Effects of a Magnetic Field on Lysozyme Crystal Nucleation and

Effects of a Magnetic Field on Lysozyme Crystal Nucleation and Growth in a Diffusive Environment Jose A. Gavira* and Juan Ma. Garcı´a-Ruiz Laboratorio de Estudios Crystalogra´ficos, Instituto Andaluz de Ciencias de la Tierra, CSIC-UniVersidad de Granada, Edf. Lo´pez Neyra, P.T.C.S., AVda. del Conocimiento, s/n. 18100 Armilla, Granada, Spain

CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 6 2610–2615

ReceiVed August 7, 2008; ReVised Manuscript ReceiVed April 22, 2009

ABSTRACT: Tetragonal hen egg white lysozyme crystals were grown in agarose gel under the influence of a 7 T homogeneous and static magnetic field. The use of agarose, gels, and polymer solutions avoids crystal sedimentation and buoyancy-driven convection providing a diffusive mass transport environment. Under these conditions, 100% of lysozyme crystals grown in 0.02% (w/v) agarose can be oriented by a 7 T magnetic field. When the agarose concentration was increased, the number of oriented crystals decreased. The results are explained by the compromise between the effect of the magnetic field and the chemical effects due to the interaction between protein and agarose, because it is known that agarose modifies the nucleation rate of lysozyme crystals. When the chemical effect of agarose was removed, it appears clear that a homogeneous and constant magnetic field influences both nucleation and growth of lysozyme tetragonal crystals in a convection-free environment. Both effects depend on supersaturation and exposure time.

1. Introduction The diamagnetic anisotropy of the peptide bonds or the paramagnetic anisotropy of prosthetic groups allows the orientation of protein molecules when they cooperatively self-arrange to form a crystal under the influence of an external magnetic field. The orientation of nonperiodic arrays of different macromolecules has been shown in cells,1,2 in photosynthetic seaweed and bacterium,3,4 and during the formation of fibrins gel.5 In 1981, Rothgeb and Oldfield observed for the first time the orientation of a suspension of microcrystals of myoglobine and cobalt-myoglobine (its Co2+ derivative) in the direction of the applied magnetic field.6 During the past decade, a large number of studies have been published on the influence of magnetic fields on (i) crystal orientation,7-11 (ii) nucleation and growth of crystal,7,12-14 (iii) crystal quality,15 and (iv) modification of the dynamic properties of protein solutions and its consequences, including crystal sedimentation.16-23 Two reviews on the subject, by Ataka and Wakayama, and Wakayama,22,24 were mainly focused on the influence of an applied magnetic field on crystal orientation and other modifications of the protein solution properties and its influence on crystal quality, while the earlier controversy on the effect of a magnetic field on nucleation and growth7,12-14 has not been fully addressed. The present study aims to investigate the influence of a homogeneous and constant magnetic field on protein crystal nucleation and growth. Until now all the reported data were obtained from experiments where crystals were grown from free protein solutions by the batch method. With this experimental setup, crystal sedimentation and fluid convection cannot be avoided. Both factors influence the experimental results making it difficult to isolate the contribution of the magnetic field on the crystal growth behavior. To remove convection and sedimentation from our experimental setup, we decided to gel the protein solution using agarose at different concentrations. The experiments were performed in a homogeneous and constant 7 T magnetic field. The effect of the magnetic field was analyzed * To whom correspondence should be addressed. E-mail: [email protected]. Phone: +34 958 181644. Fax: +34 958 181632.

after removing the chemical influence of agarose evaluated from reference experiments at 0 T. We also studied the dependence of the magnetic field effect on the supersaturation using the counter-diffusion setup.25 Finally we propose the application of this methodology to obtain aligned single crystals in capillaries as a tool for crystal quality evaluation.

