4.0 Identification of Secondary Structure

4.1 Identification in 3D Structures

Three-dimensional protein structures at atomic resolution are now available from both X-ray and NMR studies. Two important differences between structures determined from these two methods are that 1.) protons are included (necessarily) in the NMR solution structures and, with the exception of neutron diffraction studies, they are practically invisible to X-ray techniques and 2.) X-ray techniques provide a single, or at most a few, three-dimensional structures present in the unit cell as a unique analytical solution to the experimental data. On the other hand, structures determined by NMR methods are presented as groups (10-50) of structures each satisfying the experimental constraints equally well. This presents a potential problem in that either the entire ensemble of structures are evaluated or a mean conformation is produced and then evaluated. Mean structures from ill-defined portions of the polypeptide chain will have non-standard geometries and may cause problems in analyses. In any event, the lack of hydrogen in most crystallographically-determined structures is not usually a problem as their positions are, in most cases, uniquely defined by the polypeptide covalent geometry.

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.

Figure 19. Ramachandran diagrams showing (A) the potential energy distribution in the phi, psi plane for a pair of peptide units with an Ala between and (B) a plot of the backbone dihedral angles phi and psi of about 2500 residues in 13 proteins. Both (A) and (B) are taken from Schulz & Schirmer, 1979. In (A), countours are drawn at 1 kcal/mole intervals from negative to zero (dotted).

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.

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:

the proton-acceptor distance is less than 2.4 Angstroms and the angle between the proton-donor bond and the line connecting the donor and acceptor atoms is less than 35 degrees (e.g., see Berndt et al., 1993).

the proton-acceptor distance is less than 2.5 Angstroms and the angle defined by the hydrogen-acceptor-donor atoms lies between +/- 90 and 180 degrees (Baker & Hubbard, 1984)

the energy defined by an electrostatic potential function is less than a cutoff value (see Kabsch & Sander, 1983). These authors have proposed perhaps the most generous criterium (E < -0.5 kcal/mol) allowing a distance of up to 5.2 Angstroms between donor and acceptor at perfect alignment and allowing a misalignment of up to 63 degrees at the ideal length (2.9 A).

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.

Figure 20. Distance plot (contact map) of bovine pancreatic trypsin inhibitor (left). Distances shorter than 10 Å between alpha carbons are marked with a cross. The approximate positions of the secondary structure elements are indicated on the diagonal (helix:3-6 and 47-58; sheet: 18-24, 29-35, and 45). Taken from Creighton, 1993. For comparison, the three-dimensional structure of BPTI is shown with selected residue positions labeled.

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Angle plots
Hydrogen bonds
Distance plots

No Title - 31 MAY 96

written by Kurt D. Berndt

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