research papers
Semiempirical model to estimate ideal conditions for the growth of large protein crystals
^{a}Confocal Science Inc., Hayakawa 2nd Building 7F, 2122 Iwamotocho, Chiyodaku, Tokyo 1010032, Japan, and ^{b}Maruwa Foods and Biosciences Inc., 1701 Tsutsuicho, Yamatokoriyama, Nara 6391123, Japan
^{*}Correspondence email: tanakah@confsci.co.jp
A large highquality crystal is required to specify the positions of H atoms in neutron structural analysis. Consequently, several methods have been proposed for obtaining such large crystals, and theoretical considerations for growing them have been presented. However, further investigation is required to obtain a numerical model that can provide quantitative experimental conditions for obtaining a single large crystal. In the case of protein crystallization experiments, the amount of sample is often limited. Therefore, it is more realistic to make a rough estimation from a small number of experiments. This paper proposes a method of estimating the optimum experimental conditions for the growth of large protein crystals by performing a small number of experiments using a microbatch method and reporting a numerical model based on nucleation theory and a linear approximation of the crystalgrowth rate. Specifically, microbatch experiments are performed to provide the empirical parameters for the model and to help to estimate the conditions for the growth of a crystal of a predetermined size using a certain sample concentration and volume. This method is offered as a step on the path towards efficiently and rationally producing large crystals that can be subjected to neutron diffraction without depending on luck or on performing many experiments. It is expected to contribute to drug design and the elucidation of protein molecular functions and mechanisms by obtaining positional information on H atoms in the protein molecule, which is an advantage of neutron diffraction.
Keywords: large protein crystals; nucleation; crystal growth; crystallography; neutron protein crystallography; neutron diffraction; semiempirical models; numerical models.
1. Introduction
Neutron protein crystallography, a powerful neutron diffraction technique for investigating protein chemistry, has elicited considerable interest among academics and pharmaceutical companies. This growing interest stems from the building of new and improved beamlines, the development of improved software and the availability of novel techniques for growing larger crystals (Blakeley et al., 2004; Niimura & Podjarny, 2011). However, only 0.1% of the macromolecular structures deposited in the Research Collaboratory for Structural Bioinformatics Protein Data Bank (PDB) were determined using neutron diffraction (as of June, 2020). This is mainly because the neutron diffraction process requires much larger cubic crystals (∼1 mm^{3}) than Xray diffraction. Additionally, Xray diffraction is applied more generally than neutron diffraction because it requires relatively small amounts of sample. Furthermore, Xray diffraction beamlines are easier to access than neutron diffraction beamlines. Even neutron beamtime review committees are required to access Xray diffraction data first (Helliwell, 2017). Neutron diffraction can provide complementary data to Xray diffraction for the location of H atoms, since only the electronic density of H atoms is visible using Xrays. In some cases, neutron diffraction can provide insights into H atoms and hydration in protein crystal structures that is not available from Xray diffraction alone (Meilleur et al., 2006). A complement of Xray and neutron diffraction in biological science can provide the most complete biological structure possible.
To obtain large crystals, many crystallization methods have been proposed, such as vapourdiffusion (Kelpšas et al., 2019; Koruza et al., 2019; Fukuda et al., 2020), batch (Dajnowicz et al., 2017), dialysis (Zeppezauer, 1971; Maeda et al., 2004; Niimura & Podjarny, 2011) and counterdiffusion (Ng et al., 2015; Schaffner et al., 2017) methods. These methods are sometimes combined with microseeding and macroseeding (Thaller et al., 1985; Bergfors, 2003), protein feeding (Bergfors, 2003) or temperature control (BudayovaSpano et al., 2007).
