Massively Parallel Implementation of Steered Molecular Dynamics in Tinker-HP: Comparisons of Polarizable and Non-Polarizable Simulations of Realistic Systems

This paper is dedicated to the massively parallel implementation of Steered Molecular Dynamics in the Tinker-HP softwtare. It allows for direct comparisons of polarizable and non-polarizable simulations of realistic systems

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </div

A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms

International audienceIn this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self parts of the Ewald summation where different expressions can be found in literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and subsequently, all other quantities such as the electric field, the energy and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution

Tinker 8: Software Tools for Molecular Design

International audienceThe Tinker software, currently released as version 8, is a modular molecular mechanics and dynamics package written primarily in a standard, easily portable dialect of Fortran 95 with OpenMP extensions. It supports a wide variety of force fields, including polarizable models such as the Atomic Multipole Optimized Energetics for Biomolecular Applicatons (AMOEBA) force field. The package runs on Linux, macOS and Windows systems. In addition to canonical Tinker there are branches, Tinker-HP and Tinker-OpenMM, designed for use on MPI-parallel distributed memory supercomputers and state-of-the-art graphical processing units (GPUs), respectively. The Tinker suite also includes a tightly integrated Java-based graphical user interface called Force Field Explorer (FFE), which provides molecular visualization capabilities as well as the ability to launch and control Tinker calculations

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II. Towards Massively Parallel Computations using Smooth Particle Mesh Ewald

International audienceIn this article, we present a parallel implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The smooth particle mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the direct inversion in the iterative subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy and force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package, which is the first implementation of a polarizable model that makes large-scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of SPME and a noticeable improvement of the memory management, giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to nonoptimized, sequential implementations, giving new directions for polarizable molecular dynamics with periodic boundary conditions using massively parallel implementations

Addressing the issues of non-isotropy and non-additivity in the development of quantum chemistry-grounded polarizable molecular mechanics.

International audienceWe review two essential features of the intermolecular interaction energies (ΔE) computed in the context of quantum chemistry (QC): non-isotropy and non-additivity. Energy-decomposition analyses show the extent to which each comes into play in the separate ΔE contributions, namely electrostatic, short-range repulsion, polarization, charge-transfer and dispersion. Such contributions have their counterparts in anisotropic, polarizable molecular mechanics (APMM), and each of these should display the same features as in QC. We review examples to evaluate the performances of APMM in this respect. They bear on the complexes of one or several ligands with metal cations, and on multiply H-bonded complexes. We also comment on the involvement of polarization, a key contributor to non-additivity, in the issues of multipole transferability and conjugation. In the last section we provide recent examples of APMM validations by QC, which relate to interactions taking place in the recognition sites of kinases and metalloproteins. We conclude by mentioning prospects of extensive applications of APMM

A General Model for Treating Short-Range Electrostatic Penetration in a Molecular Mechanics Force Field

International audienceClassical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge–charge function previously reported (Piquemal, J.-P.; J. Phys. Chem. A 2003, 107) 10353) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101×7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (Parker, T. M.; J. Chem. Phys. 2014, 140, 094106). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields

Reconciling NMR Structures of the HIV-1 Nucleocapsid Protein (NCp7) using Extensive Polarizable Force Field Free-Energy Simulations

Using polarizable (AMOEBA) and non-polarizable (CHARMM) force fields, we compare the relative free-energy stability of two extreme conformations of the HIV-1 NCp7 nucleocapsid that had been previously experimentally advocated to prevail in solution. Using accelerated sampling techniques, we show that they differ in stability by no more than 0.75-1.9 kcal/mol depending on the reference protein sequence. While the extended form appears to be the most probable structure, both forms should thus coexist in water explaining the differing NMR findings.<br /