The Ramachandran plot is an important way of describing protein secondary structure.

<p>(a) The state of a residue within a peptide (top) and a peptoid (bottom) can be largely specified by the two dihedral angles <i>ϕ</i> and <i>ψ</i>. (b) Regular protein secondary structures, such as <i>α</i>-helices and <i>β</i>-sheets, correspond to single diffuse regions on a plot drawn in terms of <i>ϕ</i> and <i>ψ</i>, called a Ramachandran plot (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160023#sec006" target="_blank">Methods</a>). (c) Peptoid Σ-sheets [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160023#pone.0160023.ref016" target="_blank">16</a>] harbor a secondary-structure motif in which backbone residues alternate between two regions on the Ramachandran plot. In order to describe each region in terms of a single number, so that the state of each residue in a backbone can be compactly indicated, we describe in this paper the development and properties of a structurally meaningful combination of <i>ϕ</i> and <i>ψ</i> that we call the Ramachandran number, . [Panel (a) was adapted from an image found on Wikimedia Commons (<a href="https://commons.wikimedia.org/wiki/File%3AProtein_backbone_PhiPsiOmega_drawing.jpg" target="_blank">link</a>) by Dcrjsr (CC BY 3.0 (<a href="http://creativecommons.org/licenses/by/3.0" target="_blank">link</a>)). The contours in (b) and (c) represent regions within which 70% of a secondary structure resides; see Section 4.1.].