research papers
Evaluation of crystal quality of thin protein crystals based on the
of X-ray diffractionaGraduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan, bPrecursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan, and cDepartment of Education, Yokohama Soei University, 1 Mihocho, Midori-ku, Yokohama 226-0015, Japan
*Correspondence e-mail: rsuzuki@yokohama-cu.ac.jp, tachiban@yokohama-cu.ac.jp
Knowledge of X-ray diffraction in macromolecular crystals is important for not only structural analysis of proteins but also diffraction physics. Pendellösung fringes were clearly observed in the X-ray topographic images. For macromolecular crystallography, it is hard to obtain large crystals because they are difficult to crystallize. For thin crystals, can be demonstrated by analysis of the equal-thickness fringes observed by X-ray topography.
provides evidence of perfect crystals. Until now, clear in protein crystals has only been observed in glucose isomerase crystals. We wondered whether there were other protein crystals with high quality that exhibit Here we report the observation of in thin ferritin crystals by rocking-curve measurement and imaging techniques such as X-ray topography. It is generally known that in the case of thin crystals it is difficult to distinguish whether occurs from only rocking-curve profiles. Therefore, our results clarified that occurs in thin protein crystals because fringe contrasts similar toKeywords: protein crystallography; X-ray topography; rocking curves; crystal perfection; oscillatory profiles; dynamical diffraction.
1. Introduction
X-ray diffraction occurs in every crystalline material. In general, X-ray diffraction phenomena are described by kinematical and dynamical theories (Zachariasen, 1945; Batterman & Cole, 1964; Pinsker, 1978; Authier, 2001). Kinematical diffraction occurs in small or low-quality crystals. On the other hand, only occurs in perfect crystals such as Si, Ge and diamond (Kato & Lang, 1959; Lefeld-Sosnowska & Malgrange, 1969; Persson, 1971; Aldred & Hart, 1973; Bonse et al., 1977; Ishikawa, 1988; Kowalski et al., 1989; Ishikawa et al., 1991). In general, almost all crystals are not perfect, i.e. some defects exist in crystals. This leads to the conclusion that it is practical to consider only kinematical diffraction for almost all materials.
In order to reveal the protein structures by X-ray diffraction, various methods of growing high-quality protein crystals have been suggested (Chayen et al., 2010). We examine the relationship between a `perfect crystal' and `protein crystals with high quality'. In protein crystallography, crystal quality tends to be commonly evaluated by mosaic width and diffraction resolution. The crystal perfection discussed in this article should be understood to be the physical quality as a simple perfect crystal. The evaluation of several grown crystals has been carried out by X-ray rocking-curve analysis so far (Helliwell, 1988; Snell et al., 1995; Boggon et al., 2000; Volz & Matyi, 2000; Lübbert et al., 2004; Koizumi et al., 2013). Nevertheless, there has been no report on the clear observation of oscillatory profiles of rocking curves by Recently, we revealed that glucose isomerase (GI) crystals can be obtained with high quality (Suzuki et al., 2017, 2018a,b). The perfection of these crystals has been characterized by the observation of oscillatory profiles of rocking curves and fringe contrasts, i.e. Pendellösung fringes, caused by of X-rays (Suzuki et al., 2018a). The diffraction from this sample leads to the need for models; combined kinematical and models have also been suggested for a more accurate structural analysis (Suzuki et al., 2018a). However, the generality of for protein crystals cannot be clarified since the has only been observed in GI crystals.
In this study, we demonstrate that the kinematical and Pendellösung fringes. The period of the fringes can only be explained by For evaluation of the crystallinity with especially for thin crystals, it is important to perform not only the rocking-curve measurement but also diffraction imaging over the whole crystals by X-ray topography.
