Refinement of protein dynamic structure: normal mode refinement.

An x-ray crystallographic refinement method, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the effective normal modes whose amplitudes and eigenvectors are experimentally determined by the crystallographic refinement. In contrast to the conventional method, the atomic motions are treated generally as anisotropic and concerted. This method is assessed by using the simulated x-ray data given by a Monte Carlo simulation of human lysozyme. In this article, we refine the dynamic structure by fixing the average static structure to exact coordinates. It is found that the normal mode refinement, using a smaller number of variables, gives a better R factor and more information on the dynamics (anisotropy and collectivity in the motion).