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

Abstract

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 summaryProgram Title: GROMACS-VI-ExtensionCPC Library link to program files:https://doi.org/10.17632/7yvc8mmnyv.1Developer’s repository link:https://www.mpibpc.mpg.de/gromacs-vi-extension and https://www.gitlab.gwdg.de/martin.reinhardt/gromacs-vi-extensionLicensing provisions: LGPLProgramming language: C++14, CUDANature 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.