REVIEW OF SCIENTIFIC INSTRUMENTS 84, 103707 (2013)

Growth rate measurements of lysozyme crystals under microgravity conditions by laser interferometry Izumi Yoshizaki,1,a) Katsuo Tsukamoto,2,3 Tomoya Yamazaki,2 Kenta Murayama,2 Kentaro Oshi,2 Seijiro Fukuyama,4 Taro Shimaoka,5 Yoshihisa Suzuki,6 and Masaru Tachibana3 1

Japan Aerospace Exploration Agency (JAXA), 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan Graduate School of Science, Tohoku University, Aramaki, Aoba, Sendai 980-8570, Japan 3 Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto Kanazawa-ku, Yokohama 236-0027, Japan 4 Advanced Engineering Services Co., Ltd., Tsukuba Mitsui Bldg., 1-6-1 Takezono, Tsukuba, Ibaraki 305-0032, Japan 5 Japan Space Forum, 3-2-1 Surugadai, Chiyoda, Tokyo 101-0062, Japan 6 Institute of Technology and Science, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan 2

(Received 2 August 2013; accepted 4 October 2013; published online 24 October 2013) The growth rate vs. supersaturation of a lysozyme crystal was successfully measured in situ together with the crystal surface observation and the concentration measurements onboard the International Space Station. A Michelson-type interferometer and a Mach-Zehnder interferometer were, respectively, employed for real-time growth rate measurements and concentration field measurements. The hardware development, sample preparation, operation, and analysis methods are described. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4826090] I. INTRODUCTION

Numerous space experiments have been conducted to grow high quality protein crystals under microgravity conditions.1–8 The experiments are of interest because a significant number of space-grown protein crystals were found to exhibit better resolution in X-ray diffraction studies as compared to the crystals grown on Earth.9 However, the origin of such improved resolution in space environment has remained elusive, although there are many speculative discussions. One approach that aims to explain this phenomenon is based on X-ray analyses, such as rocking curve measurements and topographs. Another approach is based on crystal growth mechanisms. It is quite evident that both approaches should be coupled; however, no experiments that utilize the second approach for the above purposes have been performed under space conditions. There are several reasons for this situation. The most effective methods to analyze the growth mechanism involve growth rate measurements under different growth conditions (e.g., for supersaturation or different protein and impurity concentrations). However, the precise growth rate measurements required for the discussion of growth mechanisms are difficult to perform even under normal gravity conditions. We have solved this problem by developing a mini-laser interferometry system specifically for the space experiment “NanoStep.” This was possible because of our significant experience in using in situ observation systems for crystal growth.10 Prior to the initiation of the NanoStep project, we have performed the Foton-M3 satellite experiment in 2007 in cola) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0034-6748/2013/84(10)/103707/8/$30.00

laboration with Tohoku University, University of Granada, European Space Research and Technology Centre (ESTEC) and Japan Aerospace Exploration Agency (JAXA). During the Foton experiment, 120 protein crystals were grown in 12 days at a temperature of 20 ◦ C, following which the crystals were returned to the ground, making it possible for us to measure the growth rate from the growth striations in crystals. It should be noted that seed crystals were used for the first time in these space experiments, allowing us to conduct growth rate measurements for a given protein concentration. Although this above observation was ex situ, rather than in situ, the average macroscopic crystal growth rate before and after the launch was measured after the retrieval of the samples. We found that the growth rate on the ground and in space was almost the same, in some cases becoming a little faster for the growth in space.11, 12 This result was unexpected and opposite to what has been believed before. In order to investigate this phenomenon, we have prepared the NanoStep experiment employing a sophisticated in situ laser system for a real-time and precise measurement in microgravity conditions. In addition, the observation facility onboard the Japanese Experiment Module (KIBO) of the International Space Station (ISS) was used for the in situ visualization of the protein solution concentration field. The in situ method that allows viewing both the crystal surface and environment from a vertically crossing axis was previously reported by Tsukamoto.13 In this paper, we describe the development of hardware used in such precise observations, as well as the preparation of protein samples including a unique chemically fixed seed crystal, and methods of operation and analysis. Results of the scientific experiment, obtained by using the above procedure, will be reported elsewhere.

