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First Direct Observation of Impurity Effects on the Growth Rate of Tetragonal Lysozyme Crystals under Microgravity as Measured by Interferometry Yoshihisa Suzuki,*,† Katsuo Tsukamoto,‡ Izumi Yoshizaki,§ Hitoshi Miura,¶ and Takahisa Fujiwara# †

Institute of Technology and Science, Tokushima University, 2-1 Minamijosanjima, Tokushima 770-8506, Japan Tohoku University, Aramaki, Aoba, Sendai 980-8560, Japan § Japan Aerospace Exploration Agency (JAXA), 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan ¶ Nagoya City University, 1 Yamanohata, Mizuho-cho, Mizuho-ku, Nagoya 467-8501, Japan # Institute of Socio-Arts and Sciences, Tokushima University, 1-1 Minamijosanjima, Tokushima 770-8502, Japan Downloaded by UNIV OF LETHBRIDGE on September 9, 2015 | http://pubs.acs.org Publication Date (Web): September 9, 2015 | doi: 10.1021/acs.cgd.5b00456

‡

S Supporting Information *

ABSTRACT: The normal growth rates R and apparent step velocities (lateral growth rates of a spiral hillock) V of tetragonal hen egg-white lysozyme (HEWL) crystals were for the first time measured by Michelson interferometry in the international space station (as part of the NanoStep project) using commercialized HEWL samples containing 1.5% impurities. A significant increase in V under microgravity was confirmed compared to step velocities Vstep on the ground, while a decrease in R was also confirmed compared to that in the purified solution under microgravity as expected. Because of exact measurement of growth rates, kinetic analyses of R were conducted as a function of supersaturation, σ (σ ≡ ln(C/Ce), where C is the concentration; Ce is the solubility), using a spiral growth model and a two-dimensional (2D) nucleation growth model. For both models over a wide range of σ, R in the impure solution was significantly lower than that in the purified solution. The degree of the suppression of impurity effects was also evaluated using the difference in Vp and Vi, where Vp is the apparent step velocity in the purified solution, and Vi is that in the impure solution. The difference between Vp and Vi was smaller than the difference in step velocities on the ground, Vstep,p and Vstep,i, where Vstep,p is the step velocity in the purified solution, and Vstep,i is the step velocity in the impure solution.

1. INTRODUCTION

concentrations of impurity in crystals, protein in crystals, impurity in bulk solution, and protein in bulk solution, respectively. They showed that all Keff values of the crystals which are grown in a space shuttle (STS 95 mission) are less than that of the crystals grown on the ground. Especially, even in the case of impurities (insulin and cytochrome c) whose segregation coefficients k (k ≡ Cic/Cis) in HEWL crystals are less than unity, Keff values in space are much less than those on the ground. They concluded that these lower amounts of impurity incorporation are inconsistent with an impurity depletion zone (IDZ) hypothesis3 and they need other factors to explain strong microgravity purification effects, for instance, the dependence of Keff on growth rate, surface morphology, and so on. Chernov et al. used gel to suppress convection, and observed the crystallization process of apoferritin with the existence of

The suppression of impurity effects on protein crystallization under microgravity would be related to the origin of the higher X-ray resolution limits observed for space-grown crystals, and the mechanism by which the impurity effects are suppressed would be useful for producing high-quality protein crystals on the ground. NASA has reported that about 20% of the protein crystals grown in space exhibit higher X-ray resolution limits than those of the best crystals grown on the ground.1 Although this is the main reason so many projects on protein crystallization in space have been conducted, no one has fully clarified the mechanisms by which microgravity improves the quality of many protein crystals. To clarify the mechanisms, several space and groundbased convection-free experiments have been conducted. We introduce some representative studies as follows. Thomas et al. measured effective segregation coefficients Keff (Keff ≡ (Cic/Cpc)/(Cis/Cps)) of some impurities to be incorporated into hen egg-white lysozyme (HEWL) crystals and ferritin crystals.2 Here Cic, Cpc, Cis, and Cps show © XXXX American Chemical Society

