Importance of Hydration State around Proteins Required to Grow High

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Importance of Hydration State around Proteins required to grow High-Quality Protein Crystals Haruhiko Koizumi, Satoshi Uda, Katsuo Tsukamoto, Kenichi Kojima, Masaru Tachibana, and Toru Ujihara Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00798 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 30, 2018

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Crystal Growth & Design

Importance of Hydration State around Proteins required to grow High-Quality Protein Crystals Haruhiko Koizumi,∗, Satoshi Uda, Katsuo Tsukamoto,¶ Kenichi Kojima,∥ Masaru Tachibana,⊥ and Toru Ujihara Institute of Materials and Systems for Sustainability, Nagoya University, Furou-cho, Chikusa-ku, Nagoya 464-8603, Japan, Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan, Graduate School of Science, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai 980-8578, Japan, Department of Education, Yokohama Soei University, 1 Miho-cho, Midori-ku, Yokohama, 226-0015, Japan, and Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, 236-0027, Japan E-mail: [email protected]

*To

whom correspondence should be addressed IMaSS, Nagoya Univ. IMR, Tohoku Univ. ¶ Osaka Univ. § Tohoku Univ. ∥ Yokohama Soei Univ. ⊥ Yokohama City Univ.

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Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The explosive increase in the normal growth rates for dislocation free tetragonal hen egg white (HEW) lysozyme crystals was observed from a point of (C Ceq), corresponding to a high supersaturation ratio of 2.2. This suggests the change in the growth mode, i.e., the normal growth rates are dominated not by the surface free energy of the step edge, but by the dynamics of water around protein molecules under high supersaturation ratios. Focusing on the crystal quality at high supersaturation conditions, the quality improvement for protein crystals was also observed with an increase in water dynamics around protein molecules, despite the faster normal growth rate, as verified by the full width at half maximums (FWHMs) of X-ray diffraction (XRD) rocking curves. Moreover, the misorientation between subgrains reached the order of 104

◦

for tetragonal HEW lysozyme crystals grown with the NaCl concentration

of 0.86 M, and thus bead-like contrasts of dislocations explained by the dynamical theory of diffraction were also observed using X-ray topography conducted with a beam of monochromatic synchrotron radiation. This indicates that the grown tetragonal HEW lysozyme crystal has near-perfect quality and changes the traditional concept that high-quality protein crystals are obtained by low normal crystal growth rates. Here we show the importance of the hydration state around protein molecules required to grow high-quality protein crystals.


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Introduction Water is indispensable to maintain protein stability and function so that proteins spontaneously fold into their characteristic three-dimensional (3D) structures in the presence of water. Research concerning the stability of proteins in aqueous solution with the addition of a salt has been conducted intensively1–3 since Hofmeister revealed the order of salts in terms of their ability to precipitate proteins,4 which is referred to as the Hofmeister series, in 1888. It has since been revealed that this phenomenon is related to the change in hydration around protein molecules.3 Further studies have thus been performed with a focus on the structure of hydration around protein molecules using various methods, such as X-ray scattering,5 neutron scattering5 and nuclear magnetic resonance (NMR) spectroscopy.6–10 More recently, it has been reported that the dynamics of water around protein molecules can be varied by changing the type of salt or the salt concentration of an aqueous solution.11,12 In contrast, the elucidation of protein function has been attempted from the perspective of biochemistry by determining the 3D structures of proteins.13 The 3D structures of proteins, which are determined by X-ray diffraction, constitute approximately 90% of all the structures registered with the Protein Data Bank (PDB; http://www.rcsb.org/pdb/). Thus, the crystallization of proteins has become an important process. However, useful 3D structures of protein molecules with a resolution of less than 1.5 Å have only been achieved for 9% of all determined protein molecules, even with the use of high-brilliance synchrotron radiation facilities, such as SPring-8. Therefore, previous pioneering work has demonstrated that the quality of concanavalin A crystals having a metal-binding region depends on the metal ion homogeneity, leading to high diffraction efficiency (diffractivity).14 This means that high-quality protein crystals are required to achieve this level of resolution, and the growth of high-quality protein crystals has thus become an important subject. Protein crystals are crystallized from aqueous solution by the addition of a salt, and thus protein crystal growth is solution growth. In the case of solution growth, the dehydration process must generally be considered for all processes, such as the incorporation of atoms or molecules into the kink on a step in a crystal.15,16 Therefore, the dehydration process dominates the kinetics ACS Paragon Plus Environment