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II. HARDWARE DESCRIPTION A. SCOF and EU

The Solution Crystallization Observation Facility (SCOF) was already set up to be used onboard ISS KIBO. The facility was used for an ice crystal experiment14–16 and a phenyl salicylate crystallization experiment.17 For each experiment, the Experiment Unit (EU) was developed according to specific scientific requirements. The EU was connected to the SCOF, which provided electric power and communication lines to the EU. Cooling water (16–23 ◦ C) was supplied to a cold plate on which the EU was installed. Therefore, the size and the resources of the EU were strictly constrained. In order to meet the unique scientific requirements such as temperature control, motor control, and the requirements imposed on the observation system, each EU had to be customized and designed carefully. The SCOF was equipped with an amplitude modulation microscope (AMT), a bright field microscope, a MachZehnder type interference microscope with two wavelength light sources (532 nm and 780 nm), and two cameras (×2 and ×4). The field views were 2.4 mm × 3.2 mm and 1.2 mm × 1.6 mm. These cameras were located beneath the cold plate. There was a hole in the cold plate, offering an observation window for the EU. This enabled the in situ observation of the crystal growth process, and by using the Mach-Zehnder interference microscope, the concentration gradient of the protein solution at the growing interface could be estimated. The EU that was developed specifically for this experiment was named “NanoStep” because by measuring the interferometry fringe movements, the step growth rate could be calculated with nanometer precision. The outer and the inner views of the “NanoStep” hardware are shown in Fig. 1. The dimensions of the device are roughly 250 mm × 280 mm × 185 mm.

FIG. 1. The outer (a) and the inner (b) views of the NanoStep hardware. The arrow indicates the position of the protein sample.

shutter. The field of view of the CCD camera was 1.28 mm × 0.96 mm. Because the NanoStep’s light path was normal to the light path of SCOF, the protein crystal was observed from two different directions (Fig. 2).

C. Growth cell

The protein sample was enclosed in a quartz glass cell (Fig. 5(a)). Two capillaries for solution exchange were

B. Optical devices in NanoStep

The NanoStep hardware was equipped with a Michelsontype interferometer. The laser wavelength was 532 nm. A schematic diagram of the observation direction is shown in Fig. 2, and the light paths are shown in Fig. 3. The expanded laser light should be normally incident on the protein crystal surface. In order to fix the crystal angle, the seed crystal was glued inside the growth cell (described in detail in Secs. II C and III B). Moreover, to precisely control the crystal angle, the growth cell was set on an ultrasonic motor stage, which could control the tilting angle, rotating angle, and the focus (Fig. 4(a)). The dimensions of this ultrasonic motor stage were 40 mm × 40 mm × 17.6 mm. Because the EU was characterized by tight spatial constraints, the motor had to be designed to satisfy these constraints. The LED light source in the NanoStep was positioned behind the growth cell in order to observe the crystal in bright field (Fig. 2). The NanoStep hardware was equipped with a CCD camera to obtain the Michelson interferometer image and bright field image. Only one camera was used; thus, the light path was opened or closed by using a mechanical

FIG. 2. Schematic diagram of the observation direction. The Mach-Zehnder type interferometer in SCOF is denoted by Mz and the Michelson-type interferometer in EU is denoted by Mc. The amplitude modulation microscope in SCOF is denoted by AMT.

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connected to the growth cell. The capillaries were sealed using a special tube that suppressed evaporation. The sample holder was composed of resin, and the seed crystal was set on this holder. The holder was screwed in the internal thread helisert made of ceramics (Fig. 5(b)), allowing the seed crystal to be exchanged easily on the ground. Because the holder was composed of semitransparent material, it allowed the LED light to pass through (Fig. 5(c)). The outer dimensions of the growth cell were 15 mm × 15 mm × 9 mm excluding the capillaries, and the inner dimensions were 11 mm × 11 mm × 3 mm. D. Temperature control and measurement

FIG. 3. Schematic diagram of the light path. (a) The light path in NanoStep’s Michelson-type interferometer. (b) The light path in SCOF Mach-Zehnder type interferometer.

