Effects of a Strong Magnetic Field on Protein Crystal Growth

Lorentz force, etc. Four mechanisms are currently known to be involved in the effects of magnetic fields on protein crystal growth and all of them may...
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CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 1 17-24

Review Effects of a Strong Magnetic Field on Protein Crystal Growth Nobuko I. Wakayama* National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8565, Japan Received August 2, 2002

ABSTRACT: The effect of a strong magnetic field on protein crystal growth is a new research field. Here, we review research on protein crystallization in magnetic fields, including magnetic orientation of protein crystals, magnetic control of effective gravity on earth, formation of protein crystals in various effective gravity, magnetic improvement in crystal quality, magnetic increase in viscosity of protein aqueous solutions, damping of natural convection by Lorentz force, etc. Four mechanisms are currently known to be involved in the effects of magnetic fields on protein crystal growth and all of them may contribute to the improvement of crystal quality. High quality protein crystals are critical in determining the structure of protein molecules by using X-ray diffraction analysis. Strong magnetic fields will help to improve crystal quality. 1. Introduction Proteins are the elementary building units for living creatures, and the molecular structure of proteins provides a basis for understanding the functions of biological macromolecules. Determining the structure of protein molecules is therefore crucial. The most powerful technique for determining protein structure is X-ray crystallography. Developments in beam technology, detectors, and computational crystallography have greatly accelerated the determination of structures. However, the production of crystals of adequate size and high quality is often the “bottleneck” for three-dimensional structure analysis of macromolecular crystals. The crystallization of biological macromolecules is an empirical science of rational trial and error guided by previous studies. At present, techniques such as extensive purification, supersaturation control, seeding, genetic modification, and formation of crystals in space1,2 are commonly used in most structure improvement. In 1990, a magnetic field was suggested as one of the parameters that potentially influences the growth of protein crystals.3 In the past several years, the effects of magnetic fields on protein crystal growth have been studied. In 2000, two groups independently reported that the quality of protein crystals of orthorhombic lysozyme4,5 and snake muscle fructose-1,6-bisphosphatase6 formed under a strong magnetic field was * To whom correspondence should be addressed. Phone: +81-29861-4519. Fax: +81-298-61-4709. E-mail: [email protected].

superior to that of crystals formed in the absence of the field. In this review, first we summarize the research that clearly shows the effects of magnetic fields on protein crystal growth,7-21 such as magnetic orientation of crystals (section 2), control of effective gravity and formation of protein crystals in various effective gravity (0.7-1.3g) (section 3), improvement in crystal quality in a uniform magnetic field and decrease in both the crystal growth rate and dissolution rate of crystals (section 4), damping of natural convection by Lorentz force (section 5), and increase in viscosity in protein solutions by applying magnetic fields (section 6). Then, we discuss the potential of using strong magnetic fields as an environment to grow crystals of biomacromolecules. 2. Magnetic Orientation of Protein Crystals 2.1. Principle of Magnetic Orientation. Magnetic orientation occurs in a number of biological macromolecule crystals, organelles, and cells (see refs 22-24, and references therein). The alignment of protein crystals is considered to be caused by diamagnetic anisotropy of the peptide groups in the amino acid sequence and of aromatic residues in the molecule.25 The magnetic stabilization energy, ∆E, of a crystal is7,8

∆E )

µ0 |∆χ|H2 2

(1)

where µ0 is the absolute permeability of vacuum (4π ×

10.1021/cg025565g CCC: $25.00 © 2003 American Chemical Society Published on Web 12/07/2002

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Figure 2. Suspended protein crystals in solution in the (a) presence and (b) absence of a horizontal magnetic field.

Figure 1. Tetragonal lysozyme crystals grown in the (a) presence and (b) absence of a uniform magnetic field of 0.6 T. The direction of the magnetic field was horizontal. Photographs were taken 22 h after supersaturation. Initial concentrations of lysozyme and NaCl were 4 and 3%, respectively.

10-7 H m-1), ∆χ is the anisotropy of diamagnetic susceptibility of a crystal, and H is the magnetic field strength. When ∆E exceeds the thermal fluctuation energy kBT, the crystals become magnetically oriented. kB is Boltzman constant and T is temperature. In 1990, Kuroda found that hen egg-white lysozyme crystals that have tetragonal symmetry aligned their c-axis parallel to the direction of a magnetic field when crystals were segregated from solution under a horizontal magnetic field of 1 T.7 As an example of magnetic orientation, Figure 1 shows the photograph of lysozyme crystals formed in the presence and absence of a horizontal magnetic field of 0.6 T. After that study by Kuroda, magnetic orientation has been studied for several protein crystals grown in a magnetic field.8-13 In 1997, Sazaki et al. also reported the magnetic orientation of lysozyme crystals in a vertical magnetic field of 10 T.9 Magnetic orientation of bovine pancreatic trypsin inhibitor,10 porcine pancreatic cr-amylase,10 ribonuclease A11 and met-myoglobin crystals11 were also observed. Suspended tetragonal lysozyme crystals in solution becomes magnetically oriented, aligning their c-axis in the direction of the magnetic field when ∆E exceeds thermal energy, kBT:

