Sasmal Subarna, McCullagh Martin, Hocky Glen M
Department of Chemistry and Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, United States.
Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078, United States.
J Chem Theory Comput. 2023 Jul 25;19(14):4427-4435. doi: 10.1021/acs.jctc.3c00051. Epub 2023 May 2.
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 are not 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, whereby 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.
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下的原子位置，能够在这两种状态之间产生一个良好的反应坐标。大分子的原子坐标是大分子构型的直接表示，然而，由于缺乏旋转和平移不变性，它们未被用于增强采样研究中。我们使用我们之前工作的技术解决了这个问题，即分子构型被视为大小和形状空间中等价类的一个成员，大小和形状空间是所有可以平移和旋转到参考多元高斯分布内的单个点的构型的集合，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，在表征长分子动力学（MD）模拟中系统两种状态之间的转变方面，以及在允许我们使用增强采样MD技术沿该反应坐标轻松产生自由能估计的方面，都被证明是良好的反应坐标。
