pubs.acs.org/Langmuir © 2009 American Chemical Society
Beneficial Effect of Solubility Enhancers on Protein Crystal Nucleation and Growth Rajendrakumar A. Gosavi,† Venkateswarlu Bhamidi,‡ Sasidhar Varanasi,† and Constance A. Schall*,† †
Department of Chemical & Environmental Engineering, University of Toledo, 2801 West Bancroft Street, Toledo, Ohio 43606 and ‡Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana - Champaign, Urbana, Illinois 61801 Received September 27, 2008. Revised Manuscript Received February 9, 2009
Crystallizing solutions of proteins often contain various nonelectrolyte additives that arise from the purification process of proteins or from the reagents employed in the screening kits. Currently, limited knowledge exists about the influence of these additives on the mechanisms underlying the crystallization process, in particular on the nucleation stage of crystals. To address this need, we studied crystallization of two proteins, D-xylose isomerase and chicken egg-white lysozyme, in small batches and in the presence of two solubility-enhancing additives, acetonitrile and glycerol. We have also measured the nucleation rates of crystals of these proteins in the presence and in the absence of acetonitrile using the method of initial rates. With the addition of the solubility enhancers, both proteins exhibited an increase in crystal nucleation at any given supersaturation. Solubility enhancing additives appear to lower the energy barrier to nucleation by influencing the strength of attraction between the protein molecules. We have characterized the quality of D-xylose isomerase crystals by determining the crystal mosaicity, which showed considerable improvement for crystals grown in the presence of additives. When compared to the crystals of chicken egg-white lysozyme, D-xylose isomerase crystals required higher supersaturations to nucleate. We attribute this result to the large size of the D-xylose isomerase molecule, which influences the energy barrier to nucleation by increasing the surface area of the critical nucleus. Contrary to the common expectation that reagents that solubilize the protein may hinder the crystallization process, our results suggest that solubility enhancers, in fact, can have a beneficial effect on the nucleation and growth of crystals. These findings are of importance in formulating successful strategies toward crystallizing new proteins.
Introduction Finding optimal solution conditions that lead to the formation of large, single crystals of new proteins is a challenging task, and is often the rate-limiting step in structure determination of new proteins through X-ray diffraction. Usual strategies toward this end employ crystallization ‘screening kits’, which contain various reagents that influence the phase behavior of the protein and drive the solution toward phase transformation. Protein solutions also contain several nonelectrolyte additives that are introduced into the solution through the chromatographic purification and stabilization steps. At present, limited understanding exists on how these additives interact with protein solutions at a molecular level to influence the outcome of a crystallization experiment. Given the fact that some of these reagents can also serve as cryoprotectants during crystallographic data collection (e.g., glycerol), a significant interest exists among molecular biologists and biochemists in understanding the influence of various additives on the crystallization process. Here we present the experimental results that suggest the positive role of some additives on the crystallization processes of proteins and establish these reagents as desirable constituents in crystallizing solutions. Nonelectrolyte additives are usually classified into solubility enhancers (e.g., ethylene glycol) and precipitants (e.g., high molecular weight polyethylene glycol (PEG)). Several studies in the literature have focused on the influence of these additives on the crystallization of proteins. The majority of *Corresponding author. E-mail:
[email protected].
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these investigations have approached this problem in a qualitative manner, attempting to determine the effect of additives on the crystallization process via observing the change in the number and in the size of the resultant crystals. Sauter et al. carried out a systematic exploration of the additive space on the outcome of the crystallization experiments on proteins and nucleic acids and noted an improvement in the quality of crystals in some cases.1 Improved crystal quality with the use of additives was also observed by Wolfova et al.2 and Tanaka et al.3 In studies by Gosavi et al., solubility enhancement through buffer optimization and addition of glycerol has been shown to increase the portion of positive crystallization trials in high throughput screening of globular proteins.4 A few research groups have explored more fundamental aspects of the problem by studying the effect of different kinds of additives on the phase behavior of protein solutions, most notably on that of hen egg-white lysozyme. An increase in the solubility of chymotrypsinogen A and hen egg-white lysozyme and a decrease in the critical supersaturation for spontaneous nucleation in the presence of 1% dimethyl sulfxoide (DMSO) or 10% glycerol was reported by Lu et al.5,6 Zukoski and (1) Sauter, C.; Ng, J. D.; Lorber, B.; Keith, G.; Brion, P.; Hosseini, M. W.; Lehn, J.-M.; Giege, R. J. Cryst. Growth 1999, 196, 365–376. (2) Wolfova, J.; Grandori, R.; Kozma, E.; Chatterjee, N.; Carey, J.; Smatanova, I. K. J. Cryst. Growth 2005, 284, 502–505. (3) Tanaka, S.; Ataka, M.; Kubota, T.; Soga, T.; Homma, K.; Lee, W. C.; Tanokura, M. J. Cryst. Growth 2002, 234, 247–254. (4) Gosavi, R. A.; Mueser, T. C.; Schall, C. A. Acta Crystallogr., Sect D: Biol. Crystallogr. 2008, 64, 506–514. (5) Lu, J.; Wang, X.-J.; Ching, C.-B. Prog. Cryst. Growth Charact. Mater. 2002, 45, 201–217. (6) Lu, J.; Wang, X.-J.; Ching, C.-B. Cryst. Growth Des. 2003, 3, 83–87.
