By L. Smith
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Extra resources for Algebraic Topology, Gottingen 1984
3 Backbone fragment methods The Suppos algorithm incorporated in the WHAT IF program produces superpositions based on either structural or topological equivalence of backbone fragments, and can also permit chain reversal (Vriend and Sander, 1991). The ﬁrst of three stages identiﬁes similar fragments of a given length (10–15 residues) between the two proteins by rigid body superposition using the algorithm of Kabsch (1978). These are then iteratively grown and superposed until the same threshold is reached, thereby identifying maximal length similar fragments.
Being comformable, the matrices can be compared cell by cell and combined in a diﬀerence matrix (DM) of the same dimensions, from which an overall diﬀerence score may be computed. Most of the methods described in this section make use of this device but do not use dynamic programming to impose an alignment of the structures. 1 Distance-matrix matching Early attempts One of the ﬁrst attempts to compare proteins using this approach was Nishikawa and Ooi (1974b) who derived diﬀerence distance plots by subtracting conformable distance matrices representing the two proteins.
B) the matrices are summed with each cell (i, j) adding the best summed score in the previous sub-matrix (all with indices < i, < j) to its own. g. W:W = 12+25 = 37). (c) Two variations are shown one in which gaps are free and the other where there is a high cost resulting in an ungapped alignment. 30 The form of the gap penalty reﬂects an underlying model of protein evolution which, in part, is a reﬂection of the stability of protein structure. A simple model for the latter is that the core is very sensitive to change while the surface, and especially exposed loops, are very susceptible to change (Bajaj and Blundell, 1984).