Topology connected regions

In each SCOP class, proteins are clustered into groups based on their structure similarity. Each cluster is referred to by SCOP as a fold. Proteins share a common fold if they have the same major secondary structures in the same arrangement and with the same topological connections. Proteins with the same fold may differ at the level of their peripheral elements, which can include secondary structures and turn regions. Note that these peripheral elements can represent up to 50% of the structure. Proteins catalogued together in the same fold may have no common evolutionary origin. 

The parametrisations introduced in Sections 8.2 and 8.3 allow one to suppose that the manifold iW is (topologically) connected, and to use the theorem of analytic continuation if an analytic function equals zero in an open subset of a connected region i then it equals zero in the whole % An analytic function of the state variable z is also an analytic function of the parameters, which can be assumed to lie in a connected region of dimension D (number of degrees of freedom). By the (analytic) diffeomoiphism, to an open subset of M corresponds uniquely an open subset of. In particular if some determinant of a (sub)matrix (function of z) equals zero in some open subset of iWthen it equals zero in the whole M. Thus if the rank of some matrix M(z) equals (say) K in U where V is open in the z-space then rankM(z) < K on indeed, the determinant of any (k+l) x (/f+1) submatrix (if there is any) equals zero in thus... 

Figure S.7 The subunit structure of the neuraminidase headpiece (residues 84-469) from influenza virus is built up from six similar, consecutive motifs of four up-and-down antiparallel fi strands (Figure 5.6). Each such motif has been called a propeller blade and the whole subunit stmcture a six-blade propeller. The motifs are connected by loop regions from p strand 4 in one motif to p strand 1 in the next motif. The schematic diagram (a) is viewed down an approximate sixfold axis that relates the centers of the motifs. Four such six-blade propeller subunits are present in each complete neuraminidase molecule (see Figure 5.8). In the topological diagram (b) the yellow loop that connects the N-terminal P strand to the first P strand of motif 1 is not to scale. In the folded structure it is about the same length as the other loops that connect the motifs. (Adapted from J. Varghese et al.. Nature 303 35-40, 1983.)...

The number of possible ways to form antiparallel p structures is very large. The number of topologies actually observed is small, and most p structures fall into these three major groups of barrel structures. The last two groups—the Greek key and jelly roll barrels—include proteins of quite diverse function, where functional variability is achieved by differences in the loop regions that connect the p strands that build up the common core region. 

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