Highly Constrained ADP Refinement. Jennifer A. Kelly and Todd O. Yeates Department of Chemistry and Biochemistry University of California at Los Angeles

Protein crystals typically contain more than 50 solvent and can accommodate significant molecular motion. As a result, protein crystals diffract to much lower resolution than crystals of smaller, more rigid molecules. This presents an unfortunate situation: highly dynamic crystals require many more parameters for the accurate characterization of motion, but provide fewer observations for such an analysis. Atomic displacements modeled isotropically assign equal probability to motion in any direction and require only a single parameter. Anisotropic displacement parameters (ADP's) provide a better description of protein dynamics by allowing harmonic motion to be greater in some directions than others. Individual ADP refinement tends to over-fit macromolecular models to the limited data. Our refinement method introduces a novel form for ADP constraints and produces reliable descriptions of anisotropic motion in protein crystals. Low-order Fourier series describe the variation in individual ADP matrix elements throughout the crystal cell. An FFT-based algorithm refines the Fourier coefficients using a modified version of Agarwal's method to compute gradients. Individual ADP assignments depend on an atom's position in the cell, and ADP's vary smoothly throughout the cell since the Fourier series have few terms. Our method successfully refined ADP values for several protein models, resulting in lower R and R free values in every case.