Single-particle reconstruction from EM images of helical filaments

Abstract

Helical filaments were the first structures to be reconstructed in three dimensions from electron microscopic images, and continue to be extensively studied due to the large number of such helical polymers found in biology. In principle, a single image of a helical polymer provides all of the different projections needed to reconstruct the three-dimensional structure. Unfortunately, many helical filaments have been refractory to the application of traditional (Fourier-Bessel) methods due to variability, heterogeneity, and weak scattering. Over the past several years, many of these problems have been surmounted using single-particle type approaches that can do substantially better than Fourier-Bessel approaches. Applications of these new methods to viruses, actin filaments, pili and many other polymers show the great advantages of the new methods.

Figure 1

A schematic diagram showing the IHRSR algorithm. One cycle of IHRSR is depicted, with a reference volume at the top. This reference volume can start as a featureless solid cylinder, and has always been found to converge to the correct structure when the approximate helical symmetry can be initially determined. As one moves in a clockwise manner around the cycle: 1) projections of the reference volume are generated, which typically involve only azimuthal rotations about the filament axis (out-of-plane tilt can also be incorporated, but will be ignored here). These reference projections are used for multi-reference alignment against the images (one finds the single reference projection that gives the highest cross-correlation with an image, and this determines the azimuthal orientation of the segment being examined). The number of reference projections needed depends upon both the resolution and the diameter of the filament. 2) the multi-reference alignment determines the x-shift, y-shift and in-plane rotation needed to bring any image into register with a reference projection, and these parameters are applied to the images. 3) A back-projection is now generated using the aligned image segments. The resulting volume is clearly helical, but helical symmetry has not been imposed. A search is made within this volume for the screw operator (rotation and axial translation) that minimizes the deviation of density from points related by the screw symmetry. 4) The helical symmetry that was found for this cycle is now imposed, and the resulting helically symmetric volume (top) is used as the new reference for the next cycle. The entire procedure is run within the SPIDER software system [33], with calls to external programs that determine and impose the helical symmetry each cycle.

Figure 2

The application of IHRSR to a subset of F-actin segments that have been classified as having a common twist. A solid cylinder (left) is used as an initial reference volume for two different runs of the IHRSR procedure, starting with twist values of either -160.0° or -168.0°. Both starting values converge to a solution of ∼ -166°. The reconstructed volume on the right will be almost indistinguishable for a large range of different initial reference volumes and starting symmetries, which is why the algorithm is called “robust”.

Figure 3

A remarkably high resolution of 4-5 Å has been achieved using a single-particle approach to the helical reconstruction of Tobacco Mosaic Virus [23]. A portion of the density map is shown, along with an atomic model that has been built into it. Image courtesy of Niko Grigorieff.