radiation damage workshop
Too hot to handle? Synchrotron X-ray damage of lipid membranes and mesophases†
aBiochemistry, Biophysics, Chemistry, The Ohio State University, 100 West 18th Avenue, Columbus, OH 43210, USA
*Correspondence e-mail: caffrey.1@osu.edu
The call for brighter synchrotron X-radiation sources for use in structural biology research is barely audible as we enter the new millennium. Our brightest sources are already creating havoc when used at design specifications because of radiation damage. The time is long overdue to take stock of where we are and where we wish to go with regards to using existing sources and to designing new ones. The problem of radiation damage is particularly acute in studies involving kinetics and mechanisms where cryo-techniques are not always viable. Accordingly, we need to understand the very nature of radiation damage and to devise means of minimizing it. This is the thrust of the current report as applied to lipid membranes and mesophases. The experiments were performed at the most brilliant beamlines at CHESS, the APS and the ESRF. Two very different types of radiation damage are reported here. One involves a dramatic phase transformation and the other a disordering of lamellar stacking. How beam energy and dose rate affect damage is also discussed. The work highlights the free-radical-mediated nature of the damage process and the need for additional studies if the most efficient use is to be made of an important resource, synchrotron radiation.
Keywords: aging; cubic phase; energy effects; free radicals; heating; hexagonal phase; inverse dose-rate; lamellar phase; phase transitions.
1. Introduction
In these introductory remarks, we attempt to put our contribution to this workshop on radiation damage in a historical context. Thus, a more apt title for the report might be `Blame it on the Ring' or `The Curse of the Ring'. The workshop was conducted at the site of a very special type of ring, one that produces a torrent of X-rays that can at times be `too hot to handle'. But our problems harken back to a very different kind of ring: the one shown in Fig. 1(a). Röntgen produced this impressive image of his wife's hand, where a ring figures prominently on her finger, with the first synthetic X-rays in 1895. The exposure time was 15 min. Within four months, a company published an advertisement (Fig. 1b) claiming to have available an instrument that could produce a vastly improved image of a hand, complete with ring, in a mere 3 min, corresponding to a reduction in exposure time of a factor of five. Thus, the race was on back in the late 1800s to produce `bigger and better' X-ray machines. The race continues today and is in part responsible for this workshop, which was organized to address issues that have arisen because of what amounts to `too much of a good thing'.
In what follows, we recount our experiences with radiation damage using synchrotron radiation. The biomaterials we have worked with most intensively in this context are
one of the major components of biological membranes. We begin by providing some background on membranes and and the liquid-crystal phases that form. We are interested in physiological processes that involve membranes and have chosen to use X-rays for structure elucidation. In this work, particular attention is paid to the dynamic features of biological membranes. As a result, we have resorted to synchrotron sources because the prodigious they provide facilitates the necessary time-resolved measurements. This is where our problems with radiation damage began.1.1. and biomembranes
Fig. 2(a) shows a thin section of a rat liver cell where the darkly staining lines highlight the biomembrane. This figure suggests that membranes figure prominently in the life of the cell. The cell membrane can be viewed as a bimolecular lipid leaflet, in and on which are situated a variety of proteins and other molecules (Fig. 2b). In our work, we take a holistic view of the membrane, and study both the lipid and protein components. However, in this presentation, the lipid component alone will be addressed. A representative glycerophospholipid is shown in Fig. 2(c). are amphiphiles, with a polar and an apolar part built into the same molecule.
(d), they have the capacity to spontaneously self-assemble. With apologies to Hokusai, this woodprint has been modified to illustrate the process of self-assembly. Thus, at the air–water interface is a monomolecular Elsewhere, we see a bilayered vesicle and micelles. Spontaneous self-assembly does not require a genetic blueprint nor indeed an energy input in the form of adenosine triphosphate. It is a spontaneous process that has its origins in the hydrophobic effect. The latter in turn depends on what might be referred to as the narcissistic properties of water, the fact that water has an enormous affinity for itself. Another interesting property of lipidic materials is the fact that they can access the so-called `fourth state of matter', the liquid-crystalline state (Fig. 3). Most materials will pass from a solid to a liquid state in response to a change in temperature, pressure and/or composition. In contrast, lipidic materials pass through one or several intermediate or liquid-crystalline phases (mesophases) during the solid-to-liquid transition. Liquid crystals have order intermediate between the crystalline solid and the isotropic liquid. Some of the liquid-crystalline phases that are accessed by are shown in Fig. 3. For reference, schematics of the solid state and the liquid state are also included. The liquid-crystalline phases include the lamellar liquid-crystalline or Lα phase, cubic phases, hexagonal phases and others. The Lα phase has long been used as a successful model for the biological membrane.
