The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Optimizing potentials for a liquid mixture: a new force field for a tert-butanol and water solution

A technology for optimization of potential parameters from condensed-phase simulations (POP) is discussed and illustrated. It is based on direct calculations of the derivatives of macroscopic observables with respect to the potential parameters. The derivatives are used in a local minimization scheme, comparing simulated and experimental data. In particular, we show that the Newton trust region protocol allows for more accurate and robust optimization. We apply the newly developed technology to study the liquid mixture of tert-butanol and water. We are able to obtain, after four iterations, the correct phase behavior and accurately predict the value of the Kirkwood Buff (KB) integrals. We further illustrate that a potential that is determined solely by KB information, or the pair correlation function, is not necessarily unique.

Electrostatic free energies in translational GTPases: Classic allostery and the rest

GTPases typically switch between an inactive, OFF conformation and an active, ON conformation when a GDP ligand is replaced by GTP. Their ON/OFF populations and activity thus depend on the stabilities of four protein complexes, two apo-protein forms, and GTP/GDP in solution. A complete characterization is usually not possible experimentally and poses major challenges for simulations. We review the most important methodological challenges and we review thermodynamic data for two GTPases involved in translation of the genetic code: archaeal Initiation Factors 2 and 5B (aIF2, aIF5B). One main challenge is the multiplicity of states and conformations, including those of GTP/GDP in solution. Another is force field accuracy, especially for interactions of GTP/GDP with co-bound divalent Mg(2+) ions. The calculation of electrostatic free energies also poses specific challenges, and requires careful protocols. For aIF2, experiments and earlier simulations showed that it is a "classic" GTPase, with distinct ON/OFF conformations that prefer to bind GTP and GDP, respectively. For aIF5B, we recently proposed a non-classic mechanism, where the ON/OFF states differ only in the protonation state of Glu81 in the nucleotide binding pocket. This model is characterized here using free energy simulations. The methodological analysis should help future studies, while the aIF2, aIF5B examples illustrate the diversity of ATPase/GTPase mechanisms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Building Force Fields: An Automatic, Systematic, and Reproducible Approach

The development of accurate molecular mechanics force fields is a significant challenge that must be addressed for the continued success of molecular simulation. We developed the ForceBalance method to automatically derive accurate force field parameters using flexible combinations of experimental and theoretical reference data. The method is demonstrated in the parametrization of two rigid water models, yielding new parameter sets (TIP3P-FB and TIP4P-FB) that accurately describe many physical properties of water.

Hydration Free Energy from Orthogonal Space Random Walk and Polarizable Force Field

The orthogonal space random walk (OSRW) method has shown enhanced sampling efficiency in free energy calculations from previous studies. In this study, the implementation of OSRW in accordance with the polarizable AMOEBA force field in TINKER molecular modeling software package is discussed and subsequently applied to the hydration free energy calculation of 20 small organic molecules, among which 15 are positively charged and five are neutral. The calculated hydration free energies of these molecules are compared with the results obtained from the Bennett acceptance ratio method using the same force field, and overall an excellent agreement is obtained. The convergence and the efficiency of the OSRW are also discussed and compared with BAR. Combining enhanced sampling techniques such as OSRW with polarizable force fields is very promising for achieving both accuracy and efficiency in general free energy calculations.

Implementing electrostatic polarization cannot fill the gap between experimental and theoretical measurements for the ultrafast fluorescence decay of myoglobin

Over the past few years, time-dependent ultrafast fluorescence spectroscopy method has been applied to the study of protein dynamics. However, observations from these experiments are in a controversy with other experimental studies. Participating of theoretical methods in this debate has not reconciled the contradiction, because the predicted initial relaxation from computer simulations is one-order faster than the ultrafast fluorescence spectroscopy experiment. In those simulations, pairwise force fields are employed, which have been shown to underestimate the roughness of the free energy landscape. Therefore, the relaxation rate of protein and water molecules under pairwise force fields is falsely exaggerated. In this work, we compared the relaxations of tryptophan/environment interaction under linear response approximation employing pairwise, polarized, and polarizable force fields. Results show that although the relaxation can be slowed down to a certain extent, the large gap between experiment and theory still cannot be filled.

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

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.

Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches

Quantum mechanical (QM) calculations of noncovalent interactions are uniquely useful as tools to test and improve molecular mechanics force fields and to model the forces involved in biomolecular binding and folding. Because the more computationally tractable QM methods necessarily include approximations, which risk degrading accuracy, it is essential to evaluate such methods by comparison with high-level reference calculations. Here, we use the extensive Benchmark Energy and Geometry Database (BEGDB) of CCSD(T)/CBS reference results to evaluate the accuracy and speed of widely used QM methods for over 1200 chemically varied gas-phase dimers. In particular, we study the semiempirical PM6 and PM7 methods; density functional theory (DFT) approaches B3LYP, B97-D, M062X, and ωB97X-D; and symmetry-adapted perturbation theory (SAPT) approach. For the PM6 and DFT methods, we also examine the effects of post hoc corrections for hydrogen bonding (PM6-DH+, PM6-DH2), halogen atoms (PM6-DH2X), and dispersion (DFT-D3 with zero and Becke–Johnson damping). Several orders of the SAPT expansion are also compared, ranging from SAPT0 up to SAPT2+3, where computationally feasible. We find that all DFT methods with dispersion corrections, as well as SAPT at orders above SAPT2, consistently provide dimer interaction energies within 1.0 kcal/mol RMSE across all systems. We also show that a linear scaling of the perturbative energy terms provided by the fast SAPT0 method yields similar high accuracy, at particularly low computational cost. The energies of all the dimer systems from the various QM approaches are included in the Supporting Information, as are the full SAPT2+(3) energy decomposition for a subset of over 1000 systems. The latter can be used to guide the parametrization of molecular mechanics force fields on a term-by-term basis.

Polarizable empirical force field for hexopyranose monosaccharides based on the classical Drude oscillator

A polarizable empirical force field based on the classical Drude oscillator is presented for the hexopyranose form of selected monosaccharides. Parameter optimization targeted quantum mechanical (QM) dipole moments, solute-water interaction energies, vibrational frequencies, and conformational energies. Validation of the model was based on experimental data on crystals, densities of aqueous-sugar solutions, diffusion constants of glucose, and rotational preferences of the exocylic hydroxymethyl of d-glucose and d-galactose in aqueous solution as well as additional QM data. Notably, the final model involves a single electrostatic model for all sixteen diastereomers of the monosaccharides, indicating the transferability of the polarizable model. The presented parameters are anticipated to lay the foundation for a comprehensive polarizable force field for saccharides that will be compatible with the polarizable Drude parameters for lipids and proteins, allowing for simulations of glycolipids and glycoproteins.

Modeling organochlorine compounds and the σ-hole effect using a polarizable multipole force field

The charge distribution of halogen atoms on organochlorine compounds can be highly anisotropic and even display a so-called σ-hole, which leads to strong halogen bonds with electron donors. In this paper, we have systematically investigated a series of chloromethanes with one to four chloro substituents using a polarizable multipole-based molecular mechanics model. The atomic multipoles accurately reproduced the ab initio electrostatic potential around chloromethanes, including CCl₄, which has a prominent σ-hole on the Cl atom. The van der Waals parameters for Cl were fitted to the experimental density and heat of vaporization. The calculated hydration free energy, solvent reaction fields, and interaction energies of several homo- and heterodimer of chloromethanes are in good agreement with experimental and ab initio data. This study suggests that sophisticated electrostatic models, such as polarizable atomic multipoles, are needed for accurate description of electrostatics in organochlorine compounds and halogen bonds, although further improvement is necessary for better transferability.

Molecular dynamics study of response of liquid N,N-dimethylformamide to externally applied electric field using a polarizable force field

The behavior of Liquid N,N-dimethylformamide subjected to a wide range of externally applied electric fields (from 0.001 V/nm to 1 V/nm) has been investigated through molecular dynamics simulation. To approach the objective the AMOEBA polarizable force field was extended to include the interaction of the external electric field with atomic partial charges and the contribution to the atomic polarization. The simulation results were evaluated with quantum mechanical calculations. The results from the present force field for the liquid at normal conditions were compared with the experimental and molecular dynamics results with non-polarizable and other polarizable force fields. The uniform external electric fields of higher than 0.01 V/nm have a significant effect on the structure of the liquid, which exhibits a variation in numerous properties, including molecular polarization, local cluster structure, rotation, alignment, energetics, and bulk thermodynamic and structural properties.

An Anisotropic Coarse-Grained Model for Proteins Based On Gay-Berne and Electric Multipole Potentials

Gay–Berne anisotropic potential has been widely used to evaluate the nonbonded interactions between coarse-grained particles being described as elliptical rigid bodies. In this paper, we are presenting a coarse-grained model for twenty kinds of amino acids and proteins, based on the anisotropic Gay–Berne and point electric multipole (EMP) potentials. We demonstrate that the anisotropic coarse-grained model, namely GBEMP model, is able to reproduce many key features observed from experimental protein structures (Dunbrack Library), as well as from atomistic force field simulations (using AMOEBA, AMBER, and CHARMM force fields), while saving the computational cost by a factor of about 10–200 depending on specific cases and atomistic models. More importantly, unlike other coarse-grained approaches, our framework is based on the fundamental intermolecular forces with explicit treatment of electrostatic and repulsion-dispersion forces. As a result, the coarse-grained protein model presented an accurate description of nonbonded interactions (particularly electrostatic component) between hetero/homodimers (such as peptide–peptide, peptide–water). In addition, the encouraging performance of the model was reflected by the excellent correlation between GBEMP and AMOEBA models in the calculations of the dipole moment of peptides. In brief, the GBEMP model given here is general and transferable, suitable for simulating complex biomolecular systems.

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.