Control of Subgrain Formation in Protein Crystals by the Application of

Article pubs.acs.org/crystal

Control of Subgrain Formation in Protein Crystals by the Application of an External Electric Field H. Koizumi,*,† S. Uda,† K. Fujiwara,† M. Tachibana,‡ K. Kojima,¶ and J. 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 ¶ Department of Education, Yokohama Soei University, 1 Miho-tyou, Midori-ku, Yokohama 226-0015, Japan ‡

ABSTRACT: X-ray diffraction rocking-curve measurements were performed on tetragonal hen egg white (HEW) lysozyme crystals grown with and without the application of an external alternating current (AC) electric field. Analysis of the full width at halfmaximum (fwhm) of the rocking curves indicated that misorientation between subgrains, |θ − φ|, and local strain, ⟨ε⟩, in the crystals contributed to the broadening of the experimentally determined rocking curves for the tetragonal HEW lysozyme crystals. In particular, the data suggested that imperfections in tetragonal HEW lysozyme crystals are predominantly caused by misorientation between subgrains. Moreover, it was determined that improvements in the quality of tetragonal HEW lysozyme crystals, as assessed by a decrease in the misorientation between subgrains, can be achieved by imposing a 1 MHz electric field during crystal growth. This paper also discusses the origin of subgrain misorientation in light of the incorporation of impurities into protein crystals.

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has also been performed.23 Almost all this research used lysozyme as a model protein. Similarly, we also used hen egg white (HEW) lysozyme, which is easy to grow with relatively high-quality. We ourselves have previously studied control of the nucleation rates of proteins through the application of an external alternating current (AC) electric field. During previous studies, we succeeded in both increasing and decreasing the nucleation rates of protein crystals based on the effect of the electrostatic energy added to the chemical potentials of the liquid and solid phases.24,25 More recently, we have demonstrated that the fwhm values for X-ray rocking curves for crystals prepared in a 1 MHz external electric field are smaller than those obtained without application of the field.26 This suggests that the local crystal quality of tetragonal HEW lysozyme crystals may be improved by the application of an external electric field at 1 MHz. Moreover, our results have also indicated that not only the local crystal quality but also the overall crystal quality, that is, the homogeneity of the crystal, is improved during growth within a 1 MHz field.27 Notwithstanding these prior results, our understanding of the improvement of crystal quality in response to the application of a 1 MHz field remains incomplete. The measured fwhm of X-ray rocking curves may be increased by various effects, such as lattice tilting, lattice strain, and particle size, so the broadened profiles can be resolved into

INTRODUCTION In order to allow both structure-guided drug design and controlled drug delivery, it is important to determine the 3D structures of protein molecules. At present, these structures are primarily determined using X-ray diffraction (XRD) analysis, and therefore high-quality single crystals of proteins are required, even though these are quite difficult to obtain. This difficulty is attributed to an insufficient understanding of the potential imperfections as well as the growth mechanisms of protein crystals. Research concerning the origins of imperfections in protein crystals has been performed by several groups,1−13 and these studies have demonstrated that both impurities and dislocations have a significant effect on the quality of protein crystals. Furthermore, previous pioneering works have suggested that one possible origin of such defects may be fluctuation in the orientations of either protein molecules or smaller perfect blocks in the crystal,2,7,8 which lead to an increase in the full width at half-maximum (fwhm) values for XRD peaks. As noted, however, the origins of imperfections in protein crystals are not fully understood and therefore an improved understanding of the mechanism by which imperfections in protein crystals originate and the development of techniques to improve crystal quality are highly desirable. To date, various research groups have investigated the application of magnetic fields14−20 and microgravity1,21,22 as a means of improving the quality of protein crystals with regard to preventing an increase in the fwhm values. Moreover, research concerning the effect of the growth methods (gel and microbatch under oil) on the improvement of crystal quality © 2014 American Chemical Society

Received: June 28, 2014 Revised: August 11, 2014 Published: September 26, 2014 5662

dx.doi.org/10.1021/cg500946b | Cryst. Growth Des. 2014, 14, 5662−5667

Crystal Growth & Design

Article

an external electric field, respectively, were investigated, which had approximately 1.2 mm in dimension. By using the above procedures, the average fwhm values for the X-ray rocking curves of crystals prepared either with and without the external electric field were obtained. The fwhm values for X-ray rocking curves were also acquired while the beam spot size was varied, using a series of five tetragonal HEW lysozyme crystals prepared under each condition. Contributions to Rocking Curve Broadening. Rocking curves may be broadened by a variety of factors. Assuming that the profiles are Gaussian in shape and that the components due to lattice tilting, lattice strain, and particle size exhibit Gaussian distributions, each experimentally derived fwhm, βM, may be expressed as follows:28,29

different components depending on the lattice misorientation, the local strain, and the particle size.28,29 In this article, we report the origins of the broadening contributions to the rocking curves obtained for tetragonal HEW lysozyme crystals grown both with and without the application of an external electric field. We also discuss the origin of the misorientation between subgrains in light of the incorporation of impurities into protein crystals. This approach would be extended to a less perfect protein crystal in the future.

