The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x_i} = x that in some sense describe the essential dynamics of the system. Considering the distribution P(x) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P(x), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG(x) = −k_BT ln P(x), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.

中文翻译：

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观点：识别蛋白质动力学的集体变量和亚稳态

分子动力学模拟的统计分析需要降维技术，这会产生一组低维的集体变量（CV）{ x _i } = x，从某种意义上说，它描述了系统的基本动力学。考虑到CV的分布P（x），统计分析的主要目标是检测P（x）的特征，尤其是其最大值及其连接路径。这是因为这些特征表征了相应的自由能态势的低能区域和能垒ΔG（x）=- k _B Tln P（x），因此等于系统的亚稳态和过渡区域。从这个角度出发，我们概述了识别CV和亚稳状态的系统策略，随后可以将其用于构建动力学的Langevin或Markov状态模型。特别地，我们考虑了通常由分子动力学模拟获得的仍然有限的采样，这在实践中严重地限制了理论（例如，假设遍历性）和黑匣子软件工具（例如，使用冗余输入坐标）的适用性。我们证明了使用内部（而不是笛卡尔）输入坐标，采用避免降维误差（例如主成分分析）并执行基于密度（而不是k）的降维方法至关重要。-均值类型）聚类。最后，我们简要讨论了一种机器学习的降维方法，该方法强调了系统的基本内部坐标，并且可能揭示了隐藏的反应机制。