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Noise and functional protein dynamics.

The magnetic field dependence of the proton-spin-lattice relaxation rate in rotationally immobilized proteins shows that the one-dimensional character of the protein primary structure causes a dramatic increase in the population of low-frequency motions from 10 kHz to 20 MHz. As a consequence, the probability and rate at which functionally critical conformational states are thermally sampled in a protein are dramatically increased as well, when compared with a three-dimensional lattice structure. Studies of protein dynamics often focus on time periods far shorter than those associated with catalytic function, but we show here that the magnetic field dependence of the proton nuclear spin-lattice relaxation rate in rotationally immobilized proteins reports unambiguously the structural fluctuations in the frequency range from 10 kHz to 20 MHz. This relaxation rate decreases with increasing Larmor frequency according to a power law that derives from the distribution of dynamical states, the localization of the structural disturbances, and the spatial distribution of hydrogen atoms in the structure. The robust theoretical foundation for the spin-relaxation process, loosely characterized as a direct spin-phonon coupling, shows that the disturbances propagate in a space of reduced dimensionality, essentially along the stiff connections of the polypeptide chain. The reduced dimensionality traps the disturbance and changes the efficiency for energy redistribution in the protein and the processes that drive nuclear spin relaxation. We also show that the Larmor frequency dependence of the protein-proton-spin-lattice relaxation rate constant is related to the frequency dependence of force constants and mean-square displacement commonly observed or calculated for proteins. We believe that these approaches give additional physical insight into the character of the extremely low-frequency protein dynamics.