are interesting for several reasons. As illustrated in Fig. 21.2. Dynamic membrane processes
One of our research interests concerns the ubiquitous physiological process of membrane fusion. Much inter- and intracellular communication relies on the process. Fusion requires that two membranes come together to form a single continuous entity and that the contents of each membrane-bounded object mix in a non-leaky manner. This process involves structural rearrangements at the level of both the protein and the lipid components of the membrane. It has been proposed that fusion intermediates are reminiscent of the so-called non-lamellar phases introduced above. We investigate the dynamics and mechanism of the fusion process in simple systems and model it as a phase transformation of the lamellar-to-hexagonal or lamellar-to-cubic phase type. Such phase changes occur on a time-scale ranging from hours to milliseconds (Caffrey, 1989). The dynamics and mechanism of the transitions are studied using low- and wide-angle X-ray diffraction in the time-resolved mode. From a practical point of view, such measurements can only be made using a synchrotron source.
2. Radiation damage: background
Fig. 4 shows an example of the type of problem that we encounter with radiation damage as applied to lipidic systems. Where the beam strikes a dipalmitoylphosphatidylcholine (DPPC) or dimyristoylphosphatidylcholine (DMPC) sample, a footprint remains. The footprint probably appears as a result of chemical damage (see below), the products of which alter the dispersion state of the lipid and thus the way in which it scatters light (Caffrey, 1984). The footprints are long-lived, remaining in place for years. Note that other such as dipalmitoleoylphosphatidylethanolamine (DiPOPE) and monoolein (MO) show no evidence of footprints after similar exposures.
Fig. 5(a) shows a diffraction pattern obtained with a typical lipidic dispersion. It is a powder pattern consisting of a series of concentric rings in the low- and wide-angle regions. Most of the changes seen as a result of radiation damage occur in the low-angle region and correspond to changes in the long-range order of the sample. Scatter/diffraction at wide angles is attributed to lipid-chain packing and appears less sensitive to radiation damage. Thus far, our focus has been on the low-angle region.
2.1. Damage: type I
We have observed two types of radiation damage with lipidic mesophases. Type I damage is illustrated in Fig. 5(b) and was observed using fully hydrated phosphatidylcholine (PC) in the lamellar gel (Lβ′) phase. With time and accumulated dose, the higher-order lamellar reflections broaden and lose intensity while diffuse scatter develops, most noticeably in the region between the first- (d001) and second-order (d002) lamellar bands. `Before' and `after' diffraction patterns are shown in Fig. 5(c), where orientation in the diffuse scatter is apparent. This feature may be exploited in phasing the patterns, as described recently (Cherezov et al., 2000). Protein crystals undergoing radiation damage may yield similar phasing information, as reported in this issue (Ravelli et al., 2002).
Our initial attempts to quantify radiation damage of type I used a normalized order index (NOI; Cheng & Caffrey, 1996). The index is sensitive to the loss of diffraction and its magnitude drops as diffuse scattering grows with accumulated dose and damage. An example is shown in Fig. 6(a) for the lamellar gel Lβ′ and Lα phases of PC under conditions of full hydration. However, when the sample was exposed under conditions of water stress the NOI did not change appreciably, regardless of phase (Figs. 6b and 6c). If the NOI is an accurate measure of radiation damage, these results would indicate that the sample has not suffered damage at less than full hydration. The data shown in Fig. 7, however, prove unequivocally that damage does occur under conditions of water stress, but it is masked under these conditions.
This is a very important result because it means that X-ray diffraction is not always a reliable indicator of radiation damage.
The NOI proved to be a useful measure of the progress of radiation damage when it effected a change in the diffraction pattern. However, we have since separately quantified the development of diffraction intensity and diffuse scatter as a measure of damage-induced stacking disorder within the lamellar phase (Cherezov et al., 2000). Our long-term objective is to fit the entire diffraction curve taking into account stacking disorder and using a parameterized density of the lipid bilayer. This will allow us to obtain direct information on the growth of stacking disorder and on changes in lipid bilayer structure with accumulated dose.
