Crystallization Technique for Strain-free Protein Crystals Using Cross

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Crystallization Technique for Strain-free Protein Crystals Using Cross-linked Seed Crystals Haruhiko Koizumi,*,† Satoshi Uda,† Masaru Tachibana,‡ Katsuo Tsukamoto,¶ Kenichi Kojima,§ and Jun Nozawa† †

Institute for Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan ¶ Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan § Department of Education, Yokohama Soei University, 1 Miho-cho, Midori-ku, Yokohama 226-0015, Japan ‡

ABSTRACT: In this study, we show using X-ray diffraction (XRD) rocking-curve measurements that local strain in tetragonal hen egg white (HEW) lysozyme crystals can be removed to a large degree by utilizing seed crystals cross-linked with glutaraldehyde. We also find that misorientation between subgrains and subgrain size decrease when employing cross-linked seed crystals, which suggests that subgrain formation in tetragonal HEW lysozyme crystals can be controlled using this technique. The ideal mosaic structure of proteins that enables the collection of accurate integrated intensities of the diffracted waves is also discussed using tetragonal HEW lysozyme crystals as a model protein.

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INTRODUCTION The structural analysis of protein molecules is an active research field aimed primarily at achieving structure-guided drug design and controlled drug delivery. Thus, it is quite important to determine the 3D structures of protein molecules accurately. Although at present these structures are determined mainly by X-ray and neutron structural analysis, these techniques require high-quality single crystals of the proteins, which are difficult to obtain.1 For neutron structural analysis, in particular, large protein crystals with sizes on the order of a millimeter are needed to provide multiple diffraction spots due to the low intensity of the neutron beam. However, it is quite difficult to grow large, millimeter-sized protein crystals. Thus, the establishment of crystallization techniques for large, highquality single crystals of proteins is desirable. To this end, improvements in the crystal quality of grown protein crystals have been actively pursued by using magnetic fields,2−9 microgravity,10−17 electric fields,18−20 solution flows,21−24 and gels as growth host media25−31 because the crystal quality of simply grown protein crystals is considered to be too low. However, what is needed for X-ray and neutron structural analysis of high-quality protein crystals is not perfect crystals but crystals from which many diffraction spots with accurate integrated intensities can be collected. The integrated intensities of the diffracted waves from a perfect crystal are predominantly described by the dynamical theory of diffraction. This means that significant extinction of the integrated intensities of the diffracted waves occurs owing to multiple reflections, which reduces the accuracy of the measurement. Thus, protein crystals with an adequate mosaic structure that allows the collection of accurate integrated intensities of the diffracted waves, i.e., ideal mosaic crystals of proteins are needed in order to obtain accurate 3D structures of protein molecules. © XXXX American Chemical Society

Recently, we have observed clear equal-thickness fringes in the region of the tapered glucose isomerase crystal with wedgelike edges, using X-ray topography with monochromatic synchrotron radiation.32 The results indicate that significant dynamical diffraction due to multiple reflections occurs in this glucose isomerase crystal. The misorientation between subgrains in this glucose isomerase crystal was estimated to be on the order of 10−4 deg, indicating that this is a near-perfect crystal.32 Even for protein crystals, an adequate mosaic structure for X-ray and neutron structural analysis can be achieved by degradation of the crystal quality. Thus, it is quite important to determine whether the crystal quality of a protein crystal under analysis is adequate to obtain accurate 3D structures using X-ray and neutron structural analysis. Moreover, our X-ray diffraction (XRD) rocking-curve measurements have verified that imperfections in protein crystals are caused not only by misorientation between subgrains but also by local strain in the crystals.20 In particular, the data suggested that a large amount of local strain is accumulated in tetragonal hen egg white (HEW) lysozyme crystals, despite the low dislocation density of the crystals.20 In addition, our analysis of the full width at half-maximum (fwhm) values of the rocking curves indicated that the subgrain size in tetragonal HEW lysozyme crystals is roughly in the range of 200−600 μm.20 Such large subgrains cause significant primary extinction of the integrated intensities of the diffracted waves, which can be explained by the dynamical theory of diffraction. Therefore, obtaining ideal mosaic crystals of proteins requires the elimination Received: August 1, 2016 Revised: September 2, 2016