Published on Web 3/23/2009
DOI: 10.1021/la803185m 4579
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co-workers have studied the effects of glycerol, ethylene glycol, 2-methyl-2,4-pentanediol (MPD), and high molecular weight PEG (PEG-12000) on the solubility of bovine pancreatic trypsin inhibitor (BPTI) and hen egg-white lysozyme and related the enhancement in solubility and nucleation of protein crystals to the intermolecular interactions.7,8 Sedgwick et al. have also studied the solubility of hen eggwhite lysozyme in the presence of glycerol and modeled the protein interactions using a Derjaguin-Landau-VerweyOverbeek (DLVO) potential.9 The phase behavior of hen eggwhite lysozyme solutions in the presence of 5% glycerol and PEG-5000 was probed by Galkin and Vekilov, who found that glycerol suppressed nucleation above the liquid-liquid phase separation boundary of lysozyme, and PEG enhanced nucleation.10,11 Similar results were obtained by Chen et al. who reported enhanced nucleation of mutant hemoglobins from the dense liquid droplets induced by the addition of PEG-4000.12 Our present work investigates the effect of two nonelectrolyte additives, acetonitrile and glycerol, on both the nucleation and the growth of protein crystals in an integrated manner. Acetonitrile has been reported as a component of solutions used in protein and peptide crystallization.13 However, the role of acetonitrile in the formation of protein crystals has not, to our knowledge, been explored systematically. Glycerol is a reagent that is often present in the crystallization screening kits. It also serves as a cryoprotectant and has been reported to stabilize proteins in solution.7,14 Here, we present the influence of these additives on the solubility and nucleation kinetics of a high molecular weight protein, D-xylose isomerase (XI) from Streptomyces rubiginosis (173 kDa), and a relatively low molecular weight protein, chicken egg-white lysozyme (CEWL) from Gallus gallus (14.6 kDa), commonly referred to as hen egg-white lysozyme. We performed preliminary batch crystallization experiments in the presence of the additives for a qualitative assessment of their effect on the crystallization behavior of proteins. In addition, to quantify the observed trends in nucleation of the crystals decoupled from their growth, we have measured the rates of nucleation of orthorhombic XI crystals and tetragonal CEWL crystals at various solution conditions. To explore the effect of the added reagents on the growth of the crystals, we have also determined the mosaicity and diffraction resolution of XI crystals grown in the presence of the same additives through X-ray diffraction studies. Our results indicate that solubilityenhancing reagents can have a beneficial effect on the crystallization processes of proteins and hence are desirable additives in crystallizing protein solutions.
Experimental Section Preparation of Solutions. XI from Streptomyces rubiginosis was obtained from Hampton Research, and a buffer exchange was performed with 0.1 M, 2-amino-2-(hydroxymethyl)-1,3propanediol hydrochloride (Tris-HCl) buffer at pH 8.0, and (7) Farnum, M.; Zukoski, C. Biophys. J. 1999, 76, 2716–2726. (8) Kulkarni, A. M.; Zukoski, C. F. Langmuir 2002, 18, 3090–3099. (9) Sedgwick, H.; Cameron, J. E.; Poon, W. C. K.; Egelhaaf, S. U. J. Chem. Phys. 2007, 127, 125102. (10) Galkin, O.; Vekilov, P. G. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 6277–6281. (11) Galkin, O.; Vekilov, P. G. J. Cryst. Growth 2001, 232, 63–76. (12) Chen, Q.; Vekilov, P. G.; Nagel, R. L.; Hirsh, R. E. Biophys. J. 2004, 86, 1702–1712. (13) McPherson, A. Methods 2004, 34, 254–265. (14) Sousa, R. Acta Crystallogr., Sect D: Biol. Crystallogr. 1995, 51, 271–277.
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with 10 mM ethylenediaminetetraacetic acid (EDTA) to remove metal ions. EDTA was then exchanged three times with a buffer containing 10 mM MgCl2 using ultrafiltration with 10 kilodalton molecular weight cutoff (MWCO) membranes in a pressure concentrator (Vivascience). CEWL from Gallus gallus was purchased from Seikagaku (3X grade) and was further purified through recrystallization. For this purpose, we dissolved CEWL in 0.1 M sodium acetate (NaAc) buffer at pH 4.5 and recrystallized the protein by addition of NaCl to a final concentration of 5% (w/v). This solution was then cooled from 20 to 4 C over a period of 24 h, after which the supernatant was removed, and the crystals were washed three times with a solution of 8% (w/v) NaCl. We redissolved these crystals in a fresh batch of 0.1 M NaAc buffer at pH 4.5 and desalted the protein with buffer exchange using ultrafiltration with a 5 kDa MWCO membrane (Vivascience). The final protein solution in each case was filtered through a 0.2 μm syringe filter. We determined the concentration of the proteins by measuring their UV absorbance at 280 nm using an extinction coefficient of 1 mL/(mg 3 cm) for XI 15 and 2.64 mL/(mg 3 cm) for CEWL.16 Determination of Solubility. Solubility determination through the method of crystallization, in which crystals of a protein are allowed to equilibrate with the surrounding mother liquor over a period of time, is time-consuming. Also, with long incubation periods, denaturation, oxidation, or deamidation of proteins can occur. Such processes can result in the inhibition or cessation of crystal growth and may lead to the overestimation of solubility. Hence we employed the method of dissolution and determined the solubility of the proteins as described below. XI was dissolved in a solution containing 10% (w/v) ammonium sulfate and 0.1 M Tris-HCl at pH 8.0 with 10 mM MgCl2. Batches of about 1 mL of these concentrated XI solutions were then placed in Eppendorf tubes and were incubated in a temperature-controlled ((0.1 C) water bath at the temperature of interest until a substantial amount of crystals were observed in the batch. The batches were briefly centrifuged and the supernatant was replaced with fresh buffer at the batch temperature. The crystals were then allowed to dissolve in the new batch of buffer solution and the concentration of the protein in the supernatant was monitored with time. The batches were briefly mixed after each sampling. Crystalline material was observed to settle to the bottom of the tube and care was exercised to avoid pipetting of any visible crystalline material during sampling of the supernatant. We observed that protein concentration in the supernatant reached an equilibrium value within 24 to 48 h. We considered this steady value of concentration as the solubility of XI. Using this method, we have determined the solubility of XI in the presence and in the absence of 3% and 6% (v/v) of acetonitrile or glycerol in the solution at 4, 13, 18, and 21 C. We employed the same procedure to obtain the solubility of CEWL in 0.1 M NaAc buffer at pH 4.5 containing 2% (w/v) of NaCl. Solubility of CEWL was also determined when the solutions contained 3% and 6% (v/v) of acetonitrile or glycerol. These solubility measurements were performed at 2.5, 4, 10, 13, 18, and 21 C. All of our solubility measurements were carried out in duplicate to verify the reproducibility of results. Batch Crystallization Experiments. For a quick, qualitative assessment of the impact of acetonitrile and glycerol on the crystallization of XI and CEWL, we crystallized small batches of the protein solutions without the additives and compared these results with the outcome of the crystallization experiments in the presence of the additives. Droplets of 20 μL of protein solution with precipitant alone or precipitant along with the additives were placed in the wells of 24-well tissue culture plates (Linbro), (15) Christopher, G. K.; Phipps, A. G.; Gray, R. J. J. Cryst. Growth 1998, 191, 820–826. (16) Aune, K. C.; Tanford, C. Biochemistry 1969, 8, 4579–85.