The growth cell was sandwiched between two copper blocks with thermo-modules on both sides (Fig. 4(a)). The copper blocks were pressed using spring screws in order for the thermo-modules to remain in constant contact. Such design was absolutely necessary to cancel the volume change of the blocks and cell that would arise as a result of significant changes in temperature (ranging from 7 to 40 ◦ C). Otherwise, the cell could break or the heat might not have been removed from the thermo-modules, leading to a lower efficiency of temperature control. The maximal regulated power supply to the thermomodule was 4.2 A and 30 W at the maximum for each channel. A two-step heat transfer was applied to improve the efficiency of temperature control; first, the released heat from the first set of thermo-modules was transferred to the heat sink. The heat at the heat sink was then transferred to the Cell unit (Fig. 4(b)) by using a copper ribbon. The Cell unit is cooled with the second set of thermo-modules. The temperature was measured using the thermistors, the tip size of which was 1.5 mmϕ. The temperature measurement stability was 0.1 ◦ C, so the temperature was adjusted within this precision. E. Reference for the measurement

FIG. 4. (a) The ultrasonic motor stage (arrow) and the growth cell contained in the copper block. (b) The growth cell and the ultrasonic motor stage are inside the “Cell unit,” the black copper box (arrow).

The two reference glasses, as well as the seed crystal, were glued to the holder (Fig. 5(c)). The reference glass was used for two purposes. As the growth cell temperature changes, the interferometer fringes at the crystal and reference glass move radically because the growth cell expands or shrinks according to the temperature. This movement settles in a few minutes, following which the actual data collection process can be started. Thus, the first purpose for using the reference glass was to decide when to start the data collection. In addition, the reference glass was used for precise calculations of the crystal growth rate. Even after the radical fringe movement stops, the fringes continue to move slightly because of the temperature control algorithm or some other factor such as minute vibrations in the ISS. This slight movement causes some error to the actual crystal growth rate. By setting a reference glass beside the seed crystal, the reference glass fringe movement could be added to, or subtracted from, the growth rate data. Because the reference glass was made of

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FIG. 5. (a) Front side of the growth cell. (b) Back side of the growth cell without the holder. The arrow points at the helisert thread. (c) The protein crystal and the reference glass inside the growth cell. The chemically fixed seed crystal is slightly yellowish. The solid arrow points at the protein crystal and the dotted arrow points at the reference glass (described in Sec. II E). (d) A schematic showing that the crystal and the reference glass are rotated by 3◦ relative to the growth cell surface (described in Sec. III B).

the same quartz glass as the growth cell, the reference glass interferometer fringe movements were the same as those of the growth cell. Of course, the reference glass had to be set to an angle at which the fringes appear together with the protein crystal surface. III. SAMPLE PREPARATION A. Protein

Hen egg white lysozyme was used as a model protein. Lysozyme was purchased from Seikagaku Kogyo, and further purified to more than 99.8% purity using the method previously described.18 The purified sample was used for the Cell 1 experiment. Cells 2 and 3 were normal samples (simply dissolved and filtered). The normal sample purity was approximately 98.5%. The impurities included in the lysozyme solution were lysozyme dimers and an unknown 18 kDa protein.18 The concentrations were 30 ml mg−1 lysozyme for Cell 1 and Cell 3 and 35 ml mg−1 lysozyme for Cell 2. In all samples, the concentration of NaCl was 2.5%, and the buffer was 50 mM sodium acetate (pH 4.5). B. Seed crystal and chemical fixation

The 300 μm seed crystal was chemically fixed by glutaraldehyde.19 By using this cross-linking method, the seed could overgrow and produce a fresh surface. The epitaxially grown crystal maintained the same crystallographic axis as the seed crystal. The crystal’s lattice constant slightly

changed after chemical cross-linking. The changes in a and b axes were 0.04 Å (0.05%) each, and the c axis change was 0.16 Å (0.42%); however, the lattice constant of the overgrown crystalline layer on the cross-linked crystal was identical to that of the as-grown crystal.19 As mentioned before, the seed could be glued inside the growth cell; therefore, the crystal direction could be roughly fixed. Without chemically fixing the crystal, the protein crystal will break apart as soon as one tries to attach it to the growth cell. Another motivation to use the seed crystal is the possibility to reuse the crystal. In the case of the space experiment, the sample had to be handed to the launch team about 2 weeks prior to launch. After that, the temperature of the sample could not be controlled; thus, many micro-crystals were expected to nucleate inside the growth cell. The bulk solution concentration became unknown. By using the seed crystal, the temperature could be increased before starting the experiment to dissolve the extra crystals, leaving only the seed crystal. The surface of the crystal and the reference glass should be parallel, and they have to be oriented exactly normal to the optical axis of the interferometer. This arrangement is critical for achieving good interference fringes.20 The seed crystal was attached to the holder in a direction that was tilted by approximately 3◦ from the glass surface. This was to separate the growth cell reflection and crystal surface reflection (Fig. 5(d)). If the seed was set in the same direction as the direction of the growth cell surface, both reflections would go into the CCD camera. Because the protein surface reflection is very weak, this situation has to be avoided.