N 1 ∆E ) µ0∆KH2 . kBT 2 8

()

(2)

where ∆K is the anisotropy of the magnetic susceptibility per unit cell (about 5 × 10-27 J/T2),7 and N is the number of molecules in a crystal (i.e., size of the crystal). Magnetic orientation is expected for all the crystal symmetries except the cubic.11 Figure 2 shows a schematic of suspended small protein crystals in solution in the presence and absence of an applied magnetic field. ∆E, which determines magnetic orientation, is a function of H and N. According to eq 2, most lysozyme crystals larger than 1.3 µm are magnetically oriented when µ0H ) 1 T, whereas most crystals larger than 0.3

µm are oriented when H ) 10 T. Thus, the minimum size of magnetically oriented crystals decreases with increasing H. 2.2. Magnetic Orientation as a Method to Study the Initial Process of Protein Crystal Growth. 2.2.1. Crystal Growth and Sedimentation. Magnetic orientation has been used to study the initial stage of crystallization.8,12 A magnetic field of 1.6 T has been shown sufficient to orient most crystals in the photograph if applied over the entire period of crystallization. When the field of 1.6 T was applied only during the initial 8 h after supersaturation of the protein solution, a number of large tetragonal lysozyme crystals were observed 24 h after the supersaturation with their c-axis aligned along the direction of the magnetic field. The ratio of magnetically oriented crystals to the total number of crystals was about 70% when a field of 1.6 T was applied for the initial 8 h, and the sizes of most oriented crystals were larger than the unoriented ones. On the other hand, when the field was turned on 8 h after the supersaturation, only relatively small crystals were magnetically oriented. When µ0H ) 1.6 T, most suspended crystals larger than 0.95 µm are magnetically oriented, while magnetic orientation does not occur at the bottom of a container because of the friction between crystals and the bottom wall. The experimental results suggest that the oriented crystals had sedimented to the bottom of the container when the magnetic field was applied. Therefore, it becomes clear that protein crystals grow suspended in the solution as shown in Figure 2, sediment after reaching a critical size, and continue to grow at the bottom of the container. 2.2.2. Rate Constant of Crystal Growth and Sedimentation. By using magnetic orientation, it is possible to mark every crystal when it sediments to the bottom of the container.8,12 When a magnetic field of 1.6 T was applied immediately after supersaturation (t ) 0) for various duration times, photographs taken after crystallization showed that magnetically oriented crystals had sedimented before the field was switched off. As shown in Figure 3, the ratio of the number of magnetically oriented crystals to the total number of crystals could be approximated by ratio ) 1 - exp(kct), where kc is a rate constant of the process of crystal growth and sedimentation, and t is the application period of a 1.6-T magnetic field after supersaturation. This equation quantifies the transient behavior of crystal growth and sedimentation. When the initial lysozyme concentration, c0, was 3.2 (supersaturation ratio β ) 5.3), 4.0 (6.7), or 4.8% (8.0), the approximated

Review

Figure 3. Ratio of the number of magnetically oriented crystals to the total number of crystals as a function of application period (t) of a 1.6-T magnetic field after supersaturation for a initial lysozyme concentration c0 ) 4.8% (4), 4.0% (O), and 3.2% (b). For c0 ) 4.8, 4.0, and 3.2%, photographs were taken 24, 40, and 120 h after the supersaturation, respectively. Solid curves show the ratio calculated as ratio ) 1 - exp(-kt). Reprinted from ref 12. Copyright 1998 with permissions from Elsevier Science.

Figure 4. Ratio of the number of magnetically oriented crystals to the total number of crystals as a function of applied magnetic field strength, H. Reprinted from ref 8. Copyright 1997 with permission from Elsevier Science.

value of kc was 0.016, 0.15, and 0.48/h, respectively, indicating that kc significantly increased with c0.12 2.2.3. Critical Size of Crystal Sedimentation. From theory, sedimentation will occur if a crystal grows large enough that gravitational force exceeds viscous resistance. It can be calculated that the velocity of sedimentation is proportional to the square of the crystal size and that most nuclei less than a certain size, Nc, will stay in solution, while crystals reaching a certain size, Nc, will sediment to the bottom of a container.12 After the crystal has settled on the bottom, magnetic orientation does not occur because of the friction between crystals and the bottom wall. Thus, it is possible to determine Nc by growing crystals under various strengths (H e 1.5 T) of horizontal magnetic field and then analyzing the ratio of magnetic orientation of crystals.8,12 For example, when crystals were formed in a 0.6-T magnetic field (see Figure 1a), most of the crystals were thought to be magnetically oriented before they sedimented to the bottom. Figure 4 shows the relationship between H of a horizontally applied magnetic field and the number ratio of the magnetically oriented to the total crystals.8,12 The analysis of Figure 4 using eq 2 indicates that most of the suspended

