Crystallization Technique of High-Quality Protein Crystals Controlling

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Crystallization Technique of High-Quality Protein Crystals Controlling Surface Free Energy Haruhiko Koizumi, Satoshi Uda, Katsuo Tsukamoto, Masaru Tachibana, Kenichi Kojima, Junpei Okada, and Jun Nozawa Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01315 • Publication Date (Web): 03 Nov 2017 Downloaded from http://pubs.acs.org on November 6, 2017

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Crystal Growth & Design

Crystallization Technique of High-Quality Protein Crystals Controlling Surface Free Energy Haruhiko Koizumi,∗,† Satoshi Uda,† Katsuo Tsukamoto,‡,¶ Masaru Tachibana,§ Kenichi Kojima,∥ Junpei Okada,† and Jun Nozawa† Institute for Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, 980-8577, JAPAN, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0871, JAPAN, Graduate School of Science, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai, 980-8578, JAPAN, Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, 236-0027, JAPAN, and Department of Education, Yokohama Soei University, 1 Miho-cho, Midori-ku, Yokohama, 226-0015, Japan E-mail: [email protected]

Abstract The relationship between protein crystal quality and growth kinetics was assessed by measuring the normal growth rates vs supersaturation of the (110) and (101) faces of dislocationfree tetragonal hen egg white lysozyme crystals at three precipitant concentrations, with NaCl as the precipitant. Assuming a two-dimensional birth and spreading nucleation mechanism, an increase in the surface free energy of the step edges was realized with increasing NaCl concentration, as established by decreases in the full width at half-maximum values of X-ray ∗

To whom correspondence should be addressed Tohoku University ‡ Osaka University ¶ Tohoku University § Yokohama City University ∥ Yokohama Soei University † IMR,

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diffraction rocking curves obtained from crystals. These results demonstrate that controlling the surface free energy of the step edges is an important aspect of obtaining high-quality protein crystals. This work also proposes a mechanism for the observed improvements in the crystal quality, based on the reduced incorporation of impurities into the steps during crystal growth.


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Introduction The three-dimensional (3D) structures of protein molecules are closely related to their functions in living tissue, so determining these structures is an important aspect of drug design and controlled drug delivery. 1 Since protein structures can be elucidated using high-brilliance synchrotron radiation, many researchers have attempted to develop high-brilliance sources and/or to improve the sensitivity of detectors. 2 The goal in such cases is to obtain accurate 3D structures of protein molecules with a resolution of less than 1.5 Å, equivalent to the length of a covalent carbon-carbon bond. However, this level of resolution has only been achieved for 9% of all protein molecules registered with the Protein Data Bank (PDB; http://www.rcsb.org/pdb/), even with the use of high brilliance synchrotron radiation facilities, such as SPring-8. This lack of high resolution structures is a direct result of the difficulty associated with growing high-quality protein crystals which have high diffraction efficiency (diffractivity). Therefore, in order to obtain high-quality specimens for analysis, it is important to understand the relationship between the growth kinetics of protein crystals and the resulting crystal quality. The growth of high-quality protein single crystals has been intensively pursued using a variety of techniques, including the application of magnetic fields, 3–9 microgravity, 10–16 solution flow, 17–20

gel-based growth media 21–28 and the ceiling crystallization method. 29,30 A growth technique

mediated by screw dislocations in conjunction with minimal supersaturation has also been proposed, 31–34 while other studies have applied an electric field to protein solutions to control the nucleation rate. 35–52 Our own group has also investigated tuning the nucleation rates of proteins by changing the frequency of an applied external electric field. 53,54 Based on thermodynamic considerations, this effect is attributed to the electrostatic energy added to the chemical potentials of the liquid and solid phases in the protein solution. The same thermodynamic effects are also expected to decrease the entropy of the solid upon applying an external electric field at 1 MHz. 55 Applying this phenomenon, our past work has demonstrated improvements in the quality of tetragonal hen egg white (HEW) lysozyme crystals grown in a 1 MHz external electric field, based on acquiring X-ray diffraction (XRD) rocking curves. 55–57 More recently, we observed an increase 3 ACS Paragon Plus Environment


