Tertiary Structure of Proteins. I. Representation and Computation of the Conformations

A protein conformation can be computed by connecting peptide units of usual trans-planar structure successively with a given set of dihedral angles ϕ and ψ. It is, however, not easy to generate the native conformations such as myoglobin and lysozyme by the computation. In order to show the discrepancy between the native conformation and the computed one, we have introduced a map, where the mutual distance between C α -atoms of i -th and j -th residue , r i j , is listed against the residue number, in row and column. This map represents a tertiary structure of the protein (e. g. α-helix, β-structure) as the characteristic patterns. It becomes possible to estimate the difference of the computed conformation from the native one numerically by comparing the corresponding maps. The improvement of the dihedral angles, ϕ and ψ, as made by minimizing the deviation of the computed map from the native one on both myoglobin and lysozyme.