Resolution of the phase-ambiguity problem in the centrosymmetric P \bar{1} space group by Monte Carlo methods
Abstract
Simulated-annealing methods have been used to resolve the phase-ambiguity problem in the centrosymmetric P¿bar¿1¿ space group. First, an energy function based on the Sayre equation is introduced and a formal comparison with classical spin systems is drawn. The energy landscape is studied in detail and the validity of several energy criteria thoroughly tested. Classical Monte Carlo methods proved to be successful using a multistart optimization of the Sayre score, along with the additional monitoring of other energetic criteria. These involved the Terwilliger map quality index in reciprocal space in the absence of envelope information, and an envelope score if the shape of the molecule is known. The inherent phase-ambiguity problem of the P¿bar¿1¿ space group was therefore technically solved by Monte Carlo methods. The method should also work to resolve phase ambiguity in the SIR method of protein crystallography.