Assessment of Globularity of Protein Structures via Minimum Volume Ellipsoids and Voxel-Based Atom Representation

Abstract

A computer algorithm for assessment of globularity of protein structures is presented. By enclosing the input protein in a minimum volume ellipsoid (MVEE) and calculating a profile measuring how voxelized space within this shape (cubes on a uniform grid) is occupied by atoms, it is possible to estimate how well the molecule resembles a globule. For any protein to satisfy the proposed globularity criterion, its ellipsoid profile (EP) should first confirm that atoms adequately fill the ellipsoid’s center. This property should then propagate towards the surface of the ellipsoid, although with diminishing importance. It is not required to compute the molecular surface. Globular status (full or partial) is assigned to proteins with values of their ellipsoid profiles, called here the ellipsoid indexes (EI), above certain levels. Due to structural outliers which may considerably distort the measurements, a companion method for their detection and reduction of their influence is also introduced. It is based on kernel density estimation and is shown to work well as an optional input preparation step for MVEE. Finally, the complete workflow is applied to over two thousand representatives of SCOP 2.08 domain superfamilies, surveying the landscape of tertiary structure of proteins from the Protein Data Bank.