Polyhedral Instability of Glucose Isomerase Crystals as Revealed by

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Polyhedral Instability of Glucose Isomerase Crystals as Revealed by Confocal Scanning Fluorescence Microscopy Denis

Vivares,‡

Eric W. Kaler, and Abraham M. Lenhoff*

Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, UniVersity of Delaware, Newark, Delaware 19716

CRYSTAL GROWTH & DESIGN 2007 VOL. 7, NO. 8 1411-1415

ReceiVed NoVember 6, 2006; ReVised Manuscript ReceiVed March 27, 2007

ABSTRACT: The polyhedral stability of a crystal during its growth plays a crucial role in determining its final quality. The polyhedral instability of glucose isomerase crystals in the presence of poly(ethylene glycol) (PEG) was observed using confocal scanning fluorescence microscopy, which enabled in situ visualization and real-time determination of the variation of protein concentration around the growing crystal. The presence of a zone depleted in protein around the crystal shows that the observed polyhedral instability occurred under diffusion-limited conditions and so was governed mainly by the supersaturation, the crystal size, and the solution viscosity. The polyhedral instability of protein crystals therefore shares some common features with the instability of crystals of inorganic or small organic molecules. 1. Introduction Once protein crystals have nucleated, the quality of the ultimate crystal depends on the growth process. This process can be seen as simply the result of two consecutive steps, namely, the transport of proteins to the growing interface followed by the incorporation of the building units (one or several protein molecules) into the crystal. The transport of protein molecules occurs in general by a combination of diffusion and convection. Convective phenomena may give rise to nonuniform transport around the growing crystal and expose the crystal surface to high supersaturation and macromolecular impurities,1 phenomena that can create severe defects inside the crystalline matrix and impair its quality. Several experiments have been performed in either microgravity or gel environments to enhance crystal quality.2,3 In such environments, convection is suppressed and transport is essentially solely via diffusion, which reduces the incorporation of aggregates and other macromolecular impurities.3 Protein transport by diffusion produces a concentration depletion zone around the crystal, the size and depth of which are controlled by the balance between the rates of diffusion and the interfacial kinetics. If transport is controlled by diffusion, the depletion zone is wider and deeper than it is when kinetics controls the process, as has been experimentally observed for protein crystals mainly in microgravity experiments and by interferometric techniques1,4-9 but also by UV microscopy.10 Under some conditions (usually at conditions of high supersaturation and/or for large crystals), crystals growing under diffusion-limited conditions can lose their polyhedral stability and their quality deteriorates. The reason for this is that the depletion zone or “feeding geometry” does not coincide with the polyhedral form of the crystal. In this case, the apexes of the polyhedral crystal are the regions most efficiently supplied with protein, and the protein concentrations around the face centers are reduced. If the anisotropy of the interfacial kinetics is not sufficient to overcome these differences, the apexes will grow faster than the face centers and the crystal will lose its * To whom correspondence should be addressed. Tel.: (+1) 302-8318989; fax: (+1) 302-831-4466; e-mail: [email protected]. ‡ Present address: Laboratoire des Interactions Mole ´ culaires et Re´activite´ Chimique et Photochimique, UMR 5623, Universite´ Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France.