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crystals settled on the bottom of the container when their size reached between 2 and 6 µm, and then continued to grow there. The calculations also show that most crystals of several micrometers sediment to the bottom.12 Yanagiya et al. also studied the ratio of magnetic orientation under various strengths of vertical magnetic fields up to 10 T,13 and found that most protein crystals were magnetically oriented when H > 8 T. 2.3. Effects of Magnetic Orientation on ThreeDimensional (3D) Nucleation. The 3D nucleation is the attachment of micron-size crystals from the bulk solution onto an existing crystal surface. Atomic force microscopy (AFM) observations reveal that 3D nucleation is a common crystal growth mechanism for biological macromolecules, such as proteins and viruses, and that micron-size crystals merge onto existing large crystals.26,27 The micron-size crystals might be transported by either sedimentation or convective flow. Recently, Astier et al.28 reported similar AFM observation of R-amylase crystals, and found that a 1-µm microcrystal was incorporated into a larger crystal, thus producing a macrodefect. Astier et al. suggested that this incorporation could be the reason for poor crystal quality in X-ray diffraction. The absence of 3D nucleation caused by sedimentation in microgravity was suggested to contribute to the improvement of crystal quality.29 If the nuclei can take the same orientation as the mother crystal, formation of stacking faults and dislocations during incorporation of the nuclei may be prevented, and therefore crystal quality may improve. As described in section 2.2.3, in the presence of a 1-T horizontal magnetic field, most crystals sediment to the bottom after acquiring the magnetic orientation. Therefore, the merging 3D nuclei can acquire the same orientation as the mother crystal at the bottom of the container.6 Thus, the application of a 10-T field during the entire crystal growth process might improve crystal quality. 3. Control of Effective Gravity (Vertical Acceleration) 3.1. Method to Control Effective Gravity. Recent crystallization experiments conducted on the space shuttle indicate that about 30% of crystals grown in microgravity are larger and yield diffraction data of significantly higher resolution than the best crystals grown on earth.1,2 The remainder either showed no improvement or inferior X-ray diffraction. An obvious difference between space- and earth-based experiments is the magnitude of gravity and buoyancy. One method to damp natural convection due to gravity is the use of magnetic fields. The Lorentz force has been widely used to control natural convection in electrically highconducting fluid such as melts of metal and semiconductors.30 The electrical conductivity of molten Si is about 4 × 106 ohm-1 m-1, whereas that of a typical protein aqueous solution is several ohm-1 m-1. Therefore, damping of convection via Lorentz force is not efficient in protein solutions. At present, few known methods can efficiently damp natural convection in lowconducting fluids such as protein solutions. Recently, a newly developed method to control effective gravity uses a vertical magnetization (Kelvin) force,14,31,32 and is applicable to the control of natural

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Table 1. Volume Magnetic Susceptibility (χ), Mass Magnetic Susceptibility (χg), and Density (G) of Diamagnetic (D) and Paramagnetic Materials (P) at Room Temperature pure water acetone benzene ethanol N2 gas lysozyme O2 gas

D D D D D D P

χ

χg [kg-1 m3]

F [kg m-3]

-9.00 × 10-6 -5.82 × 10-6 -6.51 × 10-6 -7.75 × 10-6 -6.79 × 10-9 -11.31 × 10-6 +1.91 × 10-6

-9.00 × 10-9 -7.35 × 10-9 -8.82 × 10-9 -9.02 × 10-9 -5.40 × 10-9 -9.42 × 10-9 +1.34 × 10-6

1.0 × 103 0.785 × 103 0.874 × 103 0.786 × 103 1.25 1.2 × 103 1.43

convection in low and nonconducting fluids. Magnetization force is a body force and acts on every material even if it is not ferromagnetic. Generally, a unit volume of a substance in a 1-D magnetic field gradient experiences a force Fm 33

Fm ) µ0χH(dH/dy) ) Fµ0χgH(dH/dy)

(3)

where y is the site coordinate and χ is the volume magnetic susceptibility defined as the product of material density (F) and mass magnetic susceptibility (χg). Table 1 shows χ, χg, and F of diamagnetic (D) and paramagnetic (P) materials at room temperature. Most materials, such as water and a majority of proteins, are diamagnetic, and experience a weak repulsive force along the steepest gradient of the magnetic field strength because χg < 0. On the other hand, an attractive force acts on paramagnetic materials. Most diamagnetic materials have nearly the same χg (see Table 1) and χg is independent of temperature. Therefore, χ of an aqueous protein solution increases with increasing protein concentration. Because Fm is almost proportional to material density, its superposition on gravity can partially reduce or enhance effective gravity (vertical acceleration). When an upward Fm is applied along the gravitational force Fg, the total force acting on a fluid is

F ) Fg - Fm ) F{g - |µ0χgH(dH/dy)|} ) F pg p ) 1 - |(µ0χg/g)H(dH/dy)|

(4)