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Gosavi et al. and these droplets were overlaid with about 1 mL of mineral oil that was pre-equilibrated with the precipitant/additive solution. We also used the hanging drop method in some experiments in which the solutions in the reservoir and in the droplet were matched in the initial concentration of the precipitant and the additive. We monitored these crystallizing batches periodically and recorded the numbers of crystals formed in the batch after about 2 weeks. Measurement of Nucleation Kinetics. Batch crystallization studies are useful in screening the overall effect of additives on crystal nucleation and growth. To assess the influence of additives on nucleation in detail, we measured the rate of nucleation of crystals using the method of initial rates, in which we record the increase in the number density of particles with time (after the solution attains the supersaturation of interest).17 A particle counting instrument (PC2000 - Spectrex Corp.) that uses the principle of near-forward angle light scattering was used to detect and count particles in the solution. The number of particles (greater than 0.5 μm) formed in the sensing zone of the particle counter was tabulated at small time intervals. Particle counts acquired after any particle reaching a size of 10 μm were not used in nucleation rate calculations, as large crystallites tend to settle. All the solutions were equilibrated at the temperature of interest before they were mixed. Upon mixing, the solutions were quickly filtered into a clean scintillation vial using a 0.1 μm syringe filter, and the vial was then mounted on the particle counter. Temperature control to within ( 0.1 C was achieved by housing the particle counter in an incubator. In these studies, we used 4 and 8 mL batches of the crystallizing solution for XI and CEWL, respectively. Nucleation rates of the proteins were measured for three cases: (a) XI crystallizing at 13 C from solutions containing 10% (w/v) ammonium sulfate, (b) XI crystallizing at 13 C from solutions containing both 10% (w/v) ammonium sulfate and 6% (v/v) acetonitrile, and (c) CEWL crystallizing at 4 C from solutions containing 2% (w/v) NaCl and 6% (v/v) acetonitrile. The rates of nucleation of CEWL at the present experimental conditions and in the absence of acetonitrile in solution were reported in our previous publication.18 The supersaturation S, defined here as the ratio of the concentration of the protein in solution to the equilibrium solubility (C/C*), of XI explored in our nucleation studies ranged from 40 to 80, whereas this value ranged from 20 to 35 for CEWL. Estimation of Crystal Mosaicity. The quality of the X-ray diffraction pattern obtained from a crystal, and hence the usefulness of the crystal grown for structure determination, can be quantified in terms of the diffraction resolution and mosaicity of the crystal. The averaged mosaicity of a crystal is defined as the average of the full width at half-maximum height (fwhm) of peaks of scattering intensity resulting from plots of intensity versus scanning angle, and is expressed as degrees of scattering angle. To assess the influence of acetonitrile and glycerol on the quality of the resulting crystals, we estimated the change in mosaicity of XI crystals formed in the presence of the additives. XI crystals grown at 4 C in the presence of 10% (w/v) ammonium sulfate and in combination with 6% glycerol or acetonitrile using hanging drop technique were used for this purpose. To obtain a few large (approximately of size 1 mm 1 mm 0.5 mm) crystals suitable for X-ray diffraction studies, we selected the initial protein concentration such that only a small number of crystals formed in the batch. After about 2 weeks of incubation of the droplets at 4 C, we harvested these crystals and sealed them in quartz capillaries along with the mother liquor for subsequent diffraction analysis. X-ray diffraction data were collected using a Rigaku FR-E rotating (17) Bhamidi, V.; Varanasi, S.; Schall, C. A. Cryst. Growth Des. 2002, 2, 395–400. (18) Bhamidi, V.; Varanasi, S.; Schall, C. A. Langmuir 2005, 21, 9044–9050.
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Article copper anode with a Saturn 92 CCD detector. The diffraction data were processed, and the mosaicity of the crystal was estimated using d*TREK software.19
Results Solubility of Proteins. We present the solubility of XI and CEWL determined at various solution conditions in Table 1a,b, respectively. To the best of our knowledge, this is the first report of the solubility of XI in solutions containing acetonitrile or glycerol. Our measured values of XI solubility in the presence of 10% (w/v) ammonium sulfate (without the additives) are similar to the values reported by Visuri and co-workers,20,21 Chayen et al.,22 and Dalziel23 at various other solution conditions. The solubility of CEWL obtained by us differed slightly from the values reported by Pusey and co-workers,24-26 who have used the method of crystallization along with the method of dissolution and reported an averaged value of solubility. The addition of glycerol or acetonitrile appears to enhance the solubility of XI (Table 1a). This enhancement in solubility is greater at higher temperatures and concentrations of acetonitrile or glycerol. The solubility of CEWL also increases with added acetonitrile or glycerol at all temperatures (Table 1b). Acetonitrile appears to enhance the solubility of proteins to a greater extent than glycerol. Batch Crystallization. Figure 1 displays an optical micrograph of a typical result of the batch crystallization of CEWL in the presence of acetonitrile and glycerol. In our batch crystallization studies, the addition of acetonitrile or glycerol did not influence the usual morphologies of tetragonal CEWL and orthorhombic XI crystals. However, these additives increased the numbers of crystals formed. This result suggests that the additives influenced the nucleation process of the crystals to a greater extent than they affected the growth. In Table 2a,b, we summarize the effect of acetonitrile and glycerol on the numbers of crystals formed for XI and CEWL, respectively. At comparable supersaturations, for both the proteins, the addition of glycerol or acetonitrile resulted in the formation of a greater number of crystals than those obtained from solutions that contained precipitant alone. We note that the same additives also increased the solubility of the proteins. In general, to form crystals in a two-week period, batches of XI solutions needed a higher initial supersaturation than the batches of CEWL solutions. When the solution contained the precipitant alone, we observed CEWL crystals in droplets with a supersaturation of S > 5. When acetonitrile or glycerol was added to the solution, crystals were seen in batches with S > 2. For XI at 4 C, the addition of solubility enhancers reduced the minimum supersaturation needed for the formation of crystals from over 100 times (19) Pflugrath, J. W. Acta Crystallogr., Sect D: Biol. Crystallogr. 1999, 55, 1718–1725. (20) Visuri, K. In Enzyme Engineering X, International Conference, Kashikojima, Japan, September 24-29, 1989; Kashikojima, Japan, 1989. (21) Vuolanto, A.; Uotila, S.; Leisola, M.; Visuri, K. J. Cryst. Growth 2003, 257, 403–411. (22) Chayen, N. E.; Akins, J.; Campbell-Smith, S.; Blow, D. M. J. Cryst. Growth 1988, 90, 112–116. (23) Dalziel, S. M. Ph.D. Thesis, The University of Queensland, St. Lucia, QLD, Australia, 1999. (24) Cacioppo, E.; Munson, S.; Pusey, M. L. J. Cryst. Growth 1991, 110, 66–71. (25) Cacioppo, E.; Pusey, M. L. J. Cryst. Growth 1991, 114, 286–292. (26) Forsythe, E. L.; Judge, R. A.; Pusey, M. L. J. Chem. Eng. Data 1999, 44, 637–640.