2.2. Damage: type II
Type II damage is characterized by a partial or complete phase transformation that, unlike type I damage, is not accompanied by a change in phase order/disorder (Cheng et al., 1993). Two examples of type II damage are shown in Figs. 8(a) and 8(b). These include the lamellar-to-inverted hexagonal (HII) and the cubic Pn3m-to-HII phase transitions. In both cases, we see a partial or complete change in phase but no line broadening or development of diffuse scatter. Typically, a certain accumulated or threshold dose is necessary to trigger the transition. Below that threshold, no changes in the diffraction pattern are seen. The threshold dose depends on how close in temperature the sample is to the corresponding transition (Cherezov et al., 2000). The linear dependence of the threshold dose on the temperature differential indicates that the threshold drops to zero at precisely the transition temperature. This means that the closer to the transition temperature the measurement is made, the smaller is the dose needed to effect noticeable damage of type II.
2.3. X-rays `do chemistry'
In the set of experiments described in §2.1, the sample underwent radiation damage but this was not apparent in the diffraction pattern under water-stressed conditions. Accordingly, we set about identifying a more reliable indicator of radiation damage. It seemed likely that the changes induced as a result of damage had their origins in the chemical modification of the lipid, since X-rays are energetic particles with the capacity to ionize and to trigger reactions. We looked for evidence of X-ray-induced chemical change using The data in Fig. 9 show clearly that X-irradiation is accompanied by which occurs regardless of the state of hydration of the sample. This is consistent with the results noted in §2.1. In addition to chemical breakdown leading to the production of and lyso-lipids (Caffrey, 1984; Cheng et al., 1993), it is likely that lipidic polymers are produced as a consequence of damage. Evidence in support of this comes from the streaking observed close to the origin in the thin-layer (Fig. 9, lanes 3 and 4). Our intent is to use to characterize more fully these and other damage products.
2.4. Beam heating
The transitions described in §2.2 were observed when the sample was held at a temperature below the corresponding phase-transition temperature. It was suggested, therefore, that the effect seen might simply be due to beam heating. Clearly this is not the case, as the new phase formed as a result of X-irradiation persists after the beam is turned off and the sample is allowed to thermally re-equilibrate. Of course, this assumes that the high-temperature phase does not undercool. Nonetheless, we were interested in quantifying the heating capability of the X-ray beam and an experiment was set up to make the measurement illustrated in Fig. 10. This used a very small thermocouple positioned in the sample capillary to one side of the X-ray beam. A miniscule rise in temperature, amounting to 0.16 K, was recorded from an initial temperature of 288.35 K. The measurement is compromised to some degree by the fact that the thermocouple itself can act as a thermal conduit. Nevertheless, the magnitude of the temperature change is so small that it is unlikely to contribute in a significant way to the type II damage noted above. Future investigations of beam heating will use non-invasive thermal imaging as described in this issue (Snell et al., 2002).
2.5. Damage `in the dark'
It seems reasonable to expect that damage takes place while the sample is being irradiated, and, indeed, this is what is observed, as described above. Less intuitive is the possibility of witnessing damage `in the dark' following an exposure, when the X-ray beam is turned off. However, we have seen this phenomenon and it shows up in two distinct forms. In the first, radiation damage is already under way and is evident before the beam is turned off. After some delay in the dark, the sample is re-examined. Such an example is shown in Fig. 11(a), where clearly damage continues in the absence of X-irradiation. In the second form, the initial dose is low enough to cause no apparent damage (Fig. 11b). However, turning off the beam and waiting for an interval before re-examining the sample shows that damage had already set in during the initial exposure and that the process that gave rise to a change in the diffraction pattern had continued in the dark. It may be that the primary damage products are generated immediately during the exposure and that secondary products, plus the attendant phase change, happen subsequently and more slowly.
This is an important result with consequences for how samples are handled during synchrotron-based measurements. Thus, for example, the sample may be exposed to the X-ray beam transiently during capillary alignment, and the diffraction pattern may show no evidence of radiation damage after such brief exposures. The actual subsequent measurement is likely to involve a change in one or several conditions. The observed phase behavior could, therefore, be compromised by the products of a reaction that took place `in the dark' while preparations were being made for data collection. This problem could be overcome by aligning on one part of the sample and making measurements on an adjacent, previously unexposed, part of the sample. This is routine in electron diffraction and microscopic measurements.
