Computational modeling of assembly is challenging for many systems, because their timescales can vastly exceed those accessible to simulations. This article describes the multiMSM, which is a general framework that uses Markov state models (MSMs) to enable simulating self-assembly and self-organization of finite-sized structures on timescales that are orders of magnitude longer than those accessible to brute-force dynamics simulations. As with traditional MSM approaches, the method efficiently overcomes free energy barriers and other dynamical bottlenecks. In contrast to previous MSM approaches to simulating assembly, the framework describes simultaneous assembly of many clusters and the consequent depletion of free subunits or other small oligomers. The algorithm accounts for changes in transition rates as concentrations of monomers and intermediates evolve over the course of the reaction. Using two model systems, we show that the multiMSM accurately predicts the concentrations of the full ensemble of intermediates on timescales required to reach equilibrium. Importantly, after constructing a multiMSM for one system concentration, yields at other concentrations can be approximately calculated without any further sampling. This capability allows for orders of magnitude additional speedup. In addition, the method enables highly efficient calculation of quantities such as free energy profiles, nucleation timescales, flux along the ensemble of assembly pathways, and entropy production rates. Identifying contributions of individual transitions to entropy production rates reveals sources of kinetic traps. The method is broadly applicable to systems with equilibrium or nonequilibrium dynamics and is trivially parallelizable and, thus, highly scalable. Published by the American Physical Society 2024

中文翻译：

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模拟自组装的马尔可夫状态模型方法


装配体的计算建模对许多系统来说都具有挑战性，因为它们的时间跨度可能大大超过仿真所能达到的时间尺度。本文介绍了 multiMSM，这是一个通用框架，它使用马尔可夫状态模型 （MSM） 来模拟有限尺寸结构的自组装和自组织，其时间尺度比蛮力动力学仿真的时间尺度长几个数量级。与传统的 MSM 方法一样，该方法有效地克服了自由能障碍和其他动态瓶颈。与以前模拟组装的 MSM 方法相比，该框架描述了许多簇的同时组装以及随之而来的游离亚基或其他小寡聚物的消耗。该算法考虑了随着反应过程中单体和中间体浓度的变化而发生的转变速率变化。使用两个模型系统，我们表明 multiMSM 在达到平衡所需的时间尺度上准确预测了整个中间体集合的浓度。重要的是，在为一种系统浓度构建 multiMSM 后，可以近似计算其他浓度的产量，而无需任何进一步的采样。此功能允许数量级的额外加速。此外，该方法还可以高效计算自由能分布、成核时间尺度、沿装配路径集合的磁通量和熵产生速率等物理量。确定单个跃迁对熵产生率的贡献可以揭示动力学陷阱的来源。该方法广泛适用于具有平衡或非平衡动力学的系统，并且很容易并行化，因此具有高度可扩展性。美国物理学会 2024 年出版