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Gosavi et al. Table 1 (a) Solubility of XI in 0.1 M Tris-HCl Buffer at pH 8.0a,b solubility (mg/mL)
temperature (oC)
no additive
3% (v/v) Acn
6% (v/v) Acn
3% (v/v) Gly
6% (v/v) Gly
4.0 13.0 18.0 21.0
0.14 1.18 2.18 4.45
0.27 1.59 3.95 6.85
0.38 1.90 5.95 11.20
0.13 0.99 3.45 6.50
0.46 1.65 5.18 6.50
3% (v/v) Gly
6% (v/v) Gly
(b) Solubility of CEWL in 0.1 M Sodium Acetate Buffer at pH 4.5a,c solubility (mg/mL) o
temperature ( C)
no additive
2.5 4.0 10.0 13.0 18.0 21.0 a The symbols Acn and Gly values varied within 10%. b All chloride.
3% (v/v) Acn
1.80 1.91 3.37 5.95 11.50 20.30 refer to acetonitrile and solutions contained 10%
6% (v/v) Acn
2.59 4.18 2.43 2.96 2.86 5.28 2.39 3.25 6.38 9.58 6.67 6.55 10.40 15.10 10.90 11.90 18.70 29.20 14.90 20.50 26.30 33.50 24.10 31.50 glycerol, respectively. Solubility reported is the average value of two replicates whose (w/v) ammonium sulfate along with MgCl2. c All solutions contained 2% (w/v) sodium
Figure 1. Optical micrographs of CEWL crystals grown in 20 μL droplets incubated for about 2 weeks at 4 C: (a) crystals grown with no additives in solution (S = 5, N = 13), (b) crystals grown with 6% (v/v) acetonitrile (S = 5.9, N = 137), and (c) crystals grown in the presence of 6% (v/v) glycerol in solution (S = 5.8, N = 92). The scale bar applies to all three photographs. The symbols S and N refer to the supersaturation and the number of crystals formed, respectively. Additives significantly improved nucleation and did not change the morphology of crystals.
solubility (S = 100) to about S = 20 (Table 2a). Similar high supersaturations (S > 25) for the formation of XI crystals at 10 C were observed by Visuri.20 Effect of Additives on Nucleation Kinetics. We measured the nucleation rates of protein crystals using the method of initial rates, in which we monitored the number density of particles in a crystallizing batch as a function of time. The slope of the plot of number density versus time during the initial time period (when the concentration of the protein in the solution is not yet depleted due to the growth of crystals) yields the rate of crystallite formation at the initial supersaturation. In Figure 2a,b, we plot the rates of nucleation thus obtained as a function of supersaturation for CEWL and XI, respectively. From these figures, we observe that a higher supersaturation was required for a significant nucleation of XI crystals to occur as compared to that required for CEWL. The nucleation kinetic data also show that, for both the proteins, the rate of nucleation at any given 4582
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supersaturation is higher when acetonitrile is present in the solution. These observations are in accord with the results of the microbatch crystallization studies discussed above, and demonstrate the positive effect of solubility enhancers in promoting crystal nucleation. Effect of Additives on Crystal Quality. We quantified the influence of acetonitrile and glycerol on the crystal growth process by comparing the mosaicity of XI crystals grown from solutions that contained ammonium sulfate alone with those grown from solutions that also contained 6% (v/v) acetonitrile or 6% (v/v) glycerol. Crystals of similar sizes obtained from respective solutions were used in the collection of the X-ray diffraction data and in the subsequent determination of the crystal mosaicity and diffraction resolution. In Table 3, we summarize the results of these studies. We observe that crystals grown in the presence of the solubility enhancers exhibited lower mosaicity when compared to those obtained with precipitant alone in the solution. Langmuir 2009, 25(8), 4579–4587
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Article Table 2 (a) Effect of Additives on Batch Crystallization of XIa,b
no additive
3% (v/v) acetonitrile
S
N
std. dev
S
N
142.9 214.3 285.7 428.6
1 0 3 7
0.5
37.0 74.1 92.6 111.1 148.2 185.2 222.2
0 4 4 4 4 5 8
0.5 1
std. dev
6% (v/v) acetonitrile S
N
3% (v/v) glycerol S
26.3 0 76.9 0.5 52.6 3 1.2 153.8 2.0 65.8 3 1.2 192.3 1.5 78.9 6 0.6 230.8 1.2 105.3 4 1.2 307.7 1.2 131.6 5 1.2 384.6 2.6 157.9 8 2.6 461.5 (b) Effect of Additives on Batch Crystallization of CEWLa,c
no additive S
std. dev
N
6% (v/v) glycerol std. dev
S
N
N 0 0 6 6 4 5 8
6% (v/v) glycerol
std. dev
S
N
std. dev
2.0 1.0 0.6 4.0 1.7
21.7 43.5 54.4 65.2 87.0 108.7 130.4
0 3 4 4 2 4 3
1.5 0 3.0 1.2 2.6 1.7
6% (v/v) acetonitrile std. dev
S
N
std. dev
5.2 11 4 3.1 0 1.9 27 14 9.0 3 2 4.6 0 2.8 54 12 12.6 35 13 6.2 10 5 4.7 19 4 14.4 21 3 9.2 25 1 6.6 41 6 18.0 36 9 12.3 62 2 7.6 57 5 20.9 344 38 15.4 105 14 9.5 96 25 31.4 473 12 18.5 136 14 11.4 162 23 36.7 639 22 24.6 132 11 13.3 187 12 a The symbols S and N indicate the supersaturation and the average number of crystals formed, respectively. The standard deviation of the number of crystals formed for each case is also given. b The average number of XI crystals formed in three 20 μL batches, incubated at 4C for a period of two weeks, is shown. All solutions contained 10% (w/v) ammonium sulfate as precipitant and 0.1 M Tris - HCl buffer, pH 8.0. c The average numbers of CEWL crystals formed in three 20 μL batches that were incubated at 4C for a period of two weeks are shown. All the solutions contained 2% (w/v) NaCl as precipitant and 0.1 M Na acetate buffer, pH 4.5.