stability and become skeletal or dendritic.11,12 The density of defects in such crystals is usually high, due to the trapping of impurities and to the inclusion of mother liquor in the crystal lattice. These phenomena have been observed and characterized with inorganic crystals in the gas phase, in solution, and in gels,12 but very few studies have been performed for proteins. Of these, that of Nanev et al. is notable in showing with model proteins (ferritin, porcine trypsin, and lysozyme) that under conditions where diffusion was artificially hampered, cavities could form at the center of the crystal faces.13 This corresponds to the onset of crystal instability, which then should lead to skeletal and dendritic crystal shapes. Here we augment these pioneering investigations by studying the loss of stability of glucose isomerase crystals in the presence of poly(ethylene glycol) (PEG) 10 kDa. In previous work, we studied glucose isomerase crystallization via a liquid-liquidphase separation by confocal scanning fluorescence microscopy,14 an in situ and noninvasive method also recently used to trace the diffusion of organic molecules in protein crystals.15-18 A noteworthy finding was that under some conditions, the crystallization process could lead to dendritic crystals, illustrating a loss of stability as mentioned above, and in parallel a depletion zone around the growing crystal was observed. Using the same experimental technique, we have studied here the formation of skeletal and dendritic shapes as a function of the protein and PEG concentrations. The protein concentration around the growing crystal was monitored during the crystallization process and the correlation between the depletion zone and the crystal shapes was established. 2. Materials and Methods 2.1. Preparation of Protein, PEG, and Salt Solutions. All studies were carried out in 10 mM Tris buffer, pH 7, with NaCl added to a concentration of 500 mM. Glucose isomerase from Streptomyces rubiginosus was purchased from Hampton Research as a crystalline suspension in an ammonium sulfate-rich solution, dialyzed extensively at room temperature in a 10 mL Slide-A-Lyzer cassette (from Pierce) against the 10 mM Tris pH 7 buffer and concentrated using a 10 k MWCO Amicon Ultra-4 centrifuge and filter device (from Millipore) to a final concentration of about 250 mg/mL. PEG 10 kDa was purchased as a powder from Fluka. 40% (w/v) stock solutions were obtained by dissolution of the appropriate amount of polymer in the 10 mM Tris pH 7 buffer solution. Sodium chloride (from Sigma-Aldrich) was dissolved in the same buffer solution to

10.1021/cg060787q CCC: $37.00 © 2007 American Chemical Society Published on Web 07/06/2007

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Figure 1. Confocal scanning fluorescence and bright field images of the crystal growth of glucose isomerase (C ≈ 55 mg/mL) in the presence of various PEG concentrations. The protein concentration increases linearly with the fluorescence intensity. The white arrows show the directions in which the crystal growth rates (Figure 3) and the concentration profiles (Figures 4 and 5) were characterized. Dimensions of each picture: 230 × 230 µm. obtain a final concentration of 5 M. All the buffer, protein, and salt solutions were filtered through 0.22 µm Millipore sterile filters. The 40% PEG 10 kDa solutions were filtered through 0.8 µm Millipore sterile filters. 2.2. Confocal Scanning Laser Microscopy Experiments. Confocal scanning laser fluorescence microscopy experiments were performed using an inverted Zeiss LSM 510 microscope under 20× PlanApochromat and 40× (under oil immersion) Plan Neo-Fluar objectives. The glucose isomerase was labeled with Cy5, a cyanine derivative dye (Amersham Biosciences). A solution of volume approximately 0.6 mL containing about 20 mg of glucose isomerase was dialyzed against 100 mM sodium carbonate, pH 9, and directly poured into the kit vial containing 10 mg of Cy5 crystals. The solution was then gently stirred overnight. The labeled product was separated from the unreacted dye using a Sephadex G-25 size exclusion column run with the 10 mM Tris pH 7 buffer. The label ratio (dye/protein) was about 0.6. The final labeled protein solution was concentrated using a 10 k MWCO Amicon Ultra-4 centrifuge and filter device to an approximate final concentration of 20 mg/mL. For the microscopy observations, typically 1.5 µL of the 20 mg/mL labeled protein solution was mixed with 80 µL of a 240 mg/mL unlabeled protein solution to give a final label ratio of about 0.1%. From this stock solution, 2 µL of a protein solution and 2 µL of a polymer solution of desired concentrations were then mixed vigorously and placed in a 35 mm glass bottom microwell dish (Mattek Corporation) under a 2 mL layer of paraffin oil to prevent any evaporation during the experiments. Since the present study focuses on the growth of glucose isomerase crystals, to avoid the nucleation lag time the solutions were seeded with crushed microcrystals initially grown in similar PEG/protein conditions. Under the magnification of the microscope used during our experiments, no crystals were detectable at the beginning of the experiments. We controlled the seeding step to obtain only a few crystals in each solution. The distribution of the protein concentration around the crystal was obtained by exciting Cy5 using a 5 mW HeNe (λ ) 633 nm) laser source. Cy5 then emits fluorescence light in the red part of the visible spectrum. The laser powers used were low enough to avoid any photobleaching, which could lead to a continuous decrease of fluorescence intensity with time. Z-stack sections of xy horizontal planes were acquired for distances between 0 and 20 µm from the cover-slide. The resulting stable fluorescence values averaged within a single phase over the xy plane were recorded. The overall label ratio, controlled by the proportions in which labeled and unlabeled solutions were mixed, was adjusted to minimize the scattering of fluorescence by the cover-slide. Finally, the residual intensity from the buffer was subtracted before analysis. The emitted fluorescence intensities throughout each xy plane were directly correlated to the protein concentration via a linear calibration curve, determined in the protein concentration range of interest (0-100 mg/mL).

3. Results and Discussion 3.1. Supersaturation, Depletion Zone, and Polyhedral Instability. Figure 1 shows the typical crystal shapes obtained for various polymer concentrations (7, 8, and 9%) and a fixed protein concentration (≈55 mg/mL), which correspond to

Figure 2. Glucose isomerase solubility in the presence of PEG 10 kDa (filled circles). The asterisks refer to the experimental conditions described in Figure 1, and the open circles refer to those described in Figure 6.

different degrees of supersaturation according to the solubility diagram (Figure 2). At low supersaturation (CPEG ) 7%), the protein crystal retains its stability and remains well-faceted during its growth. In parallel, the fluorescence intensities show that the protein distribution around the crystal remains quite uniform. At a higher supersaturation (CPEG ) 8%), the crystal faces are still regular when the crystal is quite small (below 50 µm), but a spherical zone of depleted protein clearly appears around the crystal. As the crystal grows, it loses its stability and a typical skeletal shape develops for which the apexes of the faces grow more quickly than the centers of the faces. At the highest supersaturation investigated (CPEG ) 9%), the crystal adopts a skeletal shape as soon as it is distinguishable by microscopy (at a size around 10 µm), and a depleted protein zone is present around it. Similar effects are observed when, for a given PEG concentration, the protein concentration is increased (data not shown). From these qualitative observations, we can see that the crystal instability is directly correlated to the presence of the depletion zone and is more significant when the supersaturation and the crystal size are large. We performed similar experiments by labeling the PEG instead of the protein, but no significant difference in the repartitioning of the PEG around the growing crystal was detected. 3.2. Crystal Growth Rates and Protein Concentration Profiles. Confocal scanning laser microscopy enabled quantification of the fluorescence intensity in the xy plane, which can be used to obtain the protein concentration profile via a calibration curve. We selected the experimental condition Cprotein ) 55 mg/mL, CPEG ) 8%, at which, as described above, the crystal is well-faceted initially but loses its stability while growing (Figure 1). We followed the increase in the crystal size with time (Figure 3) at two specific points on the growing crystal: an apex (A) and a center (C) of one face (arrows shown

Polyhedral Instability of Glucose Isomerase Crystals

Figure 3. Crystal growth of glucose isomerase along the two directions described in Figure 1, i.e., an apex (A) (solid squares) and a face center (C) (open squares) of the crystal. A linear regression of the experimental points in both directions, from which the crystal growth rate is calculated, is drawn. d ) 0 µm corresponds to the crystal surface in each direction at t ) 0 s. The vertical dashed line corresponds approximately to the time from which the crystal growth rate at C starts decreasing.

