We have observed an empirical structural property that applies to the residues of any AH: the distance between the C α atoms of the ith and (i+4)th residue (denoted by D( Cα _i/Cα _{i +4})) is (almost) equal to the distance between the carbonyl oxygens of the ith and (i+4)th residue (D( O _i/O _{i +4})). We validate our hypothesis on a set of 100 high resolution, non-homologous proteins (which have 775 AHs) taken from the PISCES database ( http://dunbrack.fccc.edu/PISCES.php) ²¹ . Figure 1 shows the plot of the difference between D( Cα _i/Cα _{i +4}) and D( O _i/O _{i +4}) for AHs specified in the PDB files (in red, mean=0.16 Å, standard deviation (sd)= 0.34 Å), and for all residues separated by four residues but not part of a helix (in blue, mean=0.71 Å, sd=0.75 Å).

These results are conservative, since there are residues that are annotated as part of a helix in the PDB file which seems to be incorrect. For example, in PBD 1JET, the ninth helix spans from residues 169 to 178 - “HELIX 9 9 LYS A 169 LYS A 178 1 10”. However, the Pymol helix identification program shows part of this stretch as a random coil (Lys178 in Figure 2-a). Moreover, the distance between the carbonyl oxygen (C=O) and the alpha-amino nitrogen (N-H) of the fourth residue away from the N-terminal is 7.6 Å, which makes it improbable for them to have a hydrogen bond, the primary requisite to be part of an AH. The D( Cα _i/Cα _{i +4}) and D( O _i/O _{i +4}) for this pair is 9 Å and 8 Å, respectively: a difference of 1 Å. Even in cases where the distance between C=O and N-H is within the 3.6 Å typically required for a hydrogen bond, (PDBid: 1ELU, 12th helix), the distances D( Cα _i/Cα _{i +4}) and D( O _i/O _{i +4}) for the residue pair His292-Gly296 is 6.9 Å and 3.4 Å, respectively: a difference of 3.4 Å ( Figure 2b). In short, the helix annotation in the PDB database is often incorrect. Removing these problematic residues reduces the mean distance to 0.095 Å and the sd to 0.14 Å ( Figure 1).

There is variation in the D( Cα _i/Cα _{i +4}) even when considering the same pair of residues. For example, taking all pairs of Arg and Lys in the 775 AHs analyzed ( Table 1), we see that the values can vary from 6.5 Å in PDBid:1H16 (helix26, pair Arg583-Lys587) to 5.8 Å in PDBid:1EYH (helix5, pair Arg72-Lys76). However, as hypothesized, D( O _i/O _{i +4}) is the same as D( Cα _i/Cα _{i +4}).

The Edmundson wheel ²³ has been the standard way of visualizing AHs for a long time now, although there are other methods (Wenxiang diagram ²⁴ ) to represent AHs. The Edmundson wheel shows the alignment of residues as one looks through the helix, and gives an approximate idea of the various properties of the AH. For example, a color coding differentiation of the polar and non-polar residues gives an approximation of the hydrophobic propensity of the AH. A more mathematical representation of the hydrophobic propensity is to represent each residue with a value and a sign (direction). This results in a vector representation, called the hydrophobic moment ¹⁹ . We have chosen the hydrophobic scale from ²⁰ ( Table 2), although any other hydrophobic scale could be also used. The color coding is as follows: all hydrophobic residues (positive values in Table 2) are colored red, while hydrophilic residues (negative values in Table 2) are colored in blue: dark blue for positively charged residues, medium blue for negatively charged residues and light blue for amides. We now show the PAGAL representation of a few AH peptides.