2.6. A free-radical-mediated process
. Clearly, free-radical generation in the presence of the lipid is over and above that seen when the dispersing medium alone is subjected to X-irradiation. This study demonstrates convincingly that free radicals are produced when the hydrated lipid is exposed to X-rays. It is very likely that these reactive species go on to trigger chemical transformations that give rise to what we detect by and diffraction as radiation damage.
such as X-rays, interacts with biomaterials in ways that are expected to produce free radicals. We suspected that the damage described above was free-radical mediated. The problem with detecting free radicals is that they are usually short-lived and thus difficult to monitor. Electron spin resonance (ESR) is commonly used for measuring free radicals. However, unless the ESR measurement is made while the sample is being irradiated it is unlikely that the signal will persist and be measurable in a post-irradiation assay. Spin traps can be used to advantage here, since they react with the transient radical and produce a long-lived species that can be measured at a later time. This approach was taken in the current study, and the results of a spin-trap (2-methyl-2-nitrosopropane) measurement are shown in Fig. 122.7. Dispersing-medium effects
Since the cryo-cooling approach is not really an option in studies of lipid ). One example is shown in Fig. 13, where the X-ray sensitivity of the gel phase (Lβ′) in hydrated DPPC was evaluated in the presence of a TES/NaCl buffer system at pH 7.4. TES (N-tris[hydroxymethyl]methylaminoethane sulfonic acid) has been reported to act as a free-radical scavenger (Fiorentini et al., 1989). As judged by the changing diffraction pattern, damage was significantly reduced in the presence of the buffer system. We are currently investigating the origin of this effect. It is possible that the buffer is acting as a free-radical scavenger and in this way is minimizing damage. It is also possible that damage is taking place but the effect is being masked as a result of charge screening by the salt.
behavior, we would like to explore the possibility of adding free-radical scavengers and deoxygenation as strategies for minimizing radiation damage. These manipulations will be of use only if they do not impact on the phase properties of the system. A limited number of such studies have been performed (Cheng & Caffrey, 19962.8. Dose-rate effects
The data above demonstrate that radiation damage is free-radical mediated. Thus, the progress of damage is expected to be time-dependent in that radicals and the damage products they create must migrate in the sample to allow for the expression of damage. Regardless of how fast the latter processes are, with a hot enough beam it should be possible to deliver enough photons to the sample to produce a measurable signal (the diffraction pattern) in a time shorter than it takes for damage to develop and to reveal itself. The higher
is also associated with a greater probability of free radicals combining with one another and thereby limiting damage. This is the so-called `inverse dose-rate effect'. Specifically, damage should be less severe for a given accumulated dose as the number of incident photons per unit time and per unit area (dose-rate) rises.In the course of this work, we have studied the dose-rate effect at several synchrotron facilities and under a variety of conditions. The first result is shown in Fig. 14(a), where radiation damage of type I was examined at beamline ID2 (ESRF) using fully hydrated DPPC in the Lβ′ phase at 298 K. The loss of diffraction at low angles was monitored as a function of accumulated dose, calculated as described previously (Cherezov et al., 2000), over the dose-rate range 2–640 krad s−1. In this experiment, the dose was delivered continuously in the sense that the sample was irradiated without interruption as dose accumulated. Worthy of note in this regard is the timed structure of the source itself. The data show a distinct inverse dose-rate effect. Thus, for a given accumulated dose, the higher dose rate produced less damage.
A similar result was obtained at beamline 18ID (APS) under conditions of discontinuous irradiation (Fig. 14b). The latter course of photon delivery was necessitated by the of the detector (CCD, 4.5 s) during image readout and data transfer. Thus, the damage protocol involved a series of sequential fixed-interval exposures and data collection followed by a period of 4.5 s where the beam was turned off and the image was read out. The maximum dose rate available under these conditions (179 Mrad s−1) was more than two orders of magnitude higher than at any other source we had used. However, in contrast to previous studies, damage was generated with discontinuous as opposed to continuous irradiation. Attenuation was achieved using metal foils, and the duration of each exposure interval was adjusted to the same accumulated dose for all dose rates studied. The results in Figs. 14(b) and 14(c) show that the same inverse dose-rate effect was observed as that noted above with continuous irradiation at the lower overall dose-rate levels.