The establishment of a protein crystallization phase diagram can guide the growth of large crystals (McPherson, 1999; Chayen et al., 2010; Niimura & Podjarny, 2011; Nakamura et al., 2013; Rupp, 2015). Controlling the nucleation and crystal growth occurring in the metastable zone between the solubility and supersolubility curves in the phase diagram, where the nucleation probability is low and crystals grow, can result in the growth of one large crystal (Saridakis & Chayen, 2000; BudayovaSpano et al., 2020). However, crystal growth is not based on quantitative optimization but on many experiments, making it timeconsuming, with results that require a high consumption of protein samples. Occasionally, a large crystal is grown but cannot be reproduced. Furthermore, even using a phase diagram, it is difficult to control the number of crystals to one.
The nucleation process has been studied theoretically (Galkin & Vekilov, 2001), but it has not been applied to the problem of the growth of large crystals. Another theoretical consideration involves utilization of the free energy as a function of the charge on the protein molecule (Ng et al., 2015). (Ostwald, 1897) applies a process in which a small crystal is absorbed by a larger stable crystal. This has also been formulated qualitatively using equations related to free energy (Ng et al., 2015). However, further investigation is required to obtain a numerical method that can provide quantitative experimental conditions for obtaining one large crystal.
In this study, we developed a method for estimating the optimum experimental conditions for the growth of a large crystal using a certain volume of sample solution. This method uses a combination of a few preliminary microbatch experiments and a numerical model. The numerical model is based on nucleation theory and a linear approximation of the crystalgrowth rate. The microbatch experiments provide the empirical parameters for the model, and differential equations based on these parameters help to estimate the ideal conditions for the growth of a large single crystal in a certain sample volume. Thus, more efficient and rational crystallization experiments can be implemented to grow a single large protein crystal. In this study, Microsoft Excel 2016 was used for the data analysis and all graphs.
2. Numerical model
2.1. Sample volume
It is important to have a rough idea of the amount of protein sample that is required to grow a large crystal. For simplicity, the crystal is assumed to be a cube of dimension a (mm). The number of protein molecules in the crystal is calculated using equation (1), where V_{M} is the Matthews coefficient and M is the molecular weight,
It is converted to moles using equation (2),
and to weight (mg) using equation (3),
When the concentration of the protein sample solution is C (mg ml^{−1}) and the solubility is C_{e} (mg ml^{−1}), the required solution volume (µl) is expressed as
For example, in the case of lysozyme (PDB entry 3ijv; V_{M} = 1.84 Å^{3} Da^{−1}; E. Pechkova, S. K. Tripathi & C. Nicolini, unpublished work), if the cubic crystal size is 1 mm^{3} then the sample solution concentration is 35 mg ml^{−1}, the solubility is 4 mg ml^{−1} and the required amount of solution is approximately 29 µl. Thus, a rough estimation of the size of the crystallization container can be made before performing experiments.
It should be noted that V_{M} is an important index that is related to the solvent content and to the resolution of the diffraction data of the crystal. Generally, if V_{M} is smaller, the solvent volume in the crystal is smaller and the resolution of the crystal is higher (Kantardjieff & Rupp, 2003). The precision of the amount of protein needed and the volume required to grow a protein crystal of a certain size depends on the accuracy of V_{M}.
2.2. Estimation of C_{e} and A_{1}
It is known that protein crystal growth follows a linear differential equation (5) in the low supersaturation region, where L(t) is the of the crystal at time t if the crystal is assumed to be a cube and A_{1} is a constant (Chernov, 1998),
A_{1} is a parameter that is related to the bulk kinetic coefficient of crystal growth and is a constant which depends on the protein species, the type and concentration of the precipitant or additive, the pH, the environmental temperature etc.
To estimate C_{e} and A_{1}, crystallization experiments were performed under at least two conditions by changing the protein concentration. The time course for crystal growth was recorded from the beginning of crystal growth. Fig. 1 shows a plot of time on the horizontal axis versus crystal size on the vertical axis. The initial crystalgrowth rate can be extrapolated using a straight approximated line with a slope corresponding to the crystalgrowth rate dL(t)/dt. The horizontal intercept of this approximated straight line corresponds to the time when the nucleation started.