Figure 4. Protein concentration profiles at various times along the two directions described in Figure 1, i.e., an apex (A) (in gray) and a face center (C) (in color) of the crystal. d ) 0 µm corresponds in each case to the surface of the growing crystal. The dashed line corresponds to the protein concentration in the bulk solution, 55 mg/mL.

in the middle panel of Figure 1). The mean crystal growth rate V along each of these directions corresponds to the slope of the respective curve. As expected from the final skeletal shape of the crystal, the crystal growth rate is higher at A (VA ≈ 0.068 µm s-1) than at C (VC ≈ 0.045 µm s-1). It is also noteworthy that over the course of the experiment, the crystal growth rate remains almost constant at A, while at C it begins to decrease after a few minutes (vertical dashed line in Figure 3). The protein concentration profiles (Figure 4) show that, far from the crystal, the protein concentration is roughly equal to the initial protein concentration (i.e., 55 mg/mL), so the different crystal nucleation and growth events in the sample do not significantly modify the protein concentration during the time of the experiment. Furthermore, the concentration profile at A is essentially constant with time, while at C, it becomes slightly wider and deeper as the crystal grows. Finally, the interfacial protein concentration, and thus the supersaturation, is higher at A than at C. The crystal growth rate V is proportional to the concentration driving force and can be written as V ) βω(Cs - S), where β is the so-called kinetic parameter, ω is the volume of the growth unit, Cs is the protein concentration at the crystal surface, and S is the protein solubility (concentration units are number of protein molecules per unit volume). In most cases, the difference in the supersaturation (and so in (Cs - S)) at the apexes and at

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the centers of the faces is small and therefore compensated by the anisotropy of the kinetic parameter β such that the product of the two is constant.11 Thus, the growth rates are equal, and the crystal can maintain its regular well-faceted shape. In the microgravity and gel experiments mentioned earlier,1,4-9 the depletion zone was much shallower than in our case, and consequently the difference in the supersaturation between the apexes and the centers of the crystal faces was rather small. This explains why no polyhedral instability was detected. In our case, the anisotropy of the kinetic parameter is not sufficient to compensate for the difference between the two supersaturations. As a result, the apexes of the crystal grow faster than the centers of the crystal faces and a polyhedral instability develops. The critical size at which this instability occurs is a function of the supersaturation: the higher the supersaturation, the lower the critical size. As the polyhedral instability develops, the depletion zone becomes wider at C, and the diffusion path increases with time at this point on the crystal surface. The crystal surface therefore becomes less accessible with time, which contributes to the decreasing rate of the crystal growth at C, as observed in Figure 3. The polyhedral instability of protein crystals therefore appears to be very similar to the polyhedral instability of inorganic or organic crystals and results from a complex interplay between at least the supersaturation, the crystal size, and the kinetic parameter.11,12,19 3.3. Diffusion and Interfacial Kinetics: A Mixed Regime. The presence of a depletion zone around the crystal is evidence that the crystallization process is limited by the diffusive transport of the protein molecules to the crystal surface. If the crystal growth rate is completely limited by bulk diffusion and independent of the interfacial kinetics, the protein concentration at the crystal surface should be equal to the solubility. Even if the protein concentration is not known exactly at the crystal surface, for the PEG 8% condition the protein concentration at the crystal surface (≈20-30 mg/mL) (Figure 4) is much higher than the protein solubility (≈1.6 mg/mL) (Figure 2). The system is therefore in a mixed regime in which the crystal growth is controlled not only by the diffusion of growth units to the crystal surface but also by the kinetics of their incorporation into the crystal. Under purely diffusive mass transport, the relative importance of these two processes can be quantitatively estimated in terms of the dimensionless parameter k ) βδ/D. Here D is the protein diffusion coefficient and δ is the width of the depletion zone, and the value of k is calculated by balancing the diffusive flux of the protein molecules from solution to the crystal, JD, with the flux of their incorporation in the crystal JK ) β(Cs - S) ) V/ω.9,20 Assuming that the protein concentration profile in the depletion zone is linear, which is a reasonable approximation according to Figure 3, JD ) D/δ(Cb - Cs), where Cb and Cs are the protein concentrations far from the crystal (in the bulk) and at the crystal surface, respectively. Equating JD to JK means that β(Cs - S) ) D/δ(Cb - Cs) so k ) βδ/D ) (Cb - Cs)/(Cs - S). For k . 1, the crystal growth is therefore diffusion-limited, while for k , 1, the crystal growth is controlled by the interfacial kinetics. Experimentally, for the PEG 8% condition, Cb is 55 mg/mL, S is 1.6 mg/mL (see Figure 2), and the Cs values at A and C are 30 and 20 mg/mL, respectively (Figure 4). Thus, k is roughly equal to 1.9 and 0.9 at C and A, respectively. This confirms that these experiments are in a mixed regime and that crystal growth is more diffusionlimited at C than at A. 3.4. Kinetic Model under Diffusive Mass Transport. The presence of a depletion zone around the crystal proves unambiguously that diffusion of the protein molecules to the crystal