of solution growth, and it has been thermodynamically revealed that the rearrangement of water molecules occurs, i.e., the hydration structure changes when protein molecules are incorporated into the kink on a step during crystal growth.17 However, the relationship between the dehydration process and the crystal quality of protein crystals has never been revealed. In this article, we demonstrate that the hydration state around protein molecules has a significant effect on the crystal quality of protein crystals under high supersaturation ratios at which not the surface free energy of the step edge but the step kinetics dominates the normal growth rates of the crystal surfaces. This finding could have potential for the quality improvement of various crystals from solutions.

Experimental Procedures Crystal Growth The HEW lysozyme purchased from Wako Pure Chemical Industries, Ltd. was used in this study. The HEW lysozyme solution was employed without further purification, and thus it is considered that the impurities such as dimer were included in it. The tetragonal HEW lysozyme crystals employed for in situ observations of crystal growth, XRD rocking-curve measurements and X-ray topography were grown from the cross-linked seed crystals. Details of sample preparation are described in Ref. 23. The supersaturation ratio of each HEW lysozyme solution σ (= lnCCeq , where C is the concentration of the solution and Ceq is the solubility) was controlled by variation of the temperature. We calculated the resultant supersaturation values from data reported by Cacioppo et al..18 By using digital microscopy, replicate in situ observations of crystal growth were conducted employing two different seed crystals for each of the two different NaCl concentrations. We measured the normal growth rates R of the (110) face by tracking the crystal dimensions along the [110] direction. Details of the in situ observations are described in Ref. 23. The point of this measurement is that no dislocations occur from the seed crystals during crystal growth by control


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of the chemical cross-linking time,19 i.e., 2D nucleation and birth-and-spreading type growth is applied on the growing faces in this measurement.

XRD Rocking-Curve Measurement and Topography XRD rocking-curve measurements and monochromatic-beam X-ray topography were performed at room temperature using the BL20B beamline at the Photon Factory, part of the High Energy Accelerator Research Organization (KEK), Japan. The detailed arrangements of XRD rocking-curve measurements are described in Ref. 23. XRD rocking-curve profiles were measured using the 110 family of reflections to estimate physical values in the crystal. The instrumental resolution function (IRF’) of the 110 family of reflections was tabulated (see Table 2), which was calculated according to the DuMond diagram.20,21 The growth conditions of measured tetragonal HEW lysozyme crystals are summarized in Table 1. As shown in Table 1, the crystals grown with the same supersaturation were employed for XRD rocking-curve measurements. XRD rocking-curve profiles were obtained from two crystals under each condition. Moreover, the monochromatic-beam topography was performed using a tetragonal HEW lysozyme crystal grown with the highest NaCl concentration (NaCl: 0.86 M). The topographs were obtained using the 110 reflection and were recorded on X-ray film (Agfa D2) with an exposure time of approximately 3 min.