Figure 2. Nucleation rates of (a) tetragonal CEWL crystallizing from 0.1 M Na acetate buffer at pH 4.5 and 4 C with no additive (b) and with 6% (v/v) acetonitrile (O), and (b) orthorhombic XI crystallizing from 0.1 M Tris - HCl buffer with 10 mM MgCl2 at pH 8.0 and 13 C with no additive (9) and with 6% (v/v) acetonitrile (0), as a function of supersaturation. All CEWL solutions contained 2% (w/v) NaCl, and all XI solutions contained 10% (w/v) ammonium sulfate as precipitants. Each data point represents a single experiment. The lines drawn are predictions of eq 2 with the parameters listed in Table 4, with the solid lines indicating the case of no additive in solution, and the dotted lines indicating the case of 6% (v/v) acetonitrile. The uncertainty bars indicate a range of ( 20% of the nucleation rate measured. Data on CEWL for the case of no additive (b) are adopted from our earlier publication.18 Diffraction resolutions of crystals grown with and without additives in solution did not differ significantly. These results indicate that crystals grown with solubility enhancers in solution will have an improved quality, and as a result, are desirable for structure determination of the protein through X-ray diffraction. Langmuir 2009, 25(8), 4579–4587
Discussion Our batch crystallization studies (Table 2a,b) and the nucleation kinetic studies (Figure 2a,b) clearly demonstrate that acetonitrile and glycerol reduce the supersaturation required for the onset of nucleation of XI and CEWL crystals. DOI: 10.1021/la803185m 4583
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Table 3. Influence of Additives on the Quality of XI Crystalsa diffraction C mosaicity resolution (mg/mL) (degrees) (A˚)
crystal size (mm)
conditions
S
no additive
143 215
20 30
0.365 0.480
1.69 1.69
1.0 1.0 0.5 1.0 1.0 0.5
6% (v/v) Acn 105 132
40 50
0.273 0.181
1.69 1.69
0.8 1.0 0.5 0.7 1.0 0.5
87 20 0.100 1.94 0.7 0.8 0.4 109 40 0.250 1.54 0.8 1.0 0.5 a XI crystals used were grown at 4C in Tris-HCl buffer with 10% (w/v) ammonium sulfate as the precipitant. The symbols Acn and Gly refer to acetonitrile and glycerol, respectively. The X-ray diffraction experiments were conducted at room temperature. Initial supersaturation, S, concentration of the protein in the crystallizing batch, C, and the approximate dimensions of the crystals used, are listed. 6% (v/v) Gly
These same reagents also enhance the solubility of the proteins, as evidenced from the results of our solubility measurements (Table 1a,b). Below we discuss the relation between the solubility of a protein and the nucleation process. We first analyze the nucleation kinetic data and then associate the observed increase of nucleation to the enhancement in solubility through consideration of intermolecular interactions. Estimation of Nucleation Kinetic Parameters. Nucleation is an activated process, and an energy barrier to nucleation must be overcome by the system for a successful nucleation event to take place.27 This barrier results from the energy cost involved in the creation of the surface of the new phase. The steady-state rate of nucleation, J, decreases exponentially as the energy barrier to nucleation, ΔG*, increases. The functional dependence of J on ΔG* is expressed as ΔG J ¼ A exp kT
ð1Þ
in which k is the Boltzmann’s constant and T is the absolute temperature. Often the pre-exponential factor A (also called the prefactor), and the energy barrier ΔG* are estimated using the classical nucleation theory (CNT).27-29 The capillarity approximation used in the framework of CNT characterizes ΔG* through a solid-liquid interfacial free energy, γ (which is often simply referred to as interfacial energy, interfacial tension, or surface energy). Using the capillarity approximation for a spherical nucleus, we express eq 1, within the scope of the CNT, as28 4π3 Γ3 J ¼ A exp 27 ln2 S
! ð2Þ
in which S is the supersaturation. The dimensionless solidliquid interfacial energy Γ in eq 2 is given by Γ ¼
γd 2 kT
! ð3Þ
in which d is the diameter of the molecule. We model the dependence of nucleation rates on supersaturation observed in our experiments using eq 2. Using appropriate transformation of variables and standard nonlinear regression techniques,17,30 we regress the two parameters of eq 2 that determine the rate of nucleation-the prefactor A and the dimensionless interfacial energy Γ-for both XI and CEWL. 4584
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Table 4 lists the values of these parameters obtained for nucleation of the proteins from solutions that contained only the precipitant, and from solutions that also contained 6% (v/v) acetonitrile. The values of the interfacial energy (γ) calculated from known molecular diameters of the proteins (10.1 nm for XI31 and 3.4 nm for CEWL32) are also listed in Table 4. The predictions of eq 2 using the best fit parameters listed in Table 4 are shown in Figure 2a,b. From Table 4, we note that the values of the prefactor for the nucleation of XI and CEWL are about the same order of magnitude, from 107 - 109. These values are many orders of magnitude smaller than the values of A predicted by CNT (which are on the order of 1020-1030). This observation is a common phenomenon in numerous nucleation studies in the literature that used eq 2 to model the rate of nucleation, and forms the basis for a general perception that heterogeneous nucleation must be the dominant nucleation mechanism in these experiments.33 However, we note that, the functional dependence of J on ΔG* as expressed by eq 1 does not depend on the validity of CNT.34 In using eq 2 as a semiempirical model to relate the rate of nucleation to the driving force, we have employed only