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Figure 5. Experimental (symbols) and theoretical (lines) protein concentration profiles for the situation at t ) 0 s at the apex (A) and at the face center (B) of the crystal described in Figure 1 (Cprotein ) 55 mg/mL; CPEG ) 8%). The values of the radii taken for the fits are, from top to bottom, R ) 1, 10, and 25 µm. d ) r - R, and d ) 0 µm corresponds in each case to the surface of the growing crystal.

surface is an essential form of mass transport occurring in the crystal growth process. In the following, a simple kinetic model is used to test if purely diffusive mass transport is sufficient to explain the experimental results. For that purpose, theoretical crystal growth rates and protein concentration profiles around the growing crystal were determined and then compared to the experimental values. Assuming purely diffusive transport and a linear protein concentration profile in the depletion zone, the expected growth rate is V ) ω(D/δ)(C - Cs). Assuming that the protein adds to the crystal in its normal solution tetrameric form, the volume of the growth unit, ω, can be estimated as the protein volume ≈ 260 000 Å3 (calculated using GRASP from the PDB file of glucose isomerase 1mnz). The direct measurement of D in 8% PEG by quasielastic light scattering (QLS) is complicated due to scattering by the polymer molecules. We therefore estimated this parameter from the Stokes-Einstein equation D ) kBT/ 6πηa, where a is the mean protein radius in its tetrameric form, and η is the solvent (water) viscosity; a was calculated from the protein volume assuming a spherical geometry (a ≈ 40 Å). These values yield D ≈ 5.3 10-7 cm2 s-1 from which VA ≈ 0.057 µm s-1 and VC ≈ 0.044 µm s-1. Experimentally, VA is

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constant and equal to 0.068 µm s-1, whereas VC is between 0.050 µm s-1 (at the start of the experiment) and 0.040 µm s-1 (at the end of the experiment). Thus, this model matches the growth rate fairly well, recognizing that the appropriate viscosity sampled by a protein diffusing through a polymer solution may be different from that of water.21 Furthermore, the concentration profile in a spherical geometry around a crystal growing in a quasi-steady-state mode should be C(r) ) C - (C - Cs)R/r, where r is the distance from the center of the crystal. All the parameters are experimentally determined: C is the protein concentration far from the crystal, Cs is the protein concentration at the crystal surface, and R is the crystal radius. The theoretical protein concentration profile can be compared reasonably to the experimental one at the beginning of the experiment, i.e., when the crystal is still polyhedral and well-faceted. At that time, the mean experimental crystal radius is around 25 µm. The predicted protein concentration profiles (Figure 5) are wider than the experimental ones, and better fits are obtained for much smaller values of R than the experimental crystal radius. These two analyses show that a kinetic model based on purely diffusive mass transport matches the crystal growth rates fairly well but predicts a depletion zone wider than observed. The latter discrepancy suggests that convection may play a nonnegligible role in the crystallization process. 3.5. PEG Viscosity, a Key Parameter? Two other experiments provide additional information about the key parameters governing the polyhedral instability of glucose isomerase crystals. Crystal growth was imaged and quantified under the conditions Cprotein ) 80 mg/mL, CPEG ) 6% and Cprotein ) 25 mg/mL, CPEG ) 9% (Figure 6). For these two conditions, the crystal size and the crystal growth rate (V ≈ 0.020 µm s-1) are very similar, but the final crystal shape is well-faceted in one case and skeletal in the other. This is because for Cprotein ) 25 mg/mL, CPEG ) 9%, crystal growth is limited by the diffusion of protein molecules, as emphasized by the presence of a depletion zone, whereas for Cprotein ) 80 mg/mL, CPEG ) 6%, growth is limited by the kinetics of incorporation of protein molecules at the crystal surface, as shown by the uniform concentration profile around the growing crystal. The previous examples showed that large crystal sizes and/or supersaturation could favor diffusion-limited crystal growth. Here the crystal sizes are similar, but the supersaturation is higher in the Cprotein ) 25 mg/mL, CPEG ) 9% case (≈ 40) than in the Cprotein ) 80 mg/mL, CPEG ) 6% condition (≈ 9). Such a difference in supersaturation could

