In Situ Observation of Dislocations in Protein Crystals during Growth

Aug 4, 2005 - Synopsis. We successfully observed dislocations and relatively large inclusions inside lysozyme crystals during growth using advanced op...
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In Situ Observation of Dislocations in Protein Crystals during Growth by Advanced Optical Microscopy Gen Sazaki,*,†,§ Katsuo Tsukamoto,‡ Satomi Yai,# Masashi Okada,†,§ and Kazuo Nakajima† Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan, and Center for Interdisciplinary Research, Graduate School of Science, and Faculty of Science, Tohoku University, Aramaki, Aoba-ku, Sendai, 980-8578 Japan Received November 21, 2004;

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 5 1729-1735

Revised Manuscript Received May 26, 2005

ABSTRACT: We attempted to visualize defects in a tetragonal lysozyme crystal in situ by laser confocal microscopy combined with differential interference contrast microscopy (LCM-DIM). Birefringence microscopy (BM) and phasecontrast microscopy (PCM) were also employed for the in situ observations. LCM-DIM enabled us to observe the {1 1 0} surfaces of the crystals and visualize the strain fields around the dislocations normal to a light beam with sufficient contrast during growth for the first time. Relatively large inclusions (60 to 300 µm) inside the crystal could also be visualized during growth, with the use of BM and PCM. We found that the dislocations appeared in bundles and were probably generated at the periphery of the relatively large inclusions inside the crystal. The existence of the dislocations was confirmed by etching experiments, in which we observed two kinds of etch pits: those with a point bottom and those with a flat bottom; the former corresponded to the dislocations inside the crystal and the latter corresponded to microdefects. Two different critical undersaturations existed above which the pointbottomed and flat-bottomed etch pits started to appear. The critical undersaturation for the point-bottomed etch pits was definitely less than that for the flat-bottomed ones. In the central region of the spiral growth hillock were many point-bottomed etch pits corresponding to the dislocations but not contributing to the formation of spiral growth steps. Although the point-bottomed etch pits were formed in only the central region of the spiral growth hillock, the flat-bottomed ones were randomly formed all over the {1 1 0} surfaces. 1. Introduction The growth of single protein crystals of good quality is still a rate-determining step in the X-ray structural analysis of protein molecules. From the viewpoint of crystal growth, better-quality protein crystals have fewer defects. However, the mechanisms of defect generation in protein crystals during growth are still unclear. To investigate these mechanisms, it is necessary to observe defects incorporated in protein crystals. Furthermore, dislocations are defects that play an especially important role in the generation of spiral growth steps. Thus, we focused on the in situ observation of grown-in dislocations that govern the activity and characteristics of growth hillocks.1-3 Widely used conventional methods for observing dislocations include X-ray topography,4-9 atomic force microscopy (AFM),10-16 and etching techniques.17-21 X-ray topography is suitable for observing the distribution of dislocations in a whole single crystal and is advantageous in determining the Burgers vector. However, it requires the use of a synchrotron facility. Furthermore, in situ observation during growth is impossible since the protein solution has to be removed before the observation. AFM allows in situ observation of the distribution of dislocations in the molecular resolution of spiral growth centers and hollow cores that are exposed on a crystal surface. However, information from the inside of a * Corresponding author. Phone +81-22-215-2013; fax +81-22-2152011; e-mail [email protected]. † Institute for Materials Research. § Center for Interdisciplinary Research. ‡ Graduate School of Science. # Faculty of Science.

crystal cannot be obtained. Furthermore, the scan of a cantilever disturbs the protein concentration distribution and solution flow around a crystal. Etching is suitable for observing the kinds and distribution of defects in a crystal. However, one cannot observe defects during crystal growth since the crystal surface has to be slightly dissolved. Also, as with AFM, etching does not allow information to be acquired from the inside of a crystal. To reveal the correlation between elementary growth processes and defects generation mechanisms, it is necessary to develop a nondestructive in situ observation technique by which dislocations inside a crystal can be observed during growth. Optical observation techniques are promising alternatives that do not damage or disturb protein concentration distribution and flow around a crystal and are available for in situ observation of dislocations and other defects inside a crystal even during growth. Additionally, because of its simplicity, only optical microscopy is applicable to microgravity experiments in space. Therefore, birefringence microscopy (BM) (polarizing microscopy),22-25 laser confocal microscopy combined with differential interference contrast microscopy (LCMDIM),26 and phase-contrast microscopy (PCM)27,28 were determined to be potentially useful in this study. BM has conventionally been used for observing dislocations in inorganic crystals. After Bond and Andrus succeeded in visualizing edge dislocations in a Si crystal by transmission infrared BM,22 many studies were carried out for observing edge dislocations. BM was used to characterize screw dislocations viewed end-on in a Ba(NO3)2 crystal.23-25 Since a protein crystal contains many water molecules (40-60%),29 its photoelastic constants are believed to be much smaller than those

