Modelling the unusual temperature dependence of atomic displacements in proteins by local nonharmonic potentials.

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Abstract
Recent x-ray studies metmyoglobin at different temperatures [Frauenfelder et al., 1979] show that the dependence of the mean square displacements of individual atoms on the absolute temperature T can be described analytically by Tu, in which the parameter .mu. undergoes local variations in the range -2 to +20. This strong deviation from harmonic behavior .mu. = 1 is modeled here, in the classical limit, by local nonharmonic potentials, in which a particle spends part of its time in 1 or more weakly bound states (traps) and the rest of it as an almost free particle in a restricted volume (cavity). Analytic calculations of the mean square atomic displacement in such cavity-traps potentials for a simplified 3-dimensional geometry yield the following results: a parametrically described Tu behavior characterizes a transition region in temperature below which the particle is trapped (solid-like) and above which the particle is free (liquid-like); the magnitude of .mu. increases with an increase in the ratio of cavity volume to trap volume; .mu. > 0 type of behavior can be obtained by a single trap and .mu. < 0 type of behavior can be obtained by a single trap and .mu. < 0 by 2 symmetric traps. A comparison is made between the predictions of the model and the experimental results and the elucidation of the model parameters from x-ray data is discussed.