More precise model of <i>α</i>-helix and transmembrane <i>α</i>-helical peptide backbone structure

The 3-D structure of the β-adrenergic receptor with a molecular weight of 55,000 daltons is available from crystallographic data. Within one of the seven transmembrane ion channel helices in the β2-receptor, one loop of a helix ACADL has previously been proposed as the site that explains β2 activity (fights acute bronchitis) whereas ASADL in the β1-receptor at the corresponding site explains β1-activity (cardiac stimulation). The α-agonist responsible for this selective reaction is only 0.5% of the receptor molecular weight, and only 1.5% of the weight of the trans-membrane portion of the receptor. The understanding of the mechanism by which a small molecule on binding to a site on one single loop of a helix produces a specific agonist activity on an entire transmembrane ion channel is uncertain. A model of an α-helix is presented in which of pitch occurs at angles both smaller and larger than 180° n. Consequently, atomic coordinates in a peptide backbone α-helix match the data points of individual atom (and atom types) in the backbone. More precisely, eleven atoms in peptide backbone routinely equal one loop of a helix, instead of eleven amino acid residues equaling three loops of a helix;therefore, an α-helix can begin (or end) at any specific atom in a peptide backbone, not just at any specific amino acid. Wavefront Topology System and Finite Element Methods calculate this specific helical shape based only upon circumference, pitch, and phase. Only external forces which specifically affect circumference, pitch and/or phase (e.g. from agonist binding) can/will alter the shape of an α-helix.

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).