Langevin modes analysis of myoglobin

Langevin modes describe the behavior of atoms moving on a harmonic potential surface subject to viscous damping described by a classical Langevin equation. We present applications to myoglobin. The Langevin modes are obtained from the gas-phase normal modes using a perturbation expansion. The friction matrix in the Langevin description is assumed diagonal thus ignoring hydrodynamic interactions. The diagonal elements, which are the atomic friction constants on each atom, are weighted according to the surface area accessible to the solvent. Time-dependence of the position and velocity correlation functions are calculated for the Fe atom buried inside the protein for varying values of the external solvent viscosity. Even for negligibly small values of the viscosity, the time correlation functions are overdamped and suggest a substantial damping component from the neighboring protein atoms. The effective friction seen by the Fe atom has contributions from both the solvent friction as well as the internal protein friction. The internal protein friction is estimated to be about 14 ps(-1) and is comparable to the friction of water. The viscosity dependence of the inverse of the effective friction on the Fe atom is found to agree qualitatively with the viscosity dependence of the experimentally measured rate of conformational changes in myoglobin. (C) 1999 American Institute of Physics. [S0021-9606(99)50303-6].