GPU-based detection of protein cavities using Gaussian surfaces

Sérgio E. D. Dias, Ana Mafalda Martins, Quoc T. Nguyen, Abel J. P. Gomes

Protein cavities play a key role in biomolecular recognition and function, particularly in protein-ligand interactions, as usual in drug discovery and design. Grid-based cavity detection methods aim at finding cavities as aggregates of grid nodes outside the molecule, under the condition that such cavities are bracketed by nodes on the molecule surface along a set of directions (not necessarily aligned with coordinate axes). Therefore, these methods are sensitive to scanning directions, a problem that we call cavity ground-and-walls ambiguity, i.e., they depend on the position and orientation of the protein in the discretized domain. Also, it is hard to distinguish grid nodes belonging to protein cavities amongst all those outside the protein, a problem that we call cavity ceiling ambiguity. We solve those two ambiguity problems using two implicit isosurfaces of the protein, the protein surface itself (called inner isosurface) that excludes all its interior nodes from any cavity, and the outer isosurface that excludes most of its exterior nodes from any cavity. Summing up, the cavities are formed from nodes located between these two isosurfaces. It is worth noting that these two surfaces do not need to be evaluated (i.e., sampled), triangulated, and rendered on the screen to find the cavities in between; their defining analytic functions are enough to determine which grid nodes are in the empty space between them. This article introduces a novel geometric algorithm to detect cavities on the protein surface that takes advantage of the real analytic functions describing two Gaussian surfaces of a given protein.