How round is a protein? Exploring protein structures for globularity using conformal mapping.

Frontiers in Molecular Biosciences

卷:1

Joel eHass¹  Patrice eKoehl² 

[1] University of California, Davis;

[2] University of California;

关键词: Proteins;    Shape Analysis;    shape space;    conformal mapping;    Diffeomorphism;    Triangular mesh;   

DOI  :  10.3389/fmolb.2014.00026

来源: DOAJ

【 摘 要 】

We present a new algorithm that automatically computesa measure of the geometric difference between the surface of a protein anda round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal mapbetween these surfaces. The conformal map is chosento minimize a symmetric elastic energythat measures the distance of the constructed conformal map from an isometry. We illustrate our approachon a set ofbasic sample problems and then on a dataset of diverse protein structures. We show first that the symmetric elastic energy is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. Wethen demonstrate that the symmetric elastic energy captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that the symmetric elastic energy serves as a probe of the limits of the application of conformal mappings to parametrize protein shapes. We identifylimitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surfacegeometry.

【 授权许可】

Unknown