Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

中文翻译：

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使用 ShapeGMM 从有偏差的模拟中量化无偏差的构象系综

量化生物分子的构象集合对于描述蛋白质折叠、折叠状态之间的相互转换、配体结合和变构调节等过程的机制至关重要。由于采样不足，对除最简单分子之外的所有分子的传统分子模拟来说，这些整体的准确量化仍然是一个挑战。增强采样方法（例如元动力学）旨在克服这一挑战；然而，许多这些方法产生的不均匀帧权重对马尔可夫状态建模或结构聚类等集成量化技术提出了额外的挑战。在这里，我们提出了将非均匀框架权重严格纳入名为 shapeGMM 的结构聚类方法中。框架加权 shapeGMM 的结果是无偏系统的高维概率密度和生成模型，我们可以从中计算重要的热力学性质，例如相对自由能和构型熵。这种方法的准确性通过哈密顿重新加权计算的 GMM 与粗粒度螺旋模型系统的直接模拟之间的定量一致性得到了证明。此外，根据元动力学模拟重新加权的丙氨酸二肽的 shapeGMM 概率密度计算出的相对自由能定量地再现了盆地中潜在的自由能。最后，该方法通过在 GMM 状态上训练的线性判别分析坐标上的元动力学模拟，识别沿着肌动蛋白球状到丝状结构转变的隐藏结构，说明有偏差数据的结构聚类如何导致生物物理洞察。综合起来，这些结果表明框架加权 shapeGMM 是一种从有偏差的模拟中量化生物分子整体的强大方法。