William C. Swope

We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill’s formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.

A re-parameterization of the standard TIP4P water model for use with Ewald techniques is introduced, providing an overall global improvement in water properties relative to several popular nonpolarizable and polarizable water potentials. Using high precision simulations, and careful application of standard analytical corrections, we show that the new TIP4P-Ew potential has a density maximum at approximately 1 degrees C, and reproduces experimental bulk-densities and the enthalpy of vaporization, DeltaH(vap), from -37.5 to 127 degrees C at 1 atm with an absolute average error of less than 1%. Structural properties are in very good agreement with x-ray scattering intensities at temperatures between 0 and 77 degrees C and dynamical properties such as self-diffusion coefficient are in excellent agreement with experiment. The parameterization approach used can be easily generalized to rehabilitate any water force field using available experimental data over a range of thermodynamic points.

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). We use large-scale distributed computing to access sufficient computational resources to extensively sample molecular systems and thus reduce statistical uncertainty of measured free energies. In order to examine the accuracy of a range of common models used for protein simulation, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from recent versions of the OPLS-AA, CHARMM, and AMBER parameter sets in TIP3P water using thermodynamic integration. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02–0.05 kcal/mol, which are in general an order of magnitude smaller than those found in other studies. Notably, this level of precision is comparable to that obtained in experimental hydration free energy measurements of the same molecules. Root mean square differences from experiment over the set of molecules examined using AMBER-, CHARMM-, and OPLS-AA-derived parameters were 1.35 kcal/mol, 1.31 kcal/mol, and 0.85 kcal/mol, respectively. Under the simulation conditions used, these force fields tend to uniformly underestimate solubility of all the side chain analogs. The relative free energies of hydration between amino acid side chain analogs were closer to experiment but still exhibited significant deviations. Although extensive computational resources may be needed for large numbers of molecules, sufficient computational resources to calculate precise free energy calculations for small molecules are accessible to most researchers.

To meet the challenge of modeling the conformational dynamics of biological macromolecules over long time scales, much recent effort has been devoted to constructing stochastic kinetic models, often in the form of discrete-state Markov models, from short molecular dynamics simulations. To construct useful models that faithfully represent dynamics at the time scales of interest, it is necessary to decompose configuration space into a set of kinetically metastable states. Previous attempts to define these states have relied upon either prior knowledge of the slow degrees of freedom or on the application of conformational clustering techniques which assume that conformationally distinct clusters are also kinetically distinct. Here, we present a first version of an automatic algorithm for the discovery of kinetically metastable states that is generally applicable to solvated macromolecules. Given molecular dynamics trajectories initiated from a well-defined starting distribution, the algorithm discovers long lived, kinetically metastable states through successive iterations of partitioning and aggregating conformation space into kinetically related regions. The authors apply this method to three peptides in explicit solvent-terminally blocked alanine, the 21-residue helical F(s) peptide, and the engineered 12-residue beta-hairpin trpzip2-to assess its ability to generate physically meaningful states and faithful kinetic models.

The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.