从哈密顿观点重新审视某些非平衡化学反应的宏观动力学
Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
摘要：
活细胞中的大多数生物化学反应是通过恒化器与环境相互作用以交换能量和物质的开放系统。在介观尺度上，这些生化反应中每个物种的数量可以用随机时变泊松过程来建模。为了表征大体积极限下的宏观行为，道路空间中的大数定律确定了描述物种浓度动力学的平均场极限非线性反应速率方程，而化学主方程的WKB展开产生了Hamilton-Jacobi方程（HJE），拉格朗日给出了大偏差原理下的良好速率函数。利用HJE的定态解将一般宏观反应速率方程分解为守恒部分和耗散部分。该稳态解用于确定一般化学反应的能量景观和热力学，特别是在非平衡稳态下保持正熵产生率。证明了相应的能量耗散规律，以及从细观到宏观的过渡。此外，我们使用一个可逆的哈密顿量来研究一类非平衡酶反应，这确定了一个新的概念的平衡内相同的反应向量，由于通量分组简并。这种由化学反应跳跃过程的可逆性带来的宏观可逆性，给出了Onsager型强梯度流。可逆的哈密顿量也产生了相应的拉格朗日量的时间反演对称性。因此，修改的时间反演最小作用路径用作具有相关联的路径亲和力和能量势垒的过渡路径。
英文摘要：
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number of each species in those biochemical reactions can be modeled by a random time-changed Poisson processes. To characterize macroscopic behaviors in the large volume limit, the law of large numbers in the path space determines a mean-field limit nonlinear reaction rate equation describing the dynamics of the concentration of species, while the WKB expansion for the chemical master equation yields a Hamilton-Jacobi equation (HJE) and the Lagrangian gives the good rate function in the large deviation principle. We decompose a general macroscopic reaction rate equation into a conservative part and a dissipative part in terms of the stationary solution to HJE. This stationary solution is used to determine the energy landscape and thermodynamics for general chemical reactions, which particularly maintains a positive entropy production rate at a non-equilibrium steady state. The associated energy dissipation law is proved together with the passage from the mesoscopic to macroscopic one. Furthermore, we use a reversible Hamiltonian to study a class of non-equilibrium enzyme reactions, which identifies a new concept of balance within the same reaction vector due to flux grouping degeneracy. This macroscopic reversibility, brought by the reversibility of the chemical reaction jumping process, gives an Onsager-type strong gradient flow. The reversible Hamiltonian also yields a time reversal symmetry for the corresponding Lagrangian. Thus a modified time reversed least action path serves as the transition paths with associated path affinities and energy barriers.
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