The accuracy of empirical force fields is critical for meaningful molecular dynamics simulations of concentrated ionic solutions. Current models are typically developed on the basis of single ion properties such as the monohydrate energy in the gas phase, or the absolute hydration free energy at infinite dilution. However, the failure of these models to represent accurately the properties of concentrated solutions cannot be excluded. Here, these issues are illustrated for a polarizable potential based on classical Drude oscillators. To model accurately concentrated ionic solutions, the parameters of the potential functions are optimized to reproduce osmotic pressure data. The sodium-chloride potential of mean force in solution calculated from the empirically-adjusted model is consistent with the results from that calculated from ab initio CPMD simulations.
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 phi, psi 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 first generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns time scale 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. However, the polarizable model shows improvement for the residues with significantly underestimated S-2 order parameters in the additive model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have considerably 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 large 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.
An extremely scalable computational strategy is described for calculations of the potential of mean force (PMF) in multidimensions on massively distributed supercomputers. The approach involves coupling thousands of umbrella sampling (US) simulation windows distributed to cover the space of order parameters with a Hamiltonian molecular dynamics replica-exchange (H-REMD) algorithm to enhance the sampling of each simulation. In the present application, US/H-REMD is carried out in a two-dimensional (2D) space and exchanges are attempted alternatively along the two axes corresponding to the two order parameters. The US/H-REMD strategy is implemented on the basis of parallel/parallel multiple copy protocol at the MPI level, and therefore can fully exploit computing power of large-scale supercomputers. Here the novel technique is illustrated using the leadership supercomputer IBM Blue Gene/P with an application to a typical biomolecular calculation of general interest, namely the binding of calcium ions to the small protein Calbindin D9k. The free energy landscape associated with two order parameters, the distance between the ion and its binding pocket and the root-mean-square deviation (rmsd) of the binding pocket relative the crystal structure, was calculated using the US/H-REMD method. The results are then used to estimate the absolute binding free energy of calcium ion to Calbindin D9k. The tests demonstrate that the 2D US/H-REMD scheme greatly accelerates the configurational sampling of the binding pocket, thereby improving the convergence of the potential of mean force calculation.
The relative permeability of salt to water across an atomistic model of the FT-30 reverse osmosis (RO) membrane is studied using molecular dynamics (MD) simulations. The membrane model is built using a heuristic approach and gives a membrane density, water solubility and flux that are in good accord with the experimental values. The salt permeability is calculated from inhomogeneous solubility-diffusion theory using ion pathways from non-equilibrium targeted MD simulations, yielding an estimated salt rejection of 99.9% that is similar to the experimental value. The encouraging agreement with experimental data of FT-30 membrane suggests that MD simulations based on atomic models offer a useful way to support the experimental exploration of RD membrane development. (C) 2011 Elsevier B.V. All rights reserved.
In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.
Accurate force fields are critical for meaningful simulation studies, of highly concentrated electrolytes. The ion models that are widely used in biomolecular simulation's do not necessarily reproduce the correct behavior, at finite concentrations. In principle, the osmotic pressure is a key thermodynamic property that could be used to test and refine force field parameters for concentrated solutions. Here we describe a novel, simple, and practical method to compute the osmotic pressure directly from molecular dynamics (MD) simulation of concentrated' aqueous solutions by introducing an idealized semipermeable membrane. Simple models for Na+, K+, and Cl- are tested and calibrated to accurately reproduce the experimental osmotic pressure at high salt concentration, up to the solubility limit of 4-5 M. The methodology is general and can be extended to any type of solute as well as nonadditive polarizable force fields.
The alpha-hemolysin (alphaHL) is a self-assembling exotoxin that binds to the membrane of a susceptible host cell and causes its death. Experimental studies show that electrically neutral beta-cyclodextrin (betaCD) can insert into the alphaHL channel and significantly increase its anion selectivity. To understand how betaCD can affect ion selectivity, molecular dynamics simulations and potential of mean force (PMF) calculations are carried out for different alphaHL channels with and without the betaCD adapter. A multiscale approach based on the generalized solvent boundary potential is used to reduce the size of the simulated system. The PMF profiles reveal that betaCD has no anion selectivity by itself but can increase the Cl(-) selectivity of the alphaHL channel when lodged into the pore lumen. Analysis shows that betaCD causes a partial desolvation of ions and affects the orientation of nearby charged residues. The ion selectivity appears to result from increased electrostatic interaction between the ion and the channel due to a reduction in dielectric shielding by the solvent. These observations suggest a reasonable explanation of the ion selectivity and provide important information for further ion channel modification.