2. Materials and Methods 2.1. Proteins and Chemicals. Hen egg white lysozyme (HEWL) was purchased from Sigma (batch 65H7025, 73.000 u.a) and used without further purification. The lyophilized powder was dissolved in 50 mM sodium acetate pH 4.5 and filtered through 0.45 µm pore size (Millipore, Millex-HV13). Protein concentration was determined from the absorbance at 280 nm of the buffered solution using 2.66 mL mg-1 cm-1 as the extinction coefficient. Agarose (D5) with 310 K gel-point and 363 K melting-point was supplied by Hispanagar. 2.2. Crystallization Setup and Conditions. Three different crystallization set-ups were used during this investigation: gelled-batch (Batch), counter-diffusion in agarose gel (CD),26 and the gel acupuncture method (GAME).27 The last two methods are based on the three-chamber counterdiffusion configuration extensively discussed elsewhere.25 For the gelled-batch method, the sol was prepared by heating an agarosebuffered suspension at 368.5 K until complete dissolution. The sol was then allowed to cool down and was kept at 318.5 K. Protein, salt, and buffer solutions were incubated at 313.5 K prior to being mixed with the sol. The solution was then divided in two samples and allowed to reach room temperature and to gel. A similar procedure was used to prepare the CD samples.26 In all cases, the references were kept at the same temperature as the sample, 293 K. Table 1 shows the crystallization conditions for each setup. A nuclear magnetic resonance instrument (Bruker AM-300) was used to generate a 7 T intensity static magnetic field with 99.9% homogeneity over a 4.0 cm effective working region. The experimental setup was designed to fit the typical NMR-cell, a closed-end tube 60 mm in length and 5 mm inner diameter (Wildmad, WG-5 mm-Economy-7). Figure 1 shows a schematic representation of the experimental configurations.

3. Theoretical Aspects The diamagnetic property of a molecule can only be detected if its paramagnetic contribution is negligible. Proteins have a very low diamagnetism and are in most cases nonparamagnetic. Therefore, to have a significant contribution of their diamag-

10.1021/cg8008688 CCC: $40.75  2009 American Chemical Society Published on Web 05/12/2009

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Table 1. Experimental Configuration and Crystallization Conditions protein chamber a,b

CD GAMEc Batch

physical buffer

salt chamber

[lysozyme] 80 mg/mL [agarose] 0.025-0.5% (w/v) [agarose] 0.5% (w/v) [NaCl] 20% (w/v) [agarose] 0.5% (w/v) [lysozyme] 100 g/mL [Agarose] 0.0-0.025% (w/v) 6 mm punctuation depth [NaCl] 20% (w/v) [lysozyme] 60 mg/mL, [NaCl] 4.0% (w/v) and [agarose] 0.025-0.5% (w/v)

a The dimensions of the protein, physical buffer, and salt chambers were respectively 20, 2.5, and 30 mm. b For the extended-time experiments (>72 h), protein and salt concentrations were 50 mg/mL and 10% (w/v) with a configuration of 30, 5, and 30 mm for the protein, buffer, and salt chambers, respectively. c An individual capillary of 0.5 mm inner diameter filled with protein solution to 60 mm length was punted onto a 20 mm gel layer and 20 mm salt solution was poured onto it.

Taking φ ) 90° for an R-helix structure with NR amino acid residues and φ ≈ 60° for a β-sheet structure with Nβ residues, the anisotropy of the diamagnetic susceptibility for secondary structural elements can be calculated from

Figure 1. (A) Shows a schematic representation of a NMR instrument; (B) schematized the three experimental setups, Batch, GAME (Gel acupuncture method), and CD (counterdiffusion); (C) shows the most recent homogeneity test done over the 80 mm measurement vessel.

netism it is necessary to arrange a number of molecules, for instance, by crystallizing them. The diamagnetic properties of proteins or peptides are due to the asymmetric distribution of the electronic cloud in the peptide bonds. The contribution of each amino acid to the final diamagnetic anisotropy can be evaluated using the Lonsdale formulation28 lately applied by Worcester29 to calculate the contribution of each peptide bond to the diamagnetic susceptibility (χi) when arranged along a structure with axial distribution (R-helix or β-sheet)

