We introduce a global fitting analysis method to obtain free energies of association of noncovalent molecular clusters using equilibrated cluster size distributions from unbiased constant-temperature molecular dynamics (MD) simulations. Because the systems simulated are small enough that the law of mass action does not describe the aggregation statistics, the method relies on iteratively determining a set of cluster free energies that, using appropriately weighted sums over all possible partitions of N monomers into clusters, produces the best-fit size distribution. The quality of these fits can be used as an objective measure of self-consistency to optimize the cutoff distance that determines how clusters are defined. To showcase the method, we have simulated a united-atom model of methyl tert-butyl ether (MTBE) in the vapor phase and in explicit water solution over a range of system sizes (up to 95 MTBE in the vapor phase and 60 MTBE in the aqueous phase) and concentrations at 273 K. The resulting size-dependent cluster free energy functions follow a form derived from classical nucleation theory (CNT) quite well over the full range of cluster sizes, although deviations are more pronounced for small cluster sizes. The CNT fit to cluster free energies yielded surface tensions that were in both cases lower than those for the simulated planar interfaces. We use a simple model to derive a condition for minimizing non-ideal effects on cluster size distributions and show that the cutoff distance that yields the best global fit is consistent with this condition.

The appeal of multiscale modeling approaches is predicated on the promise of combinatorial synergy. However, this promise can only be realized when distinct scales are combined with reciprocal consistency. Here, we consider multiscale molecular dynamics (MD) simulations that combine the accuracy and macromolecular flexibility accessible to fixed-charge all-atom (AA) representations with the sampling speed accessible to reductive, coarse-grained (CG) representations. AA-to-CG conversions are relatively straightforward because deterministic routines with unique outcomes are achievable. Conversely, CG-to-AA conversions have many solutions due to a surge in the number of degrees of freedom. While automated tools for biomolecular CG-to-AA transformation exist, we find that one popular option, called Backward, is prone to stochastic failure and the AA models that it does generate frequently have compromised protein structure and incorrect stereochemistry. Although these shortcomings can likely be circumvented by human intervention in isolated instances, automated multiscale coupling requires reliable and robust scale conversion. Here, we detail an extension to Multiscale Machine-learned Modeling Infrastructure (MuMMI), including an improved CG-to-AA conversion tool called sinceCG. This tool is reliable (∼98% weakly correlated repeat success rate), automatable (no unrecoverable hangs), and yields AA models that generally preserve protein secondary structure and maintain correct stereochemistry. We describe how the MuMMI framework identifies CG system configurations of interest, converts them to AA representations, and simulates them at the AA scale while on-the-fly analyses provide feedback to update CG parameters. Application to systems containing the peripheral membrane protein RAS and proximal components of RAF kinase on complex eight-component lipid bilayers with ∼1.5 million atoms is discussed in the context of MuMMI.

Micelle cluster distributions from molecular dynamics simulations of a solvent-free coarse-grained model of sodium octyl sulfate (SOS) were analyzed using an improved method to extract equilibrium association constants from small-system simulations containing one or two micelle clusters at equilibrium with free surfactants and counterions. The statistical-thermodynamic and mathematical foundations of this partition-enabled analysis of cluster histograms (PEACH) approach are presented. A dramatic reduction in computational time for analysis was achieved through a strategy similar to the selector variable method to circumvent the need for exhaustive enumeration of the possible partitions of surfactants and counterions into clusters. Using statistics from a set of small-system (up to 60 SOS molecules) simulations as input, equilibrium association constants for micelle clusters were obtained as a function of both number of surfactants and number of associated counterions through a global fitting procedure. The resulting free energies were able to accurately predict micelle size and charge distributions in a large (560 molecule) system. The evolution of micelle size and charge with SOS concentration as predicted by the PEACH-derived free energies and by a phenomenological four-parameter model fit, along with the sensitivity of these predictions to variations in cluster definitions, are analyzed and discussed.