the capillarity approximation within the framework of CNT, which was shown by detailed statistical mechanical and molecular simulation studies to estimate ΔG* reasonably well.27,35 As a result, we believe that the low values of the prefactor observed frequently in nucleation studies need not necessarily indicate heterogeneous nucleation, but may reflect the inadequacy of the classical concepts employed in describing the origins of the prefactor. As we can observe from Table 4, the presence of acetonitrile in solution has resulted in a marginal reduction of the values of the prefactor for XI and CEWL. The additive decreased the energy barrier to nucleation, as evidenced from the lowered values of Γ (and also those of γ). While the small reduction in the value of the prefactor that we observed can reduce the rate of nucleation by an order of magnitude, a similar decrease in the interfacial energy dramatically increases the rate of nucleation as J scales as exp(- Γ3) (eq 2). The overall effect of acetonitrile observed from our batch crystallization studies and nucleation kinetic studies is the enhancement of nucleation, a result that suggests that acetonitrile primarily affects the energy barrier to nucleation. The origins of this effect are discussed below. Solubility Enhancers as Promoters of Crystal Nucleation. Solubility, Intermolecular Interactions, and Interfacial Energy. The solubility of a protein depends on the relative ease with which the solvent molecules can disrupt the bonds between the protein molecules. The crystal-solution interfacial energy, γ, is a measure of the amount of work needed to bring protein molecules from the bulk solution to the solid-liquid interface. Thus, both solubility and interfacial energy depend on the intermolecular interactions, and are (27) Debenedetti, P. G. Metastable Liquids: Concepts and Principles; Princeton University Press: Princeton, NJ, 1996. (28) Kashchiev, D. Nucleation: Basic Theory with Applications; Butterworth-Heinemann: Oxford, 2000; p 529. (29) Zettlemoyer, A. C. Nucleation; Marcel Dekker, Inc.: New York, 1969. (30) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992. (31) Kozak, M. Protein Pept. Lett. 2005, 12, 547–550. (32) Nadarajah, A.; Pusey, M. L. Acta Crystallogr., Sect D: Biol. Crystallogr. 1996, 52, 983–996. (33) Sear, R. P. J. Phys. Chem. B 2006, 110, 21944–21949. (34) Auer, S.; Frenkel, D. Nature 2001, 413, 711–713. (35) Auer, S.; Frenkel, D. Nature 2001, 409, 1020–1023.
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Article Table 4. Effect of Additives on Nucleation Rate Parameters of XI and CEWL prefactoraA, (mL-1 min-1)
condition of solution
dimensionless interfacial energy Γ
interfacial energy γ, (mJ m-2)
3.79 ( 0.43 0.15 ( 0.02 XI, no additive (1.572 ( 0.698) 109 3.46 ( 0.38 0.13 ( 0.02 XI, 6% (v/v) acetonitrile (0.923 ( 0.232) 108 3.04 ( 0.16 1.01 ( 0.06 CEWL, no additive (1.312 ( 0.405) 107 2.87 ( 0.15 0.95 ( 0.05 CEWL, 6% (v/v) acetonitrile (3.629 ( 0.450) 106 a The uncertainties given refer to the 95% confidence interval of the parameters obtained from the nonlinear parameter regression procedure.
directly affected by the strength of protein-protein interactions. We have not found detailed theoretical studies in the literature that accurately relate interfacial energy to solubility of proteins. However, approaching the problem from a colloidal perspective, we can assume a suitable potential function to represent the strength of interaction, (ε/kT), between the particles (molecules), and can relate the solubility and the interfacial energy of a compound.36,37 To link Γ and the strength of molecular interactions, here we follow the method developed by Sear.37 We demonstrate a qualitative and near-quantitative agreement between the estimates of Γ from this simple approach and the experimentally obtained values. Estimation of Interfacial Energy from the Strength of Intermolecular Interactions. To associate interfacial energy with solubility through intermolecular interactions, we need to consider a pair interaction potential. Here we use a squarewell potential to characterize the interactions between the protein molecules. Several studies in literature have established the effectiveness of a simple square-well potential in capturing the protein solution thermodynamics.8,38-40 A square-well potential represents the pair interaction energy, U(r), as a function of the strength of interaction ε and the range of interaction as 8 > ¥ > < UðrÞ ¼ -ε > > :0
red d < redð1 þ δÞ
ð4Þ
r > dð1 þ δÞ
In the above relation, δ is the parameter that denotes range of interaction, r is the intermolecular distance, and d, as defined earlier, is the diameter of the molecule. For particles whose pair interaction energy can be modeled using a square-well function, Sear developed an expression for the solid-liquid interfacial energy,37 which relates Γ to the strength of interaction (ε/kT) as Γ ¼
pffiffiffi 3 ð1 þ cδÞ2
ε kT
ð5Þ
in which c is a constant that is less than 1. To use eq 5 to estimate Γ and subsequently associate it with solubility, first we need to relate (ε/kT) to solubility. This task can be accomplished in two ways: (1) by exploiting the observed generalized correlation between solubility and the osmotic second virial coefficient (B2), which represents (36) Marr, D. W. M.; Gast, A. P. Phys. Rev. E 1995, 52, 4058–4062. (37) Sear, R. P. J. Chem. Phys. 1999, 111, 2001. (38) Asherie, N.; Lomakin, A.; Benedek, G. Phys. Rev. Lett. 1996, 77, 4832–4835. (39) Fine, B. M.; Lomakin, A.; Ogun, O. O.; Benedeck, G. B. J. Chem. Phys. 1996, 104, 326. (40) Rosenbaum, D. F.; Kulkarni, A.; Ramakrishnan, S.; Zukoski, C. F. J. Chem. Phys. 1999, 111, 9882–9890.