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EXPERIMENTAL PROCEDURES

HEW lysozyme was purchased from Wako Pure Chemical Industries, Ltd., and was used without further purification. Solutions of HEW lysozyme, at a concentration of 114 mg/mL, and 1.0 M NaCl in a 100 mM sodium acetate buffer were prepared and were mixed in equal volumes. The solutions thus produced were passed through a filter with a pore size of 0.20 μm to remove any foreign matter or large protein aggregates. The resulting solutions, containing 57 mg/mL HEW lysozyme and 0.5 M NaCl at pH 4.3, were used for the crystallization experiments. Crystallization trials were conducted at 21 ± 0.2 °C using the batch method. The details of the electrode arrangements by which the electrostatic field was applied to the protein solution have been described in ref 25. We have previously found that the strong electric field (104 V/cm) generated in the electric double layer (EDL) at the inner surface of a drop of protein solution is important with regard to controlling the nucleation rate of the proteins,30−32 so HEW lysozyme crystals grown on the sides of the electrodes were used to obtain X-ray rocking curves. The distance between the electrodes was 12 mm, and the solution volume was 2.7 mL. An external AC electric field of 400 V/cm was applied at 1 MHz, and crystals were grown over the course of 9 days, both with and without the application of this external electric field. The unit cell parameters of the crystals grown under these conditions were analyzed using XRD, as detailed in Table 1, and the

βM 2 = β0 2 + βins 2 + βα 2 + βε 2 + βL 2 + βr 2

where β0 is the intrinsic fwhm of the rocking curve for the 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. For the symmetrical Laue case, the intrinsic fwhm of the rocking curve of a perfect crystal, β0, is expressed as follows:36−38 β0 =

no electric field applied field at 1 MHz

space group

79.32 (0.15) 79.29 (0.05)

38.12 (0.02) 38.08 (0.02)

P43212 P43212

(2)

βα 2 = 2π ln 2|θ − φ|2 = Kα

(3)

βε 2 = 8 ln 2 ε tan 2 θ = Kε tan 2 θ

(4)

βL 2 = βr 2 =

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

(5)

2

Kr w = 2 r sin θ sin 2 θ 2

(6)

where |θ − φ| is the angle by which two mosaics are tilted with respect to each other, ⟨ε⟩ is the mean square strain, L is the particle size, w is the width of the X-ray beam in the diffraction plane, and r is the radius of curvature of the specimen. Substituting eqs 2−6 into eq 1, the sum of the broadening contributions, βadj, is expressed as follows:

lattice constant (SD), Å c axis

2re λ 2|Fhkl| sin 2θ πVc

where θ is the Bragg angle, re is the classical electron radius (2.82 × 10−5 Å), λ is the wavelength of the X-ray radiation, |Fhkl| is the structure factor, and Vc is the volume of the unit cell. The remaining parameters, βα, βε, βL, and βr, may be written as follows:28,29

Table 1. Comparison of Lattice Constants Obtained with and without the Application of an External AC Electric Field a axis

(1)

βadj2 = βM 2 − β0 2 − βins 2 parameters thus obtained were found to be almost identical to those previously reported in the literature, corresponding to tetragonal crystals with the P43212 space group, having lattice constants of a = 79.1 and c = 37.9 Å.33,34 It was therefore confirmed that the unit cell parameters of the protein crystals generated under these conditions were almost the same as those of the crystals produced in prior studies. XRD rocking-curve measurements were conducted at room temperature on beamline BL15B1 at the Photon Factory (PF) of the High Energy Accelerator Research Organization (KEK) in Japan. Details of the experimental procedures are described in ref 26. During these measurements, the reflected images of entire crystals for the 110 family of reflections were detected using a high spatial resolution, twodimensional, digital CCD camera (effective pixels 6.45 μm × 6.45 μm). X-ray rocking curves for the 110 family of reflections were reconstructed from the reflected intensities over a region corresponding to a beam spot size of 896.55 μm (139 pixels). Based on the above procedure, the instrumental resolution function (IRF′),35 which takes into account the dimensions of the sample and the horizontal beam divergence (0.178 mrad), can be calculated to be 1.91 × 10−3 degrees. All the X-ray rocking curves were observed to contain only single peaks. The fwhm of each rocking-curve profile measured for samples prepared with and without the external electric field was evaluated using a Gaussian function. In this study, a series of five tetragonal HEW lysozyme crystals, prepared with and without the application of

