Crystallographic modeling

The crystallography as well as the quality criteria of the crystallographic models are summarized in Table II. In NDO, the Rieske domain is formed by residues 38-155 of the a subunit only this part of the structure will be discussed in this review. 

The simplest way to account for composition variation is to include point defect populations into the crystal. This can involve substitution, the incorporation of unbalanced populations of vacancies or by the addition of extra interstitial atoms. This approach has a great advantage in that it allows a crystallographic model to be easily constructed and the formalism of defect reaction equations employed to analyze the situation (Section 1.11). The following sections give examples of this behavior. 

E. Keller, SCHAKAL99, A Computer Program for the Graphic Representation of Molecular and Crystallographic Models, University of Freiburg (Germany), 1999. 

A crystallographic example of optimization would be the minimization of a least-squares or a negative log-likelihood residual as the objective function, using fractional or orthogonal atomic coordinates as the variables. The values of the variables that optimize this objective function constitute the final crystallographic model. However, due to the... 

Macromolecular diffraction data are rarely of sufficient quality and quantity to allow construction of atomic models that would obey basic stereochemistry just based on this optimization of parameters to data. The observation-to-parameter ratio is a key factor in optimization procedures. For the optimization of a crystallographic model. 

The use of cross-validation should be widely recommended for crystallographic model refinement. Its simplicity to understand for the nonexpert and its power in discriminating models that are consistent with the experimental data make it indispensable. However, in modern crystallography model refinement is often falsely seen as the... 

The crystallographic model for martensite described above is primarily due to Wechsler et al. [1], A similar model, employing a different formalism but leading to essentially equivalent results, has also been published by Bowles and MacKen-zie [2-4]. In both models, a search is made for an invariant (or near-invariant) plane which is then proposed as the habit plane, since the selection of this plane... 

Fig. 10. Correlation of active site synthetic analog results for nuclease-T (taken from Table III) with the X-ray crystallographic model for the binding site region for nuclease [taken from Cotton and Hazen (19)]. B indicates binding of a synthetic (6—47) analog, with noted change, to nuclease-T-(49,50-149) NB, ineffective binding A, the ability of the synthetic (6-47) analog to generate at least partial enzymic activity upon addition to nuclease-T-(49, 50-149) I, little or no ability to generate such activity.

In Chapter 10, "Other Types of Models," I discuss alternative methods of structure determination NMR spectroscopy and various forms of theoretical modeling. Just like crystallographic models, NMR and theoretical models are sometimes more, sometimes less, than meets the eye. A brief description of how these models are obtained, along with some analogies among criteria of... 

In this chapter, I will discuss the strengths and limitations of molecular models obtained by X-ray diffraction. My aim is to help you to use crystallographic models wisely and appropriately, and realize just what is known, and what is unknown, about a molecule that has yielded up some of its secrets to crystallographic analysis. To demonstrate how you can draw these conclusions for yourself with regard to a particular molecule of interest, I will conclude this chapter by discussing a recent structure determination, as it appeared in a biochemical journal. Here my goals are (1) to help you learn to extract criteria of model quality from published structural reports and (2) to review some basic concepts of protein crystallography. 

More than the resolution, we would like to know the precision with which atoms in the model have been located. For years, crystallographers used the Luzzati plot (Fig. 8.3) to estimate the precision of atom locations in a refined crystallographic model. At best, this is an estimate of the upper limit of error in atomic coordinates. The numbers to the right of each smooth curve on the Luzzati plot are theoretical estimates of the average uncertainty in the positions of atoms in the refined model (more precisely, the rms errors in atom positions). The average uncertainty has been shown to depend upon R-factors derived from the final model in various resolution ranges. To prepare data for a Luzzati plot, we separate the intensity data into groups of reflections in... 

For technical reasons having to do with data collection strategies, crystal properties, and other processes essential to crystallography itself, the asymmetric unit is often mentioned prominently in papers about new crystallographic models. This discussion is part of a full description of the crystallographic methods for assessment of the work by other crystallographers. It is easy to get the impression that the asymmetric unit is the functional unit, but frequently it is not. Beyond the technical methods sections of a paper, in their interpretations and discussions of the meaning of the model, authors are careful to describe the functional form of the substance under study (if it is known), and this is the form that holds the most interest for users. 

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