Representation of Protein 3D Structures in Spherical (rho, phi, theta) Coordinates and Two of Its Potential Applications

作者：Reyes Vicente M^*

来源：Interdisciplinary Sciences, Computational Life Sciences, 2011, 3(3): 161-174.

DOI：10.1007/s12539-011-0099-0

• protein outer layer
• protein inner core
• computational epitope mapping
• spherical coordinate system
• protein double-centroid reduced representation
• protein functional site prediction
• clustering algorithm

Three-dimensional objects can be represented using Cartesian, spherical or cylindrical coordinate systems, among many others. Currently all protein 3D structures in the PDB are in Cartesian coordinates. We wanted to explore the possibility that protein 3D structures, especially the globular type (spheroproteins), when represented in spherical coordinates might find useful novel applications. A Fortran program was written to transform protein 3D structure files in Cartesian coordinates (x, y, z) to spherical coordinates (rho, phi, theta), with the centroid of the protein molecule as origin. We present here two applications, namely, (1) separation of the protein outer layer (OL) from the inner core (IC); and (2) identifying protrusions and invaginations on the protein surface. In the first application, phi and theta were partitioned into suitable intervals and the point with maximum rho in each such 'phi-theta bin' was determined. A suitable cutoff value for rho is adopted, and for each phi-theta bin, all points with rho values less than the cutoff are considered part of the IC, and those with rho values equal to or greater than the cutoff are considered part of the OL. We show that this separation procedure is successful as it gives rise to an OL that is significantly more enriched in hydrophilic amino acid residues, and an IC that is significantly more enriched in hydrophobic amino acid residues, as expected. In the second application, the point with maximum rho in each phi-theta bin are sequestered and their frequency distribution constructed (i.e., maximum rho's sorted from lowest to highest, collected into 1.50 angstrom-intervals, and the frequency in each interval plotted). We show in such plots that invaginations on the protein surface give rise to subpeaks or shoulders on the lagging side of the main peak, while protrusions give rise to similar subpeaks or shoulders, but on the leading side of the main peak. We used the dataset of Laskowski et al. (1996) to demonstrate both applications.

• 出版日期2011-9