Abstract
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).
Highlights
A helix is a line composed of only two variables: pitch and diameter [1]
We propose a model in which the eleven backbone atoms in a helix begin and end with an amide, i.e., three chiral center C* atoms and four amide groups, one before and after each C* atom
A unit cell composed of 11 amino acids equaling three loops of a helix is a model from which diameter and pitch can be calculated
Summary
A helix is a line composed of only two variables: pitch and diameter [1]. Analogous to a circumference, a loop of a helix is a measure of length, not area or volume. Wavefront Topology System and Finite Element Methods enable calculating a “scaffolding” of unit building blocks of equal unit size and volume along this linear structure, Figure 1(a) [2] [3] In this model, the pitch, diameter, volume, and shape of such volume are inputs which can have virtually any value. The structure of n loops of an α-helix is assumed to be composed only of a whole number of precise unit cells Such a more precise model of the same helical shape contains eleven peptide backbone atoms in one loop of an α-helix [1] equal to eleven amino acid residues forming three loops. We propose a molecular level mechanism for the high degree of redundancy in the peptide α-helix structure in unit cell structure even shorter than a sequence of eleven backbone atoms
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