Simulating how molecules move.

A complex molecule, whether a fullerene, protein, or strand of DNA, is an unwieldy object to describe. Though a stick-and-ball model can reveal its structure, one, can only guess how such an entity will move when it flexes and folds.

Biochemists have now joined with mathematicians to make computer programs that show how complicated molecules -- sometimes composed of thousands of atoms -- move.

Benedict J. Leimkuhler and Eric J. Barth, both mathematicians at the University of Kansas in Lawrence, report devising a model that simulates the interactive motions of a large molecule. Their algorithm, which illustrates "constrained molecular dynamics," not only captures the movements within complex molecules, it also speeds up such simulations.

"The problem we're addressing as mathematicians is to improve the algorithms used to model biomolecules," explains Leimkuhler. "The models treat molecules as a collection of point masses connected by forces. Our goal is to make those algorithms more efficient for ... more powerful simulations."

To mimic motion in a protein with 10,000 atoms, the algorithm breaks up the molecule's twisting into discrete units. "It determines the state of the molecule at each time step. At any moment, the algorithm knows where the molecule has been and then predicts where it is going," says Leimkuhler.

In a stepwise fashion, the program shows how a molecule's components interact with and affect one another. "The goal is to make an algorithm efficient so it can show realistic motions over a reasonable span of time," says Leimkuhler. "Right now we're working in femtosecond, or 10-15, increments. Ultimately, we want to show how proteins fold, or how nylon stretches, or how buckyballs lubricate a surface. These actions take place over 1 or more seconds, so we have a long way to go."