Cecropin. A synergistic combination of two critical immune functions, pathogen surface recognition and lysis, resulted in a chimeric protein with anti-microbial properties against the Gram-negative Xylella fastidiosa ¹⁵ . The lytic domain is cecropin B, which attacks conserved lipid moieties and creates pores in the X. fastidiosa outer membrane ¹⁶ . Cecropin B consists of two AHs, joined by a short stretch of random coil. Figure 3a and b shows the Edmundson wheel and hydrophobic moment of the two AHs. It can be seen that the N-Terminal AH has a large hydrophobic moment, as well as a specific positive charge distribution. The hydrophobicity of this amphipathic AH has significant bearing on the anti-microbial properties of the peptide ²⁵ . This can also be seen in a Pymol rendering of the peptide surface ( Figure 4). The Pymol script for this rendering is automatically generated by PAGAL. On the other hand, the C-Terminal AH comprises mostly of hydrophobic residues. Cecropin-like peptides use the synergy of these two helices - the N-terminal attaches to charged ion on the membrane, and the hydrophobic C-terminal permeates the hydrophobic inter-membrane region (known as the ‘carpet’ model ²⁶ ).

Cathelicidin LL-37. Cathelicidin LL-37 is a critical component of the innate human immune system that protects humans against infectious diseases by targeting anionic phosphatidylglycerols in the pathogenic bacterial membranes ²⁷ .

Recent work has demonstrated a 12-residue peptide (KR-12) corresponding to residues 18 to 29 of LL-37 is toxic to bacterial, but not human cells ¹⁷ . Figure 3c shows the Edmundson wheel and hydrophobic moment of KR-12. The demarcation of the polar and non-polar residues is quite evident. The predominance of positively charged residues in the polar side of the peptide is also clearly visible.

De novo designed AMPs for plant protection. The de novo design of small AMPs that inhibit plant pathogens was the focus of a recent work ¹⁸ . One of the most promising candidates was a small peptide (SP1-1 - RKKRLKLLKRL, Figure 3d), which was “highly active against a broad spectrum of bacteria, but showed low hemolytic activity” ¹⁸ . Although the hydrophobic moment of this peptide is much smaller than that of KR-12 ( Figure 3c), possibly due to the presence of Arg4 on the hydrophobic surface, the distribution of positively charged residues in this peptide is greater than for KR-12.

Often, it is desirable to choose a large distribution of charged residues of a certain kind (anionic or cationic) on the hydrophilic surface. One possible method for quantifying this would be to compute a ‘charge moment’, similar to the computation of hydrophobic moments. However, such an evaluation would determine certain clearly distributions to be the same. For example, assume one semicircle of the wheel comprised only positive residues, and the other hydrophobic residues ( Figure 5a). This is a slightly modified version of KR-12 from cathelicidin LL-37. If one positive residue (R5) were moved from the hydrophilic side to the hydrophobic side (I7) and replaced with a negative residue (D7) ( Figure 5b), the ‘charge moment’ would remain the same, although the two conformations are clearly not the same. Note that the hydrophobic moment is also different, as expected. Therefore, the ‘charge moment’ is not an accurate metric. This is underlined by the fact that replacing a hydrophilic serine on the hydrophobic face with a hydrophobic residue (Ala or Val) enhanced the antimicrobial peptide activity in LL-23, a natural peptide derived from the N-terminal of LL-37 ²⁸ . Thus, we resort to a simple metric to allow one to choose peptides with a large proportion of charged residue of a single kind: the ratio of the positive to the negative residues (RPNR). The two peptides mentioned above will have different RPNRs: 1 ( Figure 5a) and 0.85 ( Figure 5b). Also, the current method is unable to discriminate the possible effects of substituting similar amino acids (for example replacing an arginine by a lysine). These effects are complex and difficult to computationally model, for the ‘consequences of the substitution of arginines for lysines is also modulated by the nature of the peptide into which the substitution is made’ ¹⁴ . Such substitutions (applied to β-defensins also, and not AH peptides) also hold promise as future therapeutic drugs ²⁹ .

PAGAL generates a TikZ input file for drawing the Edmundson wheel and showing the hydrophobic moment (Supplementary File TikzInput.doc). TikZ is a package “for creating graphics programmatically” - http://www.texample.net/tikz/. PAGAL also generates a Pymol script to the peptide structure using the same color coding used in for the Edmundson wheel (Supplementary File PymolInput.doc).

http://github.com/sanchak/pagal

http://github.com/F1000Research/pagal/tree/v1.0

http://dx.doi.org/10.5281/zenodo.11136 ³⁰