This equation indicates that the level of effective gravity, p, can be modified continuously by changing the value of H(dH/dy). Figure 5 shows the cross-section schematic of a vertical superconducting magnet and the spatial distribution of the magnetic strength along a vertical central y-axis. For example, when µ02H(dH/dy) ) -685 T2/m at position A, an upward Fm of 0.5 Fg acts on pure water (χg ) -9.0 × 10-9 m3 kg-1), and thus the expected p is 0.5g. To control effective gravity, a magnet that supplies a spatially uniform distribution of H(dH/dy) is desired.32,34,35 If an upward Fm is applied, diamagnetic materials, such as water, ethanol, and acetone,36 can be levitated. Such levitation requires a strong magnetic field of 2025 T, which usually can be generated for only several hours by a massive hybrid magnet. Recent development of a liquid helium free superconducting magnet, however, has made it easy to generate a strong magnetic field of up to about 15 T in a bore of a diameter of at least 50 mm. When such a superconducting magnet is used, an environment of partially reduced or enhanced

Figure 5. Experimental setup to control effective gravity p by using a vertical superconducting magnet. Right figure shows the spatial distribution of the magnetic field strength.

effective gravity can be achieved and maintained for days or weeks. The application of this method is anticipated for material processing. Specifically, for protein crystal growth, generating a reduced gravity environment over a period of days or weeks is crucial. The protein crystal formation experiments described in 3.2 used a commercially available liquid helium free superconducting magnet that can generate an environment of 0.7g, and improvement in crystal quality was observed. Fabricating a magnet that can generate a low-gravity environment, for example, 0.1g, 0.2g, is technically feasible. Such a magnet was constructed at the Tsukuba Magnet Laboratory. Furthermore, recently developed magnetic force booster37 can supply 1335 T2/m (0.03g) when it is attached to a commercially available 10 T magnet. A new type of superconducting magnet to supply 1500 T2/m was also fabricated.38 3.2. Formation of Protein (Snake Muscle Fructose-1,6-Bisphosphatase) Crystals Under Various Magnitudes of Effective Gravity. Protein crystal formation experiments were previously done for various magnitudes of effective gravity.6 The protein used was snake muscle fructose-1,6-bisphosphatase (MW ) 36 000), which is a series of enzymes that controls the sugar level in blood. At present, details of the molecular structure of this protein have not been determined. 3.2.1. Experimental Apparatus and Procedures. The protein crystal formation experiments used a commercially available liquid helium free superconducting magnet that can generate an environment of 0.7g. Crystals were grown simultaneously in three vessels (Figure 5) at three positions (A, B, and C) inside a vertical superconducting magnet. For control, crystals were grown outside the magnet. At the center of the magnet where a strong uniform field (position B) exists, no magnetization force Fm acts on the protein solution. When µ0H is 10 T at the center of the magnet (B), at the upper position (A), a magnetic field of 7 T and an upward Fm corresponding to -400 T2/m exist simultaneously. The upward Fm acting on the protein solution corresponds to about 30% of the gravitational force (see eq 4). Thus, position A corresponds to an effective gravity of 0.7g. On the other hand, the lower position (C), where a downward Fm of the same magnitude acts

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Crystal Growth & Design, Vol. 3, No. 1, 2003 21

Figure 7. The ω - scan profiles of rocking curves for the (10 0 0) reflections of 10 T crystal compared with 0 T crystal. Reprinted from ref 4. Copyright 2000 with permission from International Union of Crystallography. Figure 6. Resolution of protein crystals (snake muscle fructose-1,6-bisphosphatase) as a function of effective gravity (vertical acceleration). Reprinted from ref 21. Copyright 2002 with permission from Elsevier Science. Experimental results are also summarized in Table 1 in ref 6.

corresponds to an effective gravity of 1.3g. Crystal formation experiments were conducted four times. Crystals were grown by batch crystallization. For each position, an X-ray oscillation photograph of a crystal of similar size was taken for comparison. The resolution shell whose signal-to-noise ratio was 2 was determined and then used as an indicator of crystal quality. 3.2.2. Results and Discussion. The results of the crystal evaluation are shown in Figure 6. When crystals were grown inside the magnet (4), the crystals grown under an effective gravity less than 1g (position A) tended to have a higher resolution than those under normal gravity (position B). Crystals grown under an effective gravity higher than 1g (position C) tended to have a lower resolution than those under normal gravity. Thus, the resolution of the crystals formed inside the magnet tended to increase with decreasing effective gravity. This tendency indicates that the level of effective gravity is an important factor in determining crystal quality. The resolution of the crystals formed in 0.7-0.8g was about 3.06 ( 0.14 Å, whereas that of crystals formed outside the magnet (O) was 4.24 ( 1.24 Å. This indicates that the lower gravity improved the resolution of crystals by about 30%. Thus, when protein crystals were formed in a low-gravity environment where natural convection was partially damped, the crystal quality was superior to the quality of crystals formed in the absence of the applied magnetic field. 3.3. Numerical Simulation of Natural Convection in Fluids at the Position A Inside the Superconducting Magnet. Since proteins are incorporated into the crystal during crystal growth, the solution density near the crystal surface becomes lower than that of bulk solution and natural convection occurs. Qi et al.15 numerically studied the effect of magnetic fields on natural convection near a growing cylindrical protein crystal (diameter of 1 mm, height of 1 mm) in a cylindrical cell (diameter of 10 mm, height of 10 mm) when a container of protein solution was set at position A inside the magnet (as shown in Figure 5) and thus