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in the surface free energy of the step edges upon applying an external electric field at 1 MHz. 58 Evaluations based on thermodynamics have also determined that this result could be caused by a decrease in the entropy associated with the shape of the steps, 58 and such shape changes would, in turn, limit the incorporation of impurities into the steps during crystal growth. The surface free energy of the step edges is determined by both entropy and energy terms (Eq. (1)). For this reason, we believe that controlling the surface free energy of the step edges, by decreasing the entropy associated with the step shape and/or increasing the energy required to form steps, could play an important role in the growth of high-quality protein crystals. In fact, Chernov has shown mathematically that the average misorientation in a protein crystal decreases with increases in the surface free energy of the step edges, taking microscopic stress centers into account. 59 In order to demonstrate the importance of the free surface energy of the step edges in determining the quality of protein crystals, the present study focused on tuning the energy required to form steps. Generally, salt precipitants such as NaCl and (NH4 )2 SO4 are added when protein crystals are grown using the batch and hanging drop techniques. The addition of these salts to protein solutions adjusts the anisotropic Coulomb interactions in a way that favors crystallization. That is, certain intermolecular orientations can be attractive by adding the salts, even if the repulsion (long-range electrostatic interactions) dominates the azimuthally average potential. 60–62 It has also been reported that the long-range electrostatic interactions in protein crystals in a low ionic environment are significant, based on analyses of macrobonding and electrostatic energy transfer. 63 These earlier reports suggest that the intermolecular interactions in protein crystals can be modified by varying the concentrations of the precipitant salt. Therefore, it was anticipated that the energy required to form steps, based on the surface free energy of the step edges, could be controlled by varying the salt concentrations in protein solutions. Such changes in the surface free energy of the step edges would, in turn, be expected to change the crystal quality, similar to improvements seen in previous research involving the application of an external electric field. 58 Herein, we report that the surface free energy of the step edges increases with increasing concentrations of the precipitant salts, based on assessing the normal growth rates, R, of tetragonal HEW lysozyme crystals.


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Moreover, we demonstrate that tuning the surface free energy in this manner improves the protein crystal quality, as verified by XRD rocking-curve measurements.

Experimental Procedures The HEW lysozyme employed in this study was purchased from Wako Pure Chemical Industries, Ltd. Because commercial HEW lysozyme typically contains a high concentration of NaCl, dialysis was employed to remove NaCl from the HEW lysozyme solutions prior to experimental trials. Tetragonal HEW lysozyme crystals grown from seed crystals were used in this work. The seed crystals were obtained by mixing equal volumes of an 80 mg/mL HEW lysozyme solution and a 1.0 M NaCl solution, both in a 100 mM sodium acetate buffer, followed by filtration (pore size: 0.20 µ m) to remove any particulate impurities or large protein aggregates. The resulting solution contained 40 mg/mL HEW lysozyme and 0.5 M NaCl in a 100 mM sodium acetate buffer at pH 4.5. The seed crystals were grown from this crystallization solution at 21 ◦ C over one day via the hanging drop technique, and then chemically fixed using a modified version of a previously reported method. 64,65 Chemical cross-linking was performed by immersing the seed crystals in a mixture of 2.5 wt% glutaraldehyde and 0.5 M NaCl in a 100 mM sodium acetate buffer for 15 min at 23 ◦ C. Following cross-linking, the seed crystals were rinsed and reused because they did not dissolve in the undersaturated solution. Subsequent to the above, tetragonal HEW lysozyme crystals were grown from the cross-linked seed crystals in a growth cell (25×25×2 mm), using the batch method. The growth solutions contained 50 mg/mL HEW lysozyme together with 0.34, 0.50 or 0.68 M NaCl in a 100 mM sodium acetate buffer at pH 4.5. The growth conditions are summarized in Table 1. The supersaturation value of each HEW lysozyme solution, σ (= ln CCeq , where C is the concentration of the solution and Ceq is the solubility), was changed by varying the temperature. The resulting supersaturation values were estimated using data reported by Cacioppo et al. 66 For each NaCl concentration, the supersaturation range was almost the same, as shown in Table 1.



