Modern X-ray maging techniques and their use in biology

Radomír Kužel

Faculty of Mathematics and Physics, Charles University, 121 16 Praha 2, Ke Karlovu 5

In the last year contribution for the Meeting of Structural Biologists, recent non-traditional applications of some X-ray techniques - powder diffraction, X-ray reflectivity, grazing incidence, standing waves method in biology were shown [1]. Here the principles of modern X-ray imaging techniques - X-ray microscopy, tomography and single-particle X-ray diffraction are explained and examples are shown.

X-ray imaging

An excellent review of the use of hard X-rays for imaging was given by J. Härtwig [2] at last year X-top conference in Pruhonice near Prague.

Imaging means revealing of inhomogeneities and singularities in the sample and recording them as a 2-D information through variations in physical effects used for probing like reflection, transmission, absorption.

There are several possibilities of imaging: Imaging with a parallel and extended beam (the spatial resolution is mainly a function of the detector), imaging by using optical elements like lenses (the spatial resolution is mainly a function of the optical element), imaging with a micro beam - scanning (the spatial resolution is mainly a function of the spot size), Bragg-diffraction-imaging (more complex dependence of the spatial resolution).

The simplest techique is the imaging based on the absorption effect. The images can be detected by high-resolution films or CCD cameras and scintillators. An interesting application is usage of absorption edge of selected elements. The image is taken at two wavelengths - below and above the absorption edge and then the images are subtracted. In that way, specific contrast can be obtained. It has been used in angiography. However, the main stream seems to be micro-tomography, a quantitative description of a slice of matter within a bulky object, based on several radiographs collected at various angles. Images are reconstructed from many projections. Important features of SR are used - high spatial and time resolution and high flux.

When a coherent wavefield propagates through an object, phase differences arise between different parts of the wavefront. These are due to spatial variations in the refractive index of the object, which for x-ray wavelengths is given by

n = 1 - d + ib

The first term (d) determines the phase of the waves and causes their refraction. The second term - absorption (b) affects the amplitude of the waves. For small wavelengths (<0.1 nm) the phase contrast dominates absorption contrast in the x-ray regime. An advantage of phase contrast is that even small spatial variations in the refractive indexcan be detected. Phase contrast x-ray imaging therefore has great potential for application in medicine and in biology, enabling one to differentiate between different kinds of soft tissue. However, for phase contrast, coherent radiation is necessary. A nice review of the coherent scattering and it use has recently been published in [3].

The structural detail in a phase contrast image depends on the distance between the object and the detector. Three regimes for imaging can be distinguished. In the contact or near-contact regime, the detector is placed directly behind the object. In this case only the absorption contrast can be seen. As one moves further away from the object, interferences build up, and one enters first the Fresnel diffraction regime, then the Fraunhofer regime. In the Fresnel diffraction regime, phase contrast can be exploited to greatest advantage.

Three-dimensional objects can be reconstructed by repeating the above imaging method for different orientations of the sample. The tomography in phase sensitive mode is called holotomography. The phases are retrieved from the images obtained at different distances in addition to different orientation.

Micro-focussing X-ray beams are obtained by means of different optical elements - capillaries, Fresnel lens, bent mirrors, refractive lens, waveguides. They can be used not only for pure imaging but also for chemical mapping of the objects in 3D (fluotomography). The techniques are based on the detection of photons coming from fluorescent emission, Compton and Rayleigh scattering [e.g. 4].

X-ray microscopy, X-ray tomography and their applications in biology

The technology of X-ray microscopes has improved considerably, in recent years [e. g. 5 - 8].

Although there are currently many powerful techniques for imaging biological cells, each with its own unique strengths and limitations, there remains a gap between the information that can be obtained with light microscopy and electron microscopy.

Soft X-ray microscopy combines features associated with both light and electron microscopy. It is fast and relatively easy to accomplish (like light microscopy), and it produces high-resolution, absorption-based images (like electron microscopy). As with light microscopy, one can examine whole, hydrated cells. In the energy range of the photons used (between the K shell absorption edges of carbon [284 eV, 4.4 nm] and oxygen [543 eV, 2.3 nm]), organic material absorbs approximately an order of magnitude more strongly than water, producing a quantifiable natural contrast and eliminating the need for contrast enhancement procedures to visualize cellular structures.

Using this approach, superb structural information can be obtained from whole, hydrated cells at better than 35-nm resolution. In addition, molecules can be localized using protocols that combine the ease of immunfluorescence labeling with the higher-resolution capabilities of X-ray imaging.

