David W. Ritchie

PROTEIN DOCKING USING SPHERICAL POLAR FOURIER CORRELATIONS

We present a new computational method of docking pairs of proteins by using spherical polar Fourier correlations to accelerate the search for candidate low‐energy conformations. Interaction energies are estimated using a hydrophobic excluded volume model derived from the notion of “overlapping surface skins,” augmented by a rigorous but “soft” model of electrostatic complementarity. This approach has several advantages over former three‐dimensional grid‐based fast Fourier transform (FFT) docking correlation methods even though there is no analogue to the FFT in a spherical polar representation. For example, a complete search over all six rigid‐body degrees of freedom can be performed by rotating and translating only the initial expansion coefficients, many infeasible orientations may be eliminated rapidly using only low‐resolution terms, and the correlations are easily localized around known binding epitopes when this knowledge is available. Typical execution times on a single processor workstation range from 2 hours for a global search (5 × 108 trial orientations) to a few minutes for a local search (over 6 × 107 orientations). The method is illustrated with several domain dimer and enzyme–inhibitor complexes and 20 large antibody–antigen complexes, using both the bound and (when available) unbound subunits. The correct conformation of the complex is frequently identified when docking bound subunits, and a good docking orientation is ranked within the top 20 in 11 out of 18 cases when starting from unbound subunits. Proteins 2000;39:178–194.

Recent Progress and Future Directions in Protein-Protein Docking

This article gives an overview of recent progress in protein-protein docking and it identifies several directions for future research. Recent results from the CAPRI blind docking experiments show that docking algorithms are steadily improving in both reliability and accuracy. Current docking algorithms employ a range of efficient search and scoring strategies, including e.g. fast Fourier transform correlations, geometric hashing, and Monte Carlo techniques. These approaches can often produce a relatively small list of up to a few thousand orientations, amongst which a near-native binding mode is often observed. However, despite the use of improved scoring functions which typically include models of desolvation, hydrophobicity, and electrostatics, current algorithms still have difficulty in identifying the correct solution from the list of false positives, or decoys. Nonetheless, significant progress is being made through better use of bioinformatics, biochemical, and biophysical information such as e.g. sequence conservation analysis, protein interaction databases, alanine scanning, and NMR residual dipolar coupling restraints to help identify key binding residues. Promising new approaches to incorporate models of protein flexibility during docking are being developed, including the use of molecular dynamics snapshots, rotameric and off-rotamer searches, internal coordinate mechanics, and principal component analysis based techniques. Some investigators now use explicit solvent models in their docking protocols. Many of these approaches can be computationally intensive, although new silicon chip technologies such as programmable graphics processor units are beginning to offer competitive alternatives to conventional high performance computer systems. As cryo-EM techniques improve apace, docking NMR and X-ray protein structures into low resolution EM density maps is helping to bridge the resolution gap between these complementary techniques. The use of symmetry and fragment assembly constraints are also helping to make possible docking-based predictions of large multimeric protein complexes. In the near future, the closer integration of docking algorithms with protein interface prediction software, structural databases, and sequence analysis techniques should help produce better predictions of protein interaction networks and more accurate structural models of the fundamental molecular interactions within the cell.

Ultra-fast FFT protein docking on graphics processors

MOTIVATION Modelling protein-protein interactions (PPIs) is an increasingly important aspect of structural bioinformatics. However, predicting PPIs using in silico docking techniques is computationally very expensive. Developing very fast protein docking tools will be useful for studying large-scale PPI networks, and could contribute to the rational design of new drugs. RESULTS The Hex spherical polar Fourier protein docking algorithm has been implemented on Nvidia graphics processor units (GPUs). On a GTX 285 GPU, an exhaustive and densely sampled 6D docking search can be calculated in just 15 s using multiple 1D fast Fourier transforms (FFTs). This represents a 45-fold speed-up over the corresponding calculation on a single CPU, being at least two orders of magnitude times faster than a similar CPU calculation using ZDOCK 3.0.1, and estimated to be at least three orders of magnitude faster than the GPU-accelerated version of PIPER on comparable hardware. Hence, for the first time, exhaustive FFT-based protein docking calculations may now be performed in a matter of seconds on a contemporary GPU. Three-dimensional Hex FFT correlations are also accelerated by the GPU, but the speed-up factor of only 2.5 is much less than that obtained with 1D FFTs. Thus, the Hex algorithm appears to be especially well suited to exploit GPUs compared to conventional 3D FFT docking approaches. AVAILABILITY http://hex.loria.fr/ and http://hexserver.loria.fr/.

