Abstract
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.
Highlights
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
Helices were proposed as the main secondary structural elements for proteins in 1951 [1] and as the only structural forms for double stranded DNAs [2] in 1953 through model building using low-resolution X-ray diffraction data well before atomic coordinates could be determined from high-resolution data [3, 4]
Even with the ready availability of many high-resolution structures at present, a biomolecular helix in either a protein or a DNA molecule has rarely been modeled as a series of genuine helical curves likely because of the difficulty to accurately fit the backbone atoms to helical curves though methods [5, 6] have been proposed in the past to compute helical parameters using backbone atoms: N, Cα, CO atoms in a protein or P atoms in a DNA
Summary
Helices were proposed as the main secondary structural elements for proteins in 1951 [1] and as the only structural forms for double stranded DNAs (dsDNA) [2] in 1953 through model building using low-resolution X-ray diffraction data well before atomic coordinates could be determined from high-resolution data [3, 4]. The deviation could not be quantified and further correlated with structural and functional significance, and (3) when applied to molecular visualization the generated helix ribbon diagrams are either choppy (wavy) or the side chains become detached from the diagrams [16]. When applied to the visualization of a helix as a ribbon diagram, the model’s closeness to a genuine helical curve makes it possible to eliminate choppiness in protein diagrams and to greatly reduce it in DNA diagrams while the minimization of the distance between a backbone atom and its closest point on the diagram achieved by the curve fitting algorithm greatly alleviates the side chain detachment problem. In addition both the deviation and correlation could be visualized by the helix diagrams generated by our model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
