An Accurate Model for Biomolecular Helices and Its Application to Helix Visualization

Helices are the most abundant secondary structural elements in proteins and the structural forms assumed by double stranded DNAs (dsDNA). Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves. In this paper we model a helix as a series of different but all bona fide helical curves; each one best fits the coordinates of four consecutive backbone Cα atoms for a protein or P atoms for a DNA molecule. An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve. Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance. When applied to helix visualization, the ribbon diagrams generated by the model are less choppy or have smaller side chain detachment than those by the previous visualization programs that typically model a helix as a series of low-degree splines.