w-Helices in Proteins
Purevjav Enkhbayar, Bazartseren Boldgiv, Norio Matsushima
A modification of the a-helix, termed the xhelix, has four residues in one turn of a helix. We searched
the x-helix in proteins by the HELFIT program which determines the helical parameters—pitch, residues per turn,
radius, and handedness—and p = rmsd/(N - 1)1/2 estimating helical regularity, where ‘‘rmsd’’ is the root mean
square deviation from the best fit helix and ‘‘N’’ is helix length. A total of 1,496 regular a-helices 6–9 residues long
with p B 0.10 A ° were identified from 866 protein chains. The statistical analysis provides a strong evidence that the
frequency distribution of helices versus n indicates the bimodality of typical a-helix and x-helix. Sixty-two right
handed x-helices identified (7.2% of proteins) show nonplanarity of the peptide groups. There is amino acid preference
of Asp and Cys. These observations and analyses insist that the x-helices occur really in proteins.
Keyword: x-helix,HELFIT,Trans-planarity,Amino acid preference,Bimodal test
The x-helix is a modification of the a-helix. The a-helix has 3.6 residue in a single turn [26, 27], while the x-helix
has four residue per turn [4, 14, 30, 33], although both are characterized by consecutive (i / i ? 4) hydrogen bonds
(Table 1; Fig. 1). Helix types are usually designated by a symbol nm, where n is the number of residues per turn and
m the number of atoms contained in the ring joined by a hydrogen bond . The a-helix and x-helix have m = 13.
Thus, the a-helix is designated 3.613-helix, while the x-helix is 4.013-helix. Similarly, the 310-helix, characterized
by (i / i ? 3) hydrogen bonds, and the p-helix, characterized by (i / i ? 5) hydrogen bonds, are called 3.010-helix and 4.416-helix, respectively [7, 23, 29]. The a-helix, 310-helix, and p-helix have been observed in protein structures; they account for 32% of residues, 4 and 0.3%, respectively [2, 10, 13, 21, 22, 25, 35]. However, the x-helix has not yet been identified, so far as we know.
Material and Methods
2.1 Composition of Data Base
The July, 2005, culled PDB data set, containing 866 protein chains with less than 20% sequence identity and B1.6 A resolution (R-value B 0.25), was used in this analysis [3, 18]. Secondary structure assignments based on threedimensional coordinates were made using the DSSP program .
2.2 Identification of a-Helix
A helical segment of the polypeptide chain may be defined either in terms of the backbone dihedral angles, / and w
(rule 6.2) or in terms of helical symmetry and H-bond arrangement (rule 6.3) . Here we employed rule 6.3,
which was used in our analysis of 310-helices . The first and the last residues of the helices are called N-cap (Nc)
and C-cap (Cc), respectively . By these conventions the residues of a helix seven residues long (N = 7) would be
labeled—Nc, 2, 3, 4, 5, 6, Cc. A total of 5,412 a-helices were identified from 866 protein chains in the nonredundant
PDB by the DSSP program . Only regular a-helices with p B 0.10 A ° as already employed as the
criterion for regular 310-helix  were selected for analyses in order to estimate reliable helix parameters.
We used the following procedures to identify x-helices in proteins. First, all a-helices in proteins were identified
using the DSSP program . Secondly, helical parameters for all the a-helices were determined using the HELFIT
program . Helix fitting of the a-helices was performed without Nc and Cc (N - 2 residues). Thirdly, the a-helices
were grouped into regular helices with p B 0.10 A ° , because the p values indicate that the deviation of helical
parameters such as r are less than 5%, and irregular helices with p[0.10 A ° .
3.1 Bimodality of the Frequency Distribution of a-Helices in Proteins Figure 2 shows the FDH of N = 6, 7, 8, and 9, regular
a-helices. The regular, 1,489 helices with 6 B N B 9 give the mean n ¼ 3:71 and its standard deviation r = 0.16.
The Shapiro–Wilk W-test (W = 0.88433 and p�.0001) indicated that the FHD is not normal. Correspondingly, the bimodality test rejects the
hypothesis H0; the FDH is bimodal at very high significance levels. The present analysis provide a strong evidence for
the presence of two distributions with n1 ¼ 3:60 having r1 ¼ 0:10 and n2 ¼ 4:00 havingr1 ¼ 0:19 (Table 2). The
low mean’s distribution corresponds to typical a-helix, while the high mean’s distribution corresponds to x-helix.
4.1 Actual Occurrence of x-Helices in Proteins Most important we have shown that the x-helix does occur
in proteins. The present analyses reveal that 62 of 866 protein chains (7.2% of proteins) contain right handed
x-helices 6–9 residues long. The average helix length of x-helices is 6.4 residues, while the highest occurrence of
a-helices is eleven residues long. The x-helices were compared with typical a-helices on the helix parameters,
the cylindrical volume, the amino acid preference, the backbone dihedral angles (/, u), and the torsion angle (x).
The present analysis identified sixty-two, regular right handed x-helices in the 866 protein chains. The x-helices
show non-planarity of the peptide groups. There is amino acid preference of Asp and Cys. The bimodal analysis of
frequency distributions of helices provides a strong evidence that the distribution consists of two those of typical a-helices and x-helices. These observations insist that the
omego-helices occur really in proteins.
National University of Mongolia
1. Aurora R, Rose GD (1998) Protein Sci 7:21–38
2. Barlow DJ, Thornton JM (1988) J Mol Biol 201:601–619
3. Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE (2000) Nucleic Acids Res 28:235–242
4. Bradbury EM, Brown L, Downie AR, Elliott A, Fraser RD, Hanby WE (1962) J Mol Biol 5:230–247
5. Chou PY, Fasman GD (1974) Biochemistry 13:222–245
6. Doig AJ, MacArthur MW, Stapley BJ, Thornton JM (1997) Protein Sci 6:147–155
7. Donohue J (1953) Proc Natl Acad Sci USA 39:470–478
8. Elango N, Yi SV (2008) Mol Biol Evol 25:1602–1608