ENHANCED SAMPLING IN MOLECULAR-DYNAMICS - USE OF THE TIME-DEPENDENT HARTREE APPROXIMATION FOR A SIMULATION OF CARBON-MONOXIDE DIFFUSION THROUGH MYOGLOBIN

To obtain enhanced sampling in the study of carbon monoxide motion through myoglobin, a classical version of the time-dependent Hartree approximation is introduced. The method is derived from the Liouville equation by separating the system of interest into two parts, each of which moves in the average field of the other. In the application to myoglobin, the method makes it possible to treat a swarm of ligand molecules in the presence of a single trajectory for the protein. This results in a calculation that is approximately a factor of N faster than the N separate protein-ligand trajectories that would have to be used in standard simulations. Corresponding savings in time can be expected in other applications of the method to appropriate condensed phase problems. The enhanced sampling (60 CO molecules with initial positions in the heme pocket) make it possible to find widely different pathways for the escape of CO from the protein. Most of the pathways involve internal cavities that have been observed in an X-ray structure of Xe saturated myoglobin. The individual trajectories spend most of the time in the cavities; the transitions between cavities are rare events that are rapid and involve the crossing of barriers. By a comparison with the results obtained with 60 high-temperature ligands in a room-temperature protein and in a rigid protein, it is shown that even high-temperature ligands are prevented from escaping in the latter. Thus, the present results confirm the conclusion from earlier work that protein fluctuations are essential for the escape of ligands. The most important exit routes arc concentrated in the region between the A, B, and E helices. Others involve the CD corner, on the proximal side of the heme and between B and G helices. A short exit path near the distal histidine found in previous simulations and supported by mutation studies is important only when the fluctuations of side chains are enhanced by increasing their temperature. This suggests that the dominant ligand pathway through the protein may depend on the system temperature. © 1990, American Chemical Society. All rights reserved.