10.1021/cg049605n CCC: $30.25 © 2005 American Chemical Society Published on Web 08/04/2005

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Figure 1. A cross-sectional view of the observation cell. The bold arrow indicates the crystal-solution interface on which in situ observations were carried out.

of an inorganic crystal. Thus, observation of birefringence in a protein crystal is considered to be more difficult. However, when the strain fields around defects in a protein crystal are strong enough, it may be possible to visualize their birefringence by BM. In addition to BM, we applied LCM-DIM to the in situ observation of dislocations inside a protein crystal. LCM-DIM recently enabled us to observe the elementary growth steps (5.6 nm in height) on the {1 1 0} surfaces of a tetragonal lysozyme crystal in situ.26 Since the contrast of the elementary steps was strong enough,26 LCM-DIM was determined to be useful for compensating for the weak contrasts of dislocations. PCM can also visualize minute phase differences in transmitted light based on the difference in refractive indices. In practice, Tsukamoto et al. succeeded in using PCM to observe elementary steps on the {1 1 0} face of a tetragonal lysozyme crystal.27,28 Thus, it is also possible to use PCM for visualizing strain fields around dislocations inside a protein crystal in situ. To clarify the generation mechanism of dislocations, in this study we sought to establish a nondestructive observation technique by which dislocations inside a protein crystal can be visualized in situ during growth. Applying BM, LCM-DIM, and PCM, we succeeded in observing the dislocations inside a tetragonal lysozyme crystal during growth in situ. With the use of the etching technique, we confirmed that the contrasts observed were dislocations. We also attempted to identify the origin of the dislocations. 2. Experiment Procedures 2.1 Crystallization. Tetragonal crystals of hen egg-white lysozyme were grown from a solution containing six times recrystallized hen egg-white lysozyme (Seikagaku Kogyo Co., Ltd.) used without further purification. All other chemicals were of reagent grade. The lysozyme was dissolved in a 50 mM sodium acetate buffer (pH 4.5). A sodium chloride solution of 50 mg/mL was prepared in the same 50 mM acetate buffer. A supersaturated solution was prepared by mixing equal volumes of the lysozyme solution and the sodium chloride solution. This solution (lysozyme: 101 mg/mL) was transferred into an observation cell and incubated at 20.0 °C for 9 days to prepare suitable seed crystals in the cell. 2.2 In Situ Observations. Growing tetragonal lysozyme crystals were observed in situ by LCM-DIM, BM, and PCM. Figure 1 presents a cross-sectional view of the observation cell, made of two glass plates of 0.17 mm thickness. The thickness of the protein solution between the two glass plates was 1.0 mm. The bold arrow in the figure indicates the crystalsolution interface on which in situ observations were carried out. The tetragonal lysozyme crystals used for the observations were 0.2-0.3 mm in height, and their {1 1 0} faces observed were almost parallel to the bottom glass plate. The temperature of the observation cell was controlled at 20.0 ( 0.1 °C, using Peltier elements.

Sazaki et al. In our previous study,26 we reported that the elementary growth steps (5.6 nm in height) on a tetragonal lysozyme crystal could be observed in situ with sufficient contrast using a LCM-DIM system (modified confocal system FV300 with an inverted microscope IX70, Olympus Optical Co., Ltd.). The same system was used for the in situ observation in this study. The crystal-solution interface was illuminated by an upward incident light (He-Ne laser; wavelength 633 nm), and reflected light from this interface was observed through the crystal from below. The objective lens used for the observation was UPlanFl 10X P, and the diameter of the confocal aperture was 60 µm. The focal depth of this system was 2.5 µm. Other details were reported in our previous study.26 BM and PCM images were observed using an upright polarizing microscope and an inverted microscope (BM51 and IX71, Olympus Optical Co., Ltd.). The crystal was illuminated by upward (BM) and downward (PCM) incident light from halogen lamps, and the light transmitted through the crystal was observed. The objective lenses used for the BM and PCM observations were UplanFl 4X P and LCPlanFl 40X Ph. The lysozyme crystals were slightly dissolved by increasing the temperature to 28 and 30 °C to confirm the source of the contrasts observed by LCM-DIM. The dissolution process was monitored by LCM-DIM and PCM.