= Kα + Kε tan 2 θ + KL

Kr λ2 + sin 2 2θ sin 2 θ

(7)

where βadj2 is the fwhm adjusted to account for the intrinsic fwhm. For example, if the local strain and the particle size both make significant contributions to the increase in the fwhm, the two contributions can be separated by measuring the fwhm for three or more rocking curves at different values of the Bragg angle, θ, and consequently a straight line, representing the well-known Williamson−Hall plot, with intercept KL and slope Kε is obtained, which provides the local strain and the particle size in the crystal. Therefore, the dominant broadening contribution can be identified by focusing on two broadening contributions.

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RESULTS AND DISCUSSION Origin of Rocking-Curve Broadening for Protein Crystals. Figure 1 shows the dependence of the measured fwhm on the X-ray beam spot size for crystals prepared without the application of an external electric field. As can be seen, the fwhm values obtained from the 220 reflections increase with increasing beam size. There are two possible explanations for this phenomenon:37 (i) the specimen is significantly curved, or (ii) the specimen contains subgrains with a size comparable to 5663



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Table 2. X-ray Rocking-Curve Data for Tetragonal HEW Lysozyme Crystals Prepared with and without the Application of an External Electric Fielda measured FWHMs, βM (SD), deg

Figure 1. Dependence of the fwhm on the X-ray spot size for crystals prepared without an external electric field, based on a series of five tetragonal HEW lysozyme crystals. The variation in IRF′ values with spot size is also shown.

tan2 θ

220 330 440 770 11 11 0 12 12 0

1.23 1.84 2.46 4.31 6.78 7.40

0.00046 0.00103 0.00184 0.00567 0.01412 0.01685

no electric field 0.00669 0.00673 0.00687 0.00711 0.00713 0.00714

(0.00119) (0.00075) (0.00131) (0.00115) (0.00109) (0.00105)

applied field at 1 MHz 0.00431 0.00461 0.00446 0.00478 0.00466 0.00490

(0.00077) (0.00052) (0.00053) (0.00047) (0.00051) (0.00037)

a 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).

increasing the order of the diffraction peaks. Using eq 2, the intrinsic fwhm of the 440 reflection rocking curve of a perfect tetragonal HEW lysozyme crystal, β0, may be estimated at 6.08 × 10−5 degrees, a value that is smaller than the experimentally obtained value by 2 orders of magnitude. The intrinsic fwhm of a perfect protein crystal is quite narrow, as mentioned in the previous report.40 Thus, the effect of β0 on the measured fwhm is negligible, and consequently the fwhm adjusted to account for the intrinsic fwhm, βadj, is expressed as the value obtained by deconvoluting the broadening contribution due to IRF′, βins, from the measured fwhm, βM. Figure 2 shows the relationship between βadj2 and tan2 θ for the tetragonal HEW lysozyme crystals prepared without an

that of the beam. If the protein crystals are indeed significantly curved, eq 6 predicts that the slope of this plot should change depending on the Bragg angle, θ. That is, the slope must decrease with increasing order of the diffraction peaks, an effect that could clearly be seen for GaN films on a curved sapphire substrate.39 In the case of the tetragonal HEW lysozyme crystals prepared without an external electric field, however, the slope of the data for the 220 reflections is almost the same as that for the 440 and the 12 12 0 reflections, as shown in Figure 1. Therefore, it appears that the beam-size dependence of the measured fwhm for crystals prepared without an external electric field cannot be attributed to curvature of the specimen, but rather is due to the presence of subgrains with a size comparable to that of the beam. It can also be seen from Figure 1 that the dependence of the fwhm on the beam size, i.e. the slope of the plot, is reduced when spot sizes in the vicinity of 100 or 700 μm are applied. The fitting line is drawn using the data of spot sizes in the range of 200−600 μm. This result suggests that, under these conditions, the beam size is not comparable to the size of the subgrains in the tetragonal HEW lysozyme crystals and therefore the size of subgrains in the tetragonal HEW lysozyme crystals is in the approximate range of 200−600 μm. The values of the measured fwhm were less than the IRF′ value when the beam size was very small. This effect could occur because the 4D slit, which is positioned just prior to the specimen, is not considered when the value of IRF′ is calculated, resulting in overestimation of the IRF′. Considering that the size of the subgrains is 200 μm, the associated broadening contribution, βL, for the 220 reflection calculated from eq 5 is 0.00075°. This value is significantly smaller than the experimentally determined fwhm, βM, obtained with a beam size of approximately 900 μm, and consequently the broadening contribution due to subgrain size is negligible. Using eq 7, therefore, the sum of the broadening contributions, βadj, for the protein crystals may be expressed as follows: βadj2 ≈ Kα + Kε tan 2 θ

reflection

Bragg angle, deg

Figure 2. Relationship between βadj2 and tan2 θ for tetragonal HEW lysozyme crystals prepared without an external electric field.

