Mapping the network of pathways of CO diffusion in myoglobin.

The pathways of diffusion of a CO molecule inside a myoglobin protein and toward the solvent are investigated. Specifically, the three-dimensional potential of mean force (PMF or free energy) of the CO molecule position inside the protein is calculated by using the single-sweep method in concert with fully resolved atomistic simulations in explicit solvent. The results are interpreted under the assumption that the diffusion of the ligand can be modeled as a navigation on the PMF in which the ligand hops between the PMF local minima following the minimum free energy paths (MFEPs) with rates set by the free energy barriers that need to be crossed. Here, all the local minima of the PMF, the MFEPs, and the barriers along them are calculated. The positions of the local minima are in good agreement with all the known binding cavities inside the protein, which indicates that these cavities may indeed serve as dynamical traps inside the protein and thereby influence the binding process. In addition, the MFEPs connecting the local PMF minima show a complicated network of possible pathways of exit of the dissociated CO starting from the primary docking site, in which the histidine gate is the closest exit from the binding site for the ligand but it is not the only possible one.