A new least-squares refinement technique based on the fast Fourier transform algorithm

A new atomic-parameters least-squares refinement method is presented which makes use of the fast Fourier transform algorithm at all stages of the computation. For large structures, the amount of computation is almost proportional to the size of the structure making it very attractive for large biological structures such as proteins. In addition the method has a radius of convergence of approximately 0.75 Å making it applicable at a very early stage of the structure-determination process. The method has been tested on hypothetical as well as real structures. The method has been used to refine the structure of insulin at 1.5 Å resolution, barium beauvuricin complex at 1.2 Å resolution, and myoglobin at 2 Å resolution. Details of the method and brief summaries of its applications are presented in the paper.