Multidimensional molecular replacement

Abstract

A method is described which attempts to simultaneously and independently determine the positional and orientational parameters of all molecules present in the asymmetric unit of a target crystal structure. This is achieved through a reverse Monte Carlo optimization of a suitable statistic (such as the R factor or the linear correlation coefficient between the observed and calculated amplitudes of the structure factors) in the 6n-dimensional space defined by the rotational and translational parameters of the n search models. Results from the application of this stochastic method - obtained with a space-group-general computer program which has been developed for this purpose - indicate that with present-day computing capabilities the method may be applied successfully to molecular-replacement problems for which the target crystal structure contains up to three molecules per asymmetric unit. It is also shown that the method may be useful in cases where the assumption of topological segregation of the self- and cross-vectors in the Patterson function is violated (as may happen, for example, in closely packed crystal structures).