Searching Distance

Fig. 18. Distribution of fitnesses as a function of mutant Hamming distance from current position on the landscape for an initial fitness of (a) 0.5 and (b) 0.543. Simulations were carried out on NK landscapes with N= 100 and K = 2, yielding the high nearest neighbor correlation of 0.97 and a correlation length of 33.3. Vertical bars show +1 and -1 standard deviation from the mean of fitnesses found at each search distance. If the best of six mutants at each distance is chosen, then the best mutant can be found at Hamming distance 33 from the fitness 0.5 point and at decreasing distances as the initial fitness increases. (From Ref. 119.)...

Figure 7 1 Pb (A) and U (B) geochemical maps compiled using MIDW interpolation method. Search distance is 3.5 km and map resolution 1 km. Pixel values have been reclassified by fractal C—A plot based on the frequency distribution of pixel values (Fig. 7.2A and B).

The stream sediment geochemical maps (Fig. 7.1 A and B) of Campania have been interpolated by MIDW using the GeoDAS program (Cheng, 2003). Search distance and map resolution are 3.5 and 1 km, respectively. 

It must be stressed that the exchange of protons between adjacent groups has no surface-enhanced directionality. A proton dissociating from one moiety can reach either the bulk or the nearby surface moiety, which sets a limit to the effectiveness of the proton antenna. Even with transfer efficiency as high as 90%, after n = 9 passages the probability that the proton will remain on the surface dwindles to e l. Because the length of a Coulomb radius on the surface is Z — 10 A, the dimension of the effective search distance is d = ly/n = 30 A. 

There are four methods for 3D data base searching distance distributions, individual distances, maximum common substructure, and atom mapping in her book, Catherine Pepperrell emphasizes the latter method, and also addresses dissimilarity (which matters when searching for new lead compounds, and one wishes to screen as many different classes as possible). 

Full structure search can be developed by using similar approaches to those employed in the case of 2D structure search. Thus, some topological indices can be modified in such a way that they include geometrical information. For example, the global index given by Eq. (4) can be modified to Eq. (11), where are real interatomic distances. 

Following the similar structure - similar property principle", high-ranked structures in a similarity search are likely to have similar physicochemical and biological properties to those of the target structure. Accordingly, similarity searches play a pivotal role in database searches related to drug design. Some frequently used distance and similarity measures are illustrated in Section 8.2.1. 

Dmparison of various methods for searching conformational space has been performed cycloheptadecane (C17H34) [Saunders et al. 1990]. The methods compared were the ematic search, random search (both Cartesian and torsional), distance geometry and ecular dynamics. The number of unique minimum energy conformations found with 1 method within 3 kcal/mol of the global minimum after 30 days of computer processing e determined (the study was performed in 1990 on what would now be considered a / slow computer). The results are shown in Table 9.1. 

The amount of computation necessary to try many conformers can be greatly reduced if a portion of the structure is known. One way to determine a portion of the structure experimentally is to obtain some of the internuclear distances from two-dimensional NMR experiments, as predicted by the nuclear Over-hauser effect (NOE). Once a set of distances are determined, they can be used as constraints within a conformation search. This has been particularly effective for predicting protein structure since it is very difficult to obtain crystallographic structures of proteins. It is also possible to define distance constraints based on the average bond lengths and angles, if we assume these are fairly rigid while all conformations are accessible. 

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