model applies to very high-quality ferritin crystals. The oscillatory profile of the rocking curves is observed in thin crystals and is in good agreement with that predicted by theory. However, the oscillatory profile is also similar to that predicted by kinematical diffraction theory when the crystal thickness is less than the extinction distance. In thin crystals, it is difficult to distinguish whether the oscillatory profile is caused by the dynamical or kinematical diffraction effect. On the other hand, X-ray topographic images clearly show the fringe contrasts similar to2. Methods
2.1. Crystallization of ferritin
A solution of equine spleen ferritin was purchased from Sigma–Aldrich Co. LLC without further purification. All other chemicals used for preparing solutions were of reagent grade. Ferritin crystals were grown by using macroseeds. First, the seed crystals were obtained using the hanging-drop vapor-diffusion method. The seed crystals were then grown from a solution containing 1.06 mg ml−1 ferritin, 0.2 M acetic acid–sodium acetate buffer (pH 5.0) and 125 mM cadmium sulfate, followed by filtration (pore size 0.1 µm) to remove any impurities and aggregates. The reservoir solution contained 250 mM cadmium sulfate. The volumes of the drop and reservoir solution were 3 µl and 1 ml, respectively. After the seed crystals were grown, they were put in a growth droplet (same condition as mentioned above) on siliconized cover glasses (Hampton Research Corp.), where the volume of the droplet was 40 µl. The droplet containing the seed crystals was kept at 20°C for five days so that ferritin crystal was grown on siliconized cover glasses from the seed crystal. Ferritin is a globular protein molecule of 12 nm in diameter and consists of 24 subunits (Vedula et al., 2009). The molecular weight of ferritin is ∼480 000 Da. The crystal has a face-centered-cubic structure with F432 and lattice constant a = 18.16 nm (Vedula et al., 2009). Fig. 1 shows a picture of a typical ferritin crystal as well as a schematic highlighting the typical growth planes.
2.2. Measurement of X-ray diffraction
X-ray topography and rocking-curve measurements were performed at room temperature in the BL14B and BL20B beamlines at the Photon Factory (PF), part of the High Energy Accelerator Research Organization (KEK). All the experiments were carried out in Laue geometry configuration, as shown in Fig. S1 in the Supporting information. Monochromatic beams of λ = 1.2 Å without focusing were selected by adjusting the double-crystal monochromator consisting of a Si (111) crystal at the PF. The incident beam with a size of 3 × 5 mm is enough to measure an entire crystal sample. The grown ferritin crystal on siliconized cover glasses was mounted on a goniometer using wax. The crystal sample on the precision goniometer was rotated about an axis perpendicular to the incident beam with a high-resolution angular step [minimum angular-step width of 0.19 arcsec (5.3 × 10−5°)] around the exact of the reflected wave. For the rocking-curve measurement, a high-resolution X-ray CCD camera (Photonic Science X-ray FDI 1.00:1, with an effective pixel size of 6.45 × 6.45 µm) was used as a detector with exposure times of 400 ms, which is enough time to measure the intensity of the diffracted beam. To obtain the high-resolution X-ray topographic images, X-ray films (Agfa D2) were used as detectors with exposure times of 180 s, which is enough time to detect the diffracted images.
3. Results and discussion
Fig. 2(a) shows a typical rocking curve of ferritin crystals taken with the reflection at BL20B at the PF, where the thickness of the ferritin crystal is ∼80 µm. The intensities of the rocking curves are shown on linear and logarithmic scales. The rocking curve is drawn as a function of W scale (Authier, 2001) as opposed to degree or mosaicity, which is more natural for diffraction experiments. The W scale is the parameter representing the deviation from the The W scale is given by
where
where Λ and ξ are the periods of the Pendellösung fringes and the extinction distance in the Laue (transmission) case, respectively. Furthermore, θB is the λ is the wavelength of the incident beam, Vc is the volume of the re is the classical electron radius (2.82 × 10−15 m) and F is the From equation (1), the is always at W = 0, so it may be easier to compare different reflections. According to equations (1) and (2), W is also scaled by the wavelength, the unit-cell volume, and the and associated with the reflections. W for the reflection of the ferritin crystal is obtained from equation (1) with θB = 0.328°, λ = 1.2 Å and Λ = 4090 µm, which is calculated from equation (2) using Vc = 5.99 × 10−24 m3 and |F| = 13 594 (PDB ID 3f32; Vedula et al., 2009).
