4.0 Identification of Secondary Structure
Angle plots
Right-handed alpha helices and beta sheets have very different backbone dihedral angles (phi and psi) which appear in two separate regions of a Ramachandran diagram (Figure 19 ). However, backbone dihedral angles are seldom used for secondary structure identification. One reason is that a given residue in a helical or extended conformation can have backbone dihedral angles which differ considerably from the "typical" mean values (and still be within the physically allowed regions). Another reason for the lack of popularity of this method of secondary structure identification is that extended conformations can exist (e.g. in loops) and not be part of a sheet. We have already seen that the backbone dihedral angles near the ends of helices are often irregular and the Ncap and Ccap residues at helix boundaries contain non-helical phi, psi values and can make identification difficult.
There is no universally correct definition of a hydrogen bond as there is no sharp border between the quantum-mechanical and electrostatic regimes and no discontinuity in energy as a function of distance or alignment that governs the interaction. From the analysis of small molecule structures, an ideal hydrogen bond has a donor-acceptor distance of 2.9 Angstroms and a hydrogen-donor-acceptor angle of 0 degrees. Some criteria commonly used in the literature are listed below. A hydrogen bond is identified if:
Hydrogen bonds
It is most natural (and in practice most common) to identify regular secondary elements (helix and sheet) based on the characteristic hydrogen-bonding patterns (3.10 helix: i, i+3; alpha helix i, i+4 etc.). There are two obstacles associated with identifying secondary structure from hydrogen bonds. One is the criteria used for identifying a hydrogen bond itself, and the other is the criteria used for identifying the secondary structure element (given exact locations of all hydrogen bonds). Each deserves consideration.
Once the definition of a hydrogen bond is adopted and all such hydrogen bonds in the protein under investigation are identified, the location and extent of the secondary structural segments remain to be determined. In principle, the core of alpha, 3.10, and pi helical segments should be unambiguous due to the repeating (i, i+4), (i, i+3), and (i, i+5) hydrogen bonds, respectively. However, as pointed out (3.1) the first and the last helical turns each contain four residues in which only one of the two potential backbone hydrogen bonds are formed. Are these first-turn and last-turn residues also to be included in the helix? According to the often used criteria of Kabsch & Sander (1983) in their "Dictionary of Protein Structure" these residues are to be included in helical definitions and set the minimum helical lengths to one turn.
Similarly, the central residues of beta strands are straightforward to align into sheets whereas the end residues of each strand can contain dihedral angles characteristic of extended conformations yet not participate in the hydrogen bonding of the sheet (see Figure 9 ). To qualify as a strand of a beta sheet, most definitions require the backbone amide nitrogen and carbonyl oxygen atoms of at least one residue
Despite all of the potential ambiguities listed above, regular hydrogen bond patterns remain the most widely used and reliable method of secondary structure identification
Distance plots
A two-dimensional plot of the distance between alpha carbons of residues i and j is a useful way to present, in two-dimensions, the overall fold of the polypeptide chain in the three-dimensional structure of a protein. Such a plot is reproduced in Figure 20 where alpha carbons closer than 10 Angstroms are indicated with a cross at the coordinates corresponding to the residue numbers. In representations such as this, helices can be identified as a strips directly adjacent to the diagonal, antiparallel beta strands by strips perpendicular to the diagonal, and parallel beta strands by off-diagonal strips parallel to the diagonal. Contacts between secondary structures are also present in this representation. The disulfide bond between residues 5 and 55 covalently attach the N- and C-terminal segments producing the correlation between the two helical segments 3-6 and 47-58. However, while the general locations of helix and strand segments can be obtained from distance plots, this method is no more reliable than others for exact location of secondary structure boundaries.
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