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.

Program summary

Program Title: GROMACS-VI-Extension

CPC Library link to program files: https://doi.org/10.17632/7yvc8mmnyv.1

Developer’s repository link: https://www.mpibpc.mpg.de/gromacs-vi-extension and https://www.gitlab.gwdg.de/martin.reinhardt/gromacs-vi-extension

Licensing provisions: LGPL

Programming language: C++14, CUDA

Nature of problem: The free energy difference between two states of a thermodynamic system is calculated using samples generated by simulations based on atomistic Hamiltonians. Due to the high dimensionality of many applications as in, e.g., biophysics, only a small part of the configuration space can be sampled. The choice of the sampling scheme critically affects the accuracy of the final free energy estimate. The challenge is, therefore, to find the optimal sampling scheme that provides best accuracy for given computational effort.

Solution method: Sampling is commonly conducted in intermediate states, whose Hamiltonians are defined based on the Hamiltonians of the two states of interest. Here, sampling is conducted in the variationally derived intermediate states that, under the assumption of uncorrelated sample points, yield optimal accuracy. These intermediates differ fundamentally from the common intermediates in that they are non-pairwise, i.e., the forces on a particle are only additive in the end state, whereas the total force in the intermediate states cannot be split into additive contributions from the surrounding particles.

References

[1] M. Reinhardt, H. Grubmüller, Determining Free-Energy Differences Through Variationally Derived Intermediates, Journal of Chemical Theory and Computation 16 (6) 3504-3512 (2020).

中文翻译：

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使用非成对的变分派生中间体进行自由能计算的GROMACS实现

自由能的梯度是物理和生化系统的驱动力。为了高精度地预测自由能的差异，分子动力学（MD）和其他基于原子哈密顿量的方法在中间热力学状态下进行了采样模拟，这些热力学状态桥接了两个目标状态（“化学转化”）之间的构型空间密度。对于不相关的采样，最新的变分派生中间体（VI）方法可产生最佳精度。VI中间体的形式与常规中间体的根本区别在于它们是非成对的，即，处于中间状态的粒子上的总力无法分解为周围粒子的累加贡献。在这项工作中，我们描述了VI在广泛使用的GROMACS MD软件包（2020年，版本1）。此外，开发了一种VI的变体，它避免了消失粒子的数值不稳定性。该实现允许使用文献中以前的非成对势形式，这在GROMACS中尚不可用。提供了关于溶剂化自由能的计算及其精度评估的示例情况。

计划摘要

程序名称：GROMACS-VI-Extension

CPC库链接到程序文件： https : //doi.org/10.17632/7yvc8mmnyv.1

开发人员的资料库链接： https : //www.mpibpc.mpg.de/gromacs-vi-extension和https://www.gitlab.gwdg.de/martin.reinhardt/gromacs-vi-extension

许可规定： LGPL

编程语言： C ++ 14，CUDA

问题的性质：热力学系统两个状态之间的自由能差是使用基于原子哈密顿量的模拟生成的样本来计算的。由于例如生物物理学中的许多应用的高维度，因此只能对配置空间的一小部分进行采样。采样方案的选择会严重影响最终自由能估算的准确性。因此，面临的挑战是要找到能够为给定的计算工作提供最佳准确性的最佳采样方案。

解决方法：采样通常在中间状态下进行，中间状态的哈密顿量是基于两个感兴趣状态的哈密顿量来定义的。在此，在不相关的采样点的假设下，以变分派生的中间状态进行采样，从而获得最佳精度。这些中间体与普通中间体的根本不同之处在于它们是非成对的，即作用在颗粒上的力仅在最终状态下相加，而中间状态下的总力无法分解为周围颗粒的相加作用。

参考

[1] M. Reinhardt，H.Grubmüller，通过变分衍生中间体确定自由能差异，化学理论与计算杂志16（6）3504-3512（2020）。