Bimolecular reaction simulation using Weighted Ensemble Brownian dynamics and the University of Houston Brownian Dynamics program.

We discuss here the implementation of the Weighted Ensemble Brownian (WEB) dynamics algorithm of Huber and Kim in the University of Houston Brownian Dynamics (UHBD) suite of programs and its application to bimolecular association problems. WEB dynamics is a biased Brownian dynamics (BD) algorithm that is more efficient than the standard Northrup-Allison-McCammon (NAM) method in cases where reaction events are infrequent because of intervening free energy barriers. Test cases reported here include the Smoluchowski rate for association of spheres, the association of the enzyme copper-zinc superoxide dismutase with superoxide anion, and the binding of the superpotent sweetener N-(p-cyanophenyl)-N'-(diphenylmethyl)-guanidinium acetic acid to a monoclonal antibody fragment, NC6.8. Our results show that the WEB dynamics algorithm is a superior simulation method for enzyme-substrate reaction encounters with large free energy barriers.

Knowledge-based interaction potentials for proteins.

We discuss the derivation of atomic-level potentials of mean force from the known protein structures and their applicability for structural evaluation applications. In the derivation process, rigorous density estimation methodology is used to estimate the probability density functions (PDFs) for the distributions of interatomic distances in the protein structures. Potentials of mean force are then derived from these density functions using simple Boltzmann's relation. We also test the potentials against pairs of current and superseded protein structures in the Protein Data Bank. Using PDF potentials to evaluate each structure pair, we are able to identify, with high accuracy, which of the two structures is of higher resolution or better quality. This result shows that the PDF potentials are sensitive to details in protein structures as the current and superseded atomic coordinates generally do not differ by more than 1 A in root-mean-square deviation, and that the PDF potentials could potentially be used for X-ray structure refinement and protein structure prediction.

Brownian dynamics simulations of protein folding: access to milliseconds time scale and beyond.

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion-collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion-collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.