of the time dependent reactions in such a way that steady states can be reached on the same time scale but with significantly fewer computational steps. The significance for applications in systems biology is discussed.

💡 Research Summary

The paper introduces a statistical‑thermodynamic reformulation of the law of mass action that is applicable to coupled chemical reactions both at steady state and during transient dynamics. Traditional kinetic models rely on experimentally determined rate constants (k) for each enzymatic step, a process that is labor‑intensive and low‑throughput, especially for large metabolic networks. To overcome this bottleneck, the authors derive a new kinetic expression from the fluctuation theorem—a result from nonequilibrium statistical mechanics that relates the probability of a forward transition to that of its reverse via the exponential of the entropy (or free‑energy) change. By substituting the chemical potential difference (Δμ) for the free‑energy change, they obtain a rate law of the form

  r = γ · exp(−Δμ/RT) · ∏