Figure 6. Crystal size evolution with time (d ) 0 corresponds in each case to the crystal surface at t ) 0 s) and confocal scanning fluorescence and bright field images, for the conditions (Cprotein ) 80 mg/mL; CPEG ) 6%) and (Cprotein ) 25 mg/mL; CPEG ) 9%).

Polyhedral Instability of Glucose Isomerase Crystals

therefore be sufficient to explain the two crystal shapes observed. Clearly, one of the key parameters inducing crystal instability is the supersaturation, and not rapid crystal growth, as could have been concluded erroneously from the experiments shown in Figure 1. The difference in the viscosity of the solutions, although small (ηPEG 9% ≈ 5.1 cp and ηPEG 6% ≈ 3.2 cp) could also play a role. Nanev and Penkova observed that lysozyme crystals could lose their stability in the presence of PEG but retain their well-faceted shape with the addition of only salt.13 Similarly, in the whole crystallization zone for glucose isomerase (the area between the solubility curve and the precipitation curve), no loss of stability was detected in the presence of only ammonium sulfate (data not shown). This observation supports the idea that PEG affects the solution in important ways to favor crystal instability. Nanev and Penkova attributed this loss of stability to the slower diffusion of proteins in the more viscous polymeric solutions. Another analysis by Tanaka et al. of the formation of a depletion zone around a growing protein crystal,22 together with experiments on the crystallization in a gel of organic and inorganic molecules,23,24 also shows the importance of viscosity. However, as mentioned above, the effective viscosity experienced by a protein molecule is lower than the viscosity of the polymer solution. As a consequence, instead of drastically decreasing the diffusivity of proteins in solution, the role of PEG could be simply to reduce mass transport by convection. 4. Conclusion The polyhedral instability of glucose isomerase crystals in the presence of PEG 10 kDa has been imaged and quantified. Confocal scanning fluorescence microscopy, an in situ and noninvasive method, shows that this loss of stability is directly correlated to the presence of a depletion zone. This technique enabled quantification of the depletion zone around the growing crystal, and the crystallization mechanism was found to be in a mixed regime between a purely diffusive and a purely kinetically limited mechanism. The analysis of the protein concentration profiles showed that mass transport was provided mainly by diffusion but also by convection. Finally, the key parameters to induce the crystal instability were found to be the supersaturation, the crystal size, and probably the solution viscosity. The instability of protein crystals therefore shares some common features with the instability of crystals of inorganic or small organic molecules. This study has also shown that the PEGglucose isomerase system appears to be an excellent system to explore the polyhedral instability of protein crystals and that confocal scanning fluorescence microscopy is a good alternative to interferometric methods for visualizing the variation of protein concentrations around a growing crystal.