Received: April 2, 2015 Revised: August 28, 2015

A

DOI: 10.1021/acs.cgd.5b00456 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Downloaded by UNIV OF LETHBRIDGE on September 9, 2015 | http://pubs.acs.org Publication Date (Web): September 9, 2015 | doi: 10.1021/acs.cgd.5b00456

Crystal Growth & Design

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holoferritin dimer as an impurity.3 They proved the formation of an IDZ of the holoferritin dimer around the apoferritin crystals, and suggested that the IDZ may reduce protein impurity incorporation and improve crystal quality in microgravity conditions. Van Driessche et al. also used gel to suppress convection, and measured two-dimensional (2D) nucleation rates Js and step velocities Vstep of tetragonal HEWL crystals with gelled and ungelled solutions.4 They used pure and impure HEWL solutions for the measurements and compared the results of the impure solution with those of the pure solution. Js values with the gelled solution were larger than that with the ungelled solution. They explained that a gel fiber act as a heterogeneous nucleation site as an impurity. Suppression of Vstep in an impure solution was relaxed in gelled solution; thus, they considered that gelled solution also acted as a diffusive impurity filter. Adawy et al. achieved the other type of ground-based convection-free experiments by growing crystals below the top wall of growth containers (ceiling crystallization method).5 They measured effective segregation coefficients of several impurities to be incorporated into tetragonal and monoclinic HEWL crystals. They concluded that the crystals grown by the ceiling method incorporated less impurity molecules in the regime of Keff > 1, while that incorporated more in the regime of Keff < 1 as expected from the viewpoint of IDZ formation around the crystals. However, they found that even in the regime of Keff < 1 the crystals grown by the ceiling method surprisingly show higher resolution. They suggested that this result is primarily due to slow growth rates of the crystals grown by the ceiling method. From the results of the above previous studies, in situ observation of growth interfaces of a crystal in space is indispensable to clarify the kinetic effects on the incorporation mechanisms of impurity molecules into protein crystals. Although Van Driessche et al. conducted in situ observation of growth interfaces under convection-free conditions, as they concluded, gel itself acts as a complex impurity, and thus, growth experiments in gelled solution are not ideal convectionfree experiments. The convection-free condition has been believed to suppress the transport of larger-sized impurities, given their smaller diffusion constant than that of the growth unit; suppression of impurity transport might improve the quality of protein crystals.6 In situ observation of growth interface enables us to clarify the suppression of impurity transport by the increase in the normal growth rates R in microgravity conditions. In 2012, for the first time, Tsukamoto et al. successfully measured R of tetragonal hen egg-white lysozyme (HEWL) crystals in purified and impure solutions as a function of supersaturation σ (σ ≡ ln(C/Ce), where C is the concentration of lysozyme and Ce is the solubility) in the NanoStep project of the international space station (ISS); with the data obtained in the NanoStep project, we can directly confirm the above supposition. To confirm it, first, we will compare R versus σ data in an impure solution in space with those in a purified solution in space. The comparison will also clarify impurity effects on growth kinetics of HEWL crystals ideally, since the complicated effects of convectional flows are negligible in ISS experiments. Second, we will discuss the degree of the suppression of impurity effects under microgravity. The difference between the apparent step velocities in a pure solution Vp and those in an impure solution Vi under microgravity is characterized, and

then the difference is compared with the difference in the step velocities Vstep,p and Vstep,i on the ground using previously published data.