Next, the initial protein concentration on the horizontal axis was plotted against dL(t)/dt as obtained in Fig. 1 on the vertical axis (Fig. 2). At low protein concentrations, the plots were almost linear. The horizontal intercept of this straight line corresponds to C_{e} and its slope corresponds to A_{1} from equation (5).
2.3. Estimation of A_{2} and A_{3}
According to nucleation theory (Galkin & Vekilov, 2001; Yoshizaki et al., 2002; GarcíaRuiz, 2003), the nucleation probability I(t) per unit time and unit volume at time t is explained by the following equation, where C(t) is the protein concentration in the solution at time t and A_{2} and A_{3} are constants,
A_{2} is related to the frequency of the attachment of molecules to the critical size of the nucleus and A_{3} is related to the thermodynamic barriers to the creation of critical and spherical clusters (Galkin & Vekilov, 2001). Both parameters are assumed to be constant and depend on the protein species, the type and concentration of the precipitant or additive, the pH, the environmental temperature etc.
Generally, if the probability of nucleation is set to a unit volume at unit time, the number of crystals will increase with time in a larger volume of the solution. Therefore, if we plot the time for nucleation on the horizontal axis against the number of crystals on the vertical axis, I(t) can be calculated from the slope of the approximated straight line (Fig. 3).
Equation (6) can be rearranged to provide equation (7),
Therefore, by plotting 1/{ln[C(t)/C_{e}]^{2}} on the horizontal axis against ln[I(t)/C(t)] on the vertical axis and making a linear approximation, A_{3} can be estimated from the slope (Fig. 4). If the vertical intercept is substituted as Y_{sec}, we obtain
2.4. Crystallization experiment: prerequisites
In the crystallization experiment, the protein concentration in the container decreases when a crystal starts to grow. Therefore, the second and subsequent crystals grow under different conditions to the first in the same container. Generally, movement of protein molecules in the container occurs because of thermal diffusion and densitydriven convection (Nerad & Shlichta, 1986). However, densitydriven convection is suppressed if the of the container is small (GarcíaRuiz et al., 2001). Therefore, we use a thin capillary placed horizontally to perform a microbatch crystallization experiment. Thermal diffusion is a phenomenon in which a molecule moves owing to thermal fluctuations over time. If the fluctuations are onedimensional, the molecules will move a distance calculated by the following equation, where D is the and is a unique value for the protein that depends on factors such as the molecular weight, shape and temperature,
In the case of lysozyme, the ^{−10} m^{2} s^{−1} in aqueous solution. However, in the case of a polymer solution containing 15% polyethylene glycol (PEG) 4000 the is approximately 0.5 × 10^{−10} m^{2} s^{−1}, as estimated by the approximate equations of Tanaka et al. (2006). From equation (9), it will take approximately 135.2 h on average to migrate 10 mm. For example, in a 15% PEG 4000 solution, if the second crystal starts growing 10 mm from the first crystal in the same capillary more than 135.2 h after the first crystal grows, the second crystal will grow with a lower protein concentration than the first.
is approximately 1.25 × 10Therefore, to carry out microbatch experiments to obtain parameters, the volume of each container should be reduced to target the first crystal in the capillary. To perform the required number of experiments, the number of capillaries can also be increased. To measure second and subsequent crystals that grow in the same container, the capillary should be sufficiently long and the second crystal should be separated by such a length that it is not affected by the first crystal (Fig. 5).
3. Experiments
3.1. Microbatch crystallization experiment
The experimental conditions are shown in Table 1. Lysozyme (Confocal Science Inc., MBPAA001) was used in the crystallization experiments. Sodium chloride and sodium acetate trihydrate were obtained from FUJIFILM Wako Pure Chemical Corporation. Acetic acid and PEG4000 were obtained from Millipore Sigma. The only variable in the experiment was the protein concentration.

The microbatch experiment was performed according to the following procedure. (i) Mix the batch solution to obtain the desired concentration and fill the capillary with it. Then seal both ends of the capillary with a sealing compound (Fig. 6). (ii) Periodically observe the inside of the capillary using a stereoscopic microscope (Nikon SMZ745) and record the images until the crystals stop growing. LED light is equipped in the microscope, so that no temperature change occurs during the observation of crystals.
