Analysis of elastic incoherent neutron scattering data beyond the Gaussian approximation

This work addresses the use of the Gaussian approximation as a common tool to extract atomic motions in proteins from elastic incoherent neutron scattering and whether improvements in data analysis and additional information can be obtained when going beyond that. We measured alpha-lactalbumin with different levels of hydration on three neutron backscattering spectrometers, to be able to resolve a wide temporal and spatial range for dynamics. We demonstrate that the Gaussian approximation gives qualitatively similar results to models that include heterogeneity, if one respects a certain procedure to treat the intercept of the elastic intensities with the momentum transfer axis. However, the inclusion of motional heterogeneity provides better fits to the data. Our analysis suggests an approach of limited heterogeneity, where including only two kinds of motions appears sufficient to obtain more quantitative results for the mean square displacement. Finally, we note that traditional backscattering spectrometers pose a limit on the lowest accessible momentum transfer. We therefore suggest that complementary information about the spatial evolution of the elastic intensity close to zero momentum transfer can be obtained using other neutron methods, in particular, neutron spin-echo together with polarization analysis.