Isomorphous Replacement : Effects of Errors on the Phase Probability Distribution

A simple framework for the analysis of the effects of errors in the method of isomorphous replacement is developed. This framework is used to derive phase probability distributions similar to those given by Blow & Crick [Acta Cryst. present analysis suggests an improved means of calculating the mean-square 'lack-of-closure' residuals and shows that they differ by a factor of two for centric and acentric reflections. It is also shown that the lack-of-closure residuals have a straightforward interpretation and that they may be used to estimate the error in the heavy-atom model and the degree of isomorphism between native and derivative structures if anomalous differences have been measured.