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Structural alignment

Structural alignment is also possible using the basic dynamic programming algorithm. The value of $S_{i,j}$ could be calculated from the RMS deviation of fixed windows centred around $A_i$ and $B_j$ fitted by least-squares superposition of atomic coordinates. Taylor and Orengotaylor:jmb89 found, however that this approach would not take into account long range interactions with small windows and larger windows lacked the flexibility to accommodate insertions and deletions. Their solution, in the program SSAP, was to apply the dynamic programming algorithm to the scoring of similarity between the structural environments around $A_i$ and $B_j$. $S_{i,j}$ is defined as the total score of the low level alignment whose equivalent pairwise suitability measure $L_{k,l}$ is calculated from the distance between interatomic vectors $V_{ik}$ and $V_{jl}$ defined using a common reference frame around carbon-$\alpha$s.

A number of other methods have also been developed to solve the structure-structure alignment problem. Rigid body superposition methods[Chothia & Lesk, 1986,Johnson et al., 1990,Russell & Barton, 1992,May & Johnson, 1994,May & Johnson, 1995,May, 1996, for example] optimise the definitions of residue equivalences between structures by the iterative application of least-squares fitting techniques. The related method of Falicov and Cohenfalicov:jmb96 uses a dynamic programming algorithm to generate the minimum soap-film area[Schulz, 1977] between arbitrarily superposed carbon-$\alpha$ backbones. The soap film area is then minimised through the sampling of superposition parameters, producing alignment and superposition simultaneously.

The DALI program by Holm and Sander[Holm & Sander, 1993] uses simulated annealing to generate alignments of structural fragments, and has the interesting feature of being able to find alignments involving chain reversals and different topologies.