2. EXPERIMENTAL SECTION Normal growth rates R and apparent step velocities (lateral growth rates of spiral hillocks) V were measured using the changes in several sets of interferograms on the {110} surface of a tetragonal lysozyme crystal on board the ISS. Details of the measurements and calculations have been described by Yoshizaki et al.7 Impure HEWL (recrystallized six times, 98.5% purity) was purchased from Seikagaku Kogyo, Co., Ltd., and used without further purification. The starting solution comprised 30 mg mL−1 HEWL and 25 mg mL−1 NaCl dissolved in 50 mM sodium acetate buffer (pH 4.5). This solution and a chemically fixed seed crystal8 were placed in Cell 3, which is the third in situ observation cell for the NanoStep project. All the conditions for the Cell 3 experiment except for the impurity content were the same as those in Cell 1 (the first cell for the NanoStep project), in which purified HEWL (99.8% purity) solution was used. Purification was conducted using the method previously described.9 Supersaturation σ of the solution was controlled by changing the temperature with Peltier elements. We measured R as a function of σ, and compared the R values of Cell 3 (Impure cell) with those of Cell 1 (Pure cell) to determine any impurity effects. 3. RESULTS AND DISCUSSION 3.1. Evaporation of Water from Impure Cell. As previously and precisely reported by Fujiwara et al.,10 the slight evaporation of water from Impure cell (2.8% by volume) occurred during the long sojourn in the ISS. Although such evaporation unfortunately altered solution properties, we successfully corrected σ by measuring a new solubility curve with careful consideration of the influence of the evaporation on the solution properties. The essence of this correction is as follows. First, the amount of the evaporation was estimated using the shift of an equilibrium temperature. Second, protein and salt concentration after the evaporation were determined. Third, a new solubility curve at the new salt concentration was measured. Finally, σ was corrected using the solubility curve. In this paper, the precise evaluation of R versus σ plots was conducted using the corrected σ values for the data from Impure cell. 3.2. R versus σ Plots as Raw Data. Measurements of R or V using interferograms of crystal surfaces have been conducted for many years.11 We conducted basically similar but more sophisticated measurements of R and V in space.7 Interferograms usually show many growth hillocks as shown in the inset of Figure 1a and b, and each hillock often results in various R and V. We can select an ideal-looking (symmetric and isolated) growth hillock from them, and R and V on the ideal-looking hillock usually show maximum values. In this section, first, we show raw and scatter R data on the several growth hillocks. And then, we selected the maximum R measured on an ideal growth hillock at a given σ for the discussion on impurity effects. Figure 1a shows the raw R values from the Pure cell (99.8% purity, open circles) plotted against σ; the maximum R values at a given σ are shown as large circles. Figure 1b similarly shows the results from Impure cell (98.5% purity, filled circles). These R values are measured repeatedly (from once to six times) at various σ, and two to four points of slopes of growth hillocks B