3. Results and Discussions In situ observation of a growing tetragonal lysozyme crystal was carried out by LCM-DIM and BM. Figure 2a,b depicts the LCM-DIM and BM images of the {1 1 0} face of the lysozyme crystal. In Figure 2a, growth steps on a spiral growth hillock could be observed with sufficient contrast (the broken curve in Figure 2a corresponds to one of the growth steps). The {1 1 0} surface of the crystal illustrated in Figure 2 was composed of only one well-developed spiral growth hillock. The cross mark in the figure corresponds to the center of the spiral growth hillock (sp). Growth sector boundaries (sb) and striations (st1 and st2) indicated by white arrows were observed in both the LCM-DIM and BM images, as shown in Figure 2a,b. After 2 days of crystallization, all the surfaces of 40 crystals were covered with two-dimensional (2D) islands, but after 9 days, the surfaces of five crystals were governed by the spiral growth hillocks because of the decreased supersaturation. This result did not mean that 35 crystals were dislocation-free: on these 35 crystals, a spiral growth hillock simply did not show up. Figure 2c,d corresponds to the areas of the white squares shown in Figure 2a,b. As shown in Figure 2c, the LCM-DIM image presented many line contrasts normal to a light beam with sufficient contrast (indicated by black arrows ln1 to ln6), in addition to the spiral growth steps. In contrast, the BM image (Figure 2d) contained evident white (w1 and w2) and black (b) contrasts, indicated by black arrows. The white and black contrasts were due to strain fields inside the crystal. The size of the strain fields was about 60 µm. The center of the spiral growth hillock (sp) in Figure 2c was located at the upper right part of the black contrast (b) depicted in Figure 2d. The line contrasts in the LCMDIM image could not be observed in the BM image, and the white and black contrasts in the BM image could not be observed in the LCM-DIM image. Line, white, and black contrasts in Figure 2c,d could also be observed in other lysozyme tetragonal crystals in the same way. The objective lens of 10× magnification gave the line contrasts depicted in Figure 2c. However,

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Figure 2. LCM-DIM images (a and c) and BM images (b and d) of the {1 1 0} face of the tetragonal lysozyme crystal during growth. LCM-DIM images were processed with a digital filter to remove interference fringes. In (a-d), cross marks (sp) correspond to the center of a spiral growth hillock; white thin arrows (c) represent the direction of the crystallographic c-axis. In (a) and (b), white squares correspond to the areas shown in (c) and (d); white arrows show growth sector boundaries (sb) and striations (st1 and st2). The broken curve in (a) presents an example of spiral growth steps. In (c), black arrows (ln1 to ln6) correspond to line contrasts developed normal to the light beam. In (d), black arrows indicate white (w1 and w2) and black (b) contrasts. Growth conditions: initial lysozyme concentration 101 mg/mL, NaCl 25 mg/mL (0.428 M), in 50 mM sodium acetate buffer (pH 4.5), at 20.0 °C, growth period 9 days.

an objective lens of larger magnification (e.g., 40×) did not present such a contrast. To determine the source of the contrasts in Figure 2, we raised the temperature of the observation cell from 20 to 28 °C to slightly dissolve the crystal surface, observing the surface by LCM-DIM. Figure 3a,b presents the LCM-DIM images of the crystal dissolved at 28 °C for 300 s (a) and 610 s (b). The lower right inset is a magnified view of the center of the spiral growth hillock.

Figure 3a depicts the 25 etch pits with point bottoms (indicated as pb) that could be observed. Such faint etch pits could be discerned only by LCM-DIM. As the dissolution proceeded (Figure 3b), the number of etch pits increased to 74, and they became larger. As illustrated in the inset of Figure 3b, a point-bottomed etch pit appeared at the center of the spiral growth hillock (sp), corresponding to a screw dislocation forming the spiral growth steps. From Figure 3a,b, it is difficult to judge whether those etch pits had point bottoms.