Results and discussion Growth kinetics under high supersaturation The normal growth rates R of crystals are determined by the balance of the surface free energy of the step edge and the step kinetics, as follows:

2

1/3 R = h(v2 J) πΩα 2 h 1/3

= h[(Ωβstep(C Ceq)) ·ϖ ΓZexp( 2 2 )] kB T σ ACS Paragon Plus Environment

,

(1)


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where vstep is the tangential step velocity, which is related to the step kinetic coefficient βstep as vstep = Ωβstep(C C eq ),22 Ω is the kink volume, C is the concentration of the solution and Ceq is the solubility, J is the rate of two-dimensional (2D) nucleus formation, which is dominated by the surface free energy of the step edge α, ϖ is the frequency of attachment of molecules

to

the critical 2D nucleus, Γ is the Zeldovich factor, Z is the steady-state admolecule surface concentration, kB is the Boltzmann constant, and T is the absolute temperature, h is the step height, C σ is the supersaturation, which is defined as ln(Ceq ). As seen in Eq. 1, the contribution of the

surface free energy of the step edge becomes larger under low supersaturation ratios, leading to the significant decrease in the normal growth rates. In our previous work,23 we have observed that the normal growth rates for tetragonal hen egg white (HEW) lysozyme crystals decrease with an increase in the NaCl concentration under low supersaturation ratios. Generally, it has been known that the impurity causes a significant decrease in the growth rates under quite low supersaturation ratios (less than σ = 1.4).24 In our measurements, however, the observations of the normal growth rates have been performed under supersaturation ratios higher than σ = 3.5. Therefore, we have concluded that the observed decrease in the normal growth rates is attributed to the increase in the surface free energy of the step edge under low supersaturation ratios.23 Figure 1 shows the dependence of the normal growth rates of the (110) face for dislocationfree tetragonal HEW lysozyme crystals on (C Ceq) at 0.34 M and 0.68 M NaCl concentrations. As shown in Figure 1, it is found that the dependence of the normal growth rates on (C Ceq) changes, respectively. In particular, the normal growth rates explosively increased in the case of crystals with higher surface free energy of the step edge (NaCl: 0.68 M) at (C Ceq) higher than 44.5 mg/mL, corresponding to a high supersaturation ratio of 2.2. In this experiment, the protein concentration is same under each condition (Lysozyme cocentration: 50 mg/mL), and therefore it is considered that ϖ, Γ and Z are same between 0.34 M and 0.68 M cases. Thus, the normal growth rates for the NaCl concentration of 0.68 M should not exceed those for that of 0.34 M, assuming that the step kinetics is constant. However, it is fact that the normal growth rates for crystals with larger surface free energy of the step edge (NaCl concentration: 0.68 M)


becomes

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faster under high supersaturation ratios, which suggests that the factor be different to dominate the normal growth rates between low and high supersaturation ratios. That is, the contribution of the surface free energy of the step edge on the normal growth rates became small due to the increase in the supersaturation, resulting in the explosive increase in the normal growth rates, which is dominated by the magnitude of the step kinetic coefficient βstep. βstep can be expressed as follows:25 βstep = an¯ ν+ exp(

∆G

k

kB T

),

(2)

1 where ∆G is the free-energy barrier for incorporation of a protein molecule into a kink, n¯ k is the

kink density, a is the molecular size of the protein being incorporated, and ν+ is the effective frequency of attempts by solute molecules to enter a kink by overcoming the energy barrier.

By

assuming that ν+ is constant because the protein concentration is the same under each condition, 1 thus, βstep is promoted when ∆G decreases or n¯ k increases. The addition of salts such as NaCl

to protein solutions generally adjusts the anisotropic coulombic interactions in a way that favours crystallization, i.e., the intermolecular interactions between protein molecules become strong,26–28 1 which means that n¯ k decreases. Therefore, the explosive increase in the normal growth rates

under high supersaturation ratios could be predominantly caused by the decrease in the free-energy barrier for incorporation of a protein molecule into a kink ∆G. Recently, the dynamics of water around protein molecules have been observed using terahertz time-domain spectroscopy.11,12 It has been reported that the dynamics of water around protein molecules are faster with an increase in the concentration of Cl ions in the protein solution.12 This is because kosmotropic anions such as Cl ions strengthen the structure of bulk water, while they weaken the structure of hydration water around the protein molecules. Therefore, hydrogen bonding with water formed around the surfaces of protein molecules becomes weaker with an increase in the NaCl concentration, which leads to a rapid change in the hydration structure around the protein molecules when the protein molecules are incorporated into the kink on a step during



