Crystallographic relationship between human and hen-egg lysozymes. II. Weighting of electron-density maps phased from an incomplete model structure and comparison with map obtained by isomorphous replacement

Abstract

Methods suitable for completing and refining a protein structure are investigated both theoretically and with human and hen lysozymes as an example. Sim (or Woolfson) weighting and the ~-synthesis are compared with unweighted maps, and while the former is an improvement over unweighted maps, the ~-synthesis is less clearly an improvement. Both WFo exp (i~c) and difference maps were found to be useful, and a comparison between the isomorphous replacement map of human lysozyme and our maps based on hen lysozyme was encouraging.

Bayesian image reconstruction from partial image and aliased spectral intensity data

“…Methods for estimating for single crystal diffraction data have been reviewed by Read [25]. We derive here two estimates for for the fiber diffraction case, based on those of Henderson and Moffat [26], and Nixon and North [27]. As noted in Section III-B, is constant for a particular set but in general varies with…”

“…Since the expected difference in each component is given by the first estimate is (47) where the averaging is over an ensemble of reflections indexed by for which is assumed to be constant. For the second method, we make use of the result of the statistical model described above [27]. Since and since and we obtain the second estimate as (48) which is an implicit equation for (since is a function of is substituted in the rhs of (48) to obtain the first estimate of This value of is substituted in the rhs (48) to obtain a new estimate, and the procedure repeated until convergence.…”

“…(The reason for deriving rather than is explained in Section IV.) Bayes theorem and the total probability theorem [22] may be applied to obtain the posterior distribution as (27) Substituting using (24) and (26) gives (28) where (29) is the normalizing constant.…”