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are selected simultaneously for the measurements from interferograms as shown in the inset of Figure 1a and b. The data is scattered in both plots, since R depends on the condition of the growth hillocks on the crystal face, and there are many kinds of growth hillocks as shown in interferograms of Figure 1a and b. Note that the extent of the variation of the data shown in Figure 1 is much larger than that of the probabilistic error of each plot. The size of the probabilistic error is smaller than the radius of large circles shown in Figure 1. By comparing Figure 1a with b, the R values of Pure cell seem to be larger than those of Impure cell, but the difference is not clear. Thus, we adopted the maximum R values from both plots to highlight the differences, since the maximum R would reflect the most ideal growth condition at a growth hillock for a given σ. Since the growth rate of crystal faces is determined by the fastest rate of growth hillocks, we discuss the kinetics of the fastest growing hillocks.12 Figure 1c compares the maximum R values of Impure cell with those of Pure cell, and clearly shows that the maximum R values of Impure cell are significantly smaller than those of Pure cell under almost all supersaturation conditions. Thus, the suppression of R is probably due to the existence and adsorption of impurities on the growth interfaces of the crystals. The underlying mechanism by which the impurities affect R is still unclear, however. To explore the phenomenon in greater detail, we analyzed R versus σ plots using two representative crystallization processes, the spiral and two-dimensional (2D) nucleation growth modes. Before discussing these growth modes, we must determine the critical supersaturation σcrit point from which 2D nucleation growth mode becomes dominant at larger σ. To estimate σcrit, a comparison of the apparent step velocities V with the step velocities Vstep should be conducted. Here V is defined as a rate of lateral expansion in the ⟨110⟩ directions of spiral growth hillocks on the {110} faces of tetragonal lysozyme crystals (Figure 2a). V was measured using a two-beam interferometer, as reported in ref 7. V corresponds to the average of the step velocities Vstep unless a new 2D nucleation occurs on a terrace between adjacent spiral steps (Figure 2b). When the 2D nucleation occurs on the terrace, a period, within which elementary steps (upper spiral step and steps around the 2D islands) sweep across the terrace completely, becomes shorter as long as the interval of adjacent steps is sufficiently larger than the width of catchment area around each step. This shorter period results in the increase in V, and then, V values becomes larger than Vstep ones. Since Vstep was obtained via in situ measurements of the advancement of elementary steps, it does not include the effects of 2D nucleation. 3.3. Apparent Step Velocities V vs C − Ce. The apparent step velocities V of Pure cell (open circles) and Impure cell (filled circles) are plotted against C − Ce in Figure 3a, since Vstep is known to be proportional to C − Ce when solute molecules are incorporated into a crystal directly at kink sites on the steps at a constant kink density.12 Larger circles indicate the maximum V values, which are defined similarly to the maximum R values shown in Figure 1a and b, whereas the smaller circles indicate the other raw V values. In Figure 3a, the trend in V values tends to curve slightly upward at first, and then, the values steeply increase in the higher C − Ce region. This steep increase in V is probably due to 2D nucleation on a terrace between two adjacent spiral steps as shown in Figure 2b. For example, if one nucleus emerges on a terrace, the step density suddenly triples around the nucleus, and as a result, the apparent step velocity V at this terrace steeply increases and

Figure 1. Normal growth rates R versus supersaturation σ under microgravity conditions. (a) R values for Pure cell (open circles, purified HEWL) versus σ in microgravity. Larger circles show the maximum values for a given σ. Inset is an interferogram of the {110} face of the tetragonal HEWL crystal. White arrows show the points at which we measured R simultaneously. Vertical and horizontal lines indicate the ⟨110⟩ and ⟨001⟩ directions, respectively. (b) R values for Impure cell (filled circles, in an impure HEWL) with supersaturation σ in microgravity. Larger circles show the maximum values for a given σ. Inset is an interferogram of the {110} face of the crystal used in the Impure cell. White arrows show the measurement points. (c) Comparison of maximum R values for Impure and Pure cells. The inset in (c) shows an expansion of the rectangular box. The maximum R values of Impure cell are clearly lower than those of Pure cell over a wide range of σ. C




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Figure 2. (a) Schematic illustration of the cross-section of a spiral growth hillock. The dashed pyramid grows and becomes the solid one over time. Here, the normal growth rate R is the rate of the advance of the hillock surface normal to the {110} face of the tetragonal lysozyme crystal. The apparent step velocity V is that parallel to the ⟨110⟩ direction of the crystal. (b) Schematic enlargements of the bold rectangle shown in (a). The upper box shows the steps on the hillock in the spiral growth mode. In this case, V corresponds to the step velocity Vstep. The lower box shows the steps in the 2D nucleation growth mode. In this mode, new 2D islands nucleate on a terrace between adjacent spiral steps. Clearly, in this case V becomes faster than Vstep. To analyze the growth mechanisms in more detail, the determination of the critical supersaturation σcrit, at which the transition from the spiral to the 2D nucleation growth mode occurs is necessary.