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Replicate in situ observations of crystal growth using digital microscopy were performed using three different seed crystals for each of the three different NaCl concentrations. The normal growth rates, R, of the (110) and (101) faces were determined by tracking the crystal dimensions along the [110] and [001] directions, as shown in Figure 1(a). The chemical cross-linking process for 15 min ensured that no dislocations were introduced from the seed crystal, although it was possible for dislocations to occur during the two-week growth process. 67 Therefore, no dislocations were present during in situ observations of the crystals, because these observations were performed over a time span of approximately seven hours. XRD rocking-curve measurements were conducted at room temperature using the BL20B beamline at the Photon Factory, part of the High Energy Accelerator Research Organization (KEK), Japan. Large protein crystals were required for these analyses, and so tetragonal HEW lysozyme crystals were grown using large quantities of the growth solutions and a thicker growth cell (25×25×4 mm), employing a growth time span of two weeks. The XRD employed a two-crystal monochromator consisting of a Si(111) crystal positioned 11 m from the source and used to select an Xray 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, ∆λ /λ , of the Si(111) monochromator was 1.29×10−4 . The monochromatic synchrotron beam was almost parallel to the ¯ [110] crystallographic direction of the crystal in the growth cell. Rocking-curve profiles for the 12 12 0 reflection were acquired using a high-spatial-resolution, two-dimensional (2D), digital CCD camera (Photonic Science X-RAY FDI 1.00:1, effective pixel size 6.45 µ m × 6.45 µ m). The beam spot size at the region being analyzed was 258 µ m (40 pixels), and therefore the instrumental resolution function (IRF’) was calculated to be 0.0012◦ according to the DuMond diagram. As shown in Figure 1(b), rocking-curve profiles were obtained from four regions (indicated by white circles), using either one or two tetragonal HEW lysozyme crystals. The associated full width at halfmaximums (FWHMs) were evaluated using a Gaussian function. No dislocations were included in the analyzed regions because dislocations did not occur from the seed crystals cross-linked for 15 min at 23 ◦ C.


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Result and discussion Figure 2 plots the crystal dimensions along the [110] and [001] directions as a function of growth time for each NaCl concentration at the highest supersaturation. The values of the supersaturation under each condition are indicated in Figure 2. It can be seen that, in both cases, the dimensions increase linearly with growth time, indicating that the supersaturation was unchanged during these measurements at each NaCl concentration. Figure 3 presents typical data summarizing the dependence of the normal growth rates of the (110) and (101) faces on the degree of supersaturation at NaCl concentrations of 0.34, 0.50 and 0.68 M. The growth rates in this figure were estimated by tracking the crystal dimensions along the [110] and [001] directions as functions of growth time, 68 similar to our previous work. 58 These data demonstrate that the dependence of the growth rate on the degree of supersaturation drastically changes as the concentration of the precipitant is varied. It seems that the critical supersaturation exists in the tendency of the change in the growth rate: one is that a higher NaCl concentration lowers the normal growth rate, and the other is that higher concentrations of the precipitant lead to more rapid normal growth rates. In addition, the errors involved in these measurements became very small. At first, we focus on the dependence of the growth rate on the degree of supersaturation at supersaturations lower than the critical supersaturation, at which a higher NaCl concentration lowers the normal growth rate. This effect implies that the surface free energy of the step edges increases with increases in the concentration of the precipitant. In situ observations were performed in a growth cell with constant volume, and thus the Helmholtz free energy should be employed when considering the free energy of the crystal surface. The Helmholtz free energy of the crystal surface, Fs , can be expressed as: Fs = Us − T Ss ,

(1)

where Us is the energy required for the formation of a step and Ss is the entropy related to the shape of the step. Therefore, the free energy of the crystal surface will increase if the energy required 7 ACS Paragon Plus Environment


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to form the steps increases or the entropy related to the shape of the steps decreases. As noted, in this work, we controlled the intermolecular interactions between protein molecules by changing the concentration of NaCl, with increases in the NaCl concentration elevating Us . The surface free energy of the step edges at each NaCl level can be estimated from the data in Figure 3. Our prior work determined that dislocations are not generated from seed crystals following 15 min of cross-linking. 67 Thus, in the case of the dislocation-free crystals grown from these seed crystals in this study, 2D nucleation and birth-and-spreading type growth should only occur on the growing faces. The formation of multiple nuclei at several points on a single growth face (representing a multiple nucleation mode) has been observed in a study using tetragonal HEW lysozyme crystals in conjunction with the same range of supersaturation. 69 Therefore, the normal growth rates observed in this experiment were analyzed using the same technique reported in the previous work. 58 In the birth-and-spreading model, the relationship between the growth rate, R, and the supersaturation, σ , is expressed as: 70–72

ln(

π Ωα 2 h 1 R ) = A − . BkB2 σ T 2 σ 1/6 (1 − e−σ )2/3

(2)

