Simulated Annealing in Crystallography

Abstract

X-ray crystallography (see Refs. 1 , 2 for reviews) is an increasingly impor­ tant tool for understanding structure, function, and control of biological macromolecules. Developments in genetics, data collection, and computer hardware have produced an unprecedented growth of macromolecular crystallographic studies. X-ray crystallography produces large amounts of diffraction data, whose interpretation is entirely dependent upon the availability of powerful computers and sophisticated algorithms. After crystallization and data collection, several computational procedures are required to solve and refine the structure. These procedures include methods of phasing, density modification, chain tracing, refinement, and correction of errors. Many of these computational procedures can be formulate:d as nonlinear optimization problems: One tries to optimize a target function, usually thc discrcpancy bctween observed and computed diffraction data, as a function of certain parameters, such as phases, scale factors between structure factors, or parameters of an atomic model. Optimization problems in macromolecular crystallography suffer from the multiple minimum problem. A case in point is crystallographic refine­ ment, in which one wants to improve the agreement of an atomic model with the diffraction data. The high-dimensionality of the parameter space of the atomic model (typically three times the number of atoms) introduces many local minima of the target function; thus, gradient descent methods, such as conjugate gradient minimization or least-squares methods (3),

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