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Figure 3. Etch figures on the {1 1 0} face of the tetragonal lysozyme crystal presented in Figure 2. Images were taken by LCM-DIM. LCM-DIM images were processed with a digital filter to remove interference fringes. The crystal was slightly dissolved at 28 °C for 300 s (a) and 610 s (b). The crystal shown in (a) and (b) was further dissolved at 30 °C for 200 s (c) and 800 s (d). In (a-d), the lower right inset is a magnified view of the center of the spiral growth hillock; white thin arrows (c) indicate the direction of the crystallographic c-axis; circles labeled sp indicate the position of the screw dislocation that provided the spiral growth steps; pb and fb in the figure correspond to point-bottomed and flat-bottomed etch pits. In (a) and (b), black arrows (ln1 to ln6) correspond to the positions at which the line contrasts appear in Figure 2c. In (b), black circles (w1, w2, and b) indicate the areas at which the white and black contrasts appeared in Figure 2d; squares correspond to the area at which the line contrasts (ln1 to ln6) ended in Figure 2c.

However, it is well-known that etch pits having deep bottoms and remaining throughout dissolution are derived from dislocations and have point bottoms.30 By AFM, Hondoh and Nakada also observed the deep etch pits on tetragonal lysozyme crystals and confirmed that the etch pits had point bottoms.20 As Figure 3b indicates, besides the screw dislocation at the center of the spiral growth hillock, many dislocations existing that provided the point-bottomed etch pits. These findings demonstrated that there were many dislocations in the central region of the spiral growth hillock that did not contribute to the formation of the spiral growth steps.

In Figure 3b, it is noteworthy that the point-bottomed etch pits always appeared at the ends of the line contrasts (ln1 to ln6) shown in Figure 2c, as indicated by squares. This result implied that the lines observed in Figure 2c were the dislocations normal to a light beam within a focal depth of 2.5 µm. Figure 3b also demonstrates that many point-bottomed etch pits appeared in the regions of the white and black contrasts (w1, w2, and b) depicted in Figure 2d. This result confirmed that many dislocations were generated from the region that had strain fields of 60 µm size, shown in Figure 2d. In the case of inorganic crystals, solid

In Situ Observation of Dislocations in Protein Crystals

inclusions incorporated during growth can be the origin of dislocations, and solid inclusions can often be observed under a spiral growth hillock.31 Thus, the white and black contrasts (w1, w2, and b) revealed in Figure 2d were probably due to the strain fields around solid inclusions or around complicated liquid inclusions associated with solid inclusions. The large size of the strain fields (Figure 2d) also supported strong strain fields around solid inclusions. As depicted in Figure 2c,d, we directly and nondestructively observed for the first time contrasts during the growth of a protein crystal that could be clearly identified as grown-in dislocations and inclusions inside a protein crystal. In principle, the Burgers vectors of the dislocations can be determined from birefringence images, as reported by Maiwa et al.23 However, in this study the image contrast was too weak for detailed analysis. Since the resolution limit of X-ray topography is several tens of micrometers,6,8 optical microscopy has much better resolution for the observation of dislocations, as shown in Figure 2c. To reveal the generation mechanism of grown-in dislocations, it is important to resolve individual dislocations. Thus, the much better resolution of the LCM-DIM image is the primary advantage of this observation technique, which was especially developed for the observation of protein crystals.26 To find defects other than dislocations, the crystal depicted in Figure 3a,b was further dissolved at 30 °C (higher undersaturation condition). Figure 3c,d presents the LCM-DIM images of the crystal dissolved further at 30 °C for 200 s (c) and 800 s (d). Although the pointbottomed etch pits in Figure 3c became larger than those in Figure 3b, their number did not increase. Therefore, all grown-in dislocations in the crystal could be revealed by the dissolution at 28 °C for 610 s. (Figure 3b). After further dissolution of the crystal at 30 °C for 800 s (Figure 3d), a different type of etch pit began to appear, together with already existing point-bottomed etch pits (pb). The new etch pits were shallow (their bottoms looked bright), although their lateral size reached 5-10 µm (comparable to that of the pointbottomed ones in Figure 3d). In addition, once the shallow etch pits appeared, their bottoms did not become deeper. Thus, we judged that the new etch pits had flat bottoms (fb). Although these flat-bottomed etch pits were observed randomly all over the {1 1 0} surfaces, the point-bottomed etch pits appeared mainly in the central region of the spiral growth hillock, where large inclusions existed just below the surface (Figure 2d). A critical undersaturation existed to form the flatbottomed etch pits,21,27,28 as observed for point-bottomed etch pits in this study. Although the critical undersaturation required to form the flat-bottomed etch pits varied by several tenths of degrees Celsius, the critical undersaturation for the flat-bottomed etch pits was definitely higher than that for the point-bottomed ones. Tsukamoto et al. concluded that these flat-bottomed etch pits originated from microdefects that were invisible to optical microscopy.27,28 Continuing this work with the use of AFM, Hondoh and Nakada reported that these flat-bottomed etch pits originated from intrinsic vacancies and impurities incorporated into a lysozyme

