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hydrophobicity plots have been used to recognize amphipathic helices as well as to build
classifiers to various protein groups. A review on these applications is in [28].
2. Comparison of 3D structures
Comparison of 3D structure is used in a variety of fields such as fold recognition, structural
evolution studies and drug design, and the protocols are as diverse as the fields themselves.
E.g. in the comparison of 3D structures produced on the same protein molecule by NMR
methods, all the equivalent atom-pairs are a priori known and can be used in the
comparison. In contrast, determination of folds is based on the backbone CD atoms only
and the equivalences have to be determined by the calculation itself. In this section we will
briefly summarize the similarity/distance functions used for backbone comparison,
concentrating on the similarity/distance measures used rather than the goal and/or
implementation of the actual algorithms. In the majority of the cases, the approach used for
structural alignments is quite similar to that used in sequence analysis (finding alignment
paths in a distance matrix or optimizing the range by successive omission or additions).
This is because 3D structures can be compared in terms of their (overlapping) peptide
fragments, and a series of peptide fragments is a linear, sequence-like representation. For
example, one can compute an
rmsd
between the peptide fragments of two proteins and
construct a distance-matrix with the resulting values [29,30]. But there are many ways to
represent peptide fragments as vectors, and then one can use any of the vector-distance
formulas to produce the values of the distance matrix. For example, vectors of torsional
angles [31,32], curvature and torsion parameters of peptide fragments [33,34] have been
used by early comparison methods, as reviewed by Orengo [35]. More recent methods
include structural alphabets described in terms of dihedral angles [36,37] or on distance
geometry [38,39]. In the latter method, the size of the alphabet (the minimum number of
fragments necessary to describe the observed data) is 27 derived from statistical
optimisation. The similarity search is then carried out by Smith-Waterman alignment.
The similarity measures described in this section can be classified according to the
use of atomic (residue-based) descriptions, or higher-order descriptions such as secondary
structure elements. Another important difference is that some of the methods can be used to
produce structural alignments while others are only preliminary filters indicating similarity
without providing a structural alignment.
Methods based on superposition of atoms use the
rmsd
distance (section x, above)
Even though the results of atom superposition methods are generally considered superior to
most computational alternatives, and very low
rmsd
values are indicative of identical
structures - rmsd can be used only with caution as a quantitative indicator of similarity. In
addition, there is no accepted and reliable statistical model that would allow to use
rmsd
as
a probabilistic score with a statistical significance, moreover
rmsd
does not penalize gaps.
Therefore there a number of alternative similarity scores have been developed for obtaining
optimal structural alignments even though the final results are always characterized in
terms of the rmsd score.
One group of similarity scores is based on vectors or sets of vectors assigned to
each position within a protein structure. The parameters of the vector represent various
features. Methods developed by Taylor and Orengo [40,41] assigned a set of intramolecular
C
D
C
D
vectors to each residue position, or used various geometric features as parameters of
the vector assigned to each residue position. As a result, a protein structure was converted
into a series of residue vectors, and two structures could be compared to give a so-called
residue matrix in which the elements are calculated as a vectorial difference (city-block