Simulations of small unilamellar lipid bilayer vesicles have been performed to model their response to an instantaneous rise in temperature, starting from an initial low-temperature structure, to temperatures near or above the main chain transition temperature. The MARTINI coarse-grained force-field was used to construct slabs of gel-phase DPPC bilayers, which were assembled into truncated icosahedral structures containing 13,165 or 31,021 lipids. Equilibration at 280 K produced structures with several (5-8) domains, characterized by facets of lipids packed in the gel phase connected by disordered ridges. Instantaneous heating to final temperatures ranging from 290 K to 310 K led to partial or total melting over 500 ns trajectories, accompanied by changes in vesicle shape and the sizes and arrangements of remaining gel-phase domains. At temperatures that produced partial melting, the gel-phase lipid content of the vesicles followed an exponential decay, similar in form and timescale to the sub-microsecond phase of melting kinetics observed in recent ultrafast IR temperature-jump experiments. The changing rate of melting appears to be the outcome of a number of competing contributions, but changes in curvature stress arising from the expansion of the bilayer area upon melting are a major factor. The simulations give a more detailed picture of the changes that occur in frozen vesicles following a temperature jump, which will be of use for the interpretation of temperature-jump experiments on vesicles.

We have performed classical molecular dynamics (MD) simulations of aqueous sodium chloride (NaCl) solutions from 298 to 674 K at 200 bars to understand the influence of ion pairing and ion self-diffusion on electrical conductivity in high-temperature/high-pressure salt solutions. Conductivity data obtained from the MD simulation highlight an apparent anomaly, namely, a conductivity maximum as temperature increases along an isobar, which has been also observed in experimental studies. By examining both velocity autocorrelation and cross-correlation terms of the Green-Kubo integral, we quantitatively demonstrate that the conductivity anomaly arises mainly from a competition between the single-ion self-diffusion and the contact ion pair formation. The velocity autocorrelation function in conjunction with structural analysis suggests that diffusive motion of ions is suppressed at high temperatures due to the persistence of an inner hydration shell. The contribution of velocity cross-correlation functions between oppositely charged ions becomes significant at the onset of the conductivity decrease. Structural analysis based on Voronoi tessellation and pair correlation functions indicates that the fraction of contact ion pairs increases as temperature increases. Spatial decomposition of the electrical conductivity also indicates that the formation of contact ion pairs significantly decreases the electrical conductivity compared to Nernst-Einstein conductivity, but the contribution of distant opposite charges cannot be ignored except at the highest temperature due to unscreened long-range interactions.

The properties of water vary dramatically with temperature and density. This can be exploited to control its effectiveness as a solvent. Thus, supercritical water is of keen interest as solvent in many extraction processes. The low solubility of salts in lower density supercritical water has even been suggested as a means of desalination. The high temperatures and pressures required to reach supercritical conditions can present experimental challenges during collection of required physical property and phase equilibria data, especially in salt-containing systems. Molecular simulations have the potential to be a valuable tool for examining the behavior of solvated ions at these high temperatures and pressures. However, the accuracy of classical force fields under these conditions is unclear. We have, therefore, undertaken a parametric study of NaCl in water, comparing several salt and water models at 200 bar–600 bar and 450 K–750 K for a range of salt concentrations. We report a comparison of structural properties including ion aggregation, hydrogen bonding, density, and static dielectric constants. All of the force fields qualitatively reproduce the trends in the liquid phase density. An increase in ion aggregation with decreasing density holds true for all of the force fields. The propensity to aggregate is primarily determined by the salt force field rather than the water force field. This coincides with a decrease in the water static dielectric constant and reduced charge screening. While a decrease in the static dielectric constant with increasing NaCl concentration is consistent across all model combinations, the salt force fields that exhibit more ionic aggregation yield a slightly smaller dielectric decrement.

Molecular dynamics (MD) simulations to understand the thermodynamic, dynamic, and structural changes in supercritical water across the Frenkel line and the melting line have been performed.

The partition‐enabled analysis of cluster histograms (PEACH) method is used to calculate the free energy surface of NaCl aggregation using cluster statistics from MD simulations of small systems (40–90 ions plus solvent) in four solvents. In all cases (pure methanol, pure water, and two methanol/water mixtures) NaCl clusters show a transition from amorphous to rocksalt structure with increasing cluster size. The crossover sizes, and the apparent kinetic barrier to ordering, increase with increasing water content. Implications for the proposed two‐step mechanism of NaCl crystal nucleation (in which the ordered structure emerges from a large disordered cluster), and how this mechanism might depend on solvent and on degree of supersaturation, are discussed. In pure water, nonideal crowding effects that promote clustering are identified from systematic concentration‐dependent deviations between simulation results and the PEACH model fit. In contrast, the ability of PEACH to fit aggregation statistics in mixed solvents is consistent with negligible interactions between ions in different clusters. © 2018 Wiley Periodicals, Inc.