Space filling designs

Fig. 4. (see facing page) Example tree. An RP tree was built using compounds selected by a space-filling design BCUT descriptors were used for the analysis. 

In contrast to optimal design, Hamprecht and co-workers recently introdnced a space-filling design techniqne for compound selection. This stochastic method nses the best linear unbiased estimator, in the form of Kriging, " to constrnct selection designs that optimize the integrated mean-square prediction error, or entropy. This... 

Space-filling design attempts to sample chemical space more evenly than D-optimal design, when the response snrface is not uniform but irregular, as is often the case with heterogeneous compound collections. 

Boyd DB. Space-filling molecular models of four-membered rings. Three-dimensional aspects in the design of penicillin and cephalosporin antibiotics. J Chem Educ 1976 53 483-8. 

The space filling in the body-centered cubic packing of spheres is less than in the closest packings, but the difference is moderate. The fraction of space filled amounts to ns/3 = 0.6802 or 68.02 %. The reduction of the coordination number from 12 to 8 seems to be more serious however, the difference is actually not so serious because in addition to the 8 directly adjacent spheres every sphere has 6 further neighbors that are only 15.5 % more distant (Fig. 14.3). The coordination number can be designated by 8 + 6. 

The space filling curve characteristic for this structure type is shown in Fig. 4.22. Strukturbericht designation Bl. 

P, and A, described later in the text the tRNA anticodons are in orange. Proteins appear as blue wormlike structures the rRNA as a blended space-filling representation designed to highlight surface features, with the bases in white and the backbone in green. The structure on the right is the 30S subunit... 

Again, our first concern must be to see how many ways there are in which the translation vectors can be related to one another (relative lengths, angles between them) to give distinct, space-filling patterns of equivalent points. We have seen (Section 11.2) that in 2D there were only 5 distinct lattices. We shall now see that in 3D there are 14. These are often designated eponymously as the Bravais lattices and are shown in Figure 11.11, in the form of one unit cell of each. 

In this fashion, it is possible to control the critical molecular design parameters (CMDPs, i.e., size, shape, topology, flexibility, and surface chemistry) and grow predictable, stoichiometric structures up to a self-limited dimension (generation) which is determined by Nc and Nb as well as by the dimensions of the structural components. Such space-filling, terminally functionalized molecular organizations have been coined Starburst dendrimers [2]. Two dimensional projections of such molecular morphogenesis [1] are as illustrated in Fig. 2. 

Each representation of a protein or nucleic acid conveys to the viewer different aspects of its structure line drawings give the bones, space-filling models the flesh, and schematic diagrams the gestalt of the design. No single representation of a protein or nucleic acid is adequate for all purposes, but the combination of several is more powerful than the total of all taken independently. 

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