Here, α is the surface free energy of the step edge, h is the step height, Ω is the crystal volume per molecule, kB is the Boltzmann constant, T is the absolute temperature and the constant B is 6 or 3 for the (110) and (101) faces, respectively. The step height of the (110) and (101) faces is assumed to be 5.6 nm and 3.4 nm, respectively. 69 Figure 4 plots typical data summarizing the dependence of R on 1/(σ T 2 ) at all three NaCl concentrations. The surface free energy of the step edges, α , for the (110) and (101) faces can be estimated using Eqs. (5) and (6), respectively. Based on the straight line fit to the data in Figure 4(a), the α values for NaCl concentrations of 0.34, 0.50 and 0.68 M were estimated to be 0.92, 1.25 and 1.74 mJ/m2 , respectively, for the (110) face. Table 2 provides the α values estimated for the (110) and (101) faces at each NaCl concentration, obtained using different seed crystals. These data show that the α values for both faces clearly increased as the NaCl concentration was


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raised. These results confirm that the intermolecular interactions in protein crystals can be modified by changing the concentration of a precipitant salt, leading to the increase in the difference in the enthalpy between the liquid and solid phases. Similar tendency has also been observed in various inorganic salt crystals crystallized from aqueous solutions. 73,74 In addition, Figure 3 demonstrates that higher concentrations of the precipitant lead to more rapid normal growth rates at supersaturations higher than the critical supersaturation. From the point of view of the surface free energy of the step edges, it becomes difficult to form 2D nucleus with increasing the concentration of a precipitant salt. At supersaturations lower than the critical supersaturation, this process is the rate-determining step of the normal growth rates, leading to the lowering of the normal growth rates with increases in the concentration of a precipitant salt. However, the tendency is completely opposite at supersaturations higher than the critical supersaturation. This suggests that the formation of 2D nucleus is not the rate-determining step in this range. Therefore, we need to focus on the term A in Eq. (6). This term primarily predominates over the step kinetic coefficient. The step kinetic coefficient, βstep , can be expressed as follows: 75

βstep = an¯ −1 k ν+ exp(−

∆G ), kB T

(3)

where ∆G is the free energy barrier for incorporation of a protein molecule into a kink, n¯ −1 k is the kink density, a is the molecular size of the protein being incorporated and ν+ is the effective frequency of attempts by solute molecule to enter a kink by overcoming the energy barrier. Thus,

βstep increases if ∆G decreases or n¯ −1 k increases, assuming that ν+ is constant because the protein concentration is the same under each condition. In these experiments, the intermolecular interactions were found to be enhanced due to the increase in the NaCl concentration, and we believe that these stronger interactions decreased the kink density. 75 Therefore, we consider that the tendency at supersaturations higher than the critical supersaturation would be predominantly caused by the decrease in ∆G, i.e. the change in the hydration structure around protein molecules. For the crystallization from aqueous solutions, the dehydration process has significant effect on the



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growth rates of the grown crystals. 76,77 That is, the normal growth rates might become faster by the destruction of the hydration shell around protein molecules with increasing the concentration of a precipitant salt. At this point, we considered the effect of the surface free energy of the step edge on the quality of the tetragonal HEW lysozyme crystals by comparing the quality of crystals grown with the same normal growth rate. Therefore, the crystals for analysis were grown at the supersaturation slightly lower than the critical supersaturation. Table 3 summarizes the growth parameters at two NaCl concentrations, from which it is evident that the supersaturation and normal growth rates were almost equivalent in each trial, while the FWHM values for the 12 12 0 reflection (obtained by deconvoluting the broadening contribution due to IRF’ from the measured values) were completely different. The FWHM was clearly reduced at the higher NaCl concentration, corresponding to an increased surface free energy of the step edge. Thus, it is concluded that high-quality protein crystal can be grown with increasing the NaCl concentration at supersaturations lower than the critical supersaturation. The quality of crystals grown at the same temperature and lysozyme concentration but using different NaCl concentrations was also assessed. In this experiment, the NaCl concentrations of 0.45 M, 0.50 M and 0.60 M were employed in order to obtain large protein crystals enough to measure XRD rocking curves. As shown in Figure 5, the FWHM values for the 12 12 0 reflection decreased with increasing NaCl concentration, even though the supersaturation was also increased. It has been previously reported that the quality of protein crystals deteriorates with increasing supersaturation when the supersaturation is determined by the protein concentration. 78 This prior result indicates that the protein crystal quality can be improved by decreasing the growth rate. However, Figure 5 indicates that high-quality protein crystals can be grown by controlling the surface free energy of the step edge, even in the case that the growth rate is faster. In particular, the crystals grown at supersaturations higher than the critical supersaturation (NaCl concentration : 0.60 M, σ : 2.38) have quite high perfection. This suggests the possibility that high-quality protein crystals can also be grown at supersaturations higher than the critical supersaturation, leading to