Thus, type I damage demonstrates the inverse dose-rate effect regardless of whether the exposure is continuous or discontinuous. In distinct contrast, type II damage to DiPOPE suggests the opposite effect under conditions of continuous exposure (Fig. 15). It must be appreciated that this experiment has not been repeated many times. Nevertheless, the threshold would appear to lengthen and the rate of damage with accumulated dose drops slightly at the lower dose rates.
To what can we attribute the opposite dose-rate effects seen with type I and type II damage? One possibility is that the inverse dose-rate effect applies to both, but the systems and the conditions are so different as to give rise to these disparate results. To begin with, type I measurements were made in the Lβ′ phase, where the lipid molecules have very limited mobility. Conversely, type II damage occurred in the Lα phase, where rapid diffusion in the plane of the membrane is a characteristic of the phase. Thus, under type I conditions, damage products are more likely to accumulate where generated and to elicit the damage effect in situ. This is in contrast to the more fluid Lα phase, where products may diffuse away from the site of production, allowing the effect to lessen with time as a result of simple dilution. Thus, at the higher dose rates, damage products will be more concentrated because they will have had less time to diffuse away for a given accumulated dose. Another factor to consider is the heating effect of the beam. The temperature along the track of the beam in the sample will be higher at the higher dose rate [see calculations in Cheng & Caffrey (1996) and Kuzay et al. (2001)]. Thus, type II damage, which happens when close to a (see above), should occur sooner at the higher dose rate. The higher associated heating effect simply shifts the system closer to the phase-transition temperature. As noted under type II damage, a smaller temperature differential corresponds to a smaller accumulated dose threshold. This may partly explain what is happening in Fig. 15.
The foregoing argument assumes that the incident beam has a uniform profile [number of photons /(unit time, unit area)] and thus is free of `hot spots'. The complicating issue of hot spots in the context of radiation damage has been addressed by Cheng & Caffrey (1996). Measurements reported in this paper that were made at the ESRF and the APS also involved beam profiling. In both cases, a Gaussian distribution was observed (in the horizontal and vertical directions).
2.9. Photon energy
One of the benefits of using a synchrotron beam is that it can be tuned over a relatively wide energy range. Each source has a characteristic output spectrum, and monochromators are commonly used to isolate particular wavelengths. Since damage due to . The data suggest that there is no large energy effect on damage in the range studied. The differences seen as a function of photon energy are similar to those due to sample variability, which can be pronounced at high accumulated doses (Fig. 14c). Note that while the latter stages of type II damage seen in Fig. 16(b) are somewhat slower to develop with accumulated dose at the lower energy, the threshold for onset of damage is insensitive to photon energy at all three energies.
depends to some degree on photon energy, we evaluated beam damage as a function of energy in the range 9–17 keV. Measurements were made at beamline ID2 (ESRF) by monitoring the progress of type I and II damage, respectively, in hydrated DPPC and DiPoPE as above. It is important to note that many properties of the system change and must be corrected and/or accounted for as photon energy is changed. These include, but are not limited to, beam size, dose rate, beam profile, beam heating, transmission (through air, windows, sample container, the sample itself), scattering/diffraction properties, and beam-intensity monitor (ion chamber, photodiode) and detector sensitivity. Although every effort was made to control these effects, we found that the dose-rate differed by a factor of two at the low and high energies used. The results of the study are included in Fig. 16Given that an energy effect was not observed in this study, our recommendation is to choose that energy which optimally combines source output, scatter/diffraction efficiency and detector sensitivity.
3. Concluding remarks
The results presented above demonstrate that studying soft condensed biomaterials, such as
and membranes, with a bright X-ray source such as that available at a synchrotron can lead to problems with radiation damage. Provision must be made in all such studies to look for the effect and to take measures to ensure that data collection is not compromised by damage.Because radiation damage was recognized only very recently as an issue worthy of study, little focused research has been carried out in the area. As a result, few useful rules or principles have emerged as to the types of materials that are more or less prone to radiation damage. Likewise, sample dispersion conditions and beam characteristics that minimize damage have not been fully investigated. Currently, therefore, each sample type must be evaluated on an individual basis. We need general guidelines, and beam time must be allocated for the purpose of establishing them. Our studies of photon energy showed little difference in radiation damage in the 9–17 keV range. Both direct and inverse dose-rate effects were observed with the different damage types examined.
