标题： 对数线性反应商动态 显示英文标题

标题： Log-Linear Reaction Quotient Dynamics

摘要： 细胞内的化学反应网络在持续扰动下远离平衡状态运行，但仍能精确控制数千种代谢物。 尽管质量作用动力学能够准确描述其基本动态，但由此产生的非线性微分方程难以分析和控制，尤其是在大型网络中。 我们提出了一种简化模型，其中反应商（衡量反应距离平衡有多远的比率）在对数尺度上呈指数方式趋向其平衡值。 这一原理导致了对数空间中的线性动力学，提供了几个关键优势：任意网络拓扑都存在解析解，通过反应商与吉布斯自由能之间的关系自动满足热力学约束，守恒定律与反应商动力学解耦，从而简化了分析和控制设计，外部能量源线性地耦合到动力学中，统一了多种生物调节机制。 显示英文摘要

摘要： Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics, the resulting nonlinear differential equations are difficult to analyze and control, particularly for large networks. We propose a simplified model where reaction quotients (the ratios that measure how far reactions are from equilibrium) evolve exponentially toward their equilibrium values when viewed on a logarithmic scale. This principle leads to linear dynamics in log-space, providing several key advantages: analytical solutions exist for arbitrary network topologies, thermodynamic constraints are automatically satisfied through the relationship between reaction quotients and Gibbs free energy, conservation laws decouple from reaction quotient dynamics simplifying both analysis and control design, and external energy sources couple linearly to the dynamics, unifying diverse biological regulatory mechanisms.