ABSTRACT
Abstract A new dihedral angle measure is presented in this chapter for protein secondary structure modeling and prediction. This new angle measure is simpler than the Ramachandran plots because it has only one degree of freedom and varies between 0 and π/2. The origin of this new dihedral angle measure was precipitated by a Steiner tree analysis of the twist angles within the individual amino acid structures. The Steiner tree structure of the amino acids revealed certain regular twist angles for the planes of atoms as defined by the Steiner tree topology. This regularity carried over into the analysis of dipeptide structures when it was shown that a planar characterization of the {N, Cα, C} set of atoms unique for each residue would synthesize the angular measure of the φ,ψ angles of the Ramachandran plots, but with one degree of freedom less. Numerous experimental results with this new angle measure are presented to characterize the α-helix and β-sheet structures of proteins.