3.2. Estimation of the parameters C_{e}, A_{1}, A_{2} and A_{3}
When a crystal was observed, its size was measured from the image data (Fig. 7). The crystal was approximated as a rectangular parallelepiped with aspect ratio a:b:c (see equation 11) and the length was measured in the longest direction. After the microbatch experiment, some crystals were taken out, their lengths in three orthogonal directions were measured and their aspect ratios were calculated. Although they were relatively small crystals, we confirmed that the aspect ratio did not change significantly. It was assumed that the aspect ratio would not change much even if the size of the crystals was on a submillimetre scale.
Under the crystallization conditions listed in Table 1, one to three crystals were obtained from each container. Fig. 7 shows an example of crystal growth with 12 mg ml^{−1} lysozyme, 0.4 M sodium chloride, 15% PEG 4000, 0.04% sodium azide in 50 mM sodium acetate buffer pH 4.5. In accordance with the procedures described in Section 2.2 and Fig. 1, Fig. 7 was plotted. In this case, the nucleation start time was estimated to be 126 ± 21 h and the initial crystalgrowth rate dL(t)/dt was estimated to be 0.65 ± 0.06 µm h^{−1}. The same estimation was also performed under other conditions.
In accordance with the procedure described in Section 2.2 and Fig. 2, the protein concentration and the initial crystallization growth rate were plotted, as shown in Fig. 8, from which C_{e} and A_{1} were estimated (Table 2). A_{1} was estimated to be 0.11 ± 0.05 µm ml mg^{−1} h^{−1} from the slope of the straight line when the lysozyme concentration was below 15 mg ml^{−1} and C_{e} was estimated to be 4.51 ± 5.78 mg ml^{−1} from the horizontal intercept. The standard deviation of C_{e} seemed to be rather large. However, it depended on the estimated standard deviations of A_{1} and the vertical intercept point of equation (5). In Fig. 8, the estimation was based on the approximated straight line up to 15 mg ml^{−1} lysozyme solution. However, the growth rate from 18 mg ml^{−1} lysozyme solution was extremely fast and deviated from the straight line. The mode of crystal growth may differ for 15 and 18 mg ml^{−1} lysozyme solutions.

In accordance with the procedure shown in Figs. 3 and 4, the plot shown in Fig. 9(a) was drawn to estimate the nucleation probability I(t) and Fig. 9(b) was drawn to estimate A_{2} and A_{3} (Table 2). Fig. 9(a) shows an example of the plot at a lysozyme concentration of 12 mg ml^{−1}, in which I(t) was estimated to be 0.029 ± 0.006 h^{−1}. The same calculation was also made under other conditions . In Fig. 9(b), A_{2} was calculated to be 8.47 ± 5.37 from the vertical intercept, and A_{3} was estimated to be 1.49 ± 1.22 from the slope of the straight line.
4. Results and discussion
4.1. Comparison with experimental results
In our previous experiments, lysozyme at various concentrations was crystallized in 15% PEG 4000, 0.04% sodium azide in 50 mM sodium acetate buffer pH 4.5 with various concentrations of sodium chloride using a batch method. The solution volume was about 3 µl for each. Crystallization was observed until six months after the experimental setup, and the solubility of lysozyme was measured using the remaining solutions after removing crystals at the end of the experiment. The results are shown in Fig. 10. When the sodium chloride concentration was 0.4 M, which is the same condition as the experimental condition in Table 1, no crystals grew, even after six months, in 5 mg ml^{−1} lysozyme solution. However, in the case of 10 mg ml^{−1} lysozyme, seven crystals, with a size of about 0.15 mm, grew after 24 h. The solubility of lysozyme was 3.02 ± 0.09 mg ml^{−1}, which was not so different from the estimated value of 4.51 ± 5.78 mg ml^{−1} in Table 2.