Docking essential dynamics eigenstructures

This article describes our attempts to dock the targets in CAPRI Rounds 3–5 using Hex 4.2, and it introduces a novel essential dynamics approach to generate multiple feasible conformations for docking. In the blind trial, the basic Hex algorithm found 1 high‐accuracy solution for CAPRI Target 12, and several further medium‐ and low‐accuracy solutions for Targets 11, 12, 13, and 14. Subsequent a posteriori docking of the targets using essential dynamics “eigenstructures” was found to give consistently better predictions than rigidly docking only the unbound or model‐built starting structures. Some suggestions to improve this promising new approach are presented. Proteins 2005;60:269–274.

FAST COMPUTATION, ROTATION, AND COMPARISON OF LOW RESOLUTION SPHERICAL HARMONIC MOLECULAR SURFACES

A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi‐Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3‐dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999

Accelerating and focusing protein–protein docking correlations using multi-dimensional rotational FFT generating functions

MOTIVATION Predicting how proteins interact at the molecular level is a computationally intensive task. Many protein docking algorithms begin by using fast Fourier transform (FFT) correlation techniques to find putative rigid body docking orientations. Most such approaches use 3D Cartesian grids and are therefore limited to computing three dimensional (3D) translational correlations. However, translational FFTs can speed up the calculation in only three of the six rigid body degrees of freedom, and they cannot easily incorporate prior knowledge about a complex to focus and hence further accelerate the calculation. Furthemore, several groups have developed multi-term interaction potentials and others use multi-copy approaches to simulate protein flexibility, which both add to the computational cost of FFT-based docking algorithms. Hence there is a need to develop more powerful and more versatile FFT docking techniques. RESULTS This article presents a closed-form 6D spherical polar Fourier correlation expression from which arbitrary multi-dimensional multi-property multi-resolution FFT correlations may be generated. The approach is demonstrated by calculating 1D, 3D and 5D rotational correlations of 3D shape and electrostatic expansions up to polynomial order L=30 on a 2 GB personal computer. As expected, 3D correlations are found to be considerably faster than 1D correlations but, surprisingly, 5D correlations are often slower than 3D correlations. Nonetheless, we show that 5D correlations will be advantageous when calculating multi-term knowledge-based interaction potentials. When docking the 84 complexes of the Protein Docking Benchmark, blind 3D shape plus electrostatic correlations take around 30 minutes on a contemporary personal computer and find acceptable solutions within the top 20 in 16 cases. Applying a simple angular constraint to focus the calculation around the receptor binding site produces acceptable solutions within the top 20 in 28 cases. Further constraining the search to the ligand binding site gives up to 48 solutions within the top 20, with calculation times of just a few minutes per complex. Hence the approach described provides a practical and fast tool for rigid body protein-protein docking, especially when prior knowledge about one or both binding sites is available.

Evaluation of protein docking predictions using Hex 3.1 in CAPRI rounds 1 and 2

This article describes and reviews our efforts using Hex 3.1 to predict the docking modes of the seven target protein–protein complexes presented in the CAPRI (Critical Assessment of Predicted Interactions) blind docking trial. For each target, the structure of at least one of the docking partners was given in its unbound form, and several of the targets involved large multimeric structures (e.g., Lactobacillus HPr kinase, hemagglutinin, bovine rotavirus VP6). Here we describe several enhancements to our original spherical polar Fourier docking correlation algorithm. For example, a novel surface sphere smothering algorithm is introduced to generate multiple local coordinate systems around the surface of a large receptor molecule, which may be used to define a small number of initial ligand‐docking orientations distributed over the receptor surface. High‐resolution spherical polar docking correlations are performed over the resulting receptor surface patches, and candidate docking solutions are refined by using a novel soft molecular mechanics energy minimization procedure. Overall, this approach identified two good solutions at rank 5 or less for two of the seven CAPRI complexes. Subsequent analysis of our results shows that Hex 3.1 is able to place good solutions within a list of ≤20 for four of the seven targets. This finding shows that useful in silico protein–protein docking predictions can now be made with increasing confidence, even for very large macromolecular complexes. Proteins 2003;52:98–106.

