Protein–protein docking by fast generalized Fourier transforms on 5D rotational manifolds

Abstract

Energy evaluation using fast Fourier transforms (FFTs) enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods, efficient acceleration is achieved only in either the translational or the rotational subspace. Developing an efficient and accurate docking method that expands FFT-based sampling to five rotational coordinates is an extensively studied but still unsolved problem. The algorithm presented here retains the accuracy of earlier methods but yields at least 10-fold speedup. The improvement is due to two innovations. First, the search space is treated as the product manifold SO(3) × (SO(3)∖S 1 ), where SO(3) is the rotation group representing the space of the rotating ligand, and (SO(3)∖S 1 ) is the space spanned by the two Euler angles that define the orientation of the vector from the center of the fixed receptor toward the center of the ligand. This representation enables the use of efficient FFT methods developed for SO(3). Second, we select the centers of highly populated clusters of docked structures, rather than the lowest energy conformations, as predictions of the complex, and hence there is no need for very high accuracy in energy evaluation. Therefore, it is sufficient to use a limited number of spherical basis functions in the Fourier space, which increases the efficiency of sampling while retaining the accuracy of docking results. A major advantage of the method is that, in contrast to classical approaches, increasing the number of correlation function terms is computationally inexpensive, which enables using complex energy functions for scoring.etermining putative protein-protein interactions using genome-wide proteomics studies is a major step toward elucidating the molecular basis of cellular functions. Understanding the atomic details of these interactions, however, requires further biochemical and structural information. Although the most complete structural characterization is provided by X-ray crystallography, solving the structures of protein-protein complexes is frequently very difficult. Thus, it is desirable to develop computational docking methods that, starting from the coordinates of two unbound component molecules defined as receptor and ligand, respectively, are capable of providing a model of acceptable accuracy for the bound receptor-ligand complex (1-4). In view of the large number of putative proteinprotein interactions, the computational efficiency of docking is also a concern.Most global docking methods start with rigid body search that assumes only moderate conformational change upon the association, accounted for by using a smooth scoring function that allows for some level of steric overlaps (3). Rigid docking was revolutionized by the fast Fourier transform (FFT) correlation approach, introduced in 1992 by Katchalski-Katzir et al. (5). The major requirement of the method is to express the interaction energy in each receptor-ligand orientation as a sum of P correlation functions, i.e., in...

New additions to the ClusPro server motivated by CAPRI

“…The fourth development, already published but not yet implemented in ClusPro, is a new algorithm and software to perform docking by employing fast generalized Fourier transforms on 5D rotational manifolds . While we started to work on such algorithms several years ago, the need for further speed‐up of the FFT‐based docking was emphasized in this round of CAPRI, since several targets, including T59, involved docking of ensembles of structures obtained by Nuclear Magnetic Resonance (NMR).…”

“…Dealing with such ensembles may require docking hundreds of multiple rigid body conformations, which significantly increases the computational costs of the docking, and would make server submissions within 48 h extremely difficult. The new algorithm, based on generalizing the FFT correlation approach to the rotational group, is an order of magnitude faster than the classical Cartesian FFT approach implemented in PIPER, while providing very similar accuracy . An additional and very significant advantage of the generalized FFT approach is that adding extra correlation function terms to the energy function leads only to very minor increases in the computational efforts required.…”

The ClusPro web server for protein–protein docking

“…According to Table 4, the relative performance of ClusPro has been improving over the years, and based on the 2016 results the server appears to be competitive with the best “human” predictor groups. We note that the PIPER scoring function has been recently used in an algorithm that expands FFT-based sampling to five rotational coordinates 81 . Working in a space with spherical coordinates defined as a manifold, the new 5D algorithm retains the accuracy of PIPER for globular proteins while providing at least 10-fold speedup.…”

“…However, moderate loss of accuracy may occur for proteins that are very elongated along some direction. An additional advantage of the method is that increasing the number of correlation function terms is computationally inexpensive, which enables using even more complex energy functions as well as accounting for any number of pairwise distance constraints 81 .…”

Monte Carlo replica-exchange based ensemble docking of protein conformations

“…The term ensemble docking typically refers to a one by one docking of each ensemble member for partner 1 to each ensemble member of partner 2 25–28 which results in a dramatic increase of the computing time with respect to the size of the conformational ensembles and becomes prohibitively expensive for large ensembles. Thus studies investigating the use of ensembles with cross docking of all ensemble members have only been performed on relatively small benchmarks or single cases, which have shown improvement over single conformation unbound docking in terms of the number of near native solutions . The representation of the receptor binding region by multiple conformations has been found beneficial for the docking success also in the area of docking of drug molecule candidates to protein binding sites .…”