χi )

∑ cos2 θijKj

(1)

j

where Kj is the diamagnetic susceptibility of the peptide bond and θij is the angle between Kj and χi. The anisotropy of the diamagnetic susceptibility of the peptide bond can be divided into a contribution parallel (k|) and a contribution perpendicular (k⊥) to the peptide plane. For an axial structure (either R-helix or β-sheets), it is enough to define two directions: one parallel (χ|) and one perpendicular (χ⊥) to the axis.

χ|| ) k|| cos2 φ + k⊥ sin2 φ

(2)

χ⊥ ) (k⊥·sin2 φ + k||·(cos2 φ + 1))/2

(3)

where φ is the angle between the axis and the direction normal to the peptide plane (Figure S1A,Supporting Information). The anisotropy of the diamagnetic susceptibility for any axial structure can then be expressed as ∆χ ) χ|| - χ⊥.

∆χR ) (N/2)∆K ) -2.68 × 10-6NR

(4)

∆χβ ) (N/8)∆K ) -6.7 × 10-7Nβ

(5)

Equations 4 and 5, given by Worcester, have been modified to use the corrected value of ∆K ) -5.36 × 10-6 (CGS) introduced by Pauling.30 Substituting in eqs 4 and 5 the total number of amino acids that forms R-helices or β-sheets in the lysozyme molecule (PDB ID 193L) and solving in ∆χT ) ∆χR+∆χβ yields the absolute value of the diamagnetic anisotropy 1.54 × 10-4 (CGS or emu/ mol). In this calculation, the contribution of the aromatic groups to the anisotropy of the diamagnetism has not been considered, since they are randomly oriented and distributed. To orient a lysozyme crystal, the energy supplied by the magnetic field must overcome the thermal fluctuation energy, kT (k is the Boltzmann constant and T is the absolute temperature). The molecular contribution to the total stabilization energy can be expressed as29

∆E ) (1/2)(N/NA)H2(cos2 φ∆χ + χ⊥)

(6)

where H is the magnetic field intensity, N is the number of molecules, NA is Avogadro’s number, and φ is the angle between the symmetry axis and the magnetic field direction. In the original work, Worcester simplified this expression for structures oriented parallel to the magnetic field lines,

∆E ) (1/2)(N/NA)H2∆χ ) (1/2)(N/NA)H2∆χT

(7)

In this formulation, each individual structure with axial distribution is considered independent, but in a protein, each secondary structure element has a fixed three-dimensional position and the packing of protein molecules in the crystals is different for each crystallographic form. Tetragonal lysozyme crystals appear oriented with their “c” axis parallel to the direction of the magnetic field. The contribution of each secondary structure element (8 R-helix and 2 β-sheet) of a tetragonal lysozyme crystal can be corrected knowing the angle (φ) between the axis of each secondary structure element and the main quaternary axis (c) (Figure S1B, Supporting Information), oriented parallel to the magnetic field (∆χT ) Σi(cos2 φi∆χR) + Σj(cos2 φj∆χβ); i ) 1-8, j ) 1-2). Applying the angular correction, the calculated absolute value of ∆χT (the diamagnetic anisotropy of lysozyme in a tetragonal crystal) is 4.08 × 10-5 (CGS). The minimum number of lysozyme molecules (N ) NH) required to orient a tetragonal crystal can be obtained from eq 7 by setting ∆E ) kT. Since we are using a sufficiently intense magnetic field (7 T), no further corrections are needed (e.g., the introduction of the correction factor 2). Knowing that

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Figure 2. Log-log plot of the minimum crystal size that can be oriented (rH) vs the magnetic field intensity obtained from eq 9 using the different published values of the diamagnetic susceptibility of tetragonal lysozyme and T ) 293 K.