an upward Fm acted on the solution. In the absence of the magnetic field (i.e., outside the magnet), the maximum velocity of natural convection was 1.11 mm/s. On the other hand, when µ20H(dH/dy) ) 685 and 1370 T2/m in eq 4, and the corresponding effective gravity levels were 0.5 and 0g, the magnitudes of maximum velocity were reduced to 0.58 mm/s and 0.1 µm/s, respectively. Thus, the natural convection was damped by the vertical magnetic field gradients, compared with the convection in the absence of the magnetic field. The damping of thermal convection in an aqueous solution of paramagnetic salts was studied experimentally for an applied vertical magnetic field gradient.39 The mechanism of magnetic damping of thermal convection in a paramagnetic solution is different from that in a diamagnetic solution. For a paramagnetic solution, the magnetic buoyancy is ∆Fm ) 0.5µ0∆χ∇H2 ) 0.5µ0(χg∆F + F∆χg)∇H2, and the second term caused by Curie’s law becomes dominant. For a diamagnetic material, such as water or protein, ∆χg ) 0 and ∆Fm is proportional to ∆F. The damping of thermal convection caused by a magnetic field gradient in electrically lowconducting diamagnetic and paramagnetic fluids has also been studied by using numerical simulations.40-42 On the basis of these experimental results and simulations, a possible method to damp natural convection in such fluids is the use of a magnetic field gradient. 4. Other Kinds of Magnetic Effects on Protein Crystal Growth 4.1. Improvement in the Quality of Orthorhombic Lysozyme Crystals by a Uniform Magnetic Field of 10 T. As shown in Figure 6, the crystals of snake muscle fructose-1,6-bisphosphatase formed in an uniform magnetic field of 10 T (position B in Figure 5) did not have a significantly higher resolution than those grown in the absence of a field. But when orthorhombic lysozyme crystals were grown in the presence of a uniform magnetic field of 10 T, crystal quality was significantly improved.4,5 Crystal perfection was evaluated using the full-width at half-maximum (fwhm) of the rocking curve. Figure 7 shows the ω - scan profiles of rocking curves for the (10 0 0) reflections of 10 T crystal compared with 0 T crystal. All the crystals grown

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Table 2. Various Mechanisms of Magnetic Effects on Protein Crystal Growth uniform magnetic field

mechanism (1) magnetic orientation (2) damping of natural convection by an upward magnetization force (3) damping of natural convection by Lorentz force (4) viscosity increase

yes no

magnetic field gradient yes yes

yes (low efficiency) yes (low efficiency) yes

yes

at 10 T showed a narrower average fwhm of the rocking curve than those grown at 0 T (in the absence of a magnetic field). The fwhms of the reflections decreased by 20-40% in the crystals grown at 10 T. As a result, the maximum resolution of X-ray diffraction increased from 1.3 Å at 0 T to 1.13 Å at 10 T. Furthermore, the magnetic field affected the dimensions of the unit cell, increments being 0.2% for the a- and c-axes and 0.1% for the b-axis, respectively. These results show that a uniform magnetic field of 10 T also improved the crystal perfection. At present, there are two reports on the magnetic-induced improvement in crystal quality.4-6 Further research is expected. 4.2. Decrease in Crystal Growth Rate and Dissolution Rate of Tetragonal Lysozyme Crystals by a Uniform Magnetic Field. Magnetic fields can be classified into uniform or gradient magnetic fields, as shown in Figure 5. Only a magnetic field gradient can induce an upward Fm and damp natural convection in electrically low-conducting fluids (see Table 2). In a recent study, the growth rate of tetragonal lysozyme crystals was reduced in the presence of a uniform magnetic field, compared with the growth rate in the absence of a field.16,17 The growth rate of tetragonal lysozyme crystals was measured under 0 and 11 T,16 and it was found that the growth rates under 11 T were 10-60% smaller than those under no magnetic field. Furthermore, the dissolution rate of the crystals was also reduced by the application of a uniform field.16,18 These experimental results suggest that even a uniform magnetic field might damp natural convection in protein aqueous solutions. 5. Damping of Natural Convection by Lorentz Force Damping of natural convection in liquid metals and semiconductors using static magnetic fields has been extensively studied since the 1960s.30 When an electrically conducting fluid moves in a magnetic field, Lorentz force dampens the fluid motion. The Hartmann number, Ha, is generally used as a parameter to estimate the efficiency of magnetic damping:

Ha ) µ0HLxσ/Fν

(5)

where σ is electric conductivity, L is the size of the container of the fluid, F is the fluid density, and ν is fluid kinematic viscosity. In general, Ha ≈ 100-400 for molten silicon. A recent study revealed magnetic damping of thermal convection in 25 wt % NaCl aqueous solution (σ ) 21 Ω-1 m-1) under 10 T.43 For this case, Ha ) 14.5.