4.2. Prediction of nucleation probability
By applying the parameters listed in Table 2 to equation (6), the nucleation probability I (in ml^{−1} h^{−1}) for a protein concentration C (in mg ml^{−1}) can be calculated as shown in Fig. 11. To show the slight difference in protein concentration in the low nucleationprobability range, the vertical axis in Fig. 11(a) is presented on a logarithmic scale. The nucleation probability increased rapidly up to 10 mg ml^{−1}, which was approximately twice the solubility of the protein. However, at higher protein concentrations the rate of nucleationprobability increase gradually slowed. To show the critical protein concentration needed for crystal growth, the vertical axis in Fig. 11(b) is shown on a linear scale. This figure indicates that the border between the socalled metastable and nucleation zones in the phase diagram was around 8 mg ml^{−1}.
4.3. Prediction of crystal number, crystal size and starting time for crystal growth
Multiplying the nucleation probability by the container volume V, the expected increase in number of crystals per unit time is expressed by the following equation, where N is the number of crystals,
In the case of the growth of one crystal, the amount of increase in crystal volume ΔV_{cryst} in a small difference time Δt is expressed by the following equation, where L(t) is one side length of the crystal and a, b and c are the aspect ratios of each side, which are 1.00, 0.84 and 0.77, based on the observation of the typical crystals:
Because the amount of protein removed from the solution part in this small difference time is C_{s}ΔV_{cryst}, where C_{s} is the protein concentration in the crystal, equation (12) can be derived,
As the number of crystals increases and each crystal grows, the protein concentration change in the solution can be calculated by equation (13) if the protein concentration in the solution decreases uniformly. Z is the total number of crystals and L_{k}(t) is one side length of the kth crystal,
The actual crystal nucleation and its growth can be calculated using the sequence of equations (10), (5) and (13), as shown in the flow chart in Fig. 12. During calculation, C_{s} was 0.901 g ml^{−1} from equation (3), assuming a V_{M} of 1.84 Å^{3} Da^{−1}.
By repeated calculation, the number of crystals and the final size of the kth crystal can be estimated. The number and size of the crystals and the starting time of crystal growth were calculated and are compared with our previous experimental results in Table 3. The experimental and calculated results were almost consistent. Thus, it can be said that the semiempirical model can predict the crystalgrowth process.

4.4. Growth of a large crystal
To obtain only one large crystal, considering the results in Table 3 and Fig. 11(b), it seems to be necessary to reduce the number of crystals while increasing the crystal size. However, it is difficult to experimentally find the optimum protein concentration and the solution volume. When using the semiempirical model, the number, crystal size and the starting time of crystal growth can be predicted finely with an initial protein concentration of lower than 10 mg ml^{−1}. Thus, it is possible to evaluate the conditions in which the size of the first crystal exceeds 1 mm^{3} while changing the solution volume and proteinsolution concentration (Table 4).

For example, if the solution volume was 400 µl and the initial protein concentration was 6.57 mg ml^{−1}, the first crystals begin to grow after 1600 h, the protein sample concentration in the container decreases and the second crystal does not grow. It should be noted that the protein concentration is significantly lower than the border between the socalled metastable and nucleation zones in the phase diagram, which is around 8 mg ml^{−1} (Fig. 11b). It is shown that the number of crystals and the initiation time for crystal growth are sensitive to the initial protein concentration. As summarized in Table 4, a concentration difference of 0.1 mg ml^{−1} or less makes a large difference in the time required and the number of crystals that begin growth. Therefore, when growing one large crystal using the batch method, one should set the initial experimental conditions carefully, paying particular attention to slight differences in protein concentrations, such as those of 0.1 mg ml^{−1}, and a precise concentration study is necessary for the final stage of optimization of the crystallization condition.
5. Conclusions
This paper proposes a semiempirical model to estimate the optimum conditions for the growth of large protein crystals. The four parameters necessary for modelling the nucleation and crystallization process were obtained by performing crystallization experiments using the microbatch method with different protein concentrations.