It should be noted that an oscillatory profile is clearly observable on the wings of the rocking curve. This oscillatory profile is quite similar to that of GI crystals, as reported previously (Suzuki et al., 2018a). The series of X-ray topographic images associated with the oscillatory rocking curve are shown in Movie S1 in the Supporting information.
According to the ), the profile of the rocking curve with absorption can be calculated by
of X-ray diffraction (Authier, 2001where
and
Here, r is the ratio of Iga/Io to with 0 ≤ r ≤ 1, and Iga, Io and are the diffraction intensity, the incident beam intensity and the averaged diffraction intensity, respectively. The ratio, 1 − r, of the average curve corresponds to the degree of smearing or background in the oscillatory curve, which originates from the resolution limit owing to the angular divergence of the beam (Bonse et al., 1977; Ishikawa, 1988). Furthermore, μ is the H is the crystal thickness, χ is the electric susceptibility and ∊ is the Fig. 2(b) shows the calculated profiles of oscillatory rocking curves by for the reflection obtained from the ferritin crystal with thickness of 80 µm. The fitting parameters were μ = 2.84 mm−1, χ = 0.001 and ∊ = 23 (Authier, 2001; Suzuki et al., 2018a; Zeldin et al., 2013). The calculated curves are in good agreement with the measured curves.
In contrast, it is well known that even if the crystal perfection is high, kinematical diffraction occurs, when the crystal thickness is quite thin compared with the extinction distance. In the case of protein crystals especially, the volume of the Vc, is large and the |F|, is small compared with those of inorganic materials. Therefore, the extinction distance of protein crystals is several hundreds of micrometres or several millimetres but that of inorganic materials such as Si is around several tens of micrometres. This means that the ratio H/Λ, where H and Λ are the thickness of the crystals and the extinction distance, respectively, is important to distinguish which predominantly occurs, kinematical or dynamical diffraction.
According to the ), the profile of rocking curves can be calculated by
of X-ray diffraction (Authier, 2001where Ih is the kinematical diffraction intensity, N is the number of unit cells and d is the plane distance. Fig. 2(c) shows the theoretical profiles of rocking curves by kinematical diffraction for the reflection obtained from the ferritin crystal with thickness of 80 µm. This curve is also in good agreement with the measured curves. This means that when the crystal thickness is quite thin compared with the extinction distance, the kinematical and cannot be distinguished. In this measurement, the ratio, H/Λ, is ∼0.02. In order to clarify the dynamical effect, the dependence of crystal thickness and wavelength is desired (Suzuki et al., 2018a). However, it is hard to perform this measurement because of the difficulty of growing large perfect protein crystals.
Fig. 3 shows the theoretical profiles of rocking curves for dynamical and kinematical diffraction over a range of different values of H/Λ. For in Laue geometry, the profile shape of the rocking curve depends on the thickness of crystals (Authier, 2001). The wings of the rocking curves of with thicker crystals show higher intensity than that of kinematical diffraction. Additionally, the calculated oscillatory rocking curve exhibits a minimum value at the exact as opposed to the expected maximum value, as shown in Fig. 3(a), when the thickness of the perfect crystal matches to the integer multiple of the extinction distance. Such a oscillatory profile with a minimum value at the exact has been measured for Si single crystals with perfection (Ishikawa et al., 1991). As shown in Fig. S2, the interesting profile with a local minimum value at the can be also measured for thicker GI crystals (H/Λ = 0.91) in which the oscillatory rocking curve caused by was first observed in protein crystals (Suzuki et al., 2018a). Thus, for thicker crystals, is easily demonstrated by the observation of strong oscillation of the rocking curve and/or the local minimum value at the exact However, it is difficult to judge the by only rocking-curve measurement for thinner crystals.