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the strength of attraction, 7,40,41 or (2) by using the generalized phase diagram, in which we equate the chemical potentials of the solid and liquid at equilibrium38,42 and relate the solubility to the strength of attraction using a suitable equation of state (EOS) for the square-well fluid.43 Below we outline both of these methods in that order and use them to estimate Γ as a function of the volume fraction of the particles at a concentration representing the solubility of crystals, jsol. For a square-well fluid, the osmotic second virial coefficient (B2) can be related to the strength of attraction via37 ( ) B2 ε -1 ¼ 1 -3δ exp kT BHS 2
ð6Þ
in which BHS is the second virial coefficient for the hard 2 sphere molecules (= 2πd3/3). The generalized correlation between the solubility and B2 of a protein, observed experimentally by Wilson and co-workers,41 provides a convenient way to estimate the B2 for XI and CEWL readily from the values of their solubility. Using this value of B2 in combination with eq 5 and eq 6, we can estimate Γ at the conditions of interest. For CEWL at a solubility of 1.91 (mg/mL) (no additive) and 5.28 (mg/mL) (with acetonitrile), we estimate a B2 of -7.58 10-4 and -4.76 10-4 (mol 3 mL/g2), respectively, from the correlation of Wilson and co-workers. Using a reasonable short-range of attraction of δ = 0.15 and with c = 0.9 in eq 5, we calculate the values of ΓCEWL as 3.16 and 2.76 (with the corresponding values of the interfacial energy γCEWL as 1.04 and 0.91 (mJ/m2)) for the cases of no additive and with acetonitrile in solution, respectively. These values agree very well with the values we have obtained from the kinetic data (ΓCEWL = 3.04 and 2.87). For the case of XI, the values of solubility at the conditions of interest are 1.18 (mg/mL) and 1.90 (mg/mL), for which we estimate the B2 as -8.91 10-4 and -7.59 10-4 (mol 3 mL/g2). These values of B2 for XI result in a ΓXI of 5.22 (γXI = 0.20 mJ/m2) with no additive in the solution, and ΓXI = 5.02 (γXI = 0.19 mJ/m2) with acetonitrile in the solution. These estimates are somewhat higher than what we have obtained from our experiments (Table 4), most likely due to the inaccuracy involved in estimating B2 from its generalized correlation with solubility, which varies sharply for the low solubility values of XI that we are interested in. Also, we note that the applicability of the generalized correlation for XI has not been verified experimentally, and that our choice of a δ of 0.15 is rather arbitrary. (41) Guo, B.; Kao, S.; McDonald, H.; Asanov, A.; Combs, L. L.; Wilson, W. W. J. Cryst. Growth 1999, 196, 424–433. (42) Lomakin, A.; Asherie, N.; Benedek, G. B. J. Chem. Phys. 1996, 104, 1646–1656. (43) Ramakrishnan, S.; Zukoski, C. F. J. Chem. Phys. 2000, 113, 1237–1248.
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In the method where we use a generalized phase diagram for protein molecules, we employ an EOS for square-well fluids developed by Ramakrishnan and Zukoski43 in conjunction with the expressions developed by Lomakin et al.42 and Asherie et al.38 for the chemical potential of the liquid phase and that of the solid phase. The EOS for a square-well fluid is expressed as43 Z ¼
4πPa3 bj 6jðε=kTÞ ¼1 þ þ f ðλÞ ð7Þ 3jkT ð1 -j=j0 Þ2 πð1 -j=jb Þ3
in which Z is the compressibility factor, P is the osmotic pressure, j is the particle volume fraction, a is the radius of the particle (= d/2), b = (4π/3), j0 = 0.8404, λ = (1+δ), and f(λ) and jb are tabulated functions of λ.43 The following equations, eqs 8 and 9, give the chemical potentials of the particles in the liquid phase, μL and solid phase, μS, respectively:38,42 Z μL ¼
0
j
! 4πPa3 dj0 4πPa3 -1 þ lnðjÞ -1 þ 3j0 kT j0 3jkT μS ¼ -
ns ε -3 lnðλ -1Þ 2 kT
ð8Þ
ð9Þ
In these equations, j0 is the variable of integration representing j, and ns is the number of nearest neighbors in the solid, which is taken as 12 in our calculations. Knowing the solubility of the protein (in terms of the volume fraction j = jsol), we estimate the strength of interaction (ε/kT) by solving μL = μS for a given range of interaction δ (= λ-1). We then use the Sear’s model (eq 5) to obtain the value of the interfacial energy. Using this procedure, for a δ of 0.15, we obtain the values of ΓCEWL as 2.71 and 2.49 (γCEWL = 0.90 and 0.83 (mJ/m2)) for the cases of without and with acetonitrile in solution, respectively. Similar estimates for XI with a δ of 0.15 result in ΓXI = 2.65 and 2.54 (with corresponding γXI = 0.10 and 0.09 (mJ/m2)) for the conditions of interest. These values of the interfacial energy are lower than the values obtained from the experimental data (Table 4). However, we again note that the choice of a δ of 0.15 is arbitrary, and in each case, a full quantitative agreement may be obtained by considering different ranges of interaction. In summary, in an effort to understand the effect of the solubility enhancers on nucleation, we have used two different methods that are available in literature to relate the interfacial energy of a compound to its solubility, which are (a) by relating jsol to (ε/kT) through the empirical correlation of jsol with B2 and using this B2 as a surrogate for (ε/kT) in Sear’s model, and (b) by directly estimating (ε/kT) from jsol via the generalized phase diagram for a simple fluid and using this (ε/kT) to estimate Γ through eq 5. While these methods estimate the absolute values of interfacial energy to different degrees of accuracy, they both predict the relative degree of reduction in Γ brought forth by the additive to the same extent, about 0.2 - 0.3, which is what we obtain from our experimental results as well. We note that the methods we have used to link interfacial energy to solubility are at best approximations and predict the interfacial energy with limited accuracy. In discussing these models that relate Γ and jsol, our aim is to understand the influence of solubility enhancers on the nucleation of protein crystals at a molecular level and to rationalize the trends we 4586
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have noticed in our experimental studies. We do not expect to achieve quantitative agreements between the model predictions and the estimated parameters. Role of Solubility Enhancers in Improving Crystal Growth. For unambiguous protein structure determination by X-ray crystallographic techniques, crystal quality is an important factor. Crystal quality can be assessed through analysis of X-ray diffraction data. Mosaicity, a metric of crystal diffraction quality, is a measure of peak broadening of scattered X-rays caused by factors that include beam divergence and crystal defects. For a given X-ray source and detector, differences in mosaicity can be attributed to differences in crystal defects. Mosaicity increases with increasingly defective crystals. Crystal diffraction resolution, which refers to the minimum d-spacing observable in X-ray diffraction data, is a second and a less sensitive measure of crystal quality. In our experiments, we observed that the degree of supersaturation needed to nucleate protein crystals was lower when acetonitrile