Figure 3. (a) Raw apparent step velocities V of Pure cell (open circles) and Impure cell (filled circles) at C = 30 mg mL−1 (Pure cell) and 30.8 mg mL−1 (Impure cell) versus C − Ce under microgravity. Larger circles indicate the maximum V values at a given C − Ce. (b) Step velocities Vstep of a purified sample measured on the ground at C = 40 mg mL−1 by Van Driessche et al.13 (open squares) and its quadratic fitting curve (solid curve) are shown with the maximum V values of Pure cell and Impure cell. Dashed vertical lines in both graphs show the critical supersaturation condition (C − Ce ≈ 17 mg mL−1) between the two growth mode regions.

becomes larger than Vstep. To confirm this supposition, the Vstep values versus C − Ce measured for purified samples on the ground by Van Driessche et al.13 were plotted against the maximum V values as open squares in Figure 3b. Both V values of Pure cell and Impure cell become larger than the Vstep values around C − Ce ≈ 17 mg mL−1. The Vstep results for the purified solution on the ground are nearly the same as the V values for Pure cell (as a purified solution) under microgravity at lower supersaturation (C − Ce < 17 mg mL−1), although the purity of the former sample (99.99%) was somewhat higher than that of the latter (99.8%). Even a slightly lower purity often results in the suppression of step velocity. However, at higher supersaturation (C − Ce ≥ 17 mg mL−1), V steeply increases and becomes larger than Vstep, since the 2D nucleation growth mode becomes dominant. The V values of Impure cell, which are slightly lower than those of Pure cell, also become larger than Vstep near this condition. Thus, around C − Ce ≈ 17 mg mL−1, there is a critical supersaturation condition between the two different growth modes, where the 2D nucleation growth mode starts on the spiral hillock. The critical supersaturation values σcrit of Pure cell and Impure cell were calculated as 0.84 and 0.80, respectively. The difference in σcrit between the cells is

due to the slight evaporation of water (2.8% by volume) which occurred during the Impure cell experiment, as already described in section 3.1. The concentration of the Impure cell solution was increased to 30.8 mg mL−1, which is slightly larger than that of Pure cell (30.0 mg mL−1), and the Ce of Impure cell at the same temperature was also lower than that of Pure cell owing to the increase in salt concentration (from 25.0 to 25.7 mg mL−1). 3.4. Spiral Growth Mode. In this study, in the low supersaturation region, kinetic analyses using the spiral growth mode were adopted, since the crystals used for Pure cell and Impure cell show spiral hillocks on the {110} faces. The crystals were obtained by regrowth on chemically fixed seed crystals, and slight differences in the lattice constants between the seed and regrown crystals induced screw dislocations on the {110} faces. In the case of the spiral growth mode, the normal growth rates R are expressed as D



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R = α1T (1 − e−σ )σ

shown in eq 2. The data from refs 14 and 15 were also calculated by assuming exact-circle-shaped 2D nuclei, and thus, the above anisotropy was not considered. In the next section, we will show calculations of γ based on the 2D nucleation growth model. 3.5. 2D Nucleation Growth Region. Under high supersaturation conditions, the 2D nucleation growth mode is considered. In this study, a polynucleation model is adopted, since all crystals we used in this study have a few spiral hillocks, and in such a situation, mononucleation model cannot be allowed. This model is expressed as

(1)

where T represents absolute temperature. α1 is expressed as

α1 ≡

hkBβst C 19γ

(2)

where h is the step height (11.2 nm as an elementary step of a spiral hillock14); kB is the Boltzmann constant; βst is a step kinetic coefficient; C is the concentration; and γ is the surface free energy (the precise derivation of eqs 1 and 2 is given in the Supporting Information). From eq 1, R should be proportional to T(1 − exp(−σ))σ in the case of spiral growth. R versus T(1 − exp(−σ))σ plots are shown in Figure 4. The solid and dashed