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IV. OPERATION

The NanoStep hardware was launched by KOUNOTORI #3 in July 2012. The hardware was set up inside the SCOF by one of the crew members. After the setup was complete, all experiments were operated from the ground at the “Space Station Integration and Promotion Center (SSIPC)” located at Tsukuba Space Center, Japan. The MPEG-2 compressed video images and temperature data were simultaneously downloaded from the ISS. During the periods at which the satellite was located at LOS (loss of signal) positions, and if necessary, the video images were recorded to a hard disk onboard the ISS so that the whole crystal growth process could be reproduced by connecting the video image files. Before a long LOS (e.g., 30 min), care had to be taken because no images and no telemetries could be downloaded in real time. Of course, no commanding could be done during LOS; thus, the experiment had to be carefully scheduled to avoid critical commanding during LOS. All telemetry data (including temperature data) during LOS were downloaded later. The microgravity environment was measured using MMA (Microgravity Measurement Apparatus) developed by JAXA.21 The level of gravity was 1 × 10−7 to 1 × 10−5 g below the frequency of 1 Hz during the night time at the ISS. In order to avoid the effect of the g-jitter, the experiments were conducted during the night time at the ISS, when the crew members were asleep. Three Cell units were prepared with different protein/impurity concentrations as described in Sec. III A. For each cell, the experiment lasted 35 days (Fig. 6). During the first week, all crystals (except for the seed crystal, which was chemically fixed) were dissolved by increasing the temperature. During the week that followed, the temperature was controlled to allow the seed crystal to grow slowly. Figure 7 shows the process of overgrowth. After the whole seed crystal was covered by an epitaxial growth layer, the ultrasonic motor stage angle was precisely controlled from the ground to obtain a good laser interferogram image showing the surface topography of a protein surface (Fig. 8(a)). Then, the temperature was controlled to change the supersaturation, and the crystal growth rate was measured with nanometer precision by calculating the movement of the interferometer fringes, and by compensating the reference glass fringe

FIG. 6. Experiment sequence. Step 1: Dissolve extra crystals. Step 2: Surface recovery to obtain molecular flat surface. Step 3: Measure the growth rate through Interferometry. TS denotes the saturation temperature.

FIG. 7. The NanoStep and SCOF observation images. The same crystal and reference glass can be observed from two directions. The solid arrow indicates the protein crystal and the dotted arrow indicates the reference glass. (a) NanoStep bright field image of the seed crystal. Image dimensions are 0.96 mm × 1.28 mm. (b) NanoStep bright field image of the seed crystal and the overgrowth crystalline layer. Image dimensions are 0.96 mm × 1.28 mm. (c) SCOF amplitude modulation microscope image of the seed crystal. Image dimensions are 2.4 mm × 3.2 mm. (d) SCOF amplitude modulation microscope image of the seed crystal and the overgrowth crystalline layer. Image dimensions are 2.4 mm × 3.2 mm.

FIG. 8. NanoStep and SCOF interferogram. (a) Surface topography of the {110} face of a tetragonal lysozyme crystal observed by using the Michelson-type interference microscope. Image dimensions are 0.96 mm × 1.28 mm. (b) The protein concentration gradient observed by using the SCOF Mach-Zehnder type interference microscope. Image dimensions are 2.4 mm × 3.2 mm.

