Several parameters are involved in completely describing a polypeptide helix or pleated sheet. Helices can be either left-handed or right-handed. The number of amino acids per repeat of the structure can vary between two and five. Also, the planes of the peptide bond ( and angles in Figure 6.2) can be rotated about the carbon. If one considers theoretically that both and can rotate 180 in either direction (+180 to -180), then one can begin to construct a graphical representation of all and rotations about a peptide bond.

Imagine that you constructed all theoretical helices in both the left- and right-handed orientations for which n=2, 3, 4, or 5 (right-handed helix) or n = -2,-3,-4,or -5 (left-handed helix). These are theoretical because some of the structures would create unstable bonds at the molecular level. A computer program could make such a set of theoretical structures, however, without the concern for stability. With a program, one could then determine the and angles of each of the secondary structures and plot the information on a graph of versus , as in Figure 6.8. The blue lines in Figure 6.8 define angles for left-handed helices and the red lines define angles for right-handed helices. The black line in the center defines angles for the pleated sheets.

Keep in mind that real molecules have rules about how stable their bonds are as a function of distance between the atoms, charge, and the angles of the bonds. One can determine which angles of and produce stable and unstable structures using this knowledge from chemistry (assuming, in this case, that all of the amino acids are alanine) and then superimpose stability information on the graph. The stable regions are shown in white in Figure 6.8 and the unstable regions are shown in blue (left-handed helix) or red (right-handed helix). Finally, the and angles for predicted secondary structures, such as the helix and pleated sheets, are plotted as yellow circles and marked accordingly.

This graph, called a Ramachandran Plot, illustrates the relatively small percentage of all theoretical and rotations that are stable for peptide bonds - at least ones involving only alanine (remember the assumption above). Real proteins, such as Bovine Pancreatic Trypsin Inhibitor have structures that largely lie within the stable regions of a Ramachandran Plot (Figure 6.10). The and angles of the protein that lie in an "unstable" region may be due to the incorrect assumptions inherent in making the plot or unknown distortions tolerated in the unique chemical environment of a protein.

The Ramachandran Plot also shows that both right- and left-handed polypeptide helices can be stable, though it turns out that right-handed helices are more stable than left-handed ones, due to the bulkiness of the side chains of the L-amino acids making up biological proteins.