While the rules and principles governing radiation damage in this area have not yet been identified, we can state with confidence that X-ray diffraction is not a reliable indicator of radiation damage. Thus, under the right conditions, radiation damage can exist and go unnoticed. The problem is that it can express itself when conditions change, thereby rendering useless the entire measurement or study.
We make extensive use of synchrotron radiation despite the problem of radiation damage, and we do so without resorting to beam attenuation. Fortunately, we work with long homogenous samples held in glass capillaries. Thus, the sample is continuously moved in the beam during a measurement to ensure that no one part is over-exposed. It is important to realize that cryo-techniques are not an option in this area of membrane/lipid research, where measurements are typically made in the temperature range 273–323 K.
Over the past two decades we have worked at the APS, CHESS, ESRF and NSLS. We have had to deal with the problem of radiation damage at all but the latter. The beam at NSLS is divergent/convergent. Further, we focus the beam at the detector, which means that the swath of radiation striking the sample is relatively large, and thus the X-ray
at the sample is relatively low. This spares the sample from noticeable damage.We have demonstrated that free radicals are produced as a result of X-irradiation. These reactive species have the capacity to `do chemistry', resulting in changes in molecular structure and, by extension,
identity and microstructure. Type II damage involves a phase transformation, which can be of the lamellar-to-non-lamellar form. In this context, it is interesting to note that biomembranes are usually of a lipid constitution, such that they exist under physiological conditions close to such a transition and are particularly sensitive to type II damage. Should a lamellar-to-non-lamellar transition take place in the lipid component of the biomembrane, its integrity would be compromised, producing a leaky structure incapable of supporting a gradient. This unhealthy state would probably lead to cell death if left unrepaired. Free-radical production is associated with aging and other physiological and non-natural processes. Excessive accumulations of free radicals could trigger a local phase transformation of the type described, leading to a loss of selective permeability and the ability to support gradients and, ultimately, to cell death. It is interesting that these insights into important physiological issues were arrived at as a spin-off from a study of the nagging problem of radiation damage.Footnotes
†Presented at the `Second International Workshop on Radiation Damage to Crystalline Biological Samples' held at Advanced Photon Source, Chicago, USA, in December 2001.
Acknowledgements
We gratefully acknowledge the assistance provided by R. Fischetti and T. Irving (APS, 18ID), N. Theyencheri and D. Panine (ESRF, ID2), and J. Clogston and H. Fersi (The Ohio State University). This work was funded in part by the National Institutes of Health (GM56969, GM61070) and the National Science Foundation (DIR9016683, DBI9981990).
References
Caffrey, M. (1984). Nucl. Instrum. Methods Phys. Res. 222, 329–338. CrossRef CAS Web of Science Google Scholar
Caffrey, M. (1989). Annu. Rev. Biophys. Biophys. Chem. 18, 159–186. CrossRef CAS PubMed Google Scholar
Cheng, A. & Caffrey, M. (1996). Biophys. J. 70, 2212–2222. CrossRef CAS PubMed Google Scholar
Cheng, A., Hogan, J. L. & Caffrey, M. (1993). J. Mol. Biol. 229, 291–294. CrossRef CAS PubMed Web of Science Google Scholar
Cherezov, V., Cheng, A., Petit, J.-M., Diat, O. & Caffrey, M. (2000). Cell. Mol. Biol. 46, 1133–1145; erratum (2001). 47, 229–230. Google Scholar
Fiorentini, D., Landi, L., Barzanti, V. & Cabrini, L. (1989). Free Radical Res. Commun. 6, 243–250. CrossRef CAS Web of Science Google Scholar
Kuzay, T. M., Kazmierczak, M. & Hsieh, B. J. (2001). Acta Cryst. D57, 69–81. Web of Science CrossRef CAS IUCr Journals Google Scholar
Ravelli, R. B. G., Theveneau, P., McSweeney, S. & Caffrey, M. (2002). J. Synchrotron Rad. 9, 355–360. Web of Science CrossRef CAS IUCr Journals Google Scholar
Snell, E. H., Judge, R. A., Larson, M. & van der Woerd, M. J. (2002). J. Synchrotron Rad. 9, 361–367. Web of Science CrossRef CAS IUCr Journals Google Scholar
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