It has been shown that the biological specimens do not suffer mass loss or morphologicla changes at radiation doses up to about 10¹⁰ Gray [6]. This makes possible studies where multiple images of the same specimen are are needed. X-ray tomography is quite straightforward and rapidly generates 3-D, quantifiable information from whole cells. Because of their low numerical aperture optics, X-ray microscopes allow one to treat high resolution images as simple projections through a specimen.

The main advantage of X-ray microscopy is its ability to study single cells in their entirety, rather than be limited to thickness of 400 nm, as in the case of electron tomography. X-ray microscopes add a unique set of capabilities to biological research. They can be used for three-dimensional imaging of intact cells, and to obtain information on the chemical and trace element markup of unlabeled cells, which cannot be done using other methods.

In [9], the yeast, Saccharomyces cerevisiae, was examined using X-ray tomography and unique views of the internal structural organization of these cells at 60-nm resolution was demonstrated. Because proteins can be localized in the X-ray microscope using immunogold labeling protocols, tomography enables 3-D molecular localization. The time required to collect the data for each cell was 3 min, making it possible to examine numerous yeast and to collect statistically significant high-resolution data.

Phase tomography by using of X-ray interferometers has been suggested recently [10]. The image of the tissue of a rat kidney was obtained with 0.1 nm X-rays and X-ray interferometer with a 40 mm analyzer.

Oversampling and single-particle diffraction

Protein crystallography using storage ring synchrotron light sources has made it possible to determine the structures of many proteins. However even the brightest storage ring x-ray sources require that the protein be prepared as a crystal – an orderly array of protein molecules, spaced and oriented identically. The millions of molecules in the crystal scatter x-rays in a distinctive pattern that can be used to determine the structure of the protein molecule. The necessary scattering data can be collected in only a few hours at a synchrotron. The difficult part of protein crystallography is producing a usable crystal – this takes 99% of the time and effort. Some of the proteins most important to life processes are difficult or impossible to crystallize. If it were possible to determine the structure of a protein without the need to form a crystal, progress in understanding proteins could be accelerated significantly.

Overcoming the crystallization difficulty requires the development of the new methodologies. One approach is to use NMR to image protein molecules in solvent. However, it is only applicable primarily to macromolecules in the lower molecular weight range. Another approach under rapid development is single molecule imaging using cryo electron microscopy (cryo-EM). The highest resolution currently achievable by this technique is ~7 C for highly symmetrical viruses. The main limitations to achieving better resolution by cryo-EM are radiation damage, specimen movement and low contrast. Due to the much weaker interaction between matter with X-rays than with electrons, the X-ray methods require much higher radiation dose to achieve the same resolution by X-rays than by electrons. Another is the difficulty of focussing X-rays. By using zone plates, the best focus currently achievable is ~30 nm for soft X-rays and ~100 nm for hard X-rays [11]. No techniques at present can provide three-dimensional imaging at nanometer resolution of the interior of particles in the micron size range.

An x-ray diffraction intensity is proportional to the square amplitude of the Fourier transform of an object image (an electron number density) in the kinematical theory. If the phase of the Fourier transform is also measured, the object image can be reconstructed by back Fourier transformation. However the phase is not directly obtained in x-ray diffraction measurement. Therefore the half of necessary information for image reconstruction is missing. The problem is known as the phase problem.
Single-particle diffraction is a methodology of extending crystallography to determine the 2D and 3D structures of nano crystals and noncrystalline samples by using coherent x-rays and electrons. In this approach, coherent diffraction patterns are recorded and then converted directly to high resolution images by using the oversampling phasing method.

The oversampling method is a solution to the phase problem [6, 12-20]. In the method a zero density region around the sample object is assumed. If the zero density region is larger than the sample region, more than half of total information is known in real space. Therefore it is in principle possible to use the zero density information to make up for the missing phase information. Thus, the method is based on the measurement of the diffraction intensity in between the Bragg peaks of a traditional crystal. Intensities must be measured at finer-than-Nyquist intervals in diffraction space. The Nyquist sampling interval (inversely related to specimen size) is as fine or finer than the Bragg interval (inversely related to the unit cell size).

The quality of image reconstruction of experimental diffraction patterns is a function of the oversampling ratio a parameter to characterize the oversampling degree. It was observed that the quality of reconstruction is strongly correlated with the oversampling ratio. When the oversampling ratio is around 5 or larger, the reconstructed images with high quality were obtained. When the oversampling ratio is less than 5, the images became noisy. When the oversampling ratio is very close to or less than 2, the images were extremely noisy and barely recognizable [22].

In the oversampling method the following iterative procedure is taken:

1. The magnitude of Fourier transform (i.e., square root of the measured diffraction intensities) is combined with the current best phase set. A random phaseset is used for the first iteration.

