To eliminate the inaccuracy introduced by a cutoff radius, Darden turned back to a much cited 1921 paper by Paul Ewald, who helped pioneer X-ray crystallography. Darden's central insight was to see how "Ewald summation" -- a method for summing up the collection of charges in a crystalline lattice -- could be combined with a very fast computational method -- fast Fourier transforms (FFT). "We're the first people to do macromolecular Ewald summation," says Darden, "because no one had a way to do it fast."
To make Ewald summation workable for the irregular charge distribution typical of MD, Darden turned to plasma physics for the "particle mesh method." As a check on the accuracy of this innovative synthesis, dubbed "particle mesh Ewald" (PME), Darden, York and Pedersen ran a one nanosecond simulation of a large protein (bovine pancreatic trypsin inhibitor) and compared results to the crystal structure. The deviation was lower than observed between different crystallized forms of the protein.
"We can now run long simulations, and we don't get the melting," says Darden. "We get high accuracy. Furthermore, simulations with PME are less expensive than with a 10 angstrom cutoff." Using PME, Darden and Pedersen have now completed the simulations of DNA and the H-ras p21 protein that previously stymied them.
To further exploit the improved realism of the new method, PSC biomedical scientist Mike Crowley has collaborated with Darden to implement a parallelized version of PME simulations on the CRAY T3D at Pittsburgh. The key stumbling block to an efficient parallel implementation was FFT, and Crowley solved this problem. "Before the T3D," says Darden, "FFT people were saying that it doesn't work well on massively parallel systems. But the T3D has such good communication bandwidth, Mike was able to come up with an efficient three-dimensional FFT routine."
Darden is also collaborating with Peter Kollman's research group at the University of California, San Francisco to incorporate PME into the AMBER package of MD routines. Because PME combines greater realism with fast performance, Darden and Pedersen see it as bridging the gap between the accuracy of structures determined by crystallography and NMR and MD's ability to simulate how biomolecules act inside the cell.
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