Cortassa S, Aon M A, Westerhoff H V
E.C. Slater Institute for Biochemical Research, University of Amsterdam, The Netherlands.
Biophys J. 1991 Oct;60(4):794-803. doi: 10.1016/S0006-3495(91)82114-2.
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.
根据非平衡态热力学原理构建了一个模拟糖酵解振荡的模型。在动力学速率方程中，每个代谢物浓度都被其化学势的指数函数所取代。这导致了速率与化学势之间的非线性关系。然后，将每个化学势围绕其稳态值展开为泰勒级数。泰勒级数的线性（一阶）项足以模拟系统的动态行为，包括在低底物输入或高自由能负荷下的阻尼振荡甚至持续振荡。糖酵解系统在前半部分是自催化的。由于仅在存在该自催化反馈回路的情况下才获得振荡，我们得出结论，这种类型的动力学非线性足以解释振荡行为。该系统的唯象系数矩阵是非对称的。我们的结果表明，正是这种对称性而非近平衡域中流 - 力关系的线性阻止了振荡。给定自催化特性，一个表现出线性流 - 力关系且处于近平衡域之外的系统可能会出现分岔，从而导致自组织行为。
