Multi-GPU-based detection of protein cavities using critical points

Highlights

• CriticalFinder is the first multi-GPU-based cavity detection algorithm.

• CriticalFinder is the first surface-based cavity detection algorithm that produces a meaningful, coarse cavity segmentation.

• CriticalFinder sustains on the theory of critical points (i.e., Morse theory).

Abstract

Protein cavities are specific regions on the protein surface where ligands (small molecules) may bind. Such cavities are putative binding sites of proteins for ligands. Usually, cavities correspond to voids, pockets, and depressions of molecular surfaces. The location of such cavities is important to better understand protein functions, as needed in, for example, structure-based drug design. This article introduces a geometric method to detecting cavities on the molecular surface based on the theory of critical points. The method, called CriticalFinder, differs from other surface-based methods found in the literature because it directly uses the curvature of the scalar field (or function) that represents the molecular surface, instead of evaluating the curvature of the Connolly function over the molecular surface. To evaluate the accuracy of CriticalFinder, we compare it to other seven geometric methods (i.e., ${\mathrm{LIGSITE}}^{CS}$, GHECOM, ConCavity, POCASA, SURFNET, PASS, and Fpocket). The benchmark results show that CriticalFinder outperforms those methods in terms of accuracy. In addition, the performance analysis of the GPU implementation of CriticalFinder in terms of time consumption and memory space occupancy was carried out.

Introduction

Many biological processes in life sciences, in particular those involving drug interactions and protein docking, occur in water. The interaction between water and molecule can tell much information about the shape of a molecule, including the location of its binding sites. As Mezey noted in  [1], this is of great importance to research in chemistry, biophysics, medicine, and nano-technology. A better interpretation and identification of such regions on a molecular surface can greatly help in discovering new drugs. Hence, the identification of those binding sites is often the first step in the study of protein functions, as in the structure-based drug design.

However, many small molecules (i.e., ligands) can bind to a given protein, depending on the number of binding sites on its molecular surface. It happens that, as noted by Henrich et al. [2], checking whether a certain molecule can bind to a particular protein takes a lot of time in lab. While, in general, binding sites correspond to concave, cleft or tunnel-shaped regions on a protein surface (cf. Kawabata and Go  [3]), called pockets or cavities, not all cavities end up being binding sites for small ligands. Thus, detecting binding sites depends on efficient computational algorithms to locate all cavities on the molecular surface.

So, in this paper, we describe a method to identify the cavities on the protein surface as tentative binding sites for ligands. The novelty of the algorithm lies in directly evaluating the curvature of the scalar field (or function) that describes the molecular surface, instead of evaluating the curvature of the Connolly function  [4] or the Mitchell–Kerr–Eyck function  [5] over the molecular surface. This provides us with an advantage over state-of-the-art techniques. In fact, the technique is more robust in identifying candidate cavities because the curvature can be evaluated not only on the protein surface, but also at any point of the domain of the scalar field from eigenvalues of the Hessian matrix; hence, we are able to identify the critical points of the scalar field.

Indeed, CriticalFinder is the first surface-based method to succeed in finding a meaningful segmentation of a molecular surface into cavities and saliences. More specifically, our method relies on the theory of critical points (also called Morse theory) to identify cavities on the protein surface. While some research works have already tried to use curvature information (see, for example, Natarajan et al.  [6]), the resulting segmentations did not prove effective for cavity detection purposes, because their charts (or segments) do not necessarily match protein cavities as tentative binding sites. Furthermore, to the best of our knowledge, CriticalFinder is the first cavity detection algorithm to take advantage of a loosely-coupled GPU cluster of computers equipped with Nvidia Tesla K40 graphics cards, over a local area network (LAN), to identify cavities on protein surfaces.

The remainder of our paper is organized as follows. Section  2 briefly surveys the most closely related work published in the literature. Section  3 describes the fundamentals of scalar field theory and theory of critical points underlying our algorithm. Section  4 describes our algorithm in detail, as well as its implementation. Section  5 briefly describes our technique to triangulate and visualize protein surfaces. Section  6 discusses the theoretical complexity of the algorithm. Section  7 describes the methodology followed in the optimization of the CUDA code. Section  8 contains the most relevant results produced by our method, including a comparison to other well-known algorithms found in the literature. Section  9 discusses the main conclusions, while providing relevant hints for future work.