each tetragonal unit cell (a ) b) contains eight lysozyme molecules, the volume of a crystal with NH molecules is expressed as

a2cNH VH ) 8

(8)

For comparative purposes, we will consider a sphere of radius rH with volume VH.

rH )

(

3a2cNAkT 1 · 16π∆χT H2

)

1/3

(9)

This equation shows that under the same experimental conditions (magnetic field intensity and temperature), rH depends only on ∆χT. Figure 2 shows the variation of the minimal crystal radius (rH) as a function of the magnetic field intensity for different values of ∆χT used in the literature. For the experimental conditions used in this work (7 T intensity and 295 K) and introducing the angular-corrected value of the diamagnetic anisotropy (4.08 × 10-5), the value of rH is 120 nm in good agreement with previously published values.7,9,11-13

4. Results and Discussion 4.1. Influence of Agarose on the Crystal Orientation. We have observed a clear effect of agarose concentration on the number of oriented crystals. Figure 3 shows the ratio, R, between the number of crystals oriented over the total number of crystals, as a function of the agarose concentration. It is notorious that at agarose concentrations higher than 0.1% (w/v) the number of crystals oriented is negligible. At lower agarose concentration, two regions can be defined. In the range from 0.02 to 0.03% (w/v) agarose, almost 100% of the crystals are oriented, while in the range between 0.03 and 0.1% (w/v) agarose concentration, the ratio of oriented crystals decreases linearly as the concentration of agarose increases. To understand this behavior, it is critical to considered that at concentration below the critical value (CR = 0.12% w/v)31 agarose cannot be considered a gel made of a homogeneous and continuous network of carbohydrates polymer. Instead, these low concentration solutions of polymeric agarose must be considered as a viscous nonNewtonian fluid.32 At low agarose concentration, the viscous

Figure 3. Shows the ratio, R, of oriented crystal (circle) and agarose pore size (square) as a function of gel concentration (plot in a log scale for clarity). The agarose critical concentration (0.12% w/v) is marked with a vertical dashed line. Values below the critical concentration (cross-square) are theoretical since agarose is not a gel but a solution of polymeric fibers.

polymeric fluid is able to suspend the crystals so they can be freely oriented by the magnetic field. As the concentration of agarose increases, the polymeric fibers interact strongly with the crystals inhibiting the orientation effect of the magnetic field. This interaction has been proven to occur, as the gel fibers are incorporated into protein crystal during the crystal growth process.26,33 This effect of agarose fibers increases linearly with concentration until the critical value, CR, when a gel network is formed. Then, in spite that at 0.1% (w/v) concentration the average pore size34 of agarose is 1 order of magnitude bigger than the minimal crystal radius (rH), the polymeric fibers already incorporated into the crystals volume26 fully cancel the effect of magnetic field. 4.2. Influence of H on the Nucleation and Crystal Habit. We also evaluated the influence of the magnetic field on the nucleation rate and habit of the lysozyme crystals. Early studies on lysozyme and ferritin crystals have shown that a magnetic field of 10 T reduces the number of crystals and changes their habit.7 On the other hand, Ataka and co-workers described an increase in the number of crystals in supersaturated lysozyme solutions exposed to a magnetic field of 0.6-1.2 T.12 According to Wakayama, this discrepancy can be explained as the effect of the magnetic field force generated by the magnetic field gradient; therefore, no influence is expected at constant intensity.13 Agarose, gels, and polymeric solutions prevent crystal sedimentation and convective mass transport but at the same time promote nucleation.35,36 The nucleation effect was subtracted by using reference samples (see Material and Methods for details). In all the experiments, batch and counter-diffusion, the number of crystals obtained under the influence of the magnetic field was higher than the number of crystals obtained in the reference sample. Although this is a general observation for all the experiments, the extent of this influence depends on the agarose concentration. The higher the agarose concentration, the stronger the influence on the nucleation and the lower the magnetic field effect on the nucleation of lysozyme. In Figure 4, the ratio of nucleation density (Rnucleation ) number of crystal at 7 T/number of crystals at 0 T) as a function of agarose concentration for batch experiments is shown. The number of crystals obtained under the influence of the magnetic field was higher at the time the experiments were removed out from the

