Seiferth David, Sollich Peter, Klumpp Stefan
Institute for the Dynamics of Complex Systems, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Institute for Theoretical Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Phys Rev E. 2020 Dec;102(6-1):062149. doi: 10.1103/PhysRevE.102.062149.
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and all steady-state fluxes except the one between the merged states. Different levels of coarse graining of the underlying microscopic dynamics can be obtained by iteration, with the result being independent of the order in which states are merged. A criterion for the optimal level of coarse graining or resolution of the process is proposed via a tradeoff between the simplicity of the coarse-grained model and the information loss relative to the original model. As a case study, the method is applied to the cycle kinetics of the molecular motor kinesin.
许多生物系统可用有限马尔可夫模型来描述。本文提出了一种基于合并相邻状态来简化主方程的通用方法。该方法保留了稳态概率分布以及除合并状态之间的通量之外的所有稳态通量。通过迭代可获得基础微观动力学不同程度的粗粒化，其结果与状态合并的顺序无关。通过在粗粒化模型的简单性与相对于原始模型的信息损失之间进行权衡，提出了该过程的最佳粗粒化水平或分辨率的标准。作为一个案例研究，该方法被应用于分子马达驱动蛋白的循环动力学。