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crystal.20,21 The appearance of the flat-bottomed etch pits at higher undersaturation (30 °C) than that of the point-bottomed ones (28 °C) confirmed that the strain energy density around the microdefects (vacancies and impurities) providing the flat-bottomed etch pits was smaller than that around the dislocations. It is well-known that impurity particles adsorbed on an inorganic crystal surface significantly influence growth kinetics.32-34 Using dislocation-free crystals of ammonium dihydrogen phosphate, Malkin et al. reported that the growth of crystals was governed by heterogeneous 2D nucleation on the crystal surfaces in a low supersaturation range.32 They concluded that impurity particles initiated heterogeneous 2D nucleation growth. In addition, the Tsukamoto group used dislocation-free crystals of barium nitrate to obtain the same results33 as those reported by Malkin et al.32 The Tsukamoto group also found that such heterogeneous 2D nucleation growth could not be observed under microgravity conditions because of the suppression of the transport of impurity particles to a crystal surface.34 We are now conducting further studies of protein crystals since the adsorption of impurity particles and resultant microdefects will also have a significant influence. Details will be reported in a forthcoming paper. The temperature of the solution was alternatively increased and decreased to clarify the correlation between the inclusion and the generation of dislocations that form spiral growth hillocks. The crystal dissolution and growth processes were observed in situ by PCM of the transmitted type. Figure 4 presents a set of PCM images of the same area during dissolution at 26.8 °C (a) and growth at 24.2 °C (b). Lysozyme concentration in the cell was 36.8 mg/mL (equilibrium at 26.5 °C); the supersaturation was σ ) -0.05 during dissolution and σ ) +0.35 during growth. Here σ is defined as σ ) ln(C/Ce), where C is protein concentration and Ce is solubility.35 The crystal observed by PCM was different from that presented in Figures 2 and 3. During dissolution (Figure 4a), point-bottomed etch pits (indicated by white arrows) began to develop in rows. Careful observation of the bottoms of the pits revealed the formation of hollow cores36,37 with dark contrast, as depicted in the inset of Figure 4a. The presence of hollow cores is evidence that these point-bottomed etch pits were generated from the outcrops of dislocations. It is noteworthy that these dislocations were outcropping above the periphery of large inclusions, appearing as white contrast in the lower right region of Figure 4a. The slightly dissolved crystal was again grown slightly at 24.2 °C (σ ) +0.35) for ∼100 min. Spiral growth hillocks developed from some of the dislocations depicted in the two white squares in Figure 4a during the growth (Figure 4b). Many dislocations were observed in the central regions of the spiral growth hillocks (inset of Figure 4a); however, a few dislocations with a screw component contributed to the development of the spiral growth hillocks. This observation indicated that, as in many inorganic crystals, sets of dislocations developed radially from inclusions or the center of the crystals as bundles, the latter of which have actually been observed by X-ray topography.6,8

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Figure 4. PCM images of the {1 1 0} face of the tetragonal lysozyme crystal during dissolution at 26.8 °C (a) and growth at 24.2 °C (b). Lysozyme concentration in the cell was 36.8 mg/mL (equilibrium at 26.5 °C); the supersaturation during the dissolution was σ ) -0.05, and during growth it was σ ) +0.35. Here σ is defined as σ ) ln(C/Ce), where C is protein concentration and Ce is solubility.35 The crystal observed by PCM was different from that shown in Figures 2 and 3. In (a) and (b), large inclusions are presented in the lower right regions of the figures. In (a), point-bottomed etch pits in rows were observed (indicated by white allows); the upper left inset is a magnified view of the point-bottomed etch pits and reveals hollow cores developed at the outcrops of dislocations. Spiral growth hillocks appeared from some dislocations inside the white squares in (a), as shown in (b).

