Detecting and analyzing protein cavities provides significant information about active sites for biological processes (e.g., protein-protein or protein-ligand binding) in molecular graphics and modeling. Using the three-dimensional structure of a given protein (i.e., atom types and their locations in 3D) as retrieved from a PDB (Protein Data Bank) file, it is now computationally viable to determine a description of these cavities. Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels, and grooves on the surface of a given protein. In this work, we survey the literature on protein cavity computation and classify algorithmic approaches into three categories: evolution-based, energy-based, and geometry-based. Our survey focuses on geometric algorithms, whose taxonomy is extended to include not only sphere-, grid-, and tessellation-based methods, but also surface-based, hybrid geometric, consensus, and time-varying methods. Finally, we detail those techniques that have been customized for GPU (Graphics Processing Unit) computing.

Computing molecular surfaces is important to measure areas and volumes of molecules, as well as to infer useful information about interactions with other molecules. Over the years many algorithms have been developed to triangulate and to render molecular surfaces. However, triangulation algorithms usually are very expensive in terms of memory storage and time performance, and thus far from real-time performance. Fortunately, the massive computational power of the new generation of low-cost GPUs opens up an opportunity window to solve these problems: real-time performance and cheap computing commodities. This paper just presents a GPU-based algorithm to speed up the triangulation and rendering of molecular surfaces using CUDA. Our triangulation algorithm for molecular surfaces is based on a multi-threaded, parallel version of the Marching Cubes (MC) algorithm. However, the input of our algorithm is not the volume dataset of a given molecule as usual for Marching Cubes, but the atom centers provided by the PDB file of such a molecule. We also carry out a study that compares a serial version (CPU) and a parallel version (GPU) of the MC algorithm in triangulating molecular surfaces as a way to understand how real-time rendering of molecular surfaces can be achieved in the future.

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BackgroundProtein 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.ResultsWe 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.ConclusionThis 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.