In this paper, we present a scalable and efficient 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-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 for a polarizable model making 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 non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.
Classical electrostatics models that take into account polarization appeared as early as the 1950s. Barker in his 1953 paper "Statistical Mechanics of Interacting Dipoles" discussed the electrostatic energy of molecules in terms of "permanent and induced dipoles". 13 Currently, polarizable models generally fall into three categories: those based on induced point dipoles, 9, 14-23 the classical Drude oscillators, 24-26 and fluctuating charges. 27-30 More sophisticated force fields that are "electronic structure-based" 31, 32 or use "machine learning methods" 33 also exist, but incur higher computational costs. Discussions of the advantages and disadvantages of each model and their applications will be presented in the following sections. Compared to fixed charge models, the polarizable models are still in a relatively early stage. Only in the past decade or so has there been a systematic effort to develop general polarizable force fields for molecular modeling. A number of reviews have been published to discuss various aspects of polarizable force fields and their development. 9, 34-40 Here, we focus on the recent development and applications of different polarizable force fields. We begin with a brief introduction to the basic principles and formulae underlying alternative models. Next, the recent progress of several well-developed polarizable force fields is reviewed. Finally, applications of polarizable models to a range of molecular systems, including water and other small molecules, ion solvation, peptides, proteins and lipid systems are presented.
We present for the first time scalable polarizable molecular dynamics (MD) simulations within a polarizable continuum solvent with molecular shape cavities and exact solution of the mutual polarization. The key ingredients are a very efficient algorithm for solving the equations associated with the polarizable continuum, in particular, the domain decomposition Conductor-like Screening Model (ddCOSMO), a rigorous coupling of the continuum with the polarizable force field achieved through a robust variational formulation and an effective strategy to solve the coupled equations. The coupling of ddCOSMO with non variational force fields, including AMOEBA, is also addressed. The MD simulations are feasible, for real life systems, on standard cluster nodes; a scalable parallel implementation allows for further speed up in the context of a newly developed module in Tinker, named Tinker-HP. NVE simulations are stable and long term energy conservation can be achieved. This paper is focused on the methodological developments, on the analysis of the algorithm and on the stability of the simulations; a proof-of-concept application is also presented to attest the possibilities of this newly developed technique.
Many biological processes are based on molecular recognition between highly charged molecules such as nucleic acids, inorganic ions, charged amino acids, etc. For such cases, it has been demonstrated that molecular simulations with fixed partial charges often fail to achieve experimental accuracy. Although incorporation of more advanced electrostatic models (such as multipoles, mutual polarization, etc.) can significantly improve simulation accuracy, it increases computational expense by a factor of 5–20×. Indirect free energy (IFE) methods can mitigate this cost by modeling intermediate states at fixed-charge resolution. For example, an efficient “reference” model such as a pairwise Amber, CHARMM, or OPLS-AA force field can be used to derive an initial estimate, followed by thermodynamic corrections to a more advanced “target” potential such as the polarizable AMOEBA model. Unfortunately, all currently described IFE methods encounter difficulties reweighting more than ∼50 atoms between resolutions due to extensive scaling of both the magnitude of the thermodynamic corrections and their statistical uncertainty. We present an approach called “simultaneous bookending” (SB) that is fundamentally different from existing IFE methods based on a tunable sampling approximation, which permits scaling to thousands of atoms. SB is demonstrated on the relative binding affinity of Mg2+/Ca2+ to a set of metalloproteins with up to 2972 atoms, finding no statistically significant difference between direct AMOEBA results and those from correcting Amber to AMOEBA. The ability to change the resolution of thousands of atoms during reweighting suggests the approach may be applicable in the future to protein–protein binding affinities or nucleic acid thermodynamics.
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