Dynamics of ligand escape from the heme pocket of myoglobin

Molecular dynamics calculations are used to study the kinetics of the process by which a dioxygen ligand leaves the heme pocket of sperm whale myoglobin. Umbrella sampling techniques are used to generate free-energy profiles at several temperatures for escape along a path between the distal histidine and valine residues, and methods for assessing the statistical precision of such profiles are explored. The results are used to compute rate constants for ligand escape, both in the transition-state approximation and with full classical dynamics. Corrections to transition-state theory rates (i.e., the transmission coefficients) are in the range 0.8 to 0.9 for this process, and the computed rate constants at room temperature are in good agreement with experiment. Near room temperature the computed activation energy is less than 1 kcal/mol, but at lower temperatures (between 180 and 270 K) this rises to 5 kcal/mol. Potential physical origins of such non-Arrhenius temperature dependence are discussed in light of models of protein fluctuations that accompany ligand escape.