Damping of thermal convection in this aqueous solution in a rectangular container by Lorentz force was numerically investigated as a function of the aspect ratio of the container (AR), Grashof number, and Ha.44 The results reveal that the magnetic damping of natural convection strongly depends on AR and that an optimum AR exists for minimizing natural convection. Thus, the shape of a container is an important factor in damping natural convection by Lorentz force. Damping of natural convection due to a Lorentz force mechanism is expected under both a uniform field and a magnetic field gradient (see Table 2). For a typical protein crystal formation experiment, σ ) 5 Ω-1 m-1, F ) 103 kg cm-3, ν ) 10-6 m2 s and L ) 5 × 10-3 m. Even when µ0H ) 10 T, Ha ≈ 3.5 and the roughly estimated efficiency of magnetic damping is small. Qi et al.15 numerically studied the effect of Lorentz force on natural convection near a growing protein crystal (size 1 mm) in a cylindrical cell (diameter of 10 mm, height of 10 mm). When a Lorentz force was generated by a magnetic field of 10 T and σ ) 4.1 Ω-1 m-1, the calculated maximum velocity of natural convection was 1.08 mm/s. The maximum velocity in the absence of a magnetic field was 1.11 mm/s, indicating that the damping of natural convection by Lorentz force was negligible. Although the efficiency of damping of convection by Lorentz force is low, such damping might help improve crystal quality. 6. Increase in Viscosity in Aqueous Protein Solutions by Applying Magnetic Fields 6.1. Viscosity Measurement Under a Strong Magnetic Field. If viscosity η of protein aqueous solutions increases in a strong magnetic field, natural convection will be damped even under a uniform field. Therefore, the magnetic effects on η of protein solutions have been examined.19 In that study, η was measured by a falling ball method. The measurement apparatus was set at the center of a vertical superconducting magnet, and the behavior of the glass ball was recorded by using a CCD camera. The η was calculated from the velocity of the ball (based on the distance l for a ball to fall per unit time). Pure water was used as a control and its η was assumed to be independent of magnetic field strength H. The η of a sample was obtained approximately by using the following relationship:

η≈

ηH2O(FG - FL)lH2O (FG - FH2O)l

≈

ηH2OlH2O l

(6)

where FG, FL and FH2O are the densities of glass, sample, and pure water, respectively. Figure 8 shows the time dependence of B ) µ0H and η of the lysozyme solution when the concentrations of lysozyme and NaCl in solution are 2.83 and 2.35%, respectively, and crystals do not grow easily. When the solution was filtered and did not contain microcrystals larger than 0.4 µm (b), η was relatively independent of the magnetic strength of the applied field. On the other hand, when the solution was not filtered and it did contain such crystals, experiment was conducted twice. For two different protein solutions (O and 4), η increased by 10 to 20% when a 10-T magnetic field was

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Crystal Growth & Design, Vol. 3, No. 1, 2003 23

Figure 8. Time dependence of magnetic field strength (B ) µ0H) and viscosity of an aqueous protein solution when concentrations of lysozyme and NaCl in solution were 2.83 and 2.35%, respectively, and crystals were not easily formed. Reprinted from ref 19. Copyright 2001 with permission from Elsevier Science. Type A did not contain microcrystals larger than 0.4 µm (i.e., filtered solution), whereas type B did contain such microcrystals (nonfiltered solution).

applied and then returned to its initial value after the field was switched off. Generally, when a liquid contains solid particles, the increase in η obeys Einstein’s viscosity formula:

η/η0 - 1 ) 2.5φ

(7)

where φ is the volume fraction of the particles. As shown in Figure 8, in the absence of magnetic field, η increased in increasing order of solution without microcrystals (b), solution with microcrystals (4), and another solution with microcrystals (O). Though η of the solutions (4, O) increased in the presence of 10 T, this order was the same as in the absence of a magnetic field. This suggests that the magnetically induced increase in η was caused by the existence of unsolved microcrystals in the solution. When a protein solution was prepared for crystals that easily segregated (lysozyme 4.0%, NaCl 3.05%) and then was filtered,19 the measured η in the absence of a magnetic field was relatively independent of time. In contrast, in the presence of a 10-T magnetic field, the measured η increased with time. After switching off the field, η did not return to the initial value. Increase in η by applying a magnetic field has been observed in magnetic fluids45 and in human blood.46 In magnetic fluids, the magnetic orientation of the chainlike clusters of magnetic particles causes the increase in η apparently when a magnetic field is applied. In human blood, a magnetically induced increase in η was explained by the magnetic orientation of red blood cells. A similar phenomenon is expected in protein aqueous solutions containing small suspended crystals. As described in section 2, there exist many suspended small crystals during the process of protein crystal growth. The magnetic orientation of these suspended crystals

