Statistical Prediction and Molecular Dynamics Simulation

We describe a statistical approach to the validation and improvement of molecular dynamics simulations of macromolecules. We emphasize the use of molecular dynamics simulations to calculate thermodynamic quantities that may be compared to experimental measurements, and the use of a common set of energetic parameters across multiple distinct molecules. We briefly review relevant results from the theory of stochastic processes and discuss the monitoring of convergence to equilibrium, the obtaining of confidence intervals for summary statistics corresponding to measured quantities, and an approach to validation and improvement of simulations based on out-of-sample prediction. We apply these methods to replica exchange molecular dynamics simulations of a set of eight helical peptides under the AMBER potential using implicit solvent. We evaluate the ability of these simulations to quantitatively reproduce experimental helicity measurements obtained by circular dichroism. In addition, we introduce notions of statistical predictive estimation for force-field parameter refinement. We perform a sensitivity analysis to identify key parameters of the potential, and introduce Bayesian updating of these parameters. We demonstrate the effect of parameter updating applied to the internal dielectric constant parameter on the out-of-sample prediction accuracy as measured by cross-validation.