Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems. To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1–40) peptide, periodically driven by an oscillating electric field.

中文翻译：

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非平衡生物分子动力学的广义马尔可夫状态建模方法：以振荡电场驱动的β淀粉样构象动力学为例

近年来，马尔可夫状态模型（MSM）的受欢迎程度得到了持续增长，因为它们非常适合于亚稳态和相关动力学的识别和分析。但是，最新的马尔可夫状态建模方法和工具强制执行详细的平衡条件，从而限制了它们对平衡MSM的适用性。迄今为止，它们不适合处理包括循环过程在内的一般主导数据结构，而循环过程本质上与非平衡系统有关。为克服此限制，我们开发了通用鲁棒性Perron聚类聚类分析的概括（PCCA +）方法，称为广义PCCA（G-PCCA）。该方法利用Schur向量而不是特征向量来处理平衡和非平衡模拟数据。G-PCCA不仅限于检测亚稳态，还可以识别一般结构的主要结构，从而阐明循环过程。G-PCCA在淀粉样β（1-4）肽的非平衡分子动力学数据上的应用得到了例证，该数据由振荡电场周期性地驱动。