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Figure 5. Sequence of pictures of the magnetically affected experiment (left pictures) and the reference (right pictures) of an extended-time counterdiffusion experiment with the protein solution gelled with 0.5% (w/v) agarose (see Table 1 for more details). Panels A and B show the experiment after 69 and 93 h, respectively, in the magnetic field. Panels C-E show the evolution of the experiment after being removed from the magnetic field for 24, 48, and 72 h, respectively.

Figure 4. Panel A shows the number of crystals in magnetic field divided by the number of crystals in the references (Rnucleation), just after being removed from the magnet (full) and after one month at 0 T (open). Panels B and C show a batch experiment in 0.055% w/v agarose just after being removed from the magnet (18 h) and 24 h later, respectively.

magnet (after 18 h). After one month the average value of Rnucleation was 1.0 ( 0.1. This indicated that when the experiments are removed from the magnet, its influence is lost. A new counter-diffusion experiment with elongated protein and salt chambers was designed to study the influence of the magnetic field on the nucleation density. The number of crystals was evaluated after 69 h and after 93 h in the magnet (Figure 5, panels A and B, respectively). Then, the evolution of the experiment at 0 T was followed at 24 h intervals for another 72 h and compared with the reference (Figure 5C-E). These results confirmed the previous observation that (i) the nucleation induction time is reduced under the magnetic field and (ii) as soon as the experiment is removed out of the magnet, this influence is lost. This behavior can be explained considering that the critical nucleus size decreases because the magnetic field increases the supersaturation or because the critical nucleus is stabilized for a longer period under the influence of the magnetic field. A similar conclusion can be deduced from the slower dissolution rate of lysozyme crystals observed under a 11 T intensity magnetic field measured by Yanagiya and co-workers.14 Although this behavior was initially explained as the damping of convection due to the magnetic field, Yin and co-workers17

Figure 6. Average development of the faces type {101} compared to the faces {110} measured as dimensions L and W, respectively (see inset representation), for induced and reference samples. The dispersion is shown as error bars.

found no influence of a magnetic field on convection in a thin layer of protein solution. In the same work, Yin and co-workers also showed that the solubility of lysozyme does not change in the presence of the magnetic field, and therefore the observed effect cannot be explained as a change of supersaturation. The magnetic field influence on the crystal habit was evaluated by measuring the characteristic dimensions, L and W (see Figure 6), of crystals grown with the batch method. In Figure 6, the average values of L and W for magnetically induce and reference samples are shown. The dispersion of the data is shown as error bars. We observed that the average crystal size is bigger for crystals grown in the magnetic field when compared with the reference. Also, the relative enhancement of the {110}