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DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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HEW lysozyme crystals were grown with and without cross-linked seed crystals using the batch method at 21 °C for 9 days from this crystallization solution containing 57 mg/mL HEW lysozyme and 0.5 M NaCl in 100 mM sodium acetate buffer at pH 4.3. The unit cell parameters of tetragonal HEW lysozyme crystals grown with and without seed crystals were almost identical to those reported previously in the literature: space group P43212 and a = 79.1 Å, c = 37.9 Å, and α = β = γ = 90°.35,36 We have previously carried out XRD rockingcurve measurements on tetragonal HEW lysozyme crystals grown without seed crystals.18−20 The details of the growth cell (12 × 12 × 45 mm) were described in our previous work.18 In those experiments, however, the crystals were grown in a plastic cell (25 × 25 × 4 mm), as shown in Figure 1a. Thus, the growth method was different from the previous work,18−20 although the growth conditions were the same. XRD rocking-curve measurements were conducted at room temperature on beamline BL20B at the Photon Factory (PF) of the High Energy Accelerator Research Organization (KEK) in Japan. A twocrystal monochromator consisting of a Si(111) crystal was located 11 m from the source and used to select an X-ray wavelength of λ = 1.2 Å. The horizontal source size, σy, and the source-to-instrument distance, L, were 0.059 mm and 14 m, respectively. The wavelength bandpass, Δλ/λ, of the Si(111) monochromator was 1.29 × 10−4. The monochromatic synchrotron beam was irradiated almost parallel to the [001] crystallographic direction while keeping the grown crystals in the growth cell. Figure 1b shows an optical micrograph of a tetragonal HEW lysozyme crystal grown in a growth cell taken from the incident direction of the monochromatic synchrotron beam. Details of the experimental procedures are the same as in our previous study.18 During these measurements, the reflected images of entire crystals for the 110 and the 11̅ 0 families of reflections were detected using a high-spatial-resolution, two-dimensional, digital CCD camera (Photonic Science X-RAY FDI 1.00:1, effective pixel size 6.45 μm × 6.45 μm). X-ray rocking curves for the 110 and the 1̅10 families of reflections were reconstructed from the reflected intensities over a region centered around the seed crystals, which corresponded to a beam spot size of 896.55 μm (139 pixels). Dislocations often extended from the interface with the cross-linked seed crystal to the surface of the grown crystal, as reported previously.32,34 However, no dislocations were observed in the analyzed regions when seed crystals cross-linked for 15 min were used because no dislocations were generated in the seed crystals, although dislocations did occur in the middle of the growth process, as shown in Figure 1c. Figure 1c shows a typical digital CCD X-ray topograph of a tetragonal HEW lysozyme crystal grown from a seed crystal that was cross-linked for 15 min; the white circle corresponds to a beam spot size of 896.55 μm. However, dislocations always originated from seed crystals when they were cross-linked for 45 min, so they were included in the analyzed regions (see Figure 3). Using a previously described procedure,18 the instrumental resolution function (IRF′),37 which takes into account the dimensions of the sample and the horizontal beam divergence (0.012 mrad), was calculated to be 1.69 × 10−3 deg. All the X-ray rocking curves were found to contain only single peaks. The fwhm of each rocking curve profile, measured for samples prepared with and without seed crystals, was evaluated using a Gaussian function. In these measurements, a set of six and two tetragonal HEW lysozyme crystals, prepared with and

of the large local strain and a decrease in subgrain size, as well as control of the misorientation between subgrains. In the case of melt growth of, e.g., Si and Ge, seed crystals are typically employed to grow the crystals. In contrast, seed crystals are seldom used for solution growth of protein crystals because of the brittleness of protein crystals. Therefore, the seed crystals must be cross-linked with glutaraldehyde because it helps to reduce the brittleness. Because chemical cross-linking changes the lattice constants of protein crystals,33 the crosslinked seed crystal is believed to induce strain in the crystal during the initial growth period. However, we have shown using X-ray topography with monochromatic synchrotron radiation that the crystal quality of glucose isomerase crystals is quite high, even when the crystals are grown from cross-linked seed crystals.32,34 This implies that strain due to cross-linked seed crystals does not give rise to the stress applied to the crystal during crystal growth. In other words, crystal growth from cross-linked seed crystals can potentially decrease the strain in the entire crystal. In this study, we demonstrate control over a large amount of local strain in tetragonal HEW lysozyme crystals by utilizing seed crystals during crystal growth, as verified by XRD rockingcurve measurements. The ideal mosaic structure that enables the collection of accurate integrated intensities of diffracted waves is also discussed using tetragonal HEW lysozyme crystals as a model protein.