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crystal growth. Thus, the decrease in ∆G with an increase in the NaCl concentration could be attributed to the faster rearrangement of hydration water around protein molecules, due to the faster dynamics of the water around protein molecules. A similar phenomenon has also been reported by the addition of acetone to insulin solutions,25,29 which indicates that the step velocity of insulin crystals is significantly faster due to the destruction of the hydration structure around protein molecules. It is thus important to regulate the dynamics of water around protein molecules for protein crystal growth, which can be controlled by changing the concentration of kosmotropic anions such as Cl and SO2.

That is, the explosive increase in the normal growth rates under

high supersaturation ratios is predominantly caused by the faster dynamics of water around protein molecules.

Effect of water dynamics on crystal quality In order to focus on the effect of the dynamics of water around protein molecules on the crystal quality, firstly, we grew tetragonal HEW lysozyme crystals at the same supersaturation ratio (see Table 1), by employing the NaCl concentrations of 0.34 M or 0.68 M. The (C Ceq) values when employing the NaCl concentration of 0.34 M and 0.68 M were 45.2 mg/mL and 45.4 mg/mL, respectively. Therefore, the normal growth rates for crystals grown with the concentration of 0.68 M were slightly faster than those for 0.34 M (see Figure 1), despite the larger surface free energy of the step edge as reported in our previous work (0.34 M NaCl: 0.92 mJ/m2, 0.68 M NaCl: 1.75 mJ/m2).23 This suggests that the water dynamics around proteins be faster for the crystals grown with the NaCl concentration of 0.68 M. The crystal quality of grown crystals was assessed using the full width at half maximums (FWHMs) βM of X-ray diffraction (XRD) rocking curves. The FWHMs of rocking-curves are broadened by various effects such as lattice tilting β α , local strain βε , particle size βL and uniform lattice bending βr. Thus, the measured FWHM βM is expressed as follows:30,31 β 2 = β 2 + β 2 + β 2 + β 2 + β 2 + β 2, M

0

ins

α

ε

L


(3) r

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where β0 is the intrinsic FWHM of the rocking curve for a perfect crystal, which can be negligible because of quite small values (see Table S1), βins is the broadening contribution due to the instrumental resolution function (IRF’). The details of other broadening contributions are described in Supplementary Information S1. Table 2 shows the average FWHM values βM from tetragonal HEW lysozyme crystals grown under high supersaturation ratios at which the dynamics of water around proteins dominates the normal growth rates. As shown in Table 2, the average FWHM values of the rocking curve profiles for the tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.34 M increased with increasing order of the diffraction peaks for the higher-order reflections. This indicates that the local strain is accumulated in the crystal. Thus, we estimate the local strain in the crystals grown with the NaCl concentration of 0.34 M, 2 ad j

according

= Kα + Kε tan2θ (The details of Kα and Kε are defined in S1). Here, β 2 ad j is the FWHM

adjusted to account for the intrinsic FWHM and IRF’ (β 2

ad j

= β 2 β 2 β 2 ). Kα and Kε are

2 and related to tilting and local strain, respectively. Figure 2 shows the relationship between β ad j

tan2θ for tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.34 M or 0.68 M. As shown in Figure 2, it is found that the values increase with a decrease in order of the diffraction peaks for the lower-order reflections. This is attributed to the broadening contribution due to subgrain size, because previous work32 has indicated that there is no large curvature in tetragonal HEW lysozyme crystals. Therefore, the local strain was calculated to be 72.3 µε for tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.34 M, using rocking-curve data of the 770, the 11 11 0 and the 12 12 0 reflections, which have smaller broadening contribution due to subgrain size. In contrast, the local strain is found to be ∼0 µε for tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.68 M, because FWHM values were almost constant for the higher-order reflections (see Table 2 and Figure 2). Next, we focused on the broadening contribution due to the misorientation between subgrains and the size of subgrains. These broadening contributions can be divided by using the following



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equation: sin22θ λ2

sin22θ

β2 ad j

=

λ2

K

(4)

K

α + L.

