Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system

A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that this is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting liner flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.