MACROMOLECULAR ANISOTROPIC TEMPERATURE-FACTOR REFINEMENT WITH STRICT CONSTRAINTS. Jennifer A. Kelly and Todd O. Yeates. The Department of Chemistry and Biochemistry and The Molecular Biology Institute, University of California at Los Angeles, USA

Macromolecular models typically have high crystallographic residuals; the discrepancy between observed and calculated structure factor amplitudes is usually from 15% to 25%. A significant component of the residual is due to inadequate representations of atomic motion in protein models. Data collected from most protein crystals are insufficient to refine individual atomic anisotropic temperature-factors. Anisotropic b-factor refinement introduces six times the number of parameters as isotropic b-factor refinement, and most often results in over-fitting macromolecular models to the data. In order to reliably model protein motion as anisotropic, strict constraints are required. Our method introduces a new form for constraints on temperature-factors described by Fourier series, and uses an FFT-based algorithm for refining the relevant values. Anisotropic temperature-factors are defined by a position-dependent B matrix whose elements are constrained to vary smoothly over the unit cell in a crystal. Each of the six matrix elements is represented by a Fourier series with few terms. Individual anisotropic temperature-factors are determined by refining the coefficients of the six Fourier series which comprise the B matrix. Gradients are computed using FFT's by a modification of the method of Agarwal*. Since each Fourier series has only a few terms, the number of refinement parameters is kept low and over-fitting is avoided.

*Ramesh C. Agarwal, Acta Cryst. (1978). A34, 791-809