⎛ ⎞ α R ⎟ = C − 22 ln⎜ 1/6 −σ 2/3 T σ σ (1 ) e − ⎝ ⎠

(3)

where α2 is given by


α2 ≡

πhΩγ 2 3kB2

(4)

where Ω is the kink volume, and h is the step height (5.6 nm as the elementary step of a 2D island17) in the case of homogeneous 2D nucleation.18 In Figure 5 the left-hand side

Figure 4. Normal growth rates R of Pure cell (open circles, purified sample) and Impure cell (filled circles, impure sample) versus T(1 − e−σ)σ under microgravity. R values of Impure cell are clearly lower than those of Pure cell over a wide range of T(1 − e−σ)σ. The solid and dashed vertical lines indicate the critical conditions at which the growth mode changes for Impure cell and Pure cell, respectively. To the left of these lines, crystals grow in the spiral growth mode.

vertical lines show the critical supersaturation conditions at which growth modes change for Impure cell and Pure cell, respectively. To the left of these lines are regions of spiral growth. From this figure, the R values for the impure sample (Impure cell) are clearly less than those of the pure sample (Pure cell), thus demonstrating the impurity effects on growth kinetics, since there is no convection in either microgravity experiment. The suppression of R probably indicates the adsorption of impurities on the growth interfaces. From eq 2, we calculated the surface free energies γ using βst in the ⟨110⟩ direction which are calculated using Figure 3b. The results are shown in Table 1. The surface free energy γ of Impure cell is nearly identical to that of Pure cell. The obtained values of γ are 1 order of magnitude larger than previously reported data.15,16 This is mainly due to the high anisotropy of the step velocities, since βst in the ⟨110⟩ direction is 1 order of magnitude larger than that in the ⟨001⟩ direction, and γ is proportional to βst as

Figure 5. Using the polynucleation model, the left-hand sides of eq 3 of Pure cell (open circles, purified sample) and Impure cell (filled circles, impure sample) are plotted against 1/(T2σ) under microgravity. The values from Impure cell are clearly lower than those of Pure cell over a wide range of σ. The solid and dashed vertical lines indicate the critical conditions where growth modes change for Impure cell and Pure cell, respectively. To the left of the lines, crystals grow in the polynucleation model. The data seem to be described by two slopes in this region. Steeper slopes probably indicate homogeneous 2D nucleation growth, and gradual ones possibly indicate heterogeneous 2D nucleation growth on spiral steps.

of eq 3 is plotted with respect to 1/(T2σ). The solid and dashed vertical lines show the critical supersaturation conditions for Impure cell (filled circles, impure sample) and Pure cell (open circles, purified sample), respectively; to the left of these lines are the regions of 2D nucleation growth mode. Clearly, even in high supersaturation regions, the R values of Impure cell are less than those of Pure cell, although impurity effects are conventionally believed to be suppressed under such conditions. Why, then, does such a decrease in R still occur? As described in section 3.1, the water in Impure cell evaporated to a small extent. As a result, the solubility in

Table 1. Results from Linear Fitting of the Data to the Left of the Critical Lines in Figure 4 α1/nm s−1 K−1 βst⟨110⟩/m s−1 γ/mJ m−2

pure cell

impure cell

0.0017 ± 0.0002 (8.6 ± 0.7) × 10−7 5.2 ± 0.6

0.0009 ± 0.0001 (4.8 ± 0.5) × 10−7 5.5 ± 0.6 E




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situation. This change in constant bulk concentrations would result in the slight differences of their results from ours. 3.6. Characterization of Impurity Effects on Step Velocities and Comparison of the Effects under Microgravity with Those on the Ground. Although impurities significantly suppress R over a wide σ range even under microgravity, as described above, this suppression due to impurities is expected to be smaller than that on the ground, given that the quality of space-grown crystals is higher than that of crystals grown terrestrially. However, at this stage, no plot of R versus σ exists for an impure sample on the ground which can be precisely and directly compared with our R versus σ plots under microgravity, although the Vstep data for purified and impure samples have been reported.13,20 Thus, to characterize the degree of the suppression of R, we compared the difference in V between purified and impure samples under microgravity with that in the Vstep values between purified and impure samples on the ground.13,20 In Figure 6, V for purified (open