Here, the details of KL is defined in Supplementary Information S1, which is related to particle 2 size. Figure 3 shows the relationship between sin 2θ β 2 and sin22θ for tetragonal HEW lysozyme λ2

ad j

λ2

crystals grown with various NaCl concentrations. At first, let us compare the results for the NaCl concentration of 0.34 M and 0.68 M. Here, the broadening contribution due to local strains is removed using the estimated value (72.3 µε) for tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.34 M. As shown in Figure 3, the relationship between

sin22θ λ2

β2

2

and sin 2θ λ2

ad j

for crystals grown with the NaCl concentration of 0.34 M has linearity, which suggests the removal of the broadening contribution due to local strains be reasonable. The slope also changes with an increase in the NaCl concentration, which means the decrease in the misorientation between subgrains in the crystal, i.e. the improvement in the crystal quality. Moreover, we also investigated the crystal quality of tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.86 M. In the case of 0.86 M NaCl concentration, there are no local strains in the crystal as same as the case of 0.68 M NaCl concentration, because the FWHM values were almost constant for the higher-order reflections (see Table 2 and Figure S2). As seen in Figure 3, it is found that the slope also drastically decreases, which suggests the more improvement in the crystal quality by employing the higher NaCl concentration. Table 3 shows the physical values estimated from tetragonal HEW lysozyme crystals grown under high supersaturation ratios at which the normal growth rates are dominated by the dynamic of water around protein molecules. Surprisingly, it was found that the misorientation between subgrains reaches the order of 104

◦

when employing the NaCl concentration of 0.86 M. This means that the crystal quality is quite high as same as Si, Ge and diamond, and thus the phenomenon explained by the dynamical theory of diffraction could also be observed using X-ray topography33,34 and XRD rocking-curve measurements,21 similar to glucose isomerase crystals.

In addition, the size of subgrains decreases


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with increasing the NaCl concentration, as shown in Table 3, which is corresponding to the crystal quality. Therefore, the grain refinement of subgrains might be important to grow high-quality protein crystals. Furthermore, dislocation contrasts explained by the dynamical theory of diffraction were observed for tetragonal HEW lysozyme crystals grown at 0.86 M NaCl concentration as expected, using X-ray topography conducted with a beam of monochromatic synchrotron radiation. The contrasts of dislocations in the crystal are generally observed as a line contrast using X-ray topography (see Figure S3).35–37 Dislocation contrasts were also observed as a line contrast even for the tetragonal HEW lyszoyme crystal grown at 0.68 M NaCl concentration, using a high spatial resolution, two-dimensional, digital CCD camera (see Figure S4). However, in the case of the tetragonal HEW lysozyme crystal grown at the highest NaCl concentration (NaCl: 0.86 M), they were observed as bead-like contrasts. Figure 4 shows a synchrotron monochromatic-beam X-ray topograph of the tetragonal HEW lysozyme crystal grown with a NaCl concentration of 0.86 M, and obtained using the 110 reflection. Bead-like contrasts are clearly observed, which is attributed to the interference between the transmitted and reflected waves.37 Therefore, this indicates that multiple reflections occur in the crystal, i.e., the grown crystal has near-perfect quality. Here, Table 4 shows the physical values estimated from tetragonal HEW lysozyme crystals grown under a low supersaturation ratio at which the normal growth rates are dominated by the surface free energy of the step edge. The (C Ceq) value was 42.7 mg/mL when employing the NaCl concentration of 0.68 M, and therefore the normal growth rates were quite low (see Figure 1). The physical values were estimated conducting the same analysis (see Figure S5).

