Myoglobin (Mb) is perhaps the most studied protein, experimentally and theoretically. Despite the wealth of known details regarding the gas migration processes inside Mb, there exists no fully conclusive picture of these pathways. We address this deficiency by presenting a complete map of all the gas migration pathways inside Mb for small gas ligands (O2, NO, CO, and Xe). To accomplish this, we introduce a computational approach for studying gas migration, which we call implicit ligand sampling. Rather than simulating actual gas migration events, we infer the location of gas migration pathways based on a free-energy perturbation approach applied to simulations of Mb's dynamical fluctuations at equilibrium in the absence of ligand. The method provides complete three-dimensional maps of the potential of meanforce of gas ligand placement anywhere inside a protein-solvent system. From such free-energy maps we identify each gas docking site, the pathways between these sites, to the heme and to the external solution. Our maps match previously known features of these pathways in Mb, but also point to the existence of additional exits from the protein matrix in regions that are not easily probed by experiment. We also compare the pathway maps of Mb for different gas ligands and for different animal species.
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