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EXPERIMENTAL PROCEDURES

HEW lysozyme was purchased from Wako Pure Chemical Industries, Ltd., and used without further purification. Tetragonal HEW lysozyme crystals were grown with and without seed crystals. To grow seed crystals, first, a 80 mg/mL HEW lysozyme solution and a 1.0 M NaCl in 100 mM sodium acetate buffer solution were prepared and mixed in equal volumes. The solutions were passed through a filter with a pore size of 0.20 μm to remove any foreign particulates or large protein aggregates. The resulting solution, consisting of 40 mg/mL HEW lysozyme and 0.5 M NaCl in 100 mM sodium acetate buffer at pH 4.3, was used. The seed crystals were grown from this crystallization solution at 21 °C for 1 day via the hanging drop technique. The grown seed crystals were chemically fixed by a modified version of a previously reported method.33,34 The solution used for chemical crosslinking was a mixture of 2.5 wt % glutaraldehyde and 0.5 M NaCl in 100 mM sodium acetate buffer. The chemical cross-linking is caused by glutaraldehyde, which reacts with lysine resides on the surfaces between neighboring lysozyme molecules, and thus, this technique can not be used if there are no lysine resides on the surface of protein molecules. It has also been revealed that tetragonal HEW lysozyme crystals can not be grown again from the seed crystals when the chemical cross-linking time is too long. Therefore, the seed crystals were immersed in the cross-linking solution for 15 or 45 min at 23 °C. After cross-linking, the seed crystals were rinsed and reused because they did not dissolve in the undersaturated solution. Next, a 114 mg/mL HEW lysozyme solution and a solution of 1.0 M NaCl in 100 mM sodium acetate buffer were prepared and mixed in equal volumes. Tetragonal

Figure 1. (a) Tetragonal HEW lysozyme crystal sealed in a growth cell. (b) Optical micrograph of a grown tetragonal HEW lysozyme crystal. (c) A typical digital CCD X-ray topograph of a tetragonal HEW lysozyme crystal grown from a seed crystal that was cross-linked for 15 min. B

DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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diffraction peaks, as described in our previous work.20 This suggests that the contributions to broadening of the rocking curve profiles can be separated into the local strain, ⟨ϵ⟩, and the misorientation between subgrains, |θ − ϕ|, for tetragonal HEW lysozyme crystals grown without seed crystals, according to βadj2 = Kα + Kϵ tan2 θ. Here, βadj is the fwhm adjusted to account for the intrinsic fwhm, which is defined as βadj2 = βM2 − β02 − βins2 (β0 is the intrinsic fwhm of the rocking curve for a perfect crystal and βins is the broadening contribution due to IRF′). Figure 2 shows the relationship between βadj2 and tan2 θ

without seed crystals, respectively, were investigated; they were all approximately 2.0 mm in size.

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RESULT AND DISCUSSION First, let us focus on the broadening contributions of the rocking curve profiles for tetragonal HEW lysozyme crystals grown without seed crystals. The measured fwhm of rocking curves, βM, may be broadened by various factors as follows:38,39 βM 2 = β0 2 + βins 2 + βα 2 + βϵ 2 + βL 2 + βr 2

(1)

where β0 is the intrinsic fwhm of the rocking curve for a perfect crystal, βins is the broadening contribution due to IRF′, and βα, βϵ, βL, and βr represent the line broadening due to lattice tilting, local strain, particle size, and uniform lattice bending, respectively. The broadening contributions can be defined as follows:38,39 βα 2 = 2π ln 2|θ − ϕ|2 = Kα

(2)

βϵ 2 = 8 ln 2⟨ϵ2⟩tan 2 θ = K ϵ tan 2 θ

(3)

4 ln 2 λ 2 λ2 = KL 2 2 2 πL sin 2θ sin 2θ

(4)

βL 2 = βr 2 =

Kr w2 = 2 2 r sin θ sin 2 θ

Figure 2. Relationship between βadj2 and tan2 θ for tetragonal HEW lysozyme crystals prepared with and without cross-linked seed crystals.

