Fast rotational matching of rigid bodies by fast Fourier transform acceleration of five degrees of freedom

Kovacs, Julio A.; Chacón, Pablo; Yao, Cong; Metwally, Essam; Wriggers, Willy

doi:10.1107/s0907444903011247

Cited by 58 publications

(50 citation statements)

References 10 publications

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“…When the center of rotation of each volume is known, the threedimensional orientation search can be further accelerated using Spherical Harmonics, which allows efficient computation of the Fourier Transform of the rotational correlation function bypassing completely the need for exhaustive search. This technique has not been used in tomography, but is well established in other applications like docking of atomic structures into electron density maps and molecular-replacement in X-ray crystallography (Crowther, 1972;Kovacs and Wriggers, 2002;Kovacs et al, 2003), and more recently applied to registration problems in computer graphics (Makadia and Daniilidis, 2006). This is a very attractive technique from the computational point of view, but in the absence of explicitly accounting for the missing wedge, it is not directly applicable to the problem of volume alignment in tomography.…”

Section: Sub-volume Alignment In Tomographymentioning

confidence: 99%

Classification and 3D averaging with missing wedge correction in biological electron tomography

Bartesaghi

Sprechmann

Liu

et al. 2008

Journal of Structural Biology

169

209

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Strategies for the determination of 3D structures of biological macromolecules using electron crystallography and single-particle electron microscopy utilize powerful tools for the averaging of information obtained from 2D projection images of structurally homogeneous specimens. In contrast, electron tomographic approaches have often been used to study the 3D structures of heterogeneous, one-of-a-kind objects such as whole cells where image-averaging strategies are not applicable. Complex entities such as cells and viruses, nevertheless, contain multiple copies of numerous macromolecules that can individually be subjected to 3D averaging. Here we present a complete framework for alignment, classification, and averaging of volumes derived by electron tomography that is computationally efficient and effectively accounts for the missing wedge that is inherent to limited-angle electron tomography. Modeling the missing data as a multiplying mask in reciprocal space we show that the effect of the missing wedge can be accounted for seamlessly in all alignment and classification operations. We solve the alignment problem using the convolution theorem in harmonic analysis, thus eliminating the need for approaches that require exhaustive angular search, and adopt an iterative approach to alignment and classification that does not require the use of external references. We demonstrate that our method can be successfully applied for 3D classification and averaging of phantom volumes as well as experimentally obtained tomograms of GroEL where the outcomes of the analysis can be quantitatively compared against the expected results.

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Section: Sub-volume Alignment In Tomographymentioning

confidence: 99%

Classification and 3D averaging with missing wedge correction in biological electron tomography

Bartesaghi

Sprechmann

Liu

et al. 2008

Journal of Structural Biology

169

209

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“…Situs is also capable of flexible docking (Rusu et al, 2008). FRM (Kovacs et al, 2003) and gEMfitter (Hoang et al, 2013) use a fast Fourier transform to fit structures into the density maps, Gorgon (Baker et al, 2011) considers secondary-structure matching, and 3SOM (Ceulemans & Russell, 2004) is based on surface-overlap maximization. Some other methods carry out segmentation of 3DEM density maps using different approaches, such as level sets (VolRover; Baker et al, 2006), elastic networks (hENM; Burger et al, 2011), watershed (Volkmann, 2002) and watershed/scale-space filtering (Segger; Pintilie et al, 2010;Pintilie & Chiu, 2012).…”

Section: Introductionmentioning

confidence: 99%

PRISM-EM: template interface-based modelling of multi-protein complexes guided by cryo-electron microscopy density maps

Kuzu

Keskin

Nussinov

et al. 2016

Acta Crystallogr D Struct Biol

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The structures of protein assemblies are important for elucidating cellular processes at the molecular level. Three-dimensional electron microscopy (3DEM) is a powerful method to identify the structures of assemblies, especially those that are challenging to study by crystallography. Here, a new approach, PRISM-EM, is reported to computationally generate plausible structural models using a procedure that combines crystallographic structures and density maps obtained from 3DEM. The predictions are validated against seven available structurally different crystallographic complexes. The models display mean deviations in the backbone of <5 Å . PRISM-EM was further tested on different benchmark sets; the accuracy was evaluated with respect to the structure of the complex, and the correlation with EM density maps and interface predictions were evaluated and compared with those obtained using other methods. PRISM-EM was then used to predict the structure of the ternary complex of the HIV-1 envelope glycoprotein trimer, the ligand CD4 and the neutralizing protein m36.

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“…This representation allows rotational searches to be accelerated by angular FFTs, and it enables translations to be calculated analytically in the Fourier basis (15). A similar approach has been developed by Chacon's group (16,17), in which translations are calculated numerically. However, both approaches were found to have lower accuracy than traditional Cartesian FFT sampling (15).…”

Section: Significancementioning

confidence: 99%

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

Padhorny

Kazennov

Zerbe

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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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...

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Fast rotational matching of rigid bodies by fast Fourier transform acceleration of five degrees of freedom

Cited by 58 publications

References 10 publications

Classification and 3D averaging with missing wedge correction in biological electron tomography

Classification and 3D averaging with missing wedge correction in biological electron tomography

PRISM-EM: template interface-based modelling of multi-protein complexes guided by cryo-electron microscopy density maps

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

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