Using these parameters, we calculated the protein concentration and the amount of solution required to grow a single crystal of a predetermined size. As shown in Table 4, when the batch solution was 6.57 mg ml^{−1} lysozyme in a volume of 400 µl only one cubic crystal appeared with a size of 1.087 mm, which began nucleation after 1600 h. However, the number of crystals increased to ten when the protein concentration was increased by 5%. Therefore, the next challenge is to perform a precise concentration study to enable the growth of only one large crystal. This means that the traditional phasediagram approach may not easily find the optimum protein concentration, which is much lower than the border between the socalled metastable area and the nucleation area in the batch method.
In our study, the number of experiments was found to be insufficient and the accuracy of the four parameters could have been improved by increasing the number of experiments. Proteins other than lysozyme should be applied in future experiments to expand the scope of this simulation.
Furthermore, only the protein concentration was changed in the crystallization conditions in this study. However, changing the concentrations of other components (for example sodium chloride and/or PEG) using other crystallization methods could create conditions under which large crystals would easily grow. The method introduced in this study can be applied to optimize the conditions in a wider range of crystallization conditions. Future studies could also evaluate how to change the abovementioned four parameters C_{e}, A_{1}, A_{2} and A_{3}. Moreover, the method presented in this study can also be applied to the design of crystallization conditions for Xray crystallography.
Because nucleation is a stochastic process, researchers should incorporate the standard deviation for multiple experiments. However, in the case of protein crystallization, the amount of sample is often limited. Therefore, it is more realistic to make a rough estimation from a smaller number of experiments. Applying the method introduced in this study would be a step on the path towards efficiently and rationally producing large crystals that can be subjected to neutron diffraction without depending on luck or on performing many experiments. We expect that this work will contribute to drug design and the elucidation of the molecular functions and biological mechanisms of proteins by obtaining positional information on H atoms in protein molecules, which is an advantage of neutron diffraction.
Acknowledgements
We would like to thank Editage (https://www.editage.com/) for Englishlanguage editing.
References
Bergfors, T. (2003). J. Struct. Biol. 142, 66–76. Web of Science CrossRef PubMed CAS Google Scholar
Blakeley, M. P., Cianci, M., Helliwell, J. R. & Rizkallah, P. J. (2004). Chem. Soc. Rev. 33, 548–557. Web of Science CrossRef PubMed CAS Google Scholar
BudayovaSpano, M., Dauvergne, F., Audiffren, M., Bactivelane, T. & Cusack, S. (2007). Acta Cryst. D63, 339–347. Web of Science CrossRef CAS IUCr Journals Google Scholar
BudayovaSpano, M., Koruza, K. & Fisher, Z. (2020). Methods Enzymol. 634, 22–46. Google Scholar
Chayen, N. E., Helliwell, J. R. & Snell, E. H. (2010). Macromolecular Crystallization and Crystal Perfection. Oxford University Press. Google Scholar
Chernov, A. A. (1998). Acta Cryst. A54, 859–872. Web of Science CrossRef CAS IUCr Journals Google Scholar
Dajnowicz, S., Johnston, R. C., Parks, J. M., Blakeley, M. P., Keen, D. A., Weiss, K. L., Gerlits, O., Kovalevsky, A. & Mueser, T. C. (2017). Nat. Commun. 8, 955. Web of Science CrossRef PubMed Google Scholar
