GROMACS Extension for Free Energy Calculations with Non-Pairwise Variationally Derived Intermediates

Non-pairwise potentials and forces in VI intermediates. Two particles i and j (red and blue, respectively) are considered that are lambda dependent, i.e., their interaction potential differs between A and B. It is assumed that direct interactions between i and j in both A and B are negligible. If particle i changes its position, then the Hamiltonians of the end states, HA and HB, respectively, change and so does the one in the intermediate HVI. Due to the form of the VI sequence, the derivative, and therefore, the force on particle j changes.

Gradients in free energies are the driving forces of physical and biochemical systems. 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.

To improve accuracy, sampling is commonly conducted in intermediate states, whose Hamiltonians are defined based on the Hamiltonians of the two states of interest. We have recently developed the variationally derived intermediates (VI) method (Link to project page). The VI intermediates yield, under the assumption of uncorrelated sample points, optimal accuracy. They 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. Furthermore, an end state dependence on the path variable lambda has been introduced to avoid divergences for vanishing particles.

VI has been implemented into the GROMACS 2020 MD software package. The implementation is conducted such that previous non-pairwise potential forms from the literature, which have so far not yet been available in GROMACS, can also be used. The package including the VI extension can be downloaded, together with documentation, test and example cases from the link below.

The source code can also be downloaded here [zip file]

Publication

Reinhardt, M.; Grubmüller, H.
GROMACS Implementation of Free Energy Calculations with Non-Pairwise Variationally Derived Intermediates
arXiv:2010.14193 [physics.comp-ph] 2020
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