Impure cell at a given temperature is lower than that in Pure cell. Lower solubility is known to induce higher surface energy in a crystal,19 which may result in the suppression of 2D nucleation and R. Here we briefly explain the reason the lower solubility induces higher surface energy. Based on the regular solution theory, Bennema and Söhnel have proven that the enthalpy of dissolution increased with decreasing the natural logarithm of the solubility of crystals.19 The surface energy also increases with decreasing solubility, since the surface energy is often suggested to be proportional to the enthalpy of dissolution. Bennema and Söhnel also confirmed the validity of their theoretical consideration using a number of experimental results of inorganic electrolyte crystals.19 However, at this stage, we have a lack of precise data on lysozyme crystals. This should be done as a future work for more detailed discussion. By assuming that 2D nucleation occurred homogeneously, we initially tried to estimate the surface free energies at the step ledges of 2D nuclei in Impure cell and Pure cell using eq 4 and the slopes of the plots to the left of the critical conditions in Figure 5. The data could be interpreted in terms of two lines with differing slopes. Regions that are more steeply sloped probably represent areas of homogeneous 2D nucleation growth, and those with more gradual slopes possibly indicate regions of heterogeneous 2D nucleation growth. Thus, we calculated two surface free energies for each cell, as shown in Table 2. In the more steeply sloped regions, the γ of Impure Table 2. Surface Free Energy γ at the Step Ledge of 2D Nuclei on the {110} Faces of Tetragonal Lysozyme Crystals

γ (steep slope)/mJ m−2 γ (gradual slope)/mJ m−2

pure cell

impure cell

Kurihara et al.15

0.58 ± 0.06

0.73 ± 0.04

1.07 ± 0.03

0.38 ± 0.02

0.36 ± 0.02

Van Driessche et al.16 0.62 ± 0.03

Figure 6. Apparent step velocities V in purified (Pure cell, open circles) and impure solutions (Impure cell, filled circles), and step velocities Vstep in purified (open squares)13 and impure (filled squares)20 solutions versus C − Ce on the ground. In the case of the purified solution, V under microgravity is nearly identical to Vstep on the ground, whereas in the case of the impure solution, V under microgravity seems to be larger than Vstep on the ground.

cell is significantly larger than that of Pure cell, whereas in the gradually sloped regions, the γ values of both cells are nearly identical. Thus, the evaporation of water must be one of the main reasons the R values of Impure cell are lower than those of Pure cell, even in a sufficiently high supersaturation region. Kurihara et al. measured growth rates R versus σ by changing concentrations of HEWL at 12.5 °C and calculated a surface free energy γ using a polynucleation model.15 Although they used the same solution condition (25 mg mL−1 NaCl is dissolved into 0.05 M sodium acetate buffer (pH = 4.5) as we used, obtained γ shows larger value as shown in Table 2. This would be due to the change in HEWL concentrations, since they changed σ by changing surface HEWL concentrations, while we used a solution with constant bulk HEWL concentration (30 mg mL−1) and changed σ by changing the temperature. On the other hand, Van Driessche et al. measured two-dimensional nucleation rates Js versus σ by changing temperature.16 In their study, γ took similar values as one of our γ which is calculated using steep slopes of purified sample. In the case of impure sample, their γ becomes smaller than ours, since they concluded that γ did not depend on impurity concentrations. Although they changed σ by changing temperature as we did, they changed constant bulk HEWL concentrations from 38 to 56 mg mL−1 depending on the

