Elsevier

Ultramicroscopy

Volume 85, Issue 4, December 2000, Pages 225-234
Ultramicroscopy

A robust algorithm for the reconstruction of helical filaments using single-particle methods

https://doi.org/10.1016/S0304-3991(00)00062-0Get rights and content

Abstract

Some of the earliest methods for three-dimensional reconstruction from electron microscopic images were developed for helical objects. Single-particle methods have been used with great success for the three-dimensional reconstruction of macromolecular assemblies that have no internal symmetry or closed point group symmetries. An approach is presented for the application of single-particle methods to helical filaments that surmounts many of the difficulties of helical image analysis, including indexing, unbending and the need to find long helically symmetric filament segments. It is shown using both human Rad51 and E. coli RecA nucleoprotein filaments that this approach converges without user intervention to a stable solution, and that it has the potential to overcome many of the problems associated with image analysis of disordered helical polymers. The method can be applied transparently to structures where Bessel overlap would greatly complicate helical analysis. In addition, the procedure allows for the ab initio determination of helical symmetry, when no prior knowledge exists.

Introduction

Many biological macromolecular assemblies exist as helical polymers. These include, among many other complexes: F-actin, microtubules, myosin thick filaments, phage tails, and bacterial pili and flagella. The bacterial RecA protein, which can be the most abundant protein in the cell after DNA damage, forms a helical nucleoprotein filament with DNA [1]. The eukaryotic Rad51 protein forms a very similar helical filament [2]. The centrality of helical polymers to biology makes methods for structural studies of such polymers important. It is thus not coincidental that the first application of electron microscopic three-dimensional reconstruction techniques was to a helical polymer [3]. In the years since, there have been many refinements and advances, and it has been possible to use such methods to image at high-resolution (better than 10 Å) specimens such as tobacco mosaic virus [4], the acetylcholine receptor [5], the sarcoplasmic reticulum calcium pump [6] and bacterial flagella [7].

However, the application of helical methods is not simple, particularly when the specimens are flexible and disordered. One initial approach to dealing with flexibility is to computationally straighten filaments [8], but this has the potential for introducing artifacts due to the assumptions that need to be made (e.g., that there is no coupling between bending and twisting, that the filament undergoes a purely elastic normal mode of bending, etc.). Another difficulty with helical analysis is that the indexing of a pattern can be ambiguous, and the wrong symmetry can be chosen [9]. Further complications exist when the filament does not have a precisely defined helical symmetry, such as F-actin that has a random, variable twist [10]. A real-space approach to dealing with the variable pitch of sickle-cell hemoglobin helical fibers has already been used [11], and other groups have also employed single-particle methods to reconstruct helical filaments [12], [13]. Real-space methods allow many advantages over helical approaches, particularly in surmounting the problem of disorder and flexibility. For highly ordered specimens, such as tobacco mosaic virus [4] or helical tubes of membrane proteins [5], [6], the advantages may be less obvious.

A method is presented here for iterative real-space reconstruction of helical filaments. The method has been successfully applied to a number of different specimens, but results are only shown here for one state each of the human Rad51 protein and the E. coli RecA protein.

Section snippets

Results

Fig. 1 shows an electron micrograph of human Rad51 (hRad51) protein bound to single-stranded DNA in the presence of ADP and aluminum fluoride, which together serve as a stable, non-hydrolyzable analog for ATP. The striations arising from the ∼98 Å pitch helix can be seen. Attempts to use conventional helical methods were limited by the paucity of long, suitably straight segments. The indexing of those segments that were found was complicated and ambiguous, as very few filament sections yielded

Conclusions

The iterative method of real-space reconstruction of helical filaments has been shown to converge to a stable solution that is different in both helical symmetry and structure from the starting model. Indeed, the method can be used to determine the helical symmetry of an unknown structure by imposing a limited averaging, assuming two subunits per turn. For the example shown, hRad51 filaments, the method actually converges to a final structure more rapidly when no assumptions are made about

Acknowledgments

I would like to thank Xiong Yu, Albina Orlova, Natalya Lukoyanova, Vitold Galkin, and Steve Jacobs, who have helped in the application of this method to Rad51, RecA and actin. I would like to thank Stephen West for generously supplying human Rad51 protein, Xiong Yu for specimen preparation and electron microscopy, and Pawel Penczek for helpful discussions. This work was supported by NIH GM35269 and AR42023.

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