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Transformation of the ϕ‐ψ plot for proteins to a new representation with local helicity and peptide torsional angles as variables
Author(s) -
Peticolas Warner L.,
Kurtz Beth
Publication year - 1980
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.1980.360190605
Subject(s) - peptide , plot (graphics) , chemistry , helicity , crystallography , torsion (gastropod) , residue (chemistry) , mathematics , physics , quantum mechanics , statistics , surgery , medicine , biochemistry
A new representation of protein structure is obtained by the angular coordinate transformations η i = (ϕ i +1 −ψ i )/2 and ξ i = ϕ i +1 +ψ i with careful mathematical attention to the cyclical boundary conditions of all of the variables involved. From published ϕ‐ψ data it is possible to obtain a new η‐ξ plot. As the angle ξ i is varied from – 180° through 0° to + 180° in this plot, the local helicity of the polypeptide chain changes continuously and contiguously without sudden reversals in handedness. The variable, η i , gives the torsional position of the i th peptide group. Some peptide groups in proteins, such as the second peptide residue in a type II β‐turn, are nonhydrogen‐bonded and can undergo considerable torsional oscillation. In such cases the η angle should be represented by a line whose length reflects the allowed dynamical variations in the peptide torsional position. Certain peptide residues in proteins may be able to undergo a complete torsional rotation of 360°. Such residues would be represented on the η‐ξ plot as a straight line across the plot parallel to the abscissa. Other examples of the possible usefulness of this plot are also given.