Zeroing in on the Cutoff Radius

Treating electrostatic forces accurately has become a problem for MD because of the sheer size of the problems researchers want to attack. Simulations of large proteins or DNA with water involve 10,000 or more atoms, making it infeasible to explicitly calculate each atom's interaction with every other. As a reasonable approximation that makes the computation possible, researchers traditionally use a "cutoff radius" -- usually around 10 angstroms -- beyond which electrostatic forces (which decrease with distance) have been considered insignificant.

This works fairly well in some cases. In others it doesn't. Pedersen and Darden started running into the melting problem when they simulated DNA and a large protein involved in cancer (H-ras p21). Both are highly charged molecules, which suggested electrostatics could be the problem. "Tom and I," says Pedersen, "were doing simulations that five years ago people would have said were all right, but we were extending them to longer times. We really wanted the answer, yet we could see before our eyes that something was fundamentally wrong." Other researchers were running into the same problem, and many began to conclude it was an inherent weakness of MD.

Pedersen and Darden began to zero in on a solution when one of their students, Darrin York, spent a summer working at the Pittsburgh Supercomputing Center. York and PSC biomedical scientist David Deerfield were running simulations that included magnesium and sodium ions, called "counterions" because their positive charges neutralize the negative charge of DNA. Pedersen visited to check on progress: "Darrin kept saying look at this. It was pretty apparent what was happening."

The ions separated from each other at exactly the distance of the cutoff radius. Because they aren't bonded to other atoms, counterions have greater freedom to move around in the water: "They respond to long range electrostatic forces," explains Darden, "and with a cutoff radius they never reach natural equilibrium. When they come closer than the cutoff, they repel each other, and as soon as they're outside, they don't feel a thing. The end result is they hang out right at the cutoff." With this strong clue that cutoff radius was the culprit, Darden set about finding a better way.

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