GROMACS implementation of free energy calculations with non-pairwise Variationally derived Intermediates

Gradients in free energies are the driving forces of physical and biochemical systems. To predict free energy differences with high accuracy, Molecular Dynamics (MD) and other methods based on atomistic Hamiltonians conduct sampling simulations in intermediate thermodynamic states that bridge the configuration space densities between two states of interest (’alchemical transformations’). For uncorrelated sampling, the recent Variationally derived Intermediates (VI) method yields optimal accuracy. The form of the VI intermediates differs fundamentally from conventional ones in that they are non-pairwise, i.e., the total force on a particle in an intermediate states cannot be split into additive contributions from the surrounding particles. In this work, we describe the implementation of VI into the widely used GROMACS MD software package (2020, version 1). Furthermore, a variant of VI is developed that avoids numerical instabilities for vanishing particles. The implementation allows the use of previous non-pairwise potential forms in the literature, which have so far not been available in GROMACS. Example cases on the calculation of solvation free energies, and accuracy assessments thereof, are provided.

自由能梯度是物理与生化系统的核心驱动力。为高精度预测自由能差值，基于原子级哈密顿量的分子动力学（Molecular Dynamics，MD）及其他相关方法，会在衔接目标两态构型空间密度的中间热力学状态中开展采样模拟，即所谓“赝化学变换”。针对无关联采样任务，近年提出的变分衍生中间体（Variationally derived Intermediates，VI）方法可实现最优精度。VI中间体的形式与传统中间体存在本质差异：其属于非成对相互作用形式，即中间态下粒子所受总合力无法拆分为周围粒子贡献的可加性分量。本研究阐述了将VI方法集成至广泛使用的GROMACS MD软件包（2020版本1.0）的具体实现流程，同时开发了VI方法的一个变体，可规避粒子消失场景下的数值不稳定性问题。该集成实现支持使用此前文献中报道的非成对相互作用势能形式，而这类势能形式此前无法在GROMACS中调用。本文还提供了溶剂化自由能计算及其精度评估的示例案例。