基于位置线性判别分析的构象转变反应坐标
Reaction Coordinates for Conformational Transitions using Linear Discriminant Analysis on Positions
AI总结：
本文提出将线性判别分析应用于原子位置，并结合尺寸-形状空间等价类方法解决旋转和平移不变性问题，从而获得可用于增强采样和自由能计算的生物分子构象转变反应坐标。
摘要：
在这项工作中，我们证明了将线性判别分析（LDA）应用于生物分子两种不同状态的原子位置，可以在这两种状态之间产生良好的反应坐标。大分子的原子坐标是大分子构型的直接表示，但由于缺乏旋转和平移不变性，它们尚未被用于增强采样研究。我们利用先前工作中的技术解决了这一问题，在该技术中，分子构型被视为尺寸-形状空间中等价类的一个成员，该等价类是可以平移和旋转到参考多元高斯分布内单个点的所有构型的集合，该参考多元高斯分布表征单个分子状态。将LDA应用于位置所产生的反应坐标被证明是良好的反应坐标，既能在长时间分子动力学（MD）模拟中表征系统两种状态之间的转变，也能使我们利用增强采样MD技术沿该反应坐标方便地得到自由能估计。
英文摘要：
In this work, we demonstrate that Linear Discriminant Analysis (LDA) applied to atomic positions in two different states of a biomolecule produces a good reaction coordinate between those two states. Atomic coordinates of a macromolecule are a direct representation of a macromolecular configuration, and yet they have not been used in enhanced sampling studies due to a lack of rotational and translational invariance. We resolve this issue using the technique of our prior work, where a molecular configuration is considered a member of an equivalence class in size-and-shape space, which is the set of all configurations that can be translated and rotated to a single point within a reference multivariate Gaussian distribution characterizing a single molecular state. The reaction coordinates produced by LDA applied to positions are shown to be good reaction coordinates both in terms of characterizing the transition between two states of a system within a long molecular dynamics (MD) simulation, and also ones that allow us to readily produce free energy estimates along that reaction coordinate using enhanced sampling MD techniques.
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