Fakharzadeh Ashkan, Moradi Mahmoud
Department of Physics, North Carolina State University , Raleigh, North Carolina 27695, United States.
Department of Chemistry and Biochemistry, University of Arkansas , Fayetteville, Arkansas 72701, United States.
J Phys Chem Lett. 2016 Dec 15;7(24):4980-4987. doi: 10.1021/acs.jpclett.6b02208. Epub 2016 Nov 23.
We present a Riemannian formalism for effective diffusion of biomolecules in collective variable spaces that provides a robust framework for conformational free energy calculation methods. Unlike their Euclidean counterparts, the Riemannian potential of mean force (PMF) and minimum free energy path (MFEP) are invariant under coordinate transformations. The presented formalism can be readily employed to modify the collective variable based enhanced sampling techniques, such as umbrella sampling (US) commonly used in biomolecular simulations, to take into account the role of intrinsic geometry of collective variable space. Although our model is mathematically equivalent to a Euclidean diffusion with a position-dependent diffusion tensor, the Riemannian formulation provides a more convenient framework for free energy calculation methods and path-finding algorithms aimed at characterizing the effective conformational dynamics of biomolecules. A simple three-dimensional toy model and a pentapeptide (met-enkephalin) simulated in an explicit solvent environment are used to illustrate the workings of the formalism and its implementation.
我们提出了一种用于生物分子在集体变量空间中有效扩散的黎曼形式，它为构象自由能计算方法提供了一个强大的框架。与欧几里得对应物不同，黎曼平均力势（PMF）和最小自由能路径（MFEP）在坐标变换下是不变的。所提出的形式可以很容易地用于修改基于集体变量的增强采样技术，例如生物分子模拟中常用的伞形采样（US），以考虑集体变量空间固有几何结构的作用。虽然我们的模型在数学上等同于具有位置依赖扩散张量的欧几里得扩散，但黎曼公式为旨在表征生物分子有效构象动力学的自由能计算方法和路径寻找算法提供了一个更方便的框架。使用一个简单的三维玩具模型和在明确溶剂环境中模拟的五肽（甲硫氨酸脑啡肽）来说明该形式的工作原理及其实现。
