Anisotropy and anharmonicity of atomic fluctuations in proteins: analysis of a molecular dynamics simulation

Positional probability density functions (pdf) for the atomic fluctuations are determined from a molecular dynamics simulation for hen egg-white lysozyme. Most atoms are found to have motions that are highly anisotropic but only slightly anharmonic. The largest deviations from harmonic motion are in the direction of the largest rms fluctuations in the local principal axis frame. Backbone atoms tend to be more nearly harmonic than sidechain atoms. The atoms with the largest anharmonicities tend to have pdfs with multiple peaks, each of which is close to harmonic. Several model pdfs are evaluated on the basis of how well they fit probability densities from the dynamics simulations when parameterized in terms of the moments of the distribution. Gram-Charlier and Edgeworth perturbation expansions, which have been successful in describing the motions of small molecules in crystals, are shown to be inadequate for the distributions found in the dynamics of proteins. Multipeaked distribution functions are found to be more appropriate.