Construction of Space-filling Models of Proteins Using Dihedral Angles

In principle the correct three-dimensional structure of a protein molecule can be reproduced by setting the dihedral angles of its backbone and side chains without the need for measuring coordinates. Dihedral angles ø, Ψ, and ω determine the conformation of a protein's backbone while angles ϰ1, ϰ2, etc., determine the dispositions of its side chains. In most cases ω is taken as 0° (Edsall et al., 1966) since peptide bonds are generally trans- and coplanar. The use of dihedral angles with C.P.K. models was initiated by Hauschka and Segal (1966) who described the use of paper dials in setting angles ø and Ψ. Their contribution led us to ask the question: Can an accurate space-filling model of a protein actually be constructed from C.P.K. models relying entirely on dihedral angles?