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Spline-Based Approach to Orientation Assignment for Three-Dimensional Electron Microscopy

S. Jonić, C.Ó. Sánchez Sorzano, P. Thévenaz, M. Unser, N. Boisset

Actes du deuxième symposium sur l'imagerie pour les sciences du vivant et la médecine (IMVIE2'05), Strasbourg, French Republic, March 1-3, 2005, pp. 40-42.

In our previous work, we have developed a volume-to-image registration algorithm for a continuous a posteriori assignment of the parameters of orientation and position to Electron Cryo-Microscopy (cryo-EM) single particle images for a high-resolution Three-Dimensional (3D) particle reconstruction [1]. To determine these parameters, our algorithm employs a Levenberg-Marquardt gradient-based iterative minimization of a least-squares measure of dissimilarity between the two-dimensional Fourier Transform (FT) of the particle image and the extracted corresponding central slice of the 3D particle model FT relying on the central-slice theorem.

The algorithm that is the most similar to ours is FREALIGN [2] which also computes continuous parameters of the particle orientation. While FREALIGN minimizes the phase dissimilarity between the experimental image and its model weighted by the amplitude of the FT of the experimental image, our algorithm minimizes both the amplitude dissimilarity and the phase dissimilarity. Also, contrary to FREALIGN which uses nearest-neighbour interpolation, our algorithm uses cubic B-splines to interpolate the data accurately. Our optimization algorithm is faster than Powell's method of FREALIGN since we have access to the gradient of the cost function. To improve the robustness of the algorithm, we use a frequency-domain weighting of the cost function.

As all iterative algorithms, our method is sensitive to the choice of the initial parameters. To improve the robustness to the initial parameters, we have developed a strategy for the assignment based on the minimum final value of the dissimilarity measure for several different initializations. In this paper, we show the performance of our algorithm when using this strategy based on three starting points. A generalization to any number of points is straightforward.

We validate the algorithm in a fully controlled simulation environment where the ground-truth solution is known a priori. We assess the assignment accuracy in terms of the warping index that is commonly used in the area of image registration. We synthesize a set of images at known poses using a 3D model of a protein from the PDB (Protein Data Bank). We first show the performance of our algorithm when initialized using the assignment by only one of the three standard quantized-parameter methods [3, 4, 5]. Then, we present the result of their joint use for initialization. We show that the “mixed” strategy can be used to refine the assignment obtained by the standard algorithms. In these experiments, we achieved the assignment with the warping index smaller than 2 voxel. At the end, we present the performance of our approach in refining a 3D model of a GroEL chaperonin using real cryoEM data with no ground-truth solution. We observe that this method improves the consistency of the volumes from the previous iteration.

Our algorithm is available in the Xmipp package [6]. In the future work, we will apply the techniques described here on other cryo-EM particles and macromolecular assemblies.


  1. S. Jonić, "Spline Projection-Based Volume-to-Image Registration," Swiss Federal Institute of Technology Lausanne, EPFL Thesis no. 2901 (2003), 160 p., December 19, 2003.

  2. N. Grigorieff, "Three-Dimensional Structure of Bovine NADH:Ubiquinone Oxidoreductase (Complex I) at 22 Â in Ice," Journal of Molecular Biology, vol. 277, no. 5, pp. 1033-1046, April 1998.

  3. P.A. Penczek, R.A. Grassucci, J. Frank, "The Ribosome at Improved Resolution: New Techniques for Merging and Orientation Refinement in 3D Cryo-Electron Microscopy of Biological Particles," Ultramicroscopy, vol. 53, no. 3, pp. 251-270, March 1994.

  4. M. Radermacher, "Three-Dimensional Reconstruction from Random Projections: Orientational Alignment via Radon Transforms," Ultramicroscopy, vol. 53, no. 2, pp. 121-136, February 1994.

  5. C.Ó. Sánchez Sorzano, S. Jonić, C. El-Bez, J.M. Carazo, S. De Carlo, P. Thévenaz, M. Unser, "A Multiresolution Approach to Orientation Assignment in 3D Electron Microscopy of Single Particles," Journal of Structural Biology, vol. 146, no. 3, pp. 381-392, June 2004.

  6. R. Marabini, I. M.Masegosa, M.C. SanMartín, S. Marco, J.J. Fernández, L.G. de la Fraga, C. Vaquerizo, J.M. Carazo, "Xmipp: An Image Processing Package for Electron Microscopy," Journal of Structural Biology, vol. 116, no. 1, pp. 237-240, January 1996.

AUTHOR="Joni{\'{c}}, S. and S{\'{a}}nchez Sorzano, C.{\'{O}} and
        Th{\'{e}}venaz, P. and Unser, M. and Boisset, N.",
TITLE="Spline-Based Approach to Orientation Assignment for
        Three-Dimensional Electron Microscopy",
BOOKTITLE="Actes du deuxi{\`{e}}me symposium sur l'imagerie pour les
        sciences du vivant et la m{\'{e}}decine ({IMVIE$^{2}$'05})",
address="Strasbourg, French Republic",
month="March 1-3,",

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