Distance maps

Fig. 12.9 A distance map indicates the distances available to specified groups. As more molecules are considered, the permitted regions get smaller.

As an alternative strategy, one might ask in a local bookshop for an altitude map and a distance map for Hawaii. A mathematically savvy shopkeeper may reply that the first (a topo map ) is readily available, because altitude is easily graphable in topographic form, whereas the second is not, because distance is inherently a path-dependent, ungraphable quantity. This reply points, by (1.16b), to the same conclusion. 

Figure 19 shows the main steps of a method of characterization of spores and generated filaments which is based on the Euclidean Distance Map. The central zone of the EDM (i.e. the zone with the highest distance value Rm) is dilated Rm times. The size of the object in Fig. 20 e gives the size of the spore. A logical subtraction of Fig. 19 e from Fig. 19 c leaves only the branches visible in Fig. 19f. 

Input/Output sequence encoding methods (see Table 9.1) PRF direct encoding of residue profile a = a-helix fi = P-sheet C = random coil t = (5-reverse turn L = loop %AA = amino acid composition FEAT = indirect encoding of sequence features MF = memory factor dist = distance Map = Kohonen map (with dimensions). 

Fig. 9. Proximity relationships for residues in Cl relative to 316 in H8. Example of R1 distance mapping in rhodopsin. For each distance measurement, only two R1 side chains were in the protein, one fixed at the reference site 316, and the other at a site in the sequence 55-75. The R1 side chains were modeled based on crystal structure data with energy minimization subject to the experimentally determined distance constraint (shown). In each case, the measured distances in solution were in good agreement with those expected from the rhodopsin crystal structure. Substituted cysteine residues 65 and 68 most rapidly formed disulfide cross-links with the reference cysteine at 316 in H8. This is indicated by the dark bars connecting the potential disulfide partners.

Two independent strategies, modulation of tertiary contact interaction and direct distance mapping, provide compelling evidence for a dominant rigid-body movement of TM6 near the cytoplasmic surface, with smaller but significant movements of TM1, TM2, TM3, and TM7. 

Discrete approaches allow computing G directly from the distance map but generally give results that are prone to high digitization effects. Our approach takes... 

The Euclidean-distance map matrix, denoted as ED, is the analogue of the geometry matrix G derived from a molecular graph. In this case, vertices of the map graph are assigned x, y) or x, y, z) coordinates, z being intended as the weighting scheme for vertices it is defined as [Bajzer, Randic et al, 2003]... 

The path-distance map matrix, denoted as PD, resembling the bond length-weighted distance matrix of a molecular graph, is defined as [Bajzer, Randic et al, 2003]... 

Euclidean-distance map matrix biodescriptors (0 proteomics maps)... 

Analogous to the Euclidean distance matrix are the data distance matrices obtained using different distance measures, such as Manhattan distance, Canberra distance, Lagrange distance, and so on. Moreover, an Euclidean-distance map matrix was defined, which encodes information about graphs used to describe proteomics maps. 

This method uses a binary image to create a "distance map" of the image, which records the distance from each pixel to the background. From the distance map, the fiber diameter at any pixel location can be determined [12]. 

Measurement of topological and spatial distribution of pores with Voronoi cells and Euclidean distance mapping (Venkataraman et al., 2007). 

The possible pharmacophoric models are then the places where the distance maps for all known active compounds intersect. If enough diverse compounds are used, a unique intersection point, and thus a unique pharmacophoric arrangement, can be identified. If there is no such intersection, either the essential groups were misidentified or there is a problem with the pharmacological information, e.g., all the compounds do not bind at the same... 

Distance Mapping Reveals Light Activation of Rhodopsin. 150... 

Altenbach C, Kusnetzow AK, Ernst OP, Hofmann KP, Hubbell WL (2008) High-resolution distance mapping in rhodopsin reveals the pattern of helix movement due to activation. Proc Natl Acad Sci USA 105(21) 7439-7444... 

More objective procedures in series design are clustering methods in multidimensional parameter space substituents from different clusters are selected for synthesis (chapter 3) [50, 154, 403]. As this approach cannot automatically avoid collinearity or multicollinearity, several different standard sets of aromatic substituents have been proposed e.g. [652, 653]). A distance mapping technique may be used to select further substituents on the basis of a nj ximum distance to the substituents which already are included [652]. A modification [654] of this approach uses the determinant of the parameter correlation matrix as the criterion for substituent selection. 

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