(Figure 2a) are considered to increase η under a strong magnetic field. Furthermore, the η of solution in which crystals easily grew did not return to the initial value after switching off the field, and some change of η might be intrinsic. Because the mechanism of magnetic increase in η has not been clarified completely,19,20 this kind of magnetic effect is classified as one of four currently known mechanisms of magnetic effects (Table 2). 6.2. Damping of Natural Convection due to Magnetically Induced Increase in Viscosity. A magnetically induced increase in η will dampen natural convection. According to a numerical study,21 when the magnetic field increases η by 30% and 50%, the maximum velocity of natural convection near a cubic crystal (100 µm size) is reduced by about 20 and 40%, respectively. This magnetically induced damping of natural convection explains the experimental results that showed a decrease in crystal growth rate16,17 and a decrease in dissolution rate of lysozyme crystals16,18 under a strong magnetic field. This kind of magnetic damping of natural convection occurs in a magnetic field gradient as well (see Table 2). 7. Conclusions This review summarizes the research that clearly shows the effects of magnetic fields on protein crystal growth. Currently, four mechanisms of magnetic effects on protein crystal growth are known (Table 2), and all of them may contribute to the improvement of crystal quality: Mechanism (1): Magnetic orientation of suspended small crystals. Effect: In 3D nucleation, if the merging nuclei can acquire the same direction as the mother crystal through magnetic orientation, it will improve the crystal quality. Mechanism (2): Low-gravity environment. Effect: By applying an upward Fm to protein solutions, effective gravity can be controlled between microgravity and 1g. The obtained low-gravity environment on earth makes it possible to partially damp natural convection during protein crystal growth. Mechanism (3): Damping of natural convection by Lorentz force. Effect: Lorentz force damps natural convection though the efficiency is low. Mechanism (4): Magnetically induced increase in viscosity. Effect: A magnetically induced increase in viscosity causes damping of natural convection during protein crystal growth. The quality of orthorhombic lysozyme crystals formed under a uniform magnetic field was superior to the quality of crystals formed in the absence of the field.4,5 In this case, mechanisms (1), (3), and (4) contributed to this improvement in crystal quality. In contrast, the quality of snake muscle fructose-1,6-bisphosphatase crystals formed in 0.7-0.8g6 was superior to the quality of such crystals formed in the absence of a field. In this case, mechanism (2) was the main contributor to this improvement in crystal quality. The effect of a strong magnetic field on protein crystal growth is a new research field. Many experimental factors, such as electrical conductivity of solution,

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protein concentration, magnetic field strength and its direction, may contribute to these magnetic effects. Clarification of the mechanisms involved in these effects will help in the development of methods to improve the crystal quality of biomacromolecules. Acknowledgment. This research was supported by the Core Research for Evolutional Science and Technology (CREST) project “Protein crystal growth under virtually variable gravity realized by magnetic force,” 1997-2002. The author thanks Dr. M. Ataka of National Institute of Advanced Industrial Science and Technology for valuable discussions. References (1) DeLucas, L. J.; Smith, C. D.; Smith, H. W.; Vijaykumar, S.; Senadhi, S. E.; Ealick, S. E.; Carter, D. C.; Snyder, R. S.; Weber, P. C.; Salemme, F. R.; Ohlendorf, D. H.; Einspahr, H. M.; Clancy, L. L.; Navia, M. A.; Mckeever, B. M.; Nagabhushan, T. L.; Nelson, G.; McPherson, A.; Koszelak, S.; Taylor, G.; Stammers, D.; Powell, K.; Darby, G.; Bugg, C. E. Science 1989, 246, 651-654. (2) Kundrot, C. E.; Judge, R. A.; Pusey, M. L.; Snell, E. D. Cryst. Growth Des. 2001, 1, 87-99. (3) McPherson, A. Eur. J. Biochem. 1990, 189, 1-23. (4) Sato, T.; Yamada, Y.; Saijo, S.; Hori, T.; Hirose, R.; Tanaka, N.; Sazaki, G.; Nakajima, K.; Igarashi, N.; Tanaka, M.; Matsuura, Y. Acta Crystallogr. 2000, D56, 1079-1083. (5) Sato, T.; Yamada, Y.; Saijo, S.; Hori, T.; Hirose, R.; Tanaka, N.; Sazaki, G.; Nakajima, K.; Igarashi, N.; Tanaka, M.; Matsuura, Y. J. Cryst. Growth 2001, 232, 229-236. (6) Lin, S. X.; Zhou, M.; Azzi, A.; Xu, G. J.; Wakayama, N. I.; Ataka, M. Biochem. Biophys. Res. Commun. 2000, 275, 274278. (7) Kuroda, R. Master Thesis, Protein Crystal Growth; Department of Applied Physics Faculty of Engineering, University of Tokyo, 1990. (8) Ataka, M.; Katoh, E.; Wakayama, N. I. J. Cryst. Growth 1997, 173, 592-596. (9) Sazaki, G.; Yoshida, E.; Komatsu, H.; Nakada, T.; Miyashita, S.; Watanabe, K. J. Cryst. Growth 1997, 173, 231-234. (10) Astier, J. P.; Veesler, S.; Boistelle, R. J. Cryst. Growth 1998, 54, 703-706. (11) Sakurazawa, S.; Kubota, T.; Ataka, M. J. Cryst. Growth 1999, 196, 325-331. (12) Wakayama, N. I. J. Cryst. Growth 1998, 191, 199-205. (13) Yanagiya, S.; Sazaki, G.; Durbin, S. D.; Miyashita, S.; Nakada, T.; Komatsu, H.; Watanabe, K.; Motokawa, M. J. Cryst. Growth 1999, 196, 319-324. (14) Wakayama, N. I.; Ataka, M.; Abe, H. J. Cryst. Growth 1997, 178, 653-656. (15) Qi, J. W.; Wakayama, N. I.; Ataka, M. J. Cryst. Growth 2001, 232, 132-137. (16) Yanagiya, S.; Sazaki, G.; Durbin, S. D.; Miyashita, M.; Nakajima, K.; Komatsu, H.; Watanabe, K.; Motokawa, M. J. Cryst. Growth 2000, 208, 645-650. (17) Yin, D. C.; Inatomi, Y.; Kuribayashi, K. J. Cryst. Growth 2001, 226, 534-542 (18) Yin, D. C.; Inatomi, Y.; Wakayama, N. I.; Kuribayashi, K.;

