Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials

Abstract

Electron and x-ray microscopes allow one to image the entire, unlabeled structure of hydrated materials at a resolution well beyond what visible light microscopes can achieve. However, both approaches involve ionizing radiation, so that radiation damage must be considered as one of the limits to imaging. Drawing upon earlier work, we describe here a unified approach to estimating the image contrast (and thus the required exposure and corresponding radiation dose) in both x-ray and electron microscopy. This approach accounts for factors such as plural and inelastic scattering, and (in electron microscopy) the use of energy filters to obtain so-called "zero loss" images. As expected, it shows that electron microscopy offers lower dose for specimens thinner than about 1 µm (such as for studies of macromolecules, viruses, bacteria and archaebacteria, and thin sectioned material), while x-ray microscopy offers superior characteristics for imaging thicker specimen such as whole eukaryotic cells, thick-sectioned tissues, and organs. The required radiation dose scales strongly as a function of the desired spatial resolution, allowing one to understand the limits of live and frozen hydrated specimen imaging. Finally, we consider the factors limiting x-ray microscopy of thicker materials, suggesting that specimens as thick as a whole mouse brain can be imaged with x-ray microscopes without significant image degradation should appropriate image reconstruction methods be identified.

Keywords: Electron; Radiation damage; Thick specimen; X-Ray.

Figure 1

Schematic diagram of the specimen model adopted for contrast parameter calculations. Features of material f are assumed to be cubes of dimension t_f on a side, embedded in an overall matrix thickness of t = t_b,o + t_f + t_b,u of background material b. For biological imaging, we will assume that the feature f is composed of protein, and the background material b is amorphous ice.

Figure 2

Normalized intensity fractions for x-rays in amorphous ice as a function of thickness at incident photon energies of (a) 5 keV, (b) 15 keV, and (c) 45 keV. Phase contrast imaging involves an interference between unscattered (I_noscat; Eq. 56) and single elastically scattered (I_1el; Eq. 58) photons, with other intensity fractions reprenting signal loss or background (these are described in Eqs. 58–62). The corresponding intensity fractions for the embedding medium EPON are shown in Fig. 3.

Figure 3

Normalized intensity fractions for x-ray in EPON as a function of thickness at incident photon energies of (a) 5 keV, (b) 15 keV, and (c) 45 keV. The corresponding intensity fractions for amorphous ice (such as for frozen hydrated specimes viewed under cryogenic conditions) are shown in Fig. 2.

Figure 4

The approximation of structure being continuous at length scales finer than the spatial resolution t_f begins to break down when molecular scattering exceeds the corresponding numerical aperture. Shown here as a series of thin lines are the small angle scattering patterns I(s) from 80 different macromolecules in small angle scattering patterns in SASBDB, the Small Angle Scattering Biological Data Bank [65]. To obtain a single parameterized representation of these patterns versus momentum transfer s, a sixth-order polynomial fit of log₁₀[I(s)] was obtained, leading to the expression of Eq. 64. This parameterized fit is shown as the thick red line.

Figure 5

Contrast parameter Θ for soft x-ray (0.5 keV) imaging of t_f = 20 nm protein features as a function of amorphous ice thicknesses t_b. At left is shown the case for Zernike phase contrast using the pure-phase thin sample approximation of Eq. 36, the conventional model of Eq. 35, and the complete model of Eq. 88 with phase contrast (ϕ = π/2). The discrepancy between the pure-phase thin sample approximation and the conventional model is due to the fact that there is significant absorption at the soft x-ray energy of 0.5 keV, even though this is within the “water window” spectral region between the carbon (0.290 keV) and oxygen (0.540 keV) x-ray absorption edges.

Figure 6

Contrast parameter Θ for Zernike phase contrast imaging with hard x-rays (15 keV) as a function of overall amorphous ice thickness. The case for a small protein feature (t_f = 20 nm) is shown at left, while the case for a larger protein feature (t_f = 1000 nm) is shown at right. The conventional Zernike phase contrast model of Eq. 35 works well for describing fine features in ice layers up to tens of micrometers thick, but the more complete model of Eq. 88 with phase contrast (ϕ = π/2) becomes necessary with thicker features and ice layers. Absorption contrast is not shown because it is quite weak for hard x-ray imaging of organic materials in ice.

