A simple two-dimensional representation for the common secondary structural elements of polypeptides and proteins

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C(α) atoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudodihedral involving four sequential C(α) atoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple φ,ψ pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor.