Consequences of Non-Uniformity in the Stoichiometry of Component Fractions within One and Two Loops Models of α-Helical Peptides

A 3-D electrostatic density map generated using the Wavefront Topology System and Finite Element Method clearly demonstrates the non-uniformity and periodicity present in even a single loop of an α-helix. The four dihedral angles (N-C*-C-N, C*-C-N-C*, and C-N-C*-C) fully define a helical shape independent of its length: the three dihedral angles, φ = -33.5°, ω = 177.3°, and Ψ = -69.4°, generate the precise (and identical) redundancy in a one loop (or longer) α-helical shape (pitch = 1.59 /residue; r = 2.25 ). Nevertheless the pattern of dihedral angles within an 11 and a 22-peptide backbone atom sequence cannot be distributed evenly because the stoichiometry in fraction of four atoms never divides evenly into 11 or 22 backbone atoms. Thus, three sequential sets of 11 backbone atoms in an α-helix will have a discretely different chemical formula and correspondingly different combinations of molecular forces depending upon the assigned starting atom in an 11-step sequence. We propose that the unit cell of one loop of an α-helix occurs in the peptide backbone sequence C-(N-C*-C)3-N which contains an odd number of C* plus even number of amide groups. A two-loop pattern (C*-C-N)7-C* contains an even number of C* atoms plus an odd number of amide groups. Dividing the two-loop pattern into two equal lengths, one fraction will have an extra half amide (N-H) and the other fraction will have an extra half amide C=O, i.e., the stoichiometry of each half will be different. Also, since the length of N-C*-C-N, C*-C-N-C*, and C-N-C*-C are unequal, the summation of the number of each in any fraction of n loops of an α-helix in sequence will always have unequal length, depending upon the starting atom (N, C*, or C).