Potential for Protein Surface Shape Analysis Using Spherical Harmonics and 3D Zernike Descriptors

Abstract

With structure databases expanding at a rapid rate, the task at hand is to provide reliable clues to their molecular function and to be able to do so on a large scale. This, however, requires suitable encodings of the molecular structure which are amenable to fast screening. To this end, moment-based representations provide a compact and nonredundant description of molecular shape and other associated properties. In this article, we present an overview of some commonly used representations with specific focus on two schemes namely spherical harmonics and their extension, the 3D Zernike descriptors. Key features and differences of the two are reviewed and selected applications are highlighted. We further discuss recent advances covering aspects of shape and property-based comparison at both global and local levels and demonstrate their applicability through some of our studies.

Improved protein surface comparison and application to low-resolution protein structure data

“…the input 3D function) [17,28]. The mathematical foundation of the 3DZD was laid out by Canterakis (1999) and was applied on 3D object retrieval by Novotni and Klein (2003).…”

“…Thus, development of a new generation of structure analysis tools, which allow a fast screening of large structure databases and can handle low resolution structure data, is needed. With this in mind, we represent protein structures as surface shapes by the 3D Zernike descriptors (3DZD) [13-17]. There have been previous works which employ a protein surface representation [15], such as volumetric representation [18], convex hull [19], and the spin image [20].…”

Accurate single-sequence prediction of solvent accessible surface area using local and global features

“…Recently Klenin et al introduced a fast analytical method to calculate the ASA using power diagrams [15]. Other efforts in characterizing the surface of proteins were also carried out [16, 17, 18, 19, 20, 21, 22]. Since the ASA describes the amount of surface a given residue has that is accessible to the solvent or for other intermolecular interactions, it is easy to understand why the ASA is important for recognizing functional sites along the chain [23].…”

Modelo computacional para la generación de indicaciones en la localización de objetos en entornos virtuales : aspectos espaciales y perceptivos

“… In molecular biology, shape descriptors have been applied to analyze molecular surfaces (Ankerst et al, 1999;Venkatraman et al, 2009) and molecule stability (Chung, 1997).…”

“…The 3D Zernike descriptor will be used, also known as descriptor of geometric moments with orthogonal bases. This descriptor has been used effectively as a method to represent the global shape of a 3D object (Esquivel-Rodriguez and Kihara, 2012;Kihara et al, 2011;Sael et al, 2008;Venkatraman et al, 2009). …”