Generally,

it is considered that high-quality crystals can be grown under lower supersaturation conditions. However, the misorientation between subgrains for the crystals grown under a high supersaturation ratio was smaller compared with that under a low one, despite the same surface free energy of the step edge (see Table 3 and Table 4). This means that the growth mode dominated by the faster dynamics (rearrangement) of water around protein molecules is important to obtain high-quality protein crystals, even if the normal growth rates are faster. It has also been reported that the ordered



water molecules around proteins increase when protein crystals were grown under microgravity.38 That is, the degree of the order of water around proteins could have a significant effect on the crystal quality of protein crystals. This result changes the traditional concept that high-quality protein crystals are obtained by maintaining low normal growth rates during crystal growth. Therefore, the control of the hydration water on protein molecules could be a key methodology to achieve accurate 3D structural analysis of proteins. We consider that various protein crystals can be grown as perfect crystals by control of the dynamics of water around protein molecules. We have recently confirmed that multiple reflections also occur in glucose isomerase crystals,21,33,34 although such a phenomenon had previously been observed only with limited crystals such as Si, Ge and diamond.36,37,39 However, we could not state why high-quality crystals were grown in the case of glucose isomerase crystals. This could be explained from the perspective of the change in the dynamics of water around the protein molecules. In our previous work, glucose isomerase crystals were grown using (NH4)2SO4 as the precipitant.21,33,34 It has been revealed that kosmotropic anions such as SO2 weaken even more the hydration water structure around protein molecules using terahertz time-domain spectroscopy, which leads to faster dynamics of the water around protein molecules.11,12 Moreover, the glucose isomerase crystals used in our previous work21,33,34,34 were grown under a high precipitant concentration of 0.91 M, although the precipitant concentration generally employed is in the range from 0.3 M to 0.5 M. Thus, the fast dynamics (rearrangement) of water around protein molecules could lead to the formation of glucose isomerase crystals with near-perfect quality. Furthermore, it has been reported that the hydration structure around protein molecules is destroyed by the addition of acetone to protein solutions, which leads to an increase in the step velocity of insulin crystals.25,29 Thus, the improvement in the crystal quality of protein crystals could also be achieved by the addition of acetone to protein solutions. Therefore, this approach with a focus on the hydration structural design around protein molecules could become a novel crystallization technique to obtain high-quality protein crystals with faster normal growth rates.


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Conclusion We observed the explosive increase in the normal growth rates for tetragonal HEW lysozyme crystals grown with the higher NaCl concentration, under high supersaturation ratios at which the dynamics of water around protein molecules dominates the normal growth rates. The quality improvement in protein crystals was also demonstrated with an increase in water dynamics around proteins, despite the faster normal growth rates. Moreover, for the tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.86 M, it was found that the misorientation between subgrains reaches the order of 104 ◦ . This means that the crystal quality is quite high as same as Si, Ge and diamond. In addition, bead-like contrasts explained by the dynamical theory of diffraction were also observed as expected, using X-ray topography conducted with a beam of monochromatic synchrotron radiation. These results could indicate the importance of the regular arrangement of not only protein molecules but also water molecules around proteins, i.e., the dehydration process in solution growth has a significant effect on the crystal quality. This finding could have potential for the quality improvement of various crystals from solutions.

Acknowledgement This work was supported in part by a Grant-in-Aid for Scientific Research (C) (No. 16K06708) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The authors thank Dr. H. Sugiyama and Dr. K. Hirano of KEK for their help with the synchrotron radiation Xray topography. Monochromatic-beam X-ray topography and XRD rocking-curve measurements were performed at the Photon Factory under the auspices of the Photon Factory Program Advisory Committee of KEK (Proposal Nos. 2016G673).



