A general phasing algorithm for multiple MAD and MIR data

A phasing algorithm is presented for combining multiple wavelength anomalous dispersion (MAD) data from multiple types of anomalous scatterers, either in the same or in different derivative crystals, as well as for combining MAD data with multiple isomorphous replacement (MIR) data from different derivative crystals. A heavy-atom phasing and refinement program originally written by Rossmann [(1967) HATOMLSQ program, Purdue University, West Lafayette, Indiana, USA] has been modified to refine the parameters that define the anomalous and isomorphous scatterers and to determine protein phases by using all MAD and MIR derivatives simultaneously. The technique allows for appropriate weighting of every data set, including the native data, which contains neither an anomalous nor an isomorphous component. This method is a generalization of currently used heavy-atom methods. Numerical tests are presented for different experimental scenarios, including a double MAD experiment on the same crystal (diffraction data at two absorption edges), combination of two MAD experiments on different crystals, and combination of MAD data with MIR data from multiple crystals. An appendix shows how the Karle equations used in MAD phasing can be reformulated as a particular case of this algorithm.