circles) and impure (filled circles) samples are shown with Vstep for purified (open squares) and impure (filled squares) samples. As discussed in section 3.3, at C − Ce < 17 mg mL−1, V should correspond to Vstep. Thus, in this region, we can compare V with Vstep directly. In Figure 6, V and Vstep in the purified solutions seem to be larger than those in the impure solutions both under microgravity and on the ground. V (open circles) and Vstep (open squares) in the purified solutions are nearly identical, whereas the V of Impure cell (filled circles) seems to be larger than Vstep in the impure solutions (filled squares). In practice, six circles (in space) are clearly larger than squares (on the ground), while one circle is clearly smaller. Thus, the suppression of step velocity due to impurities under microgravity would be less than that on the ground. This decrease in the suppression probably indicates a decrease in impurity adsorption on the growing crystal surfaces under microgravity owing to the reduced convective flow around the crystals. In the case of HEWL, the major impurity molecules are known to be the covalently bound dimer and 18 kDa impurity.9,21 Thus, under microgravity, the transport of the F



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dimer to the growing surface of a crystal is probably reduced due to the smaller diffusion constant of the dimer molecules and lack of convective flows. This suppression is one of the most probable mechanisms by which many protein crystals grown in space have shown higher resolution limits than those of the best crystals grown on the ground. However, if this mechanism were true, then similarly sized impurities would equally deteriorate the quality of crystals even under microgravity. The effects of 18 kDa impurity on transportation process under microgravity would be negligible, since the molecular weight is not so much different from HEWL monomer (14 kDa); the amount of incorporation of 18 kDa impurity molecules into crystals under microgravity would not be different from that on the ground. Furthermore, smaller impurities would worsen the impurity effects under microgravity. To confirm these expectations, we will need to conduct additional experiments with smaller or similarly sized impurities (i.e., impurity size screenings) in the future.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-88-656-7415. Fax: +81-88-655-7025. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank Professor Gen Sazaki of Hokkaido University for valuable discussion on impurity effects on step intervals of spiral hillocks. The authors also thank Professor Alexander Chernov of Lawrence Livermore National Laboratory for valuable suggestions and discussion. Y.S. was partially supported by JSPS KAKENHI Grant No. 24656016 and 26390054. K.T. was supported by JSPS KAKENHI Grant No. 22244066.

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4. CONCLUSIONS As part of the NanoStep project of the international space station, we successfully measured the dependence of the normal growth rates R of the {110} faces of tetragonal hen egg-white lysozyme crystals on supersaturation σ under microgravity for both pure and impure samples. This is the first space experiment in which impurity effects on growth kinetics were precisely studied. R values in impure solutions were lower than those in purified solutions, not only in the lower σ regions, but also the higher σ regions. The key findings obtained in this study are summarized as follows: (1) R values in the impure solution (Impure cell) were clearly lower than those in the purified solution (Pure cell) over a wide range of σ. (2) Apparent step velocities V start to increase steeply around C − Ce ≈ 17 mg mL−1 for both impure and pure solutions. This indicates that the dominant growth mode changes from spiral to 2D nucleation growth at this critical concentration. (3) In the spiral-growth-mode region, the R values in the impure solution were clearly lower than those in the purified solution, as conventionally expected. (4) In the 2D-nucleation-mode region, the R values in the impure solution were also clearly lower than those in the purified solution. The surface free energy at the step ledge of the {110} faces of the tetragonal lysozyme crystal in Impure cell was higher than that in Pure cell in the high supersaturation region. This increase is probably due to the decrease in the solubility in Impure cell after the slight evaporation of water. (5) Suppression of step velocities in the presence of the impurity under microgravity seems to be less than that on the ground; thus, the suppression of impurity effects under microgravity is quantitatively confirmed.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.5b00456. Precise derivation of eqs 1 and 2 (PDF) G



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(20) Sleutel, M.; Sazaki, G.; Van Driessche, A. E. S. Cryst. Growth Des. 2012, 12, 2367−2374. (21) Nakada, T.; Sazaki, G.; Miyashita, S.; Durbin, S. D.; Komatsu, H. J. Cryst. Growth 1999, 196, 503−510.

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