Semi-classical quantization of protein dynamics: Novel NMR relaxation formalism and its application to prion

Novel nuclear spin relaxation mechanism in proteins on a timescale of micro to milliseconds has been proposed using the Berry-phase interference between periodic orbits within the semi-classical quantization formalism. In order to examine the proposed formalism, susceptibility has been represented by an analytical formulation as a function of the frequency of the periodic orbits, using a Riemann function. Numerically obtained profile of the susceptibility has been quantitatively compared with that of experimentally obtained slow exchange rates in a stable globular protein, p8(MTCP1) and in a hamster prion protein. Behavior of amide nitrogen atoms in p8(MTCP1) was almost uniform between residues, and consistent with that of theoretically obtained ones. On the other hand, that of hamster prion was not uniform and quite different than that of theoretical one, suggesting that the slow dynamics of a hamster prion might not be well described by the periodical orbits around the unique saddle point. Local trajectories in the phase space around the native conformation of the hamster prion may be connected to the complicated geometry, corresponding to multiple conformational states, for instance, PrPC, PrP* or PrPSc.