Quantification of Twist from the Central Lines of β-Strands

Since the discovery of right-handed twist of a β-strand, many studies have been conducted to understand the twist. Given the atomic structure of a protein, twist angles have been defined using atomic positions of the backbone. However, limited study is available to characterize twist when the atomic positions are not available, but the central lines of β-strands are. Recent studies in cryoelectron microscopy show that it is possible to predict the central lines of β-strands from a medium-resolution density map. Accurate measurement of twist angles is important in identification of β-strands from such density maps. We propose an effective method to quantify twist angles from a set of splines. In a data set of 55 pairs of β-strands from 11 β-sheets of 11 proteins, the spline measurement shows comparable results as measured using the discrete method that uses atomic positions directly, particularly in capturing twist angle change along a pair, different levels of twist among different pairs, and the average of twist angles. The proposed method provides an alternative method to characterize twist using the central lines of a β-sheet.