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movement. In most cases, the temperature was kept constant for more than 30 min. The protein concentration gradient at the crystal’s interface was obtained at the same time by using the SCOF Mach-Zehnder type interference microscope (Fig. 8(b)). Mach-Zehnder interference was also used to check the equilibrium temperature (as described in Sec. VI). The experiment was carried out from August 2012 to December 2012. Following the completion of one cell experiment (after 35 days of experiment), the crew member exchanged the Cell unit. V. GROWTH RATE ANALYSIS

By using the Michelson-type interferometer, we calculated the advancement of a crystal face from the decrease in the optical path length between the interferometer and the crystal face (Fig. 3(a)). The face growth rate, R, is expressed as λ dx , (1) R= 2nl dt where λ is 532 nm, n is the refractive index of lysozyme solution (n = 1.34), l is the fringe interval, x is the fringe shift, and t is time.22 In this calculation, we neglect the dependence of n on temperature and concentration because the change is smaller than the R value scatter at a certain temperature. Measurements of R were performed using shifts of interference fringes on the {110} face of a crystal, as shown in Secs. V A and V B. We analyzed the interference fringe images in movie files by using a software (Toyo Corporation). This software mainly outputs (1) periodic changes of brightness when interference fringes pass through a point on a crystal surface and (2) space-time plots of moving interference fringes at a line on a crystal surface. We selected an appropriate data set for the measurements from these two outputs depending on R values, as follows. A. Growth rate measurements for fast rates

For growth rates higher than 0.4–0.5 nm s−1 , periodic changes in brightness of the fringes that passed through one point on a crystal surface were used for the measurements (Fig. 9). Because the fringes moved sufficiently fast, we were able to count sufficient number of fringes to be used in calculations for this condition. The number of passing fringes N corresponds to x/l, where x indicates the shift of fringes during the time t. Using these values and Eq. (1) we calculated R as λ x/ l λ N λ dx = = . (2) R= 2nl dt 2n t 2n t

FIG. 9. A plot of intensity vs. time at a certain point on the crystal surface (arrow).

time plot indicate the position of a line on a crystal and the time, respectively. Tilted dark lines show the shifts of interference fringes with time. We drew a line segment along the fringe in the space-time plot and measured the space-time coordinates (xi , ti ) and (xf , tf ) of both ends of the segment (Fig. 10). Using these coordinates and Eq. (1) we calculated R as λ x λ xf − xi λ dx = = . (3) R= 2nl dt 2nl t 2nl tf − ti

B. Growth rate measurements for slow rates

For relatively small values of R, we had to use a space-time plot of interference fringes for the measurements (Fig. 10) because in this regime, the quantity N ≡ x/l becomes less than 1. Horizontal and vertical axes in the space-

FIG. 10. Example of the surface topography (a) and its space-time plot at the solid line (b). The vertical axis in (b) is time. The dotted box is schematically shown in (c).

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Then, if the shape of a cross-section of an ideal spiral hillock is isosceles triangle, ϕ can be expressed as ϕ1 + ϕ2 . (5) 2 Second, using ϕ 1 , ϕ 2 , and ϕ, we calculated the angle between the real crystal surface and the crystal surface normal to the laser light axis θ as ϕ=

θ = ϕ − ϕ1 = ϕ2 − ϕ.

(6)

Third, by using R1 and R2 we calculated the increasing rate of thickness of a growth hillock R as R  = R1 cos ϕ1 = R2 cos ϕ2 .

(7)

Finally, we obtained the real growth rate Rreal and the average step velocity Vstep as Rreal =

R cos ϕ

(8)

Vstep =

R . sin ϕ

(9)

and

VI. SATURATION POINT MEASUREMENT

The protein concentration gradient around a growing crystal was visualized by using a Mach-Zehnder type interferometer (Fig. 8(b)). Because the refractive index correlates with the concentration, the bending at the solution/crystal interface reflects the concentration gradient. The concentration at the crystal interface can be calculated as follows:23 FIG. 11. (a) Schematic presentation of an ideal interferometer fringe and the real growth rate. (b) Schematic presentation of the slanted growth hillock. The area below the bold dotted line exists, but it is not estimated from the fringes.