Fukuda, Y., Hirano, Y., Kusaka, K., Inoue, T. & Tamada, T. (2020). Proc. Natl Acad. Sci. USA, 117, 4071–4077. CrossRef CAS PubMed Google Scholar
Galkin, O. & Vekilov, P. G. (2001). J. Cryst. Growth, 232, 63–76. Web of Science CrossRef CAS Google Scholar
GarcíaRuiz, J. M., Novella, M. L., Moreno, R. & Gavira, J. A. (2001). J. Cryst. Growth, 232, 165–172. Google Scholar
GarcíaRuiz, J. M. (2003). J. Struct. Biol. 142, 22–31. Web of Science CrossRef PubMed Google Scholar
Helliwell, J. R. (2017). Biosci. Rep. 37, BSR20170204. Web of Science CrossRef PubMed Google Scholar
Kantardjieff, K. A. & Rupp, B. (2003). Protein Sci. 12, 1865–1871. Web of Science CrossRef PubMed CAS Google Scholar
Kelpšas, V., Lafumat, B., Blakeley, M. P., Coquelle, N., Oksanen, E. & von Wachenfeldt, C. (2019). Acta Cryst. F75, 260–269. CrossRef IUCr Journals Google Scholar
Koruza, K., Mahon, B. P., Blakeley, M. P., Ostermann, A., Schrader, T. E., McKenna, R., Knecht, W. & Fisher, S. Z. (2019). J. Struct. Biol. 205, 147–154. CrossRef CAS PubMed Google Scholar
Maeda, M., Chatake, T., Tanaka, I., Ostermann, A. & Niimura, N. (2004). J. Synchrotron Rad. 11, 41–44. Web of Science CrossRef CAS IUCr Journals Google Scholar
McPherson, A. (1999). Crystallization of Biological Macromolecules. New York: Cold Spring Harbor Laboratory Press. Google Scholar
Meilleur, F., Myles, D. A. A. & Blakeley, M. P. (2006). Eur. Biophys. J. 35, 611–620. Web of Science CrossRef PubMed CAS Google Scholar
Nakamura, A., Ishida, T., Fushinobu, S., Kusaka, K., Tanaka, I., Inaka, K., Higuchi, Y., Masaki, M., Ohta, K., Kaneko, S., Niimura, N., Igarashi, K. & Samajima, M. (2013). J. Synchrotron Rad. 20, 859–863. Web of Science CrossRef CAS IUCr Journals Google Scholar
Nerad, B. A. & Shlichta, P. J. (1986). J. Cryst. Growth, 75, 591–608. CrossRef CAS Web of Science Google Scholar
Ng, J. D., Baird, J. K., Coates, L., GarciaRuiz, J. M., Hodge, T. A. & Huang, S. (2015). Acta Cryst. F71, 358–370. Web of Science CrossRef IUCr Journals Google Scholar
Niimura, N. & Podjarny, A. (2011). Neutron Protein Crystallography, pp. 50–74. Oxford University Press. Google Scholar
Ostwald, W. (1897). Z. Phys. Chem. 22, 289–330. CAS Google Scholar
Rupp, B. (2015). Acta Cryst. F71, 247–260. Web of Science CrossRef IUCr Journals Google Scholar
Saridakis, E. & Chayen, N. E. (2000). Protein Sci. 9, 755–757. Web of Science CrossRef PubMed CAS Google Scholar
Schaffner, I., Mlynek, G., Flego, N., Pühringer, D., LibisellerEgger, J., Coates, L., Hofbauer, S., Bellei, M., Furtmüller, P. G., Battistuzzi, G., Smulevich, G., DjinovićCarugo, K. & Obinger, C. (2017). ACS Catal. 7, 7962–7976. Web of Science CrossRef CAS PubMed Google Scholar
Tanaka, H., Yoshizaki, I., Takahashi, S., Yamanaka, M., Fukuyama, S., Sato, M., Sano, S., Motohara, M., Kobayashi, T., Yoshitomi, S. & Tanaka, T. (2006). Microgravity Sci. Technol. 18, 91–94. Web of Science CrossRef CAS Google Scholar
Thaller, C., Eichele, G., Weaver, L. H., Wilson, E., Karlsson, R. & Jansonius, J. N. (1985). Methods Enzymol. 114, 132–135. CrossRef CAS PubMed Web of Science Google Scholar
Yoshizaki, I., Nakamura, H., Fukuyama, S., Komatsu, H. & Yoda, S. (2002). Int. J. Micrograv. Sci. Appl. 19, 30–33. Google Scholar
Zeppezauer, M. (1971). Methods Enzymol. 22, 253–266. CrossRef Google Scholar
This is an openaccess article distributed under the terms of the Creative Commons Attribution (CCBY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.