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

By D. Padhorny, Andrey M. Kazennov, B. Zerbe, Kathryn A. Porter, Bing Xia, Scott E. Mottarella, Y. Kholodov, D. Ritchie, Sandor Vajda, Dima Kozakov. 2016

56 citations recorded by the source corpus.

Significance Expressing the interaction energy as sum of correlation functions, fast Fourier transform (FFT) based methods speed the calculation, enabling the sampling of billions of putative protein–protein complex conformations. However, such acceleration is currently achieved only on a 3D subspace of the full 6D rotational/translational space, and the remaining dimensions must be sampled using conventional slow calculations. Here we present an algorithm that employs FFT-based sampling on the 5D rotational space, and only the 1D translations are sampled conventionally. The accuracy of the results is the same as those of earlier methods, but the calculation is an order of magnitude faster. Also, it is inexpensive computationally to add more correlation function terms to the scoring function compared with classical approaches. 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)∖S1), where SO(3) is the rotation group representing the space of the rotating ligand, and (SO(3)∖S1) 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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Molecular Biology

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Citations in the corpus

New additions to the ClusPro server motivated by CAPRI (2017, methodology): “…much poorer.13 However, in 2012 we have introduced a special DARS-type potential for this type of interactions, which provided some improvement.16 The last CAPRI evaluation meeting in April 2016 focused on the results of rounds 28–29 and 31–35 that included targets 59–67 and 95–105, respectively.”
Protein Docking Model Evaluation by Graph Neural Networks (2020, methodology): “These include docking conformational searches, such as fast Fourier transform (Katchalski-Katzir et al., 1992; Padhorny et al., 2016), geometric hashing (Fischer et al.”