external electric field. Based on the straight line fit to the data, the intercept, Kα, and the slope, Kε, were calculated to be 1.28 × 10−8 radian2 and 1.37 × 10−7 radian2, respectively. According to eqs 3 and 4, the misorientation between subgrains, |θ − φ|, and the local strain, ⟨ε⟩, were estimated to be 0.0031° and 157με, respectively. From these data, the individual broadening contributions of βα and βε can be calculated using eqs 3 and 4. The broadening contribution due to the local strain, βε, depends on the Bragg angle and, using eq 4, is calculated to be 0.0013° in the case of the 440 reflection and 0.0026° for the 12 12 0 reflection. In contrast, the broadening contribution due to the misorientation between subgrains, βα, is independent of the Bragg angle, and therefore βα is estimated to be 0.0065°, using eq 3. This value is almost equal to the experimentally derived fwhm value, βM, as presented in Table 2, suggesting that imperfections in the protein crystals are primarily the result of misorientation between subgrains.

(8)

That is, the experimentally determined fwhm for the protein crystals can be separated into the effects of local strain, ⟨ε⟩, and misorientation between subgrains, |θ − φ|. Table 2 shows X-ray rocking-curve data for tetragonal HEW lysozyme crystals prepared without an external electric field, in which the fwhm values, βM, represent average values. As shown in Table 2, the observed fwhm values slightly increased with 5664



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Effect of the Electric Field on the Misorientation between Subgrains. Figure 3 shows the dependence of the

Figure 4. Relationship between βadj2 and tan2 θ for tetragonal HEW lysozyme crystals prepared with a 1 MHz external electric field.

calculated to be 4.97 × 10−9 and 6.40 × 10−8 radian2, respectively, and the misorientation between subgrains, |θ − φ|, and the local strain, ⟨ε⟩, were estimated to be 0.0019° and 107με. These results suggest that misorientation between subgrains and the local strain are both reduced as the result of applying an external electric field at 1 MHz. However, the predominant broadening contribution in the case of the crystals prepared with an external electric field at 1 MHz was not the local strain, βε (0.0019° for the 12 12 0 reflection) but rather the misorientation between subgrains, βα (0.0040°), according to eqs 3 and 4. This is obvious because the misorientation between subgrains, βα, is almost the same as the measured fwhm values, βM, as shown in Table 2. That is, the improvement of the crystal quality under a 1 MHz applied field is achieved by a decrease in the misorientation between subgrains in the crystal. Finally, let us consider the origin of the misorientation between subgrains in protein crystals. In general, such misorientation can be attributed to dislocations in the crystals, as approximated by estimation of the dislocation density, D, as follows:29

Figure 3. Dependence of the fwhm of the 220 and the 12 12 0 reflections of crystals prepared with a 1 MHz external electric field, the 12 12 0 reflection of crystals prepared without an external electric field and IRF′ with the X-ray beam size. These data were obtained using a series of five tetragonal HEW lysozyme crystals.

fwhm on the X-ray beam size for the crystals prepared with a 1 MHz external electric field. The dependence is seen to be weaker than that for crystals grown without the application of the electric field. This suggests the possibility of reducing misorientation between subgrains in protein crystals by applying an external electric field at 1 MHz. In the case of a 1 MHz applied field, the slope of the data for the 220 reflections was almost the same as that for the 12 12 0 reflections, as seen in Figure 3, demonstrating that, in the case of the crystals grown with an electric field, the dependence of the fwhm on the beam size is also responsible for the generation of subgrains with sizes comparable to that of the beam. Moreover, it appears that the dependence of the fwhm on the beam size when the 1 MHz field is applied deviates from a straight line at a larger beam size than that observed for the samples obtained without the application of an external electric field. This result implies that the average size of the subgrains in the crystals prepared with an external electric field at 1 MHz is larger than that of the subgrains in crystals grown without the field. As a result, it is expected that the fwhm for tetragonal HEW lysozyme crystals prepared with a 1 MHz external electric field can also be separated into contributions due to the local strain, ⟨ε⟩, and the misorientation between subgrains, |θ − φ|. It is, however, difficult to discuss the sizes of subgrains in the crystals prepared with and without an external electric field in detail, since the measured fwhm values were almost equal to the broadening contribution due to IRF′, βins, at small beam sizes. Table 2 shows the fwhm values for tetragonal HEW lysozyme crystals prepared with an external electric field at 1 MHz. It should be noted that the observed fwhm values significantly improve for all diffraction peaks under a 1 MHz applied field. Figure 4 summarizes the relationship between βadj2 and tan2 θ for the tetragonal HEW lysozyme crystals prepared with an external electric field at 1 MHz. As shown in Figure 4, the slope and the intercept are significantly smaller than those obtained without an electric field (Figure 2). From the straight line fit to the data in Figure 4, the intercept, Kα, and the slope, Kε, were

