Three-dimensional reconstruction of helical polymers

Abstract

The field of three-dimensional electron microscopy began more than 45years ago with a reconstruction of a helical phage tail, and helical polymers continue to be important objects for three-dimensional reconstruction due to the centrality of helical protein and nucleoprotein polymers in all aspects of biology. We are now witnessing a fundamental revolution in this area, made possible by direct electron detectors, which has led to near-atomic resolution for a number of important helical structures. Most importantly, the possibility of achieving such resolution routinely for a vast number of helical samples is within our reach. One of the main problems in helical reconstruction, ambiguities in assigning the helical symmetry, is overcome when one reaches a resolution where secondary structure is clearly visible. However, obstacles still exist due to the intrinsic variability within many helical filaments.

Keywords: Direct electron detectors; Helical polymers; Variable twist.

Fig. 1

Averaged power spectrum showing that the distance of a peak from the meridian is not always simply related to the Bessel order n on any given layer line. For example, the first maxima on the layer line labeled n=-12 is at a larger distance R from the meridian than the peak on the layer line labeled n=-14. For a helical structure containing an array of atoms all at the same radius, the distance of these peaks from the meridian is a simple function of n, the Bessel order on that layer line. For a real structure, which extends over a range of radial values, this simple relationship breaks down.

Fig. 2

Power spectra from ASC PYD filaments (Lu et al., 2014a) recorded either on film using a Tecnai F20 microscope (A), or using a Falcon II direct electron detector on a Titan Krios (B). Both sets of images have been sorted based upon the pitch of the six-start helices (red arrows), with one twist state shown in (A), and two different twist states shown in (b). Although the twist is variable in the PYD filaments, the axial rise per subunit (which is actually three identical molecules, due to the C3 rotational symmetry in these filaments) is relatively fixed, and indicated by the blue arrow in (B) at ∼ 1/(14 Å). Surprisingly, this meridional layer line is not seen in (A) due to the much weaker modulation transfer function of the film on the F20 compared to the Falcon II on the Titan Krios. An atomic model can be built into the reconstruction (C), confirming that the correct symmetry has been used.

Fig. 3

A power spectrum from a thin helical nanotube formed by a 29-residue peptide (A), and the reconstruction of the nanotube with an atomic model (B) (Egelman et al., 2015). The layer line at 1/(9.0 Å) (A, arrows) is clearly visible when using a K2 direct electron detector on a Titan Krios, but absent when using either film on an F20 or a CCD camera on the Titan Krios. Most of the large side chains can be clearly seen in the density map (B).

Fig. 4

Map (mesh) and model (magenta) from the interior of the Type Six Secretion System sheath of Vibrio cholerae (Kudryashev et al., 2015). An α-helix is shown at the bottom, and two β-strands forming part of a β-sheet are seen at the top. The resolution of the map (∼ 3.2 Å in the most ordered parts) allowed for the ab initio tracing of > 600 residues in the two chains that form the heterodimer of the asymmetric unit.