(5)

where θ is the Bragg angle, λ is the wavelength of the X-ray radiation, |θ − ϕ| is the misorientation between adjacent subgrains, ⟨ϵ⟩ is the mean square strain, L is the subgrain size, w is the width of the X-ray beam in the diffraction plane, and r is the radius of curvature of the specimen. Table 1 shows the

for tetragonal HEW lysozyme crystals prepared without seed crystals. Based on a linear fit to the data, the misorientation between subgrains, |θ − ϕ|, and the local strain, ⟨ϵ⟩, were estimated to be 0.0030° and 177 μϵ, respectively. These are almost equal to previously obtained values (|θ − ϕ|, 0.0031°; ⟨ϵ⟩, 137 μϵ).20,40 This indicates that these variables are dominated by growth conditions such as temperature, concentration of protein solutions, and pH, but not by the growth method. In contrast, the average fwhm values for tetragonal HEW lysozyme crystals grown with seed crystals that were crosslinked for 15 or 45 min were almost constant for the high-order reflections, while those for the low-order reflections increased slightly, as shown in Table 1 and Figure 2. The fwhm values for high-order reflections exhibited completely different trends for tetragonal HEW lysozyme crystals grown with and without seed crystals. This suggests that there is no local strain in tetragonal HEW lysozyme crystals grown with cross-linked seed crystals. In contrast, it is thought that the increase in the average fwhm values for the low-order reflections is attributable to the specimen curvature or subgrain size, as expressed in eqs 4 and 5. Thus, it must be determined which broadening contributions are predominant. However, our previous study showed that there is no large curvature in tetragonal HEW lysozyme crystals.20 Therefore, the broadening contributions for tetragonal HEW lysozyme crystals grown with cross-linked seed crystals can be divided into the misorientation between subgrains, βα, and the subgrain size, βL:

Table 1. X-ray Rocking-Curve Data for Tetragonal HEW Lysozyme Crystals Prepared with and without Cross-Linked Seed Crystals with seed crystal βM (SD) without seed crystal reflection 220 330 440 770 11 11 0 12 12 0

cross-linking time

βM (SD)

(βadj2 − βϵ2)1/2

15 min

45 min

0.00657° (0.00118°) 0.00658° (0.00137°) 0.00660° (0.00104°) 0.00685° (0.00169°) 0.00708° (0.00200°) 0.00727° (0.00202°)

0.00632°

0.00517° (0.00041°) 0.00505° (0.00041°) 0.00510° (0.00037°) 0.00485° (0.00038°) 0.00485° (0.00041°) 0.00491° (0.00058°)

0.00471° (0.00045°) 0.00463° (0.00031°) 0.00467° (0.00047°) 0.00448° (0.00022°) 0.00437° (0.00014°) 0.00438° (0.00023°)

0.00631° 0.00629° 0.00639° 0.00625° 0.00635°

The measured FWHM values, βM, represent the average values obtained from each rocking curve. Profiles were acquired using a beam spot size of 896.55 μm (139 pixels). SD = standard deviation. a

average fwhm values, βM, from tetragonal HEW lysozyme crystals, obtained from the 110 and 11̅ 0 families of reflections. As shown in Table 1, the average fwhm values of the rocking curve profiles for the tetragonal HEW lysozyme crystals grown without seed crystals increased with increasing order of the

βadj2 ≈ βα 2 + βL 2 = Kα + KL

λ2 , sin 2 2θ

sin 2 2θ 2 sin 2 2θ βadj = Kα + KL 2 λ λ2 C

(6)

DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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their growth. It was also found that the misorientation between subgrains and the size of subgrains in the crystal decreased by growing the crystals from cross-linked seed crystals. Furthermore, the misorientation between subgrains and the subgrain size in the crystal were found to decrease with increasing chemical cross-linking time. Dislocations were observed in the analyzed regions when seed crystals cross-linked for 45 min were used. Thus, the presence of dislocations might lead to a decrease in the misorientation between subgrains in protein crystals, as seen in Figure 3. Finally, let us consider the criterion for ideal mosaic crystals of proteins. In previous researches, it has been considered that the extinction effect of protein crystals is not impressively large because the extinction distance of protein crystals is comparable to the dimension of the analyzed crystals.41 Figure 4 shows the Figure 3. Relationship between

sin 2 2θ λ2

βadj2 and

sin 2 2θ λ2

for tetragonal

HEW lysozyme crystals prepared with and without cross-linked seed crystals. The inset shows a digital CCD X-ray topograph of a typical tetragonal HEW lysozyme crystal grown from a seed crystal crosslinked for 45 min.

Figure 3 shows the relationship between

sin 2 2θ βadj2 λ2

and

sin 2 2θ λ2

for tetragonal HEW lysozyme crystals prepared with seed crystals that were cross-linked for 15 or 45 min. Table 2 Table 2. Estimated Local Strain and Misorientation between Subgrains and Size of Subgrains in Tetragonal HEW Lysozyme Crystals Grown with and without Cross-linked Seed Crystals

Figure 4. Dependence of X-ray wavelength on the extinction distance for the 110 reflection obtained from tetragonal HEW lysozyme crystals. The extinction distance of each wavelength was calculated using the structure factor estimated from X-ray structural analysis.

with seed crystal cross-linking time strain misorientation subgrain size

without seed crystal

15 min

45 min

177 μϵ 0.0030° 193 μm

no strain 0.0022° 83 μm

no strain 0.0019° 54 μm

dependence of X-ray wavelength on the extinction distance for the 110 reflection obtained from tetragonal HEW lysozyme crystals in the range from 0.3 to 5 Å under which the structural analysis of proteins is generally performed. The extinction distance of each wavelength was calculated using the structure factor (|F110| = 1096) estimated from X-ray structural analysis. As shown in Figure 4, the extinction distance of protein crystals is quite large under the short wavelength less than 1 Å, although it approximates the general dimension of the analyzed protein crystals when using the wavelength more than 3 Å. However, we have recently observed clear equal-thickness fringes in a region of the tapered glucose isomerase crystal with wedge-like edges using X-ray topography with monochromatic synchrotron radiation of 1.2 Å,32 in spite of the thickness of about 0.9 mm. We attributed these fringes to the Pendellösung effect. This finding indicates that the integrated intensities of the diffracted waves for glucose isomerase crystals are predominantly governed by the dynamical theory of diffraction, which means that the glucose isomerase crystal is a near-perfect crystal. Moreover, we indicated that the periodicity of these fringes estimated from structure factor, which is obtained from X-ray structure analysis, does not correspond with that on the topographic image, and this discrepancy might be attributed to the underestimation of the structure factor used to calculate the periodicity of the fringes. This results in the smaller extinction distance of protein crystals according to ξ ≈ VC/|Fhkl| (ξ, the extinction distance; VC, the unit cell volume; |Fhkl|, the structure factor); therefore, the extinction effect described by the dynamical theory of diffraction is considered even in the case of protein crystals.

tabulates the misorientation between subgrains, |θ − ϕ|, and the subgrain size, L, of tetragonal HEW lysozyme crystals grown with and without seed crystals, obtained from a linear fit to the data. Moreover, the subgrain size in tetragonal HEW lysozyme crystals grown without seed crystals can also be estimated by removing the broadening contribution due to the local strain in the crystal (see Table 1). From the slope of the plot in Figure 3, the misorientation between subgrains, |θ − ϕ|, and the subgrain size, L, in tetragonal HEW lysozyme crystals grown without seed crystals were estimated to be 0.0030° and 193 μm, respectively. The misorientation between subgrains estimated from Figure 3 is almost equal to that estimated from Figure 2. Thus, the estimates of the subgrain size for tetragonal HEW lysozyme crystals grown without seed crystals are considered to be reasonable. Table 2 shows the physical values estimated from tetragonal HEW lysozyme crystals grown with and without cross-linked seed crystals. As can be seen in Table 2, a large amount of local strain is accumulated in tetragonal HEW lysozyme crystals grown without seed crystals, which it is avoided by using crosslinked seed crystals. Such control over the local strain enabled by using cross-linked seed crystals would be expected to facilitate the growth of larger protein crystals because it is thought that the local strain accumulating in protein crystals could impede D

DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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The clear equal-thickness fringes were observed for a glucose isomerase crystal.32 This means that the secondary extinction described by the dynamical theory of diffraction occurs in the glucose isomerase crystal. It was estimated that the misorientation between subgrains in glucose isomerase crystals was on the order of 10−4 deg. In contrast, equal-thickness fringes have not been experimentally observed in X-ray topographs of tetragonal HEW lysozyme crystals, and the misorientation between subgrains in tetragonal HEW lysozyme crystals was estimated to be on the order of 10−3 deg. This indicates that dynamical diffraction due to multiple reflections does not occur significantly in tetragonal HEW lysozyme crystals. Thus, the threshold below which no secondary extinction occurs, as described by the dynamical theory of diffraction, is presumably on the order of 10−3 deg. Next, we must consider the extinction effect of the integrated intensities for the diffracted wave due to primary extinction because the subgrain size in protein crystals is quite large. In a typical example, such as the strongest reflection of α-quartz for which |Fhkl|/VC = 0.348 × 1024 cm−3, the subgrain size that enables accurate measurement of integrated intensities of the diffracted waves, as explained by the kinematical theory of diffraction, is calculated to be less than 1.02 μm for CuKα radiation (λ = 1.54 Å).42 That is, primary extinction is negligible if the size of subgrains in α-quartz is less than 1 μm. For the 110 reflection obtained from tetragonal HEW lysozyme crystals, however, it is estimated to be less than 10.8 μm for a wavelength of 1.2 Å, which is significantly larger than that for the strongest reflection of α-quartz. This is because the X-ray scattering power, |Fhkl|/VC, for tetragonal HEW lysozyme crystals (0.462 × 1022 cm−3) is smaller than that for α-quartz by 2 orders of magnitude. As seen in Table 2, the size of subgrains decreased significantly with increasing chemical crosslinking time; therefore, the criterion for the subgrain size of ideal mosaic crystals of proteins (L = 10.8 μm) could be achieved by further control of the roughness of the surface of seed crystals due to the chemical cross-linking. Accordingly, the crystallization of protein crystals from cross-linked seed crystals can potentially be used to obtain ideal mosaic crystals, by controlling the subgrain formation in the crystals during crystal growth, leading to the more detailed electron density for accurate 3D structures of proteins.

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by a Grant-in-Aid for Challenging Exploratory Research (No. 15K14484) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. We thank Dr. H. Sugiyama and Dr. K. Hirano of KEK for their help on synchrotron radiation X-ray topography. X-ray diffraction rocking-curve measurements were performed at the Photon Factory (PF) under the auspices of the Photon Factory Program Advisory Committee of KEK (Proposal Nos. 2014G601 and 2015G142).

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REFERENCES

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CONCLUSION XRD rocking-curve measurements, performed using tetragonal HEW lysozyme crystals grown with and without cross-linked seed crystals, indicated that local strain is largely removed in the former case. The same approach can potentially be used in neutron structural analysis, which requires large, millimetersized protein crystals, because it is thought that local strain accumulating in protein crystals can impede the growth process. It was also revealed that the misorientation between subgrains and the subgrain size decrease with increasing chemical cross-linking time. This suggests that subgrain formation in protein crystals can be controlled by using cross-linked seed crystals. Thus, the present technique of crystal growth from cross-linked seed crystals is useful for obtaining adequate mosaic structures that enable the collection of accurate integrated intensities of diffracted waves during X-ray and neutron structural analysis. E

DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

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DOI: 10.1021/acs.cgd.6b01136 Cryst. Growth Des. XXXX, XXX, XXX−XXX