for Biomolecular Simulation
The research goal is to develop new computational techniques that contribute to scientific understanding of life at the molecular level. Current work involves physics-based models, numerical algorithms, and massive computation in collaborations with biophysicists.
Molecular simulations are used most often for sampling configuration space to determine structure and free energy profiles, but they are also used directly for kinetic calculations. The computational costs are very high for all-atom models, and it is an important research problem to systematically construct less detailed models that capture the essential features. Current research embraces three computational challenges: (i) the problem of sampling very high dimensional configuration space, (ii) the problem of doing dynamics simulations on biological time scales, and (iii) the problem of calculating energies and forces for large numbers of particles. Results from this work are implemented in the parallel molecular dynamics program NAMD.
The nature of biomolecular phenomena requires sampling enormous numbers of points or short trajectories in configuration space or a more modest number of long trajectories. Currently we are completing a project involving the novel use of importance sampling to bring down by orders of magnitude the cost of calculating the reaction rate between a ligand and an enzyme. We plan to adapt these and other techniques to other contexts such as calculations of reactions paths, potentials of mean force, and/or conformational dynamics.
For atomic-resolution molecular dynamics, the time step is severely limited. Also, there are difficult questions concerning the accuracy of long-time numerical integrations. We have obtained theoretical results that have excellent predictive power for the stability and accuracy of typical integrators and have created a scheme, Langevin MOLLY, that permits a much longer time step. The current goal is to construct other more efficient methods and to develop theoretical justification for long-time numerical integrations.
The cost of direct evaluation of energies and forces is proportional to the square of the number of degrees of freedom. Methods such as the celebrated fast multipole method reduce the cost to being linear. However, the constant can be quite large due to the moderately high accuracy needed to maintain stability. For this reason we have developed a fast algorithm based on the use of multiple grids that generates forces that are continuous as functions of particle positions. Results published recently show a great improvement over the fast multipole method for accuracies needed in molecular dynamics. The method is being extended to the case of periodic boundary conditions and then to force fields incorporating polarizability.