Protein topology, representation

Protein topology cartoons (TOPS) are two-dimensional schematic representations of protein structures as a sequence of secondary structure elements in space and direction (Flores et al, 1994 Sternberg and Thornton, 1977). The TOPS of trypsin domains as exemplified in Figure 4.9 have the following symbolisms ... 

Figure 5. Three-dimensional and two-dimensional topological representations of flavodoxin (A and B) and adipocyte lipid-binding protein (C and D). In both projections, individual P-strands are numbered in order from the amino- to the carboxyl-terminus.

Visualization is an efficient way to utilize the human ability to process laige amounts of data. Traditional visualization methods are based on clustering and tree representation, and are complemented by projecting objects onto a Euclidean space to reflect theh stractural or functional differences. The data are visualized without preclustering and can be explored dynamically and interactively, e.g., in protein topology and gene expression. 

Figure 89 illustrates two different tries at simplified representation of the globin structure. For reference, Fig. 89a shows the hemoglobin /3 chain in stereo. Figure 89b shows the globin structure schematically as two layers of helices with the elements in one layer approximately perpendicular to those in the other layer this can be contrasted with a possible description of the up-and-down helix bundles as two layers with their elements approximately parallel to each other. The perpendicular layers provide a rather successful simple schema for the globin structure, but unfortunately there are no other proteins that can be adequately described as two perpendicular layers of helices. Also, specification of the topology in this scheme is cumbersome, since the chain skips back and forth between layers. 

Koch et al. [111] have discussed the use of graph theoretical techniques in an attempt to find rules to relate beta sheet topology to amino acid sequence and for the comparison of beta sheet structures. They defined a graph representation for every protein in the PDB that contains beta sheets, notations and graphic representations for sheets which described the sequential and topological neighbourhoods of the strands, and constructed tools for substructure searches of this database. 

Fig. 7. Topological modifications to increase a FRET signal between two variants of the green fluorescent protein (GFP) fused to interacting proteins, (a) Schematic representation of interacting proteins and GFP variants with the location of the N- and C-termini indicated, (b) The GFP variants fused to the ends of the interacting proteins are too far apart to generate a FRET signal, (c) Insertion of one of the GFP variants into an interacting protein brings the two GFP variants close enough for FRET to be detected.

Special cases are discussed in some detail in the literature [112,197,198], where the shape representation P is chosen as a space curve representing a protein backbone and the topological descriptors Fj(s) on the local tangent plane projections are either graphs or knots defined by the crossing pattern on the planar projection at each tangent plane T(s) of the sphere S. 

The ribbon model in Figure 5.5d shows the organization of the structural path of the secondary structure elements of the protein chain (a-helix and j8-sheet regions). This representation is very often used, with the arrowheads indicating the N-to-C-terminal direction of the secondary structure elements, and is most effective for identifying secondary structures within complex topologies. 

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