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faces (dimension W), perpendicular to the direction of the magnetic field, is larger than the {101} faces (dimension L). This can be further described as an increase of the aspect ratio (W/L), which can be understood as a rise in supersaturation.37 The results contrast with the observation of Yanagiya and coworkers14 who observed a decrease in the growth rate for both faces of lysozyme crystals, but they applied a magnetic field which was perpendicular to the c axis. This influence of the magnetic field on the crystal habit was further investigated using the counter-diffusion setup with extended-time experiments (see Table 1 for details). Counterdiffusion techniques develop a spatiotemporal pattern of supersaturation that varies along the length of the protein chamber in a single experiment.25 The protein solution was gelled with low agarose concentration (e0.035% w/v) to avoid as much as possible the gel interference. Upon completion of the experiments, the variation of the aspect ratio (i.e., corresponding to the change of supersaturation, if magnetic field effects on growth kinetics can be ignored) was measured along the protein chamber. We observed that at high supersaturation values, corresponding to the beginning of the protein chamber, both reference and induced experiments run parallel while at lower supersaturation values the aspect ratio (W/L) was bigger for the samples grown in the magnetic field in agreement with our observation in the batch experiments (Figure S2, Supporting Information). Therefore, there is a threshold of supersaturation at which the influence of the magnetic field becomes significant. Above this supersaturation value, the magnetic field influence is negligible. There are two hypotheses to explain the observed effects of a homogeneous and constant magnetic field on the nucleation, size, and habit of tetragonal lysozyme crystals in a convention free media. The first hypothesis is that the magnetic field increases the supersaturation and therefore is a thermodynamic effect. The second possibility is that the magnetic field provokes a kinetic effect by the stabilization of the critical nucleus long enough to favor its growth. Both hypotheses could fully describe the nucleation and growth data presented in this work, but none of them could explain the slower growth rate observed by Yanagiya and co-workers. Since kinetic studies are difficult to implement, further investigation to determine the effect of a magnetic field on the thermodynamic supersaturation (i.e., in terms of lysozyme activity not concentration) will be necessary to discriminate one of two hypotheses. 4.3. Capillary Grown Protein Crystals in a Magnetic Field. We have also performed counterdiffusion experiments using the GAME setup (see Figure 1 and Table 1). In absence of agarose, we got oriented individual single crystals, “rod”, filling the capillary diameter. When the protein solution contains low agarose concentration a higher number of oriented individual crystals were obtained (Figure 7). We propose the use of capillaries to evaluate the influence of magnetic field on crystal quality since capillaries grown crystals avoid the stress due to manipulation and handling any previous X-ray diffraction experiment.38 Also, the use of capillaries minimized the volume of protein needed to carry out the magnetic field experiments and therefore could facilitate its application to new proteins.

Gavira and Garcı´a-Ruiz

Figure 7. Magnetically oriented lysozyme crystal grown in 0.5 mm inner diameter capillaries by the gel acupuncture method. Panel A shows multiple crystals grown in 0.025% (w/v) agarose. Panel B shows the time evolution of a single crystal filling completely the diameter of the capillary.

secondary structure element with respect to the magnetic field direction introduced for the first time in this work. This calculation can be applied for any protein and crystal form. A homogeneous and constant magnetic field of 7 T can orient 100% of lysozyme crystals using low agarose concentration gels as a physical support. The percentages of oriented crystals decrease as the gel concentration increases due to the higher number of fibers crossing the crystals and the reduction of the pore size. Using agarose to avoid crystal sedimentation and convective flow, we have found that a homogeneous and constant magnetic field reduces the nucleation induction time provoking a higher nucleation density and larger crystal size. Both the development of the faces perpendicular to the magnetic field and the reduction of the induction time could be interpreted as an increment of the supersaturation under the magnetic field influence (thermodynamic effect). Those effects disappear when the experiments are removed from the magnet. The magnetic field influence is time dependent in such a way that any factor that reduces the nucleation induction time, for example, high supersaturation values or high agarose concentrations, reduces its influence pointing to a possible kinetic effect of the magnetic field. Further investigations are necessary to discern which type of effect, thermodynamic or kinetic, is provoked by the magnetic field. Acknowledgment. This work was supported by the Andalusian Regional Government (Project RNM1344) and Grant Intramural-200730I013 of the Consejo Superior de Investigaciones Cientı´ficas. This is a product of the Project “Factorı´a Espan˜ola de Crystalizacio´n” Consolider-Ingenio 2010. We thank Dr. Gen Sazaki for his helpful comments and discussions. We also would like to thank E. Onorato-Gutie´rrez and A. H. Benamin of the Servicios de Instrumentacio´n Cientifica, U. of Granada, for their technical support during the use of the NMR instruments. Supporting Information Available: This information is available free of charge via the Internet at http://pubs.acs.org/.

5. Conclusion

References

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