EMPIRICAL TORSIONAL POTENTIAL FUNCTIONS FROM PROTEIN STRUCTURE DATA Phi‐ and Psi‐Potentials for Non‐glycyl Amino Acid Residues

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Abstract
The torsional potential functions Vt(φ) and Vt(ψ) around single bonds N–Cα and Cα-C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (φ, ψ)-plane with the value of Vtot(φ, ψ), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in l-configuration, are Vt(φ) = – 1.0 cos (φ + 60°); Vt(ψ) = – 0.5 cos (ψ + 60°) – 1.0 cos (2ψ + 30°) – 0.5 cos (3ψ + 30°). The dipeptide energy maps Vtot(φ, ψ) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line ψ = 0°. These functions, derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.