An isomorphous replacement method for phasing twinned structures

A linear least-squares formulation of the method of isomorphous replacement is presented. With data from untwinned crystals, this approach is shown to be equivalent to the phasing representation developed by Hendrickson & Lattman [Acta Cryst. (1970). B26, 136-143]. A general method for calculating the most probable phase is described and applied to the higher- dimensional problem of phase determination for twinned structures. A method for calculating the best phase with intensity data from twinned crystals is also presented. The dependences of these phasing procedures on the number of derivatives and accuracy of the data sets are evaluated in test calculations.