Although small liquid inclusions do not generate dislocations, the present study clearly demonstrated that complicated inclusions did generate bundles of dislocations, some of which became the centers of spiral growth hillocks. The flat-bottomed etch pits that appeared with increased temperature, namely, at higher undersaturation (Figure 3d), were concluded to be formed at the points of microdefects or small inclusions. These microdefects did not contribute to the generation of spiral growth hillocks. Detailed results will be presented in a forthcoming paper. Conclusions We observed the {1 1 0} faces of the tetragonal lysozyme crystal in situ by LCM-DIM, BM, and PCM. Key results found in this study were as follows. (1) The strain fields around the dislocations normal to a light beam could be observed in situ during growth by LCM-DIM with much higher resolution than possible with X-ray topography. (2) Slight dissolution of the crystal at 28 °C provided point-bottomed etch pits at the outcrops of the dislocations observed in (1). At the center of the spiral growth hillock, the point-bottomed etch pit appeared, corresponding to the screw dislocation providing the spiral growth steps. (3) Further dissolution of the crystal at 30 °C yielded flat-bottomed etch pits that originated from the microdefects. (4) Relatively large inclusions incorporated in the crystal could be visualized in situ by BM and PCM. Bundles of the dislocations were generated from the large inclusions.

We directly and nondestructively observed the birefringence images of the dislocations and inclusions inside a protein crystal during growth for the first time. LCM-DIM and PCM also enabled us to observe elementary growth steps at the same time. The optical techniques reported in this study will contribute to the discrimination of individual defects inside a protein crystal and to the explanation of the defect-generation mechanisms. Acknowledgment. The authors would like to thank Dr. H. Hondoh of Ritsumeikan University for valuable discussions. One of the authors (G.S.) is grateful for the partial support by Grants-in-Aid (Nos. 16360001 and 17034007) of Scientific Research of the Ministry of Education, Science and Culture Japan. This work was partially supported by Project Research B in the Center for Interdisciplinary Research, Tohoku University. This work has been carried out as a part of “Ground-based Research Announcement for Space Utilization” promoted by the Japan Space Forum. References (1) Sunagawa, I.; Tsukamoto, K.; Yasuda, T. In Materials Science of Earth’s Interior; Sunagawa, I., Ed.; Terra Scientific Publishing Company: Tokyo, 1984; pp 331-349. (2) Durbin, S. D.; Feher, G. J. Mol. Biol. 1990, 212, 763-774. (3) Durbin, S. D.; Carlson, W. C. J. Cryst. Growth 1992, 122, 71-79. (4) Izumi, K.; Sawamura, S.; Ataka, M. J. Cryst. Growth 1996, 168, 106-111. (5) Stojanoff, V.; Siddons, D. P. Acta Crystallogr. 1996, A52, 498-499. (6) Izumi, K.; Taguchi, K.; Kobayashi, Y.; Tachibana, M.; Kojima, K.; Ataka, M. J. Cryst. Growth 1999, 206, 155158.