Figs. 4(a) and 4(b) show typical X-ray topographic images of ferritin crystals taken with reflection at BL14B at the PF. As seen in Figs. 4(a) and 4(b), the fringe contrasts at the wedge-like edges of the crystals are clearly observed at different values of W. The fringe contrasts are caused by the of X-rays. Here, the period of fringe contrasts was analyzed. The average periods of the fringes on the wedge-like edges of the crystal shown by the arrows are measured to be 7.78 and 9.95 µm. According to the of X-ray diffraction, the period of the fringes depends on the degree of the inclination of the wedge-like edges at each W (Ishikawa, 1988). Using the angle of the wedge shape as shown in Fig. 1, the average periods of the peak tops at W values of −198.58 and −132.38 are calculated to be 7.28 and 10.9 µm, respectively. The calculated profiles and average values are in good agreement with the measured ones, as shown in Figs. 4(c), 4(d) and Table 1. This match between measurement and theory is strong evidence of Even though it is difficult to distinguish the origin of the diffraction by measurement of rocking curves with thin crystals, the X-ray topographic image shows clear evidence of the For evaluation of the crystal quality, especially for thin crystals, it is important to perform not only the rocking-curve measurement but also the diffraction imaging with high-resolution X-ray topography. In previous research on Si crystals, the precise has been experimentally determined from the analysis of equal-thickness fringes observed by using high-collimated X-ray (Kato, 1969). In protein crystals, it is possible to estimate the precise by analyzing the fringe contrasts as mentioned above.
|
Finally, we consider the origin of the crystal quality of protein crystals. Recently, it has been reported that the crystal quality of hen egg-white lysozyme (HEWL) crystals is improved when the concentration of the precipitant in growth solution is higher (Koizumi et al., 2019). This is attributed to the faster dynamics of water around the protein molecules (Koizumi et al., 2019; Aoki et al., 2013, 2016). However, the quality might be inferior to that of GI crystals since the oscillatory profiles of rocking curves by has not been observed yet. One of the distinct features of GI, ferritin and HEWL molecules is the molecular shape. GI and ferritin molecules have a spherical shape composed of 4 and 24 subunits, respectively, as shown in Figs. 5(a) and 5(b) (Nowak et al., 2002; Vedula et al., 2009). On the other hand, HEWL molecule has a croissant shape (not spherical), as shown in Fig. 5(c) (Diamond, 1974). Therefore, it may be possible to produce the low crystallinity by non-spherical molecular shape. More extensive and quantitative analysis of the relationship between the crystal quality and molecular shapes with other proteins is now in progress.
4. Summary
We have measured the oscillatory profile of rocking curves for thin ferritin crystals. The oscillatory profile can be explained by both dynamical and kinematical diffraction models. For thin crystals, it is difficult to judge from only the rocking-curve profiles whether Pendellösung fringes in X-ray topographic images is clearly observed in thin crystals and can be explained by In brief, occurs even in thin ferritin crystals. This knowledge will be useful for the evaluation of crystal quality in thin crystals. Furthermore, the observation of using ferritin crystals provides a second example in addition to glucose isomerase. It will be received with considerable interest for a more accurate structural analysis by the physical crystallography community and the macromolecular crystallography community and beyond.
and/or kinematical diffraction occurs. Measurement of the fringe contrasts similar toSupporting information
Supporting figures and Supporting movie caption. DOI: https://doi.org/10.1107/S2052252520007393/yu5019sup1.pdf
Movie S1. Serial images of digital X-ray topographs taken as a function of the angle. DOI: https://doi.org/10.1107/S2052252520007393/yu5019sup2.avi
Acknowledgements
We thank Dr K. Hirano and Dr H. Sugiyama of the High Energy Accelerator Research Organization (KEK) for their help with the synchrotron radiation X-ray experiments. X-ray topography and the rocking-curve measurements were performed in BL14B and BL20B at the Photon Factory of KEK under the approval of the Program Advisory Committee (Proposal 2019G103).
Funding information
The following funding is acknowledged: PRESTO, Japan Science and Technology Agency (grant No. JPMJPR1995); Japan Society for the Promotion of Science (JSPS) KAKENHI Grants-in-Aid for Scientific Research (grant Nos. 16K06708, 17K06797 and 19K23579); Iketani Science and Technology Foundation (grant No. 0291078-A).
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