Abstract
Substantial highly correlated differences sometimes exist between a series of heavy-atom derivatives of a macromolecule and the native structure. Use of such a series of derivatives for phase determination by multiple isomorphous replacement (MIR) has been difficult because MIR analysis has treated errors as independent. A simple Bayesian approach has been used to derive probability distributions for the phase in the case where a group of MIR derivatives have correlated errors. The utility of the resulting 'correlated-phasing' method has been examined by applying it to both simulated and real MIR data sets that contain sizeable correlated errors and it has been found that it can dramatically improve MIR phase estimates in these cases. Correlated phasing is applicable to situations where derivatives exhibit substantial correlated changes in protein conformation or crystal packing or where correlated errors in heavy-atom models are large. Correlated phasing does not substantially increase the complexity of phase computation and is suitable for routine use.
Highlights
In the method of multiple isomorphous replacement (MIR), the phase problem of crystallography is solved using information from X-ray diffraction data on crystals of the 'native' macromolecule and on several 'derivative' crystals that differ from the native through binding of heavy atoms at a small number of sites in each asymmetric unit
We examined how high the correlation among errors in the derivatives must be before correlated phasing has a substantial effect, and we examined the use of correlated phasing in cases where there were substantial errors in the measurement of the amplitude of the native structure factor
Data from a selenomethionine-containing derivative that was isomorphous to the native had been collected and was potentially useful for phasing, but the positions of the selenium atoms could not be identified with the MIR phases obtained from the three non-isomorphous derivatives
Summary
In the method of multiple isomorphous replacement (MIR), the phase problem of crystallography is solved using information from X-ray diffraction data on crystals of the 'native' macromolecule and on several 'derivative' crystals that differ from the native through binding of heavy atoms at a small number of sites in each asymmetric unit. A serious lack of isomorphism that leads to differences between amplitudes of native and derivative structure factors of 40%, for example, makes the derivative almost worthless for MIR It is both common and disappointing to obtain nonisomorphous derivatives, and it would be very helpful if some way were available to use such derivatives in phasing. Others could arise from undetected sites of heavy-atom substitution that are present in each crystal but missing in the heavyatom models, errors in data collection or scaling in common for all derivatives, or (since MIR phase calculations involve differences between each derivative and the native amplitude for each structure factor). We take advantage of correlations among errors in a way that can substantially improve estimates of phases
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