Model refinement methods, chain models

As the above results show, the gross features of the cellulose I crystal structure predicted by various methods do not differ appreciably, but the accompanying deviations in the R -factors are significant. When these predictions are used to assess, for example, whether the cellulose I crystal structure is based on parallel- or antmarallel-chains, the range in the R"-factors seen for the parallel models (cf. Table II) is comparable to that between the two different polarity models. As shown in Fig. 5, the most probable parallel- and antiparallel-chain structures of cellulose I, refined by minimizing the function O, differ in R -factors by approximately the same extent as the three predictions for the parallel model shown in Fig. 4 and Table II. 

In terms of the refinement illustrated here, the function Y is the function Fix], The first point, Xj, is represented by all variable bond lengths, bond angles, conformation angles, chain position parameters, coordinates of the solvent of crystallization, etc., of the initial model. All other points X2,. .., Xj, represent trial values for the same n variables within the desired interval limits and subject to any other constraints, such as coupling of variables or hydrogen bond formation. Clearly, the number and type of variables, and their limits and constraints are easily changed in this procedure, as is the form of the function. The search procedure is also relatively rapid and does not suffer from a slowdown in the vicinity of the minimum, as may occur in steep-est-descent methods. 

This paper is a review of x-ray diffraction work in the authors laboratory to refine the structures of cellulose I and II, and a- and B-chitin, concentrating on the methods used to select between alternate models. Cellulose I is shown to consist of an array of parallel chains, and this conclusion is supported by a separate refinement based on electron diffraction data. In the case of cellulose II, both parallel and antiparallel chain... 

The first structure of human renin was obtained from prorenin produced by expression of its cDNA in transfected mammalian cells. Prorenin was cleaved in the laboratory to renin using the protease trypsin. Because the carbohydrates in renin are not required for bioactivity, oligosaccharides were removed enzymatically. This process facilitates crystallization in some cases and also removes the contribution of the heterogeneous sugar chains to the diffraction pattern. The structure was determined without the use of heavy-atom derivatives, by application of molecular replacement techniques based on the atomic coordinates of porcine pepsinogen as the model. The molecular dynamic method of refinement was used extensively to arrive at a 2.5 A resolution structure. However, some of the loop regions were not well resolved in this structure (Sielecki et al, 1989 Sail et al, 1990). 

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