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Acknowledgment. We are grateful to Dr. Kirk Czymmek (Delaware Biotechnology Institute) for his help with the confocal microscopy experiments and to NASA for financial support under Grant No. NAG8-1830. The Bioimaging Facility at DBI is supported by NIH Grants P20 RR16472 and P20 RR15588 from the INBRE and COBRE programs, respectively, of the National Center for Research Resources. References (1) 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. (2) DeLucas, L. J.; Smith, C. D.; Smith, H. W.; Vijay-Kumar, S.; Senadhi, S. E.; Ealick, S. E.; Carter, D. C.; Snyder, R. S.; Weber, P. C.; Salemme, F. R.; Ohlendorf, D. H.; Einspahr, H. M.; Clancy, L. L.; Navia, M. A.; McKeever, B. M.; Nagabhushan, T. L.; Nelson, G.; McPherson, A.; Koszelak, S.; Taylor, G.; Stammers, D.; Powell, K.; Darby, G.; Bugg, C. E. Science 1989, 246, 651-654. (3) Lorber, B. Biochem. Biophys. Acta 2002, 1599, 1-8. (4) Komatsu, H.; Miyashita, S.; Suzuki, Y. Jpn J. Appl. Phys. 1993, 32, L1855-L1857. (5) Kurihara, K.; Miyashita, S.; Sazaki, G.; Nakada, T.; Suzuki, Y.; Komatsu, H. J. Cryst. Growth 1996, 166, 904-908. (6) Miyashita, S.; Komatsu, H.; Suzuki, Y.; Nakada, T. J. Cryst. Growth 1994, 141, 419-424. (7) Hou, W. B.; Kudryavtsev, A. B.; Bray, T. L.; DeLucas, L. J.; Wilson, W. W. J. Cryst. Growth 2001, 232, 265-272. (8) Otalora, F.; Novella, M. L.; Gavira, J. A.; Thomas, B. R.; Chernov, A. A. Acta Crystallogr. D 2001, 57, 412-417. (9) Otalora, F.; Garcia-ruiz, J. M.; Carotenuto, L.; Novella, M. L.; Chernov, A. A. Acta Crystallogr. D 2002, 58, 1681-1689. (10) Kam, Z.; Shore, H. B.; Feher, G. J. Mol. Biol. 1978, 123, 539-555. (11) Chernov, A. A. Modern Crystallography III. Growth of Crystals; Berlin, 1984. (12) Nanev, C. N. Prog. Cryst. Growth Charact. 1997, 35, 1-26. (13) Nanev, C. N.; Penkova, A. N. J. Cryst. Growth 2002, 237-239, 283288. (14) Vivares, D.; Kaler, E. W.; Lenhoff, A. M. Acta Crystallogr. D 2005, 61, 819-825. (15) Cvetkovic, A.; Straathof, A. J. J.; Krishna, R.; Van, der Wielen, L. A. M. J. Am. Chem. Soc. 2005, 127, 875-879. (16) Cvetkovic, A.; Straathof, A. J. J.; Krishna, R.; Van, der Wielen, L. A. M. Langmuir 2005, 21, 1475-1480. (17) Iimura, Y.; Yoshizaki, I.; Nakamura, H.; Yoda, S.; Komatsu, H. Cryst. Growth Des. 2005, 5, 301-305. (18) Iimura, Y.; Yoshizaki, I.; Yoda, S.; Komatsu, H. Cryst. Growth Des. 2005, 5, 295-300. (19) Nanev, C. N. J. Cryst. Growth 2000, 212, 516-521. (20) Chernov, A. A. J. Struct. Biol. 2003, 142, 3-21. (21) Fan, T.-H.; Dhont, J. K. G.; Tuinier, R. Phys. ReV. E 2007, 75, 011803. (22) Tanaka, H.; Inaka, K.; Sugiyama, S.; Takahashi, S.; Sano, S.; Sato, M.; Yoshitomi, S. Ann. N.Y. Acad. Sci. 2004, 1027, 10-19. (23) Oaki, Y.; Imai, H. Cryst. Growth Des. 2003, 3, 711-715. (24) Petrova, R. I.; Swift, J. A. Cryst. Growth Des. 2002, 2, 573-578.

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