Non-Gaussian behavior of elastic incoherent neutron scattering profiles of proteins studied by molecular dynamics...

Elastic incoherent neutron scattering (EINS) data can be approximated with a Gaussian function of q in a low q region. However, in a higher q region the deviation from a Gaussian function becomes non-negligible. Protein dynamic properties can be derived from the analyses of the non-Gaussian behavior, which has been experimentally investigated. To evaluate the origins of the non-Gaussian behavior of protein dynamics, we conducted a molecular dynamics (MD) simulation of staphylococcal nuclease. Instead of the ordinary cumulant expansion, we decomposed the non-Gaussian terms into three components: (i) the component originating from the heterogeneity of the mean-square fluctuation, (ii) that from the anisotropy, and (iii) that from higher-order terms such as anharmonicity. The MD simulation revealed various dynamics for each atom. The atomic motions are classified into three types: (i) "harmonic," (ii) "anisotropic," and (iii) "anharmonic." However, each atom has a different degree of anisotropy. The contribution of the anisotropy to the total scattering function averages out due to these differences. Anharmonic motion is described as the jump among multiple minima. The jump distance and the probability of the residence at one site vary from atom to atom. Each anharmonic component oscillates between positive and negative values. Thus, the contribution of the anharmonicity to the total scattering is canceled due to the variations in the anharmonicity. Consequently, the non-Gaussian behavior of the total EINS from a protein can be analyzed by the dynamical heterogeneity.