Versatile Rigid-Body and Group Refinement in Real Space

A procedure is described for performing least-squares rigid-body or group refinements in real space. The necessary derivatives are obtained from gradients in a difference Fourier map [Jack & Levitt (1978). Acta Cryst. A34, 931-935] allowing the use of fast Fourier transforms for rapid calculations. The computation time is nearly independent of the number of rigid groups being refined. The orientational transformation of the molecule or group is represented in a linear matrix form. The inherent non-linearity is treated outside of the refinement calculations, and trigonometric calculations are avoided. The linear approximation provides versatility in the types of constraints that may be applied during the refinement. Errors in unit-cell parameters may be detected through the strain component of the transformation matrix. The results of refinement of two protein structures are described as examples.