C. Calculation of Rreal

In this study, interference fringes usually had sharp oval shapes, as shown in Fig. 8(a). These oval shapes reflect the shapes of spiral hillocks on a crystal surface; thus, these shapes have to be ideally symmetrical, as shown in Fig. 11(a). However, in many cases, the shapes of the fringes were not perfectly symmetrical. This occurred primarily because the extra-precise mechanical control of the ultrasonic motor stage was difficult to achieve; thus, the laser light beam that arrived at a crystal surface deviated from normal incidence. Such asymmetrically oval shapes caused the scatter of R values because, as shown in Fig. 11(b), the rate R1 was smaller than the true normal growth rate Rreal , while the rate R2 of the same hillock was larger than Rreal . We corrected the scatter by analyzing the asymmetric fringes. First, we estimated the base angles of the isosceles triangle cross-section of a hillock by using the fringe intervals of both sides of asymmetric interference fringes l1 and l2 (Fig. 11(b)). Using l1 and l2 as shown in Fig. 11(b), we determined the values of ϕ 1 and ϕ 2 as  λ  , ϕ1 = tan−1 2nl  λ1  (4) −1 ϕ2 = tan . 2nl2

λx , (10) bdl where l is the fringe interval, x is the fringe shift at the crystal interface, d is the thickness of the crystal, and b is the coefficient determined by the concentration dependence of the refractive index n. In this case, the value of b was approximately 1.8 × 10−4 ml mg−1 , and it was determined each time from the refractive index data obtained in-house. The light path in the Mach-Zehnder type interferometer is shown in Fig. 3(b). The solubility curve we used was the one that was previously reported by Sazaki et al.24 There was a possibility that the concentration may have changed because of evaporation; thus, as a first step, the saturation point measurements were performed. After dissolving the extra micro-crystals, we let the seed crystal overgrow on the seed. Next, the saturation point (temperature) was checked by inspecting the SCOF Mach-Zehnder image to determine whether the fringes bend at the crystal surface. It was found that the saturation point for Cell 1 was the same as the saturation temperature before launch. Regarding Cells 2 and 3, a slight evaporation was found. The saturation point was checked several times during the experiment because as the crystal grows, the bulk protein concentration is expected to decrease. However, no change was detected. This is reasonable considering the solution volume (approximately 360 μl). In the case of Cell 1, the protein concentration was 30 ml mg−1 ; therefore, the amount of Cbulk − Cinterf ace =

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protein in the solution was 10.8 mg. If the seed crystal with dimensions of 0.3 mm × 0.3 mm × 0.15 mm grew to double its dimensions, the epitaxial crystalline layer volume would become (0.6 mm × 0.6 mm × 0.3 mm) – (0.3 mm × 0.3 mm × 0.15 mm) = 0.0945 mm3 . Because the tetragonal lysozyme density in the crystal is approximately 0.8 mg/mm3 , the mass of the protein incorporated into the epitaxial crystalline layer will be 0.0756 mg, which will change the bulk concentration to 29.79 ml mg−1 . However, this change is negligible. In addition, the concentration change could be neglected in our experiments because we did not grow the crystals to double their initial sizes. The NanoStep interferogram was also inspected to determine whether the fringes had stopped completely. However, the movement at very low levels of supersaturation was too slow, and it was difficult to determine the exact saturation point by using this method. VII. CONCLUSIONS

NanoStep experiment was performed onboard the ISS from August to December 2012 to elucidate the growth mechanisms of lysozyme crystals in microgravity conditions. All three crystals, having different protein/impurity concentrations, were successfully studied to obtain the surface morphology, the normal growth rate R and the step velocity Vstep as a function of supersaturation. The success of the experiment was supported by the hardware development and the sample preparation, which was accompanied by many trials and errors. The key points that determined the success of this experiment were the fixation of the seed crystal, the development of the ultrasonic motor stage to control the crystal angle, and the development of the temperature controlling system. ACKNOWLEDGMENTS

The authors are thankful to Mr. Daiki Fujii, Mr. Shiro Tsukashima, Mr. Kohei Hosokawa, and Mr. Daisuke Ito for helping them with the on-site analysis. We acknowledge Mr. Takehiko Sone, Mr. Toshiyuki Tomobe, Mr. Takao Maki, and Mr. Jong Il Kim for developing the hardware. We also thank Mr. Makoto Yokomine of Toyo Corporation for developing the plug-ins for the analysis software. K.T. was supported by Tohoku University “Program Research” in the Center for Interdisciplinary Research (Gakusai Center, Sendai, Japan) and JSPS KAKENHI Grant No. 22244066. 1 L.

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Growth rate measurements of lysozyme crystals under microgravity conditions by laser interferometry.

The growth rate vs. supersaturation of a lysozyme crystal was successfully measured in situ together with the crystal surface observation and the conc...
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