Global topology

In the standard approaches to the systems in which monolayers or bilayers are formed, one assumes that the width of the film is much smaller than the length characterizing the structure (oil or water domain size, for example). In such a case it is justified to represent the film by a mathematical surface and the structure can be described by the local invariants of the surface, i.e., the mean H and the Gaussian K curvatures and by the global (topological)... 

Observation 1 Since primitive graph decompositions are not particularly representative of global topologies, it can hardly be surprising to find a large number of nonisomorphic topologies supporting virtually the same dynamics. 

As for Cl, the global topology of the TM7-H8 sequence was mapped in detail by direct distance measurements between pairs of spin labels (A1 tenbach et al., 2001c) and by disulfide cross-linking (Klein-Seetharaman et al., 2001). For direct distance measurement using spin-spin interactions, a reference R1 side chain was placed at site 65 in Cl, and a second R1 placed at each site in the sequence 306-316. Figure 14 shows the pairs and indicates the interspin distances... 

SE-vectors describe the global topology of a molecule, also taking into account the presence of heteroatoms and multiple bonds as well as their numbers and relative positions. However, they do not encode information about stereochemistry of molecules. 

Moreover, a global topological charge index J is defined as... 

Kim H, Melen K, Osterherg M, von Heijne G (2006) A global topology map of the Saccharomyces cerevisiae membrane proteome. Proc Natl Acad Sci USA 103 11142-11147... 

The word shape is loaded with strong personal intuitions of what each of us thinks defines an object in three-dimensional (3D) space. Sometimes, we may view an object as a distribution of points in space and conceive its shape in terms of distances and angles, that is, local geometrical measures. More often, we associate the notion of shape with a solid object defined by an envelope surface. In this case, a precise geometrical characterization may lose its relevance, and it may be sufficient to characterize shape in a more qualitative fashion. Global topological measures are better suited here. Therefore, we... 

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