Abstract
A method for generating a complete polypeptide backbone structure from a set of C^α^ coordinates is presented. Initial trial values of ϕ and ψ for a selected residue are chosen (essentially from an identification of the conformational region of the virtual‐bond backbone, e.g., and α‐helical region), and values of ϕ and ψ for the remaining residues (both towards the N‐ and C‐terminus) are then computed, subject to the constraint that the chain have the same virtual‐bond angles and virtual‐bond dihedral angles as the given set of C^α^ coordinates. The conversion from C^α^ coordinates to full backbone dihedral angles (ϕ,ψ) involves the solution of a set of algebraic equations relating the virtual‐bond angles and virtual‐bond dihedral angles to standard peptide geometry and backbone dihedral angles. The procedure has been tested successfully on C^α^ coordinates taken from standard‐geometry full‐atom structures of bovine pancreatic trypsin inhibitor (BPTI). Some difficulty was encountered with error‐sensitive residues, but on the whole the backbone generation was successful. Application of the method to C^α^ coordinates for BPTI derived from simplified model calculations (involving nonstandard geometry) showed that such coordinates may be inconsistent with the requirement that ϕ~Pro~ be near −75°. In such a case, i.e., for residues for which the algebraic method failed, a leastsquares minimizer was then used in conjunction with the algebraic method; the mean‐square deviation of the calculated C^α^ coordinates from the given ones was minimized by varying the backbone dihedral angles. Thus, these inconsistencies were circumvented and a full backbone structure whose C^α^ coordinates had an rms deviation of 0.26 Å from the given set of C^α^ coordinates was obtained.