Review Huang, W. D. Acta Crystallogr. D, in press. (19) Zhong, C. W.; Wakayama, N. I. J. Cryst. Growth 2001, 226, 327-332. (20) Zhong, C. W.; Wang, L. B.; Wakayama, N. I. J. Cryst. Growth 2001, 233, 561-566. (21) Wang, L. B.; Zhong, C. W.; Wakayama, N. I. J. Cryst. Growth 2002, 237-239, 312-316. (22) Torbet, J.; Freyssinet, J. M.; Hudry-Clergeon, G. Nature 1981, 289, 91-93. (23) Yamagishi, A. J. Magn. Magn. Mater. 1990, 90, 43-46. (24) Rothgeb, T. M.; Oldfield, E. J. Biol. Chem. 1981, 256, 14321446. (25) Worcester, D. L. Proc. Natl. Acad. Sci. U.S.A. 1978, 75, 5475-5477. (26) Malkin, A. J.; Kuznetsov, Y. G.; Land, T. A.; DeYoreo, J. J.; McPherson, A. Nat. Struct. Biol. 1995, 2, 956-959. (27) Malkin, A. J.; Kuznetsov, Y. G.; McPherson, A. Proteins Struct. Funct. Genet. 1996, 24, 247-252. (28) Astier, J. P.; Bokern, D.; Lapena, L.; Veesler, S. J. Cryst. Growth 2001, 226, 294-302. (29) McPherson, A. In Crystallization of Biological Macromolecules; Cold Spring Harbor Laboratory Press: New York, 1999; p 453. (30) Series, R. W.; Hurle, D. T. J. J. Cryst. Growth 1991, 113, 305-328. (31) Wakayama, N. I. Control of Effective Gravity; Japan patent 3278685, applied in 1996. (32) Wakayama, N. I.; Zhong, C. W.; Kiyoshi, T.; Itoh, K.; Wada, H. AIChE J. 2001, 47, 2640-2643. (33) McGraw-Hill Encyclopedia of Science and Technology, 7th ed; McGraw-Hill: New York, 1992; Vol. 10, p 315, (34) Kiyoshi, T.; Ozaki, O.; Morita, H.; Nakayama, H.; Jin, H. B.; Wada, H.; Wakayama, N. I.; Ataka, M. IEEE Appl. Supercond. 1999, 9, 362-365. (35) Kiyoshi, T.; Wada, H.; Wakayama, N. I. Uniform Magnetic Force Generation Magnet; US Patent US 6362712. (36) Beangnon, E.; Tournier, R. Nature 1991, 349, 470-470. (37) Ozaki, O.; Kiyoshi, T.; Koyanagi, K.; Fujihira, J.; Wada, J. In Proceeding of 6th Symposium on New Magneto-Science; National Institute for Materials Science: Tsukuba, Japan, November 6-8, 2002, p 59. (38) Hirose, R.; Saito, K.; Watanabe, Y.; Tanimoto, Y., J. In Proceedings of 6th Symposium on New Magneto-Science; National Institute for Materials Science: Tsukuba, Japan, November 6-8, 2002, p 60. (39) Braithwaite, D.; Beaugnon, E.; Tournier, R. Nature 1991, 354, 134-136. (40) Qi, J. W.; Wakayama, N. I.; Yabe, A. Int. J. Heat Mass Transfer 2001, 44, 3043-3052. (41) Qi, J. W.; Wakayama, N. I. Mater. Trans., JIM 2001, 41, 970-975. (42) Ramachandran, N.; Leslie, F. W. AIAA-2001-0618. (43) Sazaki, G.; Durbin, S. D.; Miyashita, S.; Ujihara, T.; Nakajima, K.; Motokawa, M. Jpn. J. Appl. Phys. 1999, 38, L842-L844. (44) Wang, L. B.; Wakayama, N. I. Int. J. Heat Fluid Flow 2002, 23, 92-95. (45) Taketomi, S.; Chikazumi, S. In Magnetic Fluid; NikkanKogyo-Shinbun; 1998; pp 226-237 (in Japanese). (46) Haik, Y.; Pai, V.; Chen, C. J. J. Magn. Magn. Mater. 2001, 225, 180-186.

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