Picosecond timescale rigid-helix and side-chain motions in deoxymyoglobin

The contribution of rigid-body motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two types of rigid-body motions are considered: one in which the helices are rigid units and one in which the side-chains are rigid units. Using a quaternion-based algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid-body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean-square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen; rigid-helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the helix atom (backbone and side-chain) mean square displacements and only 1.1% of total kinetic energy. Only very low-frequency motions contribute to the rigid-helix dynamics; the rigid-body analysis allows characteristic rigid-helix vibrations to be identified and described. Treating the side-chains as rigid bodies is found to be an excellent approximation to both their diffusive and vibrational mean-square displacements: 96% of side-chain atom mean-square displacements originate from rigid side-chain motions. However, the errors in the side-chain atomic positional fits are not always small. An analysis is made of factors contributing to the positional error for different types of side-chain.