Collective motions in proteins investigated by X-ray diffuse scattering

We have developed theoretical models for analysis of X-ray diffuse scattering from protein crystals. A series of models are proposed to be used for experimental data with different degrees of precision. First, we propose the normal mode model, where conformational dynamics of a protein is assumed to occur mostly in a limited conformational subspace spanned by a small number of low-frequency normal modes in the protein. When high precision data are available, variances and covariances of the normal mode variables can be determined from experimental data using this model. For experimental data with lower degrees of precision, we introduce a series of simpler models. These models express the covariance matrix using relatively simple empirical correlation functions by assuming the correlation between a pair of atoms to be isotropic. As an application of these simpler models, we calculate diffuse-scattering patterns from a human lysozyme crystal to examine how each adjustable parameter in the models affects general features of the resulting patterns. The results of the calculation are summarized as follows. (1) The higher order scattering makes a significant contribution at high resolutions. (2) The resulting simulated patterns are sensitive to changes in correlation lengths of about 1 A, as well as to changes of the functional form of the correlation function. (3) But only the "average" value of the intra- and intermolecular correlation lengths seems to determine the gross features of the pattern. (4) The effect of the atom-dependent amplitude of fluctuations is difficult to observe.