Comprehensive Comparison of Ligand-Based Virtual Screening Tools Against the DUD Data set Reveals Limitations of Current 3D Methods

In recent years, many virtual screening (VS) tools have been developed that employ different molecular representations and have different speed and accuracy characteristics. In this paper, we compare ten popular ligand-based VS tools using the publicly available Directory of Useful Decoys (DUD) data set comprising over 100 000 compounds distributed across 40 protein targets. The DUD was developed initially to evaluate docking algorithms, but our results from an operational correlation analysis show that it is also well suited for comparing ligand-based VS tools. Although it is conventional wisdom that 3D molecular shape is an important determinant of biological activity, our results based on permutational significance tests of several commonly used VS metrics show that the 2D fingerprint-based methods generally give better VS performance than the 3D shape-based approaches for surprisingly many of the DUD targets. To help understand this finding, we have analyzed the nature of the scoring functions used and the composition of the DUD data set itself. We propose that to improve the VS performance of current 3D methods, it will be necessary to devise screening queries that can represent multiple possible conformations and which can exploit knowledge of known actives that span multiple scaffold families.

Comparison of Ligand-Based and Receptor-Based Virtual Screening of HIV Entry Inhibitors for the CXCR4 and CCR5 Receptors Using 3D Ligand Shape Matching and Ligand−Receptor Docking

HIV infection is initiated by fusion of the virus with the target cell through binding of the viral gp120 protein with the CD4 cell surface receptor protein and the CXCR4 or CCR5 co-receptors. There is currently considerable interest in developing novel ligands that can modulate the conformations of these co-receptors and, hence, ultimately block virus-cell fusion. This article describes a detailed comparison of the performance of receptor-based and ligand-based virtual screening approaches to find CXCR4 and CCR5 antagonists that could potentially serve as HIV entry inhibitors. Because no crystal structures for these proteins are available, homology models of CXCR4 and CCR5 have been built, using bovine rhodopsin as the template. For ligand-based virtual screening, several shape-based and property-based molecular comparison approaches have been compared, using high-affinity ligands as query molecules. These methods were compared by virtually screening a library assembled by us, consisting of 602 known CXCR4 and CCR5 inhibitors and some 4700 similar presumed inactive molecules. For each receptor, the library was queried using known binders, and the enrichment factors and diversity of the resulting virtual hit lists were analyzed. Overall, ligand-based shape-matching searches yielded higher enrichments than receptor-based docking, especially for CXCR4. The results obtained for CCR5 suggest the possibility that different active scaffolds bind in different ways within the CCR5 pocket.

Protein Docking Using Case-Based Reasoning

Protein docking algorithms aim to calculate the three‐dimensional (3D) structure of a protein complex starting from its unbound components. Although ab initio docking algorithms are improving, there is a growing need to use homology modeling techniques to exploit the rapidly increasing volumes of structural information that now exist. However, most current homology modeling approaches involve finding a pair of complete single‐chain structures in a homologous protein complex to use as a 3D template, despite the fact that protein complexes are often formed from one or more domain–domain interactions (DDIs). To model 3D protein complexes by domain–domain homology, we have developed a case‐based reasoning approach called KBDOCK which systematically identifies and reuses domain family binding sites from our database of nonredundant DDIs. When tested on 54 protein complexes from the Protein Docking Benchmark, our approach provides a near‐perfect way to model single‐domain protein complexes when full‐homology templates are available, and it extends our ability to model more difficult cases when only partial or incomplete templates exist. These promising early results highlight the need for a new and diverse docking benchmark set, specifically designed to assess homology docking approaches. Proteins 2013; 81:2150–2158.