In Situ Observation of Dislocations in Protein Crystals (7) Hu, Z. W.; Lai, B.; Chu, Y. S.; Cai, Z.; Mancini, D. C.; Thomas, B. R.; Chernov, A. A. Phys. Rev. Lett. 2001, 87, 148101-1-148101-4. (8) Tachibana, M.; Koizumi, H.; Izumi, K.; Kajiwara, K.; Kojima, K. J. Synchrotron Radiat. 2003, 10, 416-420. (9) Capelle, B.; Epelboin, Y.; Ha¨rtwig, J.; Moraleda, A. B.; Ota´lora, F.; Stojanoff, V. J. Appl. Crystallogr. 2004, 37, 6771. (10) Malkin, A. J.; Kuznetsov, Y. G.; McPherson, A Proteins 1996, 24, 247-252. (11) Land, T. A.; Malkin, A. J.; Kuznetsov, Y. G.; McPherson, A.; De Yoreo, J. J. Phys. Rev. Lett. 1995, 75, 2774-2777. (12) McPherson, A.; Malkin, A. J.; Kuznetsov, Y. G.; Koszelak, S.; Wells, M.; Jenkins, G.; Howard, J.; Lawson, G. J. Cryst. Growth 1999, 196, 572-586. (13) Land, T. A.; De Yoreo, J. J. J. Cryst. Growth 2000, 208, 623637. (14) Yau, S.-T.; Thomas, B. R.; Vekilov, P. G. Phys. Rev. Lett. 2000, 85, 353-356. (15) Malkin, A. J.; McPherson, A. J. Phys. Chem. B 2002, 106, 6718-6722. (16) Waizumi, K.; Plomp, M.; van Enckevort, W. Colloids Surf. B 2003, 30, 73-86. (17) Monaco, L. A.; Rosenberger, F. J. Cryst. Growth 1993, 129, 465-484. (18) Malkin, A. J.; Kuznetsov, Yu. G.; McPherson, A. J. Cryst. Growth 1999, 196, 471-488. (19) Ko, T. P.; Day, J.; Malkin, A. J.; McPherson, A. Acta Crystallogr. 1999, D55, 1383-1394. (20) Hondoh, H.; Nakada, T. Jpn. J. Appl. Phys. 2004, 43, 45294532. (21) Hondoh, H.; Nakada, T. J. Cryst. Growth 2005, 275, e1423e1429. (22) Bond, W. L.; Andrus J. Phys. Rev. 1956, 101, 1211-1211.

Crystal Growth & Design, Vol. 5, No. 5, 2005 1735 (23) Maiwa, K.; Tsukamoto, K.; Sunagawa, I.; Ge, C. Z.; Ming, N. B. J. Cryst. Growth 1989, 98, 590-594. (24) Ge, C. Z.; Ming, N. B.; Tsukamoto, K.; Maiwa, K.; Sunagawa, I. J. Appl. Phys. 1991, 69, 7556-7564. (25) Ge, C. Z.; Wang, H. W.; Ming, N. B. J. Appl. Phys. 1993, 74, 139-145. (26) Sazaki, G.; Matsui, T.; Tsukamoto, K.; Usami, N.; Ujihara, T.; Fujiwara, K.; Nakajima, K. J. Cryst. Growth 2004, 262, 536-542. (27) Tsukamoto, K.; Yai, S.; Sazaki, G. J. Jpn. Assoc. Cryst. Growth 2003, 30, 81 (in Japanese). (28) Yai, S. Graduation thesis, Tohoku University, Sendai, Japan, 2003. (29) Drenth, J. Principles of Protein X-ray Crystallography; Springer-Verlag: New York, 1999; p 12. (30) Tsukamoto, K.; Giling, L. J.; Yasuda, T. J. Cryst. Growth 1982, 57, 412-427. (31) Maiwa, K.; Tsukamoto, K.; Sunagawa, I. J. Cryst. Growth 1987, 82, 611-620. (32) Malkin, A. J.; Chernov, A. A.; Alexeev, I. V. J. Cryst. Growth 1989, 97, 765-769. (33) Maiwa, K.; Tsukamoto, K.; Sunagawa, I. Corrected abstracts of the Fourth Topical Meeting on Crystal Growth Mechanism, Tokyo, January 16-17, 1990; Tokyo, 1991; pp 6770. (34) Tsukamoto, K.; Yokoyama, E.; Maruyama, S.; Maiwa, K.; Shimizu, K.; Sekerka, R. F.; Morita, T. S.; Yoda, S. J. Jpn. Soc. Microgravity Appl. 1998, 15, 2-9. (35) Sazaki, G.; Kurihara, K.; Nakada, T.; Miyashita, S.; Komatsu, H. J. Cryst. Growth 1996, 169, 355-360. (36) Frank, F. C. Acta Crystallogr. 1951, 4, 497-501. (37) Cabrera, N.; Levine, M. M. Philos. Mag. 1956, 1, 450-458.

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