BACKGROUND: 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. RESULTS: 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. CONCLUSION: 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.

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.

Current GPU-based workstations are inadequate to triangulate and rendering large molecular datasets with thousands and hundreds of thousands, not to say millions, of atoms. The problem is not so the lack of processing power, but the memory limitations of current GPU graphics cards. For example, the NVidia GeForce GTX 590 graphics card comes with two 1.5GB GPUs. We tackle here this problem using a OpenMP-CUDA solution that runs on a loosely-coupled GPU cluster. Basically, we propose a fast, scalable, parallel triangulation algorithm for molecular surfaces that takes advantage of multicore processors of CPUs and GPUs of modern hardware architectures, where each CPU core works as the master of a single GPU, being the processing burden distributed over the CPU cores available in a single computer or a cluster. As much as we know, this is the first marching cubes algorithm that triangulates molecular surfaces on multiple GPUs using CUDA and OpenMP.

SUMMARY Computing the surface of a molecule (e.g., a protein) plays an important role in the analysis of its geometric structure as needed in the study of interactions between proteins, protein folding, protein docking, and so forth. There are a number of algorithms for the computation of molecular surfaces and their triangulations, but only a few take advantage of graphics processing unit computing. This paper describes a graphics processing unit‐based marching cubes algorithm to triangulate molecular surfaces. In the end of the paper, a performance analysis of three implementations (i.e., serial CPU, CUDA, and OpenCL) of the marching cubes‐based triangulation algorithm takes place as a way to realize beforehand how molecular surfaces can be rendered in real‐time in the future. Copyright © 2011 John Wiley & Sons, Ltd.

The problem addressed in this paper consists in triangulating the van der Waals surface without computing the geometric intersections of its atoms. Recall that the van der Waals surface is useful in computational molecular biology and biochemistry to, for example, determine the volume occupied by a molecule, as well as other important geometric properties. Assuming that every atom is represented by a ball, this amounts to compute the surface of the union of a number of balls. The novelty of our method lies in avoiding the computation of surface-surface intersections (SSI) of two or more balls.

Previous work on implicit surfaces has almost exclusively focused on homogeneously 2-dimensional surfaces, regardless of whether they are manifold or not. Consequently, current geometric and graphical systems, and even commercial mathematical software packages, cannot generate non-homogeneous implicit surfaces such as, for example, the Steiner surface or the Whitney surface correctly. This paper overcomes these difficulties by introducing a new uniform space partitioning-based algorithm that generates a polygonization for implicit surfaces possibly with self-intersections and isolated 0-and 1-dimensional singularities.

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.