2. Applying the inverse fast Fourier transform, a new electron density function is obtained.

3. Constraints are enforced on the electron density function. By pushing the electron density outside the support and the negative electron density inside the support close to zero, and retaining the positive electron density inside the support, a new electron density is defined.

4. Applying the fast Fourier transform to the new electron density, a new set of phases is calculated. After setting the phase of central pixel to zero, this new phase set is used for the next iteration.

This can also be expressed as follows:

..... ® Image of n-th iteration ® Fourier transformation ® Set Fourier amplitudes to known (measured) values ® Back Fourier transformation ® Set the density in the zero density region and at negative density pixels gradually to zero ® Image of (n+1)-th iteration ® ..

By employment of an iterative algorithm, the phase information could be recovered from computer-generated oversampled diffraction patterns of small specimens that are perfect or imperfect crystals, or have a repeated motif without orientational regularity, or are an unrepeated motif, such as an amorphous glass, a single molecule or a single biological cell [15].

It is expected that extention of the current crystallographic methodology to crystals as small as a single unit cell will be possible, i.e. to non-crystals and individual biomolecules could be studied by using the beam of a free-electron-laser source of X-rays [23]. The resulting continuous diffraction patterns would be invertible into atomic-resolution images of the molecule. The method does not require any structural knowledge concerning the specimen and does not require data to atomic resolution (although it can use such data if present). After a few hundred to a few thousand iterations, the correct phase set and image are recovered.

However, the oversampling technique imposes a high radiation dose on the specimens compared with the situation in crystallography, in which it is usual for the pattern to be sampled at the (much less fine) Bragg spacing (the inverse of the size of the unit cell). An approach to overcoming the degrading effects of radiation damage is to record the diffraction pattern in a time shorter than the time of the damage process itself.

Theoretical simulations by Hajdu and collaborators [24] show that, within about 10 femtoseconds, biomolecules can withstand an X-ray intensity of ~3.8 x 10^{6 photons/C2} with minimal structural changes. A 2D diffraction pattern can hence be obtained from a single exposure of a biomolecule before the radiation manifests itself.

To get 3D images, it is necessary to record a series of diffraction patterns by rotating the specimen perpendicular to the beam. Unfortunately, any biological sample is destroyed in a single shot. However, if the sample is reproducible, and that single-shot diffraction images can be collected from individual sample particles exposed to the beam one-by-one in unknown orientations. The images can be sorted into classes that correspond to a distinct view (orientation) of the sample [25]. Images within each class are then averaged; if the classification is correct, the signal adds constructively but the noise does not. It was shown that less then one photon per independent pixel can be enough for classification, even in the presence of a Poisson-type photon noise [25].

The method of single-particle diffraction is especially useful in two fields - structural study of nanoparticles and study of macromolecules. In the former field, several successfull experiments have been performed [26, 27] for example on gold nanoparticles. The method has been used for imaging of whole Escherichia coli bacteria [28] using coherent x-rays with a wavelength of 2 C. A real space image at a resolution of 30 nm was directly reconstructed from the diffraction pattern. An R factor used for characterizing the quality of the reconstruction was in the range of 5%, which demonstrated the reliability of the reconstruction process. The distribution of proteins inside the bacteria labeled with manganese oxide has been identified and this distribution confirmed by fluorescence microscopy images.

Review of the single-particle diffraction method and discussion of its possibilities for biological applications can be found in [29]. The main hope is given to new XFELs (X-ray free lectron laser) The X rays produced by LCLS (Linac Coherent Light Source) will be fully transversely coherent. The pulse (> 10¹² photons) length, initially in the range of 100–200 fs, can be shortened to below100 fs, and with additional research and development it is expected to approach 1 fs.

Summary

The method of coherent X-ray diffractive imaging has been dramatically developed during last few years (in addition to the above papers, see for example also [30, 31]). It has a great potential especially in physics, materials science and biology. In life sciences such a technique is needed to determine the internal structure of assemblies of macromolecules, protein complexes, and virus particles at a resolution sufficient to recognize known proteins and determine their relationship to each other.

X-ray diffraction microscopy, a combination of coherent and bright X-rays with the oversampling phasing method, is a newly developed methodology that may overcome the need of crystallization for obtaining diffraction data. Due to the loss of the amplification from a large number of unit cells inside crystals, the major limitation of the application to structural biology seems to be radiation damage. It is hoped to overcome this problem by cryo technologies and femtosecond-pulsed X-ray lasers enabling to get a record from a biomolecule before it is destroyed.

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