or glycerol was added to solution as compared to the supersaturation required for crystallization with precipitants alone. We also observed a corresponding decrease in crystal mosaicity (Table 3). We believe this improvement in the quality of the crystals is a direct result of the low supersaturation at which they were grown. Reduced supersaturation provides a smaller driving force for crystal growth, which leads to the formation of more ordered crystals.44 Thus solubility enhancers, through their effect on nucleation, also play a positive role in the growth of well-ordered protein crystals. Threshold Supersaturation for the Crystallization of XI. During the present study, we observed that XI (173 kDa) needed fairly higher degrees of supersaturation for the onset of nucleation when compared to those required by CEWL (14.6 kDa). In our batch studies at 4 C, crystals of CEWL formed in solutions with precipitant alone at conditions where the initial protein concentration was in excess of 5 times equilibrium solubility (S > 5). This threshold supersaturation was about S = 2 for solutions that contained acetonitrile or glycerol. For XI, when these additives were present in the solution, we observed crystal formation in a period of 2 weeks at solution conditions where S > 20, whereas a supersaturation of 100 or above was needed to observe crystals in the same period in the absence of these reagents. From Tables 1 and 2, we note that the solubility of XI at 4 C (∼ 0.1 to 0.5 mg/mL) is an order of magnitude lower than that of CEWL at the same temperature (∼2 to 5 mg/mL). To assess the relative ease of crystallization of XI in comparison to that of CEWL at similar conditions of solubility, we crystallized XI at 18 C (at which the solubility of XI is ∼2-6 mg/mL, comparable to that of CEWL at 4 C) with and without acetonitrile in solution. We observed crystals formed at S > 13 when acetonitrile was present in solution, and a supersaturation of 18 and above was needed with no additive. Thus, even at solution conditions at which the solubility of the proteins is comparable, higher supersaturation was required to crystallize XI (S > 13) than that needed for CEWL (S > 2). These results highlight an interesting balance between the driving force for protein crystal nucleation (the supersaturation) and the resistance toward the formation of crystals (44) Yoshizaki, I.; Sato, T.; Igarashi, N.; Natsuisaka, M.; Tanaka, N.; Komatsu, H.; Yoda, S. Acta Crystallogr., Sect D: Biol. Crystallogr. 2001, 57, 1621–1629.
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(the energy barrier). From our above analysis of nucleation studies, we note that the dimensionless interfacial energy of XI is higher than that of CEWL, regardless of the presence of additive in solution (ΓXI > ΓCEWL for the concentration of 6% (v/v) acetonitrile we studied). We note that, within the scope of CNT and the applicability of the capillarity approximation that we used to estimate the energy barrier, the resistance to nucleation scales as exp(-Γ3), whereas the driving force for nucleation varies as exp(-ln-2 S). As a result, a solute with even moderately large values of Γ requires a significantly high driving force to overcome the energy barrier. From Table 4, we see that the interfacial energy (γ) that we calculate is in fact smaller for XI when compared to that of CEWL (γXI < γCEWL). This result shows that the size of the XI molecule contributes significantly to Γ (and hence the energy barrier). Indeed, from eqs 2 and 3, we observe that the energy barrier scales as exp(-d 6), a result that explains the high supersaturations required by XI for the onset of crystallization. On the basis of these observations, we hypothesize that larger protein molecules, in general, may require a higher supersaturation to nucleate in a reasonable period of time when compared to that needed for smaller molecules.
Conclusions In summary, we have examined the role of two nonelectrolyte additives, acetonitrile and glycerol, on the solubility, nucleation, and growth of crystals of two proteins, XI and CEWL. We observed that these additives enhance the solubility of the proteins. Batch crystallization studies followed by the measurements of rates of nucleation reveal that these solubility enhancers promote nucleation and affect the growth process of crystals in a favorable manner. We also observed that XI, a relatively large protein when compared to CEWL, required higher supersaturation for the onset of nucleation than that required by CEWL. To understand the effect of these solubility-enhancing additives on nucleation, we have analyzed the kinetic data and have obtained the parameters that dictate the rate of nucleation. For this purpose, we used a semi-empirical model that employs the capillarity approximation within the scope of
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CNT to approximate the energy barrier to nucleation. We observed that the additives influenced the intermolecular interactions such that the pre-exponential factor was not altered substantially, whereas the energy barrier to nucleation was reduced significantly. Within the framework of CNT, this effect is manifested as a reduction of the solid-liquid interfacial energy of the protein crystal. We have used two approximate methods that are available in the literature to associate the change in the strength of interactions between protein molecules caused by the additive to the reduction of the energy barrier to nucleation. Interestingly, these methods predicted the observed relative change in the dimensionless interfacial energy reasonably well for the case of nucleation in the presence of a solubility enhancer. We assert that our experimental results that demonstrate enhanced nucleation of XI and CEWL in the presence of acetonitrile or glycerol are not dependent on the validity of the models used in the analysis of our nucleation data. Additives such as acetonitrile and glycerol enter the solutions of proteins used in crystallization attempts at various stages of preparation. Some of these additives can increase the solubility of the protein in solution. In our previous work that focused on high throughput screening of crystallization conditions, we observed an increase in the portion of positive results when solubility enhancement was achieved through buffer optimization and addition of glycerol.4 In the present work, we have shown that additives that increase the solubility of a protein also enhance the nucleation kinetics of its crystals, allowing the protein crystals to nucleate at a low supersaturation. Subsequent growth of these crystals at this low supersaturation allows them to grow into wellordered crystals with fewer defects, as evidenced from the improved mosaicity measurements we obtained in this study. These results demonstrate that solubility enhancing reagents have beneficial effects on the outcome of protein crystallization experiments and hence are desirable additives in the solution. Acknowledgment. This research was sponsored in part by the National Aeronautics and Space Administration Grant NAG8-1838.
DOI: 10.1021/la803185m 4587