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(19) Koizumi, H.; Uda, S.; Tachibana, M.; Tsukamoto, K.; Kojima, K.; Nozawa, J. Crystallization Technique for Strain-free Protein Crystals Using Cross-linked Seed Crystals. Cryst. Growth Des. 2016, 16, 6089–6094. (20) DuMond, J. W. Theory of the use of more than two successive x-ray crystal reflections to obtain increased resolving power. Phy. Rev. 1937, 52, 872. (21) Suzuki, R.; Koizumi, H.; Hirano, K.; Kumasaka, T.; Kojima, K.; Tachibana, M. Analysis of oscillatory rocking curve by dynamical diffraction in protein crystals. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, 3634–3639. (22) Vekilov, P. G.; Alexander, J. I. D. Dynamics of layer growth in protein crystallization. Chem. Rev. 2000, 100, 2061–2090. (23) Koizumi, H.; Uda, S.; Tsukamoto, K.; Tachibana, M.; Kojima, K.; Okada, J.; Nozawa, J. Crystallization Technique of High-Quality Protein Crystals Controlling Surface Free Energy. Cryst. Growth Des. 2017, 17, 6712–6718. (24) Van Driessche, A. E.; Sazaki, G.; Otálora, F.; González-Rico, F. M.; Dold, P.; Tsukamoto, K.; Nakajima, K. Direct and noninvasive observation of two-dimensional nucleation behavior of protein crystals by advanced optical microscopy. Cryst. Growth Des. 2007, 7, 1980–1987. (25) Vekilov, P. G. What determines the rate of growth of crystals from solution? Cryst. Growth Des. 2007, 7, 2796–2810. (26) Elcock, A. H.; McCammon, J. A. Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient. Biophys. J. 2001, 80, 613–625. (27) Chan, H. Y.; Lankevich, V.; Vekilov, P. G.; Lubchenko, V. Anisotropy of the Coulomb interaction between folded proteins: consequences for mesoscopic aggregation of lysozyme. Biophys. J. 2012, 102, 1934–1943.


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Table and Figure captions • Table 1: Growth conditions of the tetragonal HEW lysozyme crystals grown to access the crystal quality under high supersaturation conditions at which the water dynamics around proteins dominates the normal growth rates. • Table 2: X-ray rocking-curve data for tetragonal HEW lysozyme crystals grown under various NaCl concentrations. Profiles were acquired using a beam spot size of 258 µm (40 pixels). SD is standard deviation. IRF’ values are also tabulated, which were calculated according to the DuMond diagram.20,21 • Table 3: Estimated local strain, misorientation between subgrains and size of subgrains in tetragonal HEW lysozyme crystals grown under high supersaturation ratios, at which the normal growth rates are dominated by the dynamics of water around proteins. • Table 4: Estimated local strain, misorientation between subgrains and size of subgrains in tetragonal HEW lysozyme crystals grown under a low supersaturation ratio at which the normal growth rates are dominated by the surface free energy of the step edge. • Figure 1: Typical effects of (C Ceq) on the growth rates of the (110) face of tetragonal HEW lysozyme crystals at NaCl concentrations. Lysozyme concentrations were 50 mg/mL in both cases. The solubility of each HEW lysozyme solution Ceq was changed by variation of the temperature. 2 • Figure 2: Relationship between β ad and tan2θ for tetragonal HEW lysozyme crystals grown j

with the NaCl concentration of 0.34 M or 0.68 M.strain-estimation. 2

2

λ2

ad j

• Figure 3: Relationship between sin 2θ β

2 and sin 2θ for tetragonal HEW lysozyme crystals

λ2

grown with the NaCl concentration of 0.34 M or 0.68 M. • Figure 4: Synchrotron monochromatic-beam X-ray topograph of the tetragonal HEW lysozyme crystal grown with a NaCl concentration of 0.86 M, obtained using the 110 reflection. The ACS Paragon Plus Environment


bead-like contrasts explained by the dynamical theory of diffraction are clearly evident.


