Computational Methods for Protein Structure Prediction & Modeling V1 - Xu Xu and Liang

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Further Reading

Jones, N.C., and Pevzner P.A. 2004. An Introduction to Bioinformatics Algorithms.

Cambridge, MA, MIT Press.

Konopka, A.K., and Crabbe, M.J.C. (Eds.). 2004. Compact Handbook of Computational Biology. New York, Dekker.

chain or to the backbone of the two residues (Fariselli and Casadio, 1999; Mirny and Domany, 1996). The following definitions of the interresidue distance Di j have appeared at some time in the literature, each associated with a threshold distance:

1.The distance between alpha carbons (CA)

2.The distance between beta carbons (CB), using alpha carbon for glycine

3.The minimum distance between the van der Waals (vdW) spheres of heavy atoms (HS)

4.The minimum distance between the vdW spheres of backbone heavy atoms (BB)

5.The minimum distance between the vdW spheres of side-chain heavy atoms or alpha carbons (SC)

By one informed account, the best definition for interresidue distance is SC, the minimum distance between side-chain or alpha-carbon atoms (Berrera et al., 2003). Using

˚

a cutoff distance of around 1.0 A between vdW spheres, SC-based contact maps efficiently recognized homologue sequences in a “threading” experiment, where a query sequence is assigned an energy score for every possible alignment of the sequence to a set of template structures. In a threading experiment, the definition of a contact determines which residues in the sequence are used to sum the energy. Using the minimum distance between residues and using a short distance cutoff makes the definition of a contact more energetically realistic, and this makes the sum of amino acid contact potentials a better approximation of the true energy. Contact potentials are energy functions that measure the pairwise side-chain-dependent free energy of residue–residue contacts, irrespective of the side-chain conformations. Contact potentials may be derived from contact maps statistics, as described in a later section.

Simpler, backbone atom-based definitions (CA or CB) with longer distance cutoffs are more readily projected into three dimensions, since the atomic positions used to calculate the distance depend only on the backbone angles. CB is slightly more meaningful than CA in an energetic sense, since side chains that point toward each other, and therefore have a shorter CB distance than CA distance, are more likely to make an actual physical contact. Using the minimum distance measures (HS, BB, or SC) can make projection into three dimensions more difficult because we have not saved the precise identity of the contacting atoms in the Boolean matrix.

˚

CB distances with a cutoff of 8 A were chosen for use in the Critical Assessment of Structure Prediction (CASP) experiments (Moult et al., 2003), and this is the definition that we will discuss here, unless otherwise specified.

Having defined what we mean by the distance Di j , the definition of a contact map is a straightforward distance threshold. For a protein of N amino acids the contact map is an N × N matrix C whose elements are given, for all i, j = 1, . . . , N , by

The set of all Di j is commonly referred to as the “distance matrix.” Therefore, we can think of Ci j as a thresholded distance matrix. The mean difference between two