Figure 7

Contrast parameter Θ for Zernike phase contrast imaging with hard x-rays (15 keV) as a function of feature thickness t_f for protein in amorphous ice. In this case no overlying or underlying thickness was assumed (that is, t_b,o = t_b,u = 0 in Fig. 1), so this is just for a protein feature of the indicated thickness in an equal thickness slab of ice. As can be seen, the pure-phase thin sample expression of Eq. 36 gives inaccurate predictions for ice thicknesses of even a few tens of micrometers; the conventional model of Eq. 35 works well for thicknesses up to several hundreds of micrometers at which point the more complete expression of Eq. 88 with ϕ = π/2 gives correct results.

Figure 8

Electron Energy Loss Spectroscopy (EELS) of amorphous ice and of the plastic embedding medium EPON. The EPON EELS spectrum shows a increase at the carbon K edge at 290 eV, while the ice EELS spectrum shows an increase at the oxygen K edge at 540 eV. For amorphous ice, the as-recorded spectrum is shown along with the single-inelastic-scatter spectrum obtained by Fourier-log deconvolution; for EPON, only the single-inelastic-scatter spectrum is shown with arbitrary absolute scaling. Also shown are the locations of the plasmon mode peaks of the inelastic spectra, and the values of the mean energy loss 〈ΔE〉 as calculated using Eq. 103. Amorophous ice spectra courtesy Richard Leapman, National Institutes for Health. The EPON spectra are from a sample prepared by Qiaoling Jin, with assistance on EELS spectrum recording provided by Kai He, both of Northwestern University.

Figure 9

Normalized intensity profiles for phase contrast electron imaging in amorphous ice as a function of thickness at incident electron energies of (a) 100 and (b) 300 keV. The structural information in the image is contributed through the interference between unscattered electrons (I_noscat, Eq. 108) and single elastic scattered electrons (I_1el, Eq. 109). The intensities for EPON are shown in Fig. 10.

Figure 10

Normalized intensity profiles for phase contrast electron imaging in EPON as a function of thickness at incident electron energies of (a) 100 and (b) 300 keV. The intensities for amorphous ice are shown in Fig. 9.

Figure 11

Estimated radiation dose associated with 10 nm resolution imaging of protein features in amorphous ice. This shows the case for soft x-ray microscopy at 0.5 keV and hard x-ray microscopy at 10 keV, both for absorption and Zernike phase contrast. In the case of electron microscopy, acclerating voltages of 100 and 300 kV are shown for phase contrast imaging with and without the use of a zero-loss energy filter. In all cases, the imaging system is assumed to have 100% efficiency.

Figure 12

Combined contour and brightness map of the required x-ray radiation dose in Gray for imaging 10 nm features in amorphous ice as a function of both x-ray photon energy and overall ice thickness. This figure shows the lower of absorption or phase contrast imaging at each point; in nearly all cases phase contrast provides the lowest dose. The grayscale image shows log₁₀(Gray), with the overlaying contour line labeled 6 representing a dose of 10⁶ Gray and so on. The soft x-ray “water window” energy range [84] between the carbon K edge at 0.29 keV and the oxygen K edge at 0.54 eV provides minimum dose imaging for specimens in ice layers up to about 10–20 μm thick, while phase contrast requires a slightly higher dose at multi-keV energies while accommodating thicker specimens overall. Note that the presence of sulfur in our model protein leads to the contour feature at the S K edge at 2.47 keV.

Figure 13

Required radiation dose as a function of resolution. In this case of imaging protein in 10 μm of amorophous ice, the dose for SNR=5 imaging was calculated as t_F was varied, for both soft x-rays in the water window (0.5 keV) or for hard X rays (10 keV), for the better of absorption or Zernike phase contrast at each thickness. The trend of required dose increasing as the fourth power of improvements in spatial resolution (decreases in t_f) as expected from Eqs. 94 and 95 is clearly seen. Also shown are the radiation doses associated with various detrimental effects in biological specimens, as discussed in Sec. 7.3.

Figure 14

Combined contour and brightness map of the required x-ray radiation dose in Gray for imaging 100 nm features in amorphous ice as a function of both x-ray photon energy and overall ice thickness. This figure shows the lower of absorption or phase contrast imaging at each point; in nearly all cases phase contrast provides the lowest dose. The grayscale image shows log₁₀(Gray), with the overlaying contour line labeled 6 representing a dose of 10⁶ Gray and so on. Of course it would be very challenging to obtain amorphous ice over these organ-scale thicknesses, but on the other hand ice crystal artifacts that obscure features in few-nanometer-resolution cryo electron microscopy studies might be unnoticeable in 100 nm resolution imaging.