D = Kα /(4.36b2)

(9)

where b is Burgers vector. For tetragonal HEW lysozyme crystals grown without an external electric field, dislocations with a ⟨110⟩ Burgers vector (111.8 Å) have been observed, exhibiting a screw character.41 According to eq 9, therefore, the dislocation density in tetragonal HEW lysozyme crystals grown without an external electric field can be estimated to be approximately 2 × 103 cm−2. However, the actual dislocation density observed by X-ray topography is ∼102 cm−2 for tetragonal HEW lysozyme crystals,41 which is smaller than the estimated value by 1 order of magnitude. This discrepancy is quite large, although the dislocation density that can be accurately determined using this X-ray rocking-curve technique ranges from 105 to 109 cm−2. These findings suggest that the origin of the misorientation between subgrains in protein crystals cannot be explained solely by the presence of dislocations in the crystal. It is known that lysozyme solutions include lysozyme dimers, which act as impurities and are incorporated into the steps on the surface during crystal growth.42,43 It is also considered that the incorporated impurities could cause the generation of dislocations in the crystal. The misorientation between subgrains was estimated to be 0.0031° for the crystals grown without an external electric field, leading to a gap between subgrains of 10.8−32.5 nm because the size of subgrains is discussed to be 200−600 μm, in the previous section. The 5665



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Figure 5. Model demonstrating the origin of misorientation between subgrains in protein crystals and the effect of an external electric field on the misorientation.

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dimensions of lysozyme molecules are 4.5 × 3.0 × 3.0 nm3, and therefore the size of dimers will be approximately 3−9 nm. This value is almost the same as the calculated gap between two subgrains, and the coincidence between these two values might indicate that the misorientation between subgrains can be attributed to the incorporation of lysozyme dimers between adjacent subgrains, as shown in Figure 5. It was also determined that the misorientation between subgrains is reduced in the case of tetragonal HEW lysozyme crystals prepared with an external electric field at 1 MHz. Using eq 9, the dislocation density in crystals grown with the external electric field at 1 MHz can be estimated to be approximately 9 × 102 cm−2 based on the misorientation between subgrains (0.0019°), and this value is approaching the dislocation density determined from X-ray topography. This finding implies that the external electric field prevents the lysozyme dimers from being incorporating into the steps on the surface during crystal growth, leading to decreased misorientation between subgrains and consequently increasing the size of the subgrains, as shown in Figure 5. However, all incorporated impurities would not contribute to the generation of dislocations in protein crystals, because the estimated dislocation density of the crystals prepared with an external electric field is larger than that observed experimentally. Therefore, it is important to suppress the incorporation of impurities into the steps on the surface during crystal growth in order to obtain high-quality single crystals of proteins. In situ observations of the crystal growth of tetragonal HEW lysozyme crystals both with and without the application of an external electric field are now underway in our laboratory.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Professor M. Saito and Dr. S. Nambu at IMRAM, Tohoku University, for X-ray analysis of lysozyme crystals. This work was supported in part by a Grant-in-Aid for Challenging Exploratory Research (Grant No. 25650017) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. 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. 2011G073 and 2012G504).

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REFERENCES

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CONCLUSION

We have found that the broadening contributions to measured X-ray rocking curves can be separated into the misorientation between subgrains and the local strain for tetragonal HEW lysozyme crystals grown with and without an external electric field. It was also determined that the imperfections in protein crystals are predominantly caused by misorientation between subgrains in the crystal. Moreover, this study showed that improvement of the quality of crystals grown under a 1 MHz applied field is achieved by a decrease in the misorientation between subgrains in the crystal. This might be attributable to suppression of the incorporation of lysozyme dimers into the steps on the surface during crystal growth. 5666



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Control of Subgrain Formation in Protein Crystals by the Application of

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