Long‐time overdamped Langevin dynamics of molecular chains

We present a novel algorithm of constrained, overdamped dynamics to study the long‐time properties of peptides, proteins, and related molecules. The constraints are applied to an all‐atom model of the molecule by projecting out all components of the nonbonding interactions which tend to alter fixed bond lengths and angles. Because the overdamped dynamical equations are first order in time, the constraints are satisfied by inversion of a banded matrix at each timestep, which is computationally efficient. Thermal effects are included through a Langevin noise term in the equation of motion. Because high‐frequency components of the motion have been eliminated, the timestep of the algorithm is determined by the nonbonding forces, which are two to three orders of magnitude weaker than the bonding forces. Using polyalanine as a test example, we demonstrate that trajectories simulating a microsecond of motion can be run about 103 times faster than an equivalent molecular dynamics simulation. © 1994 by John Wiley & Sons, Inc.