Three-dimensional similarity, computational techniques

The emerging techniques for computer recognition of the similarity of three-dimensional properties of molecules will be discussed in this review. In particular, we will concentrate on methods or computer programs that examine a database of three-dimensional structures. However, to place such programs in context we will introduce the concepts of chemical information and the terminology, usually derived from molecular graphics, of three-dimensional similarity. Since much of the impetus for this research has been from research on computer-assisted design of bioactive molecules, this field will be introduced also. 

Pepperrell, C. A. and Willett, P. (1991) Techniques for the calculation of three-dimensional structural similarity using inter-atomic distances. J. Comput.-Aided Mol. Design 5, 455-474. 

Computed tomography (CT) techniques share a common mechanism for spatial encoding. A two dimensional projection of the object (similar to a standard x-ray or a single read out in MRI without phase encoding) at multiple angles can be reconstructed into two or three dimensional images. Data... 

The new set of varied DF found in the previous section can be studied in the same way as the well-known eDF maps are represented since the first plots used in Quantum Chemistry [53a)]. Here an alternative point of view, similar as the one used by Mezey [9a)], will be chosen. Three-dimensional maps of isodensity surfaces can be generated with available computational techniques [84]. This corresponds to follow several steps, some of them so trivial that appear to be irrelevant in a study as the present. The representation process starts with the evaluation of DF grids, enveloping the molecular co-ordinates, which can origin wireframe structures related with the isodensity values. After that, they can be rendered and rotated in space as virtual objects, until some adequate point of view is found. Finally, the chosen object snapshot can be manipulated, represented on a screen and, if necessary, printed into a paper surface. The processing detail, the computational techniques and the required programs and data are briefly commented in Appendix E. All the necessary items are available to the interested reader and permit to generate surfaces of his own [93-96]. 

Now we return to the example of Fig. 4a and analyze it in more detail. We take, as shown in Fig. 7, a problem with 256 grid points arranged as a 16 x 16 mesh. We decompose it onto 16 processors. We replace the wave equation of a seismic simulation by the similar iterative solution to Laplace s equation where potential (/, j) is to be determined at grid points (/, j). Iteration is not the best way to tackle this particular problem. However, more sophisticated iterative techniques are probably the best approach to large three-dimensional finite-difference or finite-element calculations. Thus, although the simple example in Fig. 7 is not real or interesting itself, it does illustrate important issues. The computational solution consists of a simple algorithm... 

C. A. Pepperrell and P. Willett,/. Comput.-Aided Mol. Design, 5,455 (1991). Techniques for the Calculation of Three-Dimensional Structural Similarity Using Inter-Atomic Distances. 

Similar equations maybe written for gradients along the x- andy-directions. Exposure of the sample to radiation of frequency v z) results in a signal with an intensity that is proportional to the number of protons at the position z. This procedure is an example of slice selection, the use of radiofrequency radiation that excites nuclei in a specific region, or slice, of the sample. It follows that the intensity of the NMR signal will be a projection of the number of protons on a line parallel to the field gradient. The image of a three-dimensional object such as a flask of water can be obtained if the slice selection technique is applied at different orientations (Fig. 13.28). In projection reconstruction, the projections can be analyzed on a computer to reconstruct the three-dimensional distribution of protons in the object. 

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