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the growth of larger high-quality protein crystals. The comparison of the quality of crystals grown in this range is a future work. Therefore, modifying the surface free energy of the step edge has a remarkable effect on the protein crystal quality. Our previous work has also demonstrated that the FWHMs of rocking-curve profiles are predominantly determined by the misorientation between subgrains in the case of protein crystals grown from seed crystals. 67 This finding suggests that variations in the experimentally determined FWHM values can be attributed to changes in the misorientations, because seed crystals were also employed in the present study. Therefore, high-quality protein crystals with fewer misorientations can be achieved by increasing the surface free energy of the step edges, in good agreement with the results of theoretical calculations by Chernov. 59 Finally, we consider the mechanism by which the crystal quality is improved upon increasing the surface free energy of the step edge, focusing on supersaturations lower than the critical supersaturation. Crystallization of almost all proteins is employed in this range. Under supersaturations lower than the critical supersaturation, the formation of 2D nucleus is the rate-determining step of the normal growth rates. Chernov has suggested that impurities act as macroscopic stress centers, resulting in an average mosaic misorientation due to randomly misoriented 2D nuclei. 59 An increase in the surface free energy of the step edges could make 2D nucleus more difficult to form, leading to a flatter crystal surface. This effect, in turn, would prevent impurities from being incorporated into the steps during crystal growth, resulting in decreased misorientation. At supersaturations higher than the critical supersaturation, on the other hand, we consider that the rate-determining step could not be the formation of 2D nucleus but the destruction of the hydration shell around protein molecules. Under such high supersaturations, one intuitively consider that it is difficult to grow high-quality crystals. However, we observed that protein crystals with large surface free energy of the step edge have quite high perfection, even under high supersaturations. This might suggest that the hydration structure around protein molecules have significantly effect on the crystal quality.



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Conclusion We have found that the surface free energy of the step edges increases as the concentration of the precipitant is raised. This is attributed to increases in the energy required for step formation. We have also found that the critical supersaturation exists in the tendency of the change in the growth rate. At supersaturations lower than the critical supersaturation, the formation of 2D nucleus is the rate-determining step, leading to the reduction in misorientations in the protein crystals with increases in the precipitant concentration. On the other hand, the destruction of the hydration shell around protein molecules could be the rate-determining step at supersaturations higher than the critical supersaturation. It was also found that protein crystals with large surface free energy of the step edge have quite high perfection, even in the case that the growth rate is faster. This might suggest that the hydration structure around protein molecules have significantly effect on the crystal quality. That is, these results confirm that the protein crystal quality can be greatly affected by changes in the surface free energy of the step edge and that this factor therefore plays an important role in the growth of high-quality protein crystals.

Acknowledgement The authors thank Dr. H. Sugiyama and Dr. K. Hirano of KEK for their assistance in acquiring synchrotron radiation X-ray topography data. Monochromatic-beam X-ray topography and XRD rocking-curve analyses were performed at the Photon Factory under the approval of the Photon Factory Program Advisory Committee of KEK (Proposal Nos. 2016G673 and 2017G087).


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Table and Figure captions Table 1: Comparison of the tetragonal HEW lysozyme crystal growth conditions. The normal growth rates were determined using three different crystals under each set of initial conditions.

Table 2: Comparison of the surface free energy of the step edges, α , as estimated from the normal growth rates vs supersaturation of the (110) and (101) faces at different NaCl concentrations.

Table 3: Comparison of the FWHM values for the 12 12 0 reflections obtained from tetragonal HEW lysozyme crystals grown using the same degree of supersaturation. These data were obtained by deconvoluting the broadening contribution due to IRF’ from the experimental values. The standard deviations are also provided.