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Supporting Information Available The following files are available free of charge. • S1: Broadening Contribution to FWHMs. • S2: Strains in tetragonal HEW lysozyme crystals grown with the NaCl concentration of 0.86 M. • S3: Typical X-ray topograph of the tetragonal HEW lysozyme crystal grown at 0.50 M NaCl concentration. • S4: Digital X-ray topograph of the tetragonal HEW lyszoyme crystal grown at 0.68 M NaCl concentration. • S5: Separation of local strain, misorientation between subgrains and size of subgrains in tetragonal HEW lysozyme crystals grown under a low supersaturation ratio. This material is available free of charge via the Internet at http://pubs.acs.org.



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Table 1: Growth conditions of the tetragonal HEW lysozyme crystals grown to access the crystal quality under high supersaturation conditions at which the water dynamics around proteins dominates the normal growth rates (Supersaturation σ)


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Table 2: X-ray rocking-curve data for tetragonal HEW lysozyme crystals grown under various NaCl concentrations. Profiles were acquired using a beam spot size of 258 µm (40 pixels). SD is standard deviation. IRF’ values are also tabulated, which were calculated according to the DuMond diagram.20,21 βM under each NaCl concentration Reflection 220 0.00073

◦

330 0.00076◦ 440 0.00078◦ 770 0.00085◦ 11 11 0 0.00094◦ 12 12 0 0.00097◦

(0.00038◦ ) 0.00270◦ (0.00036◦ ) 0.00275◦ (0.00034◦ ) 0.00275◦ (0.00030◦ ) 0.00272◦ (0.00022◦ ) 0.00279◦ (0.00017◦ ) 0.0029◦ (0.00021◦ )

(0.00026◦ ) 0.00224◦ (0.00021◦ ) 0.00217◦ (0.00022◦ ) 0.00213◦ (0.00031◦ ) 0.00208◦ (0.00037◦ ) 0.00201◦ (0.00035◦ ) 0.0020◦ (0.00039◦ )


(0.00014◦ ) 0.00202◦ (0.00011◦ ) 0.00189◦ (0.00009◦ ) 0.00179◦ (0.00015◦ ) 0.00170◦ (0.00011◦ ) 0.00150◦ (0.00026◦ ) 0.00151◦ (0.00020◦ )


Table 3: Estimated local strain, misorientation between subgrains and size of subgrains in tetragonal HEW lysozyme crystals grown under high supersaturation ratios, at which the normal growth rates are dominated by the dynamics of water around proteins

(2.0 w/v%)

∼0 µε ∼0 µε


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Table 4: Estimated local strain, misorientation between subgrains and size of subgrains in tetragonal HEW lysozyme crystals grown under a low supersaturation ratio at which the normal growth rates are dominated by the surface free energy of the step edge. NaCl conc.

Lysozyme conc.

0.68 M (4.0 w/v%)

50 mg/mL

Solubility Ceq (Supersaturation σ) 7.3 mg/mL (1.92)

Strain

Misorientation

Subgrain size

0 µε

0.00133◦

63.4 µm



Figure 1: H. Koizumi et al.


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For Table of Contents Use Only

Title: "Importance of Hydration State around Proteins required to grow High-Quality Protein Crystals" Author(s): Koizumi, Haruhiko; Uda, Satoshi; Tsukamoto, Katsuo; Kojima, Kenichi; Tachibana, Masaru; Toru Ujihara

Hydration state around proteins has a significant effect on the crystal quality of protein crystals. That is, the growth mode dominated by the faster water dynamics around proteins is important to obtain high-quality protein crystals, even if the normal growth rates are faster. In fact, the protein crystals with nearperfect quality can be grown by maintaining the faster dynamics of the water around proteins. This finding changes the traditional concept that high-quality protein crystals are obtained by maintaining low normal growth rates during crystal growth, and moreover it could have potential for the quality improvement of various crystals from solutions. Therefore, this approach could be a key methodology to achieve accurate 3D structural analysis of


proteins.

Importance of Hydration State around Proteins Required to Grow High

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