Figure 1: (a) A typical digital microscopy image of a tetragonal HEW lysozyme crystal grown using a NaCl concentration of 0.68 M, and (b) a typical digital CCD X-ray topograph of a tetragonal HEW lysozyme crystal grown from a seed crystal cross-linked for 15 min, produced using a NaCl concentration of 0.50 M. The four circles indicate the regions analyzed, which correspond to the beam spot size of 258 µ m (40 pixels).

Figure 2: Crystal dimensions along the (a) [110] and (b) [001] directions as functions of growth time using different NaCl concentrations with the greatest degree of supersaturation.

Figure 3: Typical effects of supersaturation on the growth rates of the (a) (110) and (b) (101) faces of tetragonal HEW lysozyme crystals at each NaCl concentration.

Figure 4: Typical plots of the growth rates, R, of the (a) (110) and (b) (101) faces at each NaCl concentration as functions of 1/(σ T 2 ). 19 ACS Paragon Plus Environment


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Figure 5: Trends in the quality of tetragonal HEW lysozyme crystals grown at the same temperature as the concentration of the precipitant is varied. The FWHM data were obtained by deconvoluting the broadening contribution due to IRF’ from the experimental values. The standard errors are also provided.


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Table 1: Comparison of the tetragonal HEW lysozyme crystal growth conditions. The normal growth rates were determined using three different crystals under each set of initial conditions. NaCl concentration 0.34 M (2.0 w/v%) 0.50 M (3.0 w/v%) 0.68 M (4.0 w/v%)

Lysozyme concentration Growth temperature 50 mg/mL 8∼12 ◦ C 50 mg/mL 18∼22 ◦ C 50 mg/mL 26∼30 ◦ C


Supersaturation 1.88∼2.20 1.86∼2.28 1.91∼2.15


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Table 2: Comparison of the surface free energy of the step edges, α , as estimated from the normal growth rates vs supersaturation of the (110) and (101) faces at different NaCl concentrations. Surface free energy of the step edge, α (mJ/m2 ) (110) face (101) face NaCl concentration Crystal 1 Crystal 2 Crystal 3 Crystal 1 Crystal 2 Crystal 3 0.34 M (2.0 w/v%) 0.92±0.03 0.86±0.07 0.99±0.02 1.01±0.04 0.96±0.07 1.15±0.03 Average : 0.92±0.04 Average : 1.04±0.06 0.50 M (3.0 w/v%) 1.25±0.03 1.19±0.01 1.08±0.07 1.38±0.03 1.33±0.04 1.22±0.09 Average : 1.17±0.05 Average : 1.31±0.05 0.68 M (4.0 w/v%) 1.74±0.03 1.81±0.07 1.69±0.06 1.94±0.04 1.99±0.08 1.91±0.07 Average : 1.75±0.04 Average : 1.95±0.02


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Table 3: Comparison of the FWHM values for the 12 12 0 reflections obtained from tetragonal HEW lysozyme crystals grown using the same degree of supersaturation. These data were obtained by deconvoluting the broadening contribution due to IRF’ from the experimental values. The standard deviations are also provided.

NaCl concentration 0.34 M (2.0 w/v%) 0.50 M (3.0 w/v%)

Supersaturation Normal growth rate (µ m/h) FWHM (Growth temperature) R(110) R(101) (Standard deviation) 2.04 5.37±0.03 8.56±0.06 0.0031◦ (10 ◦ C) (0.0003◦ ) 1.95 4.28±0.03 7.82±0.04 0.0022◦ (21 ◦ C) (0.0003◦ )



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Figure 1: H. Koizumi et al.


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For Table of Contents Use Only

Title: "Crystallization Technique of High-Quality Protein Crystals Controlling Surface Free Energy" Author(s): Koizumi, Haruhiko; Uda, Satoshi; Tsukamoto, Katsuo; Tachibana, Masaru; Kojima, Kenichi; Junpei Okada; Nozawa, Jun

Typical growth rates, R, for the (110) face of tetragonal hen egg white lysozyme crystals as function of 1/(σT2). It is found that the surface free energy of the step edge increases with increasing the concentration of the precipitant. It is also reveal that high-quality protein crystals with reduced misorientation can be achieved by increasing the surface free energy of the step edges, even in the case that the growth rate is faster.

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Crystallization Technique of High-Quality Protein Crystals Controlling

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