An Investigation of the Crystallogenesis of an Icosahedral RNA Plant

CRYSTAL GROWTH & DESIGN

An Investigation of the Crystallogenesis of an Icosahedral RNA Plant Virus with Solubility Phase Diagrams Bernard Lorber*,† and Jean Witz‡,§ Architecture et Re´actiVite´ de l’ARN and formerly Immunochimie des Peptides et des Virus, UniVersite´ Louis Pasteur de Strasbourg, CNRS, IBMC, 15 rue Rene´ Descartes, 67084 Strasbourg, France

2008 VOL. 8, NO. 5 1522–1529

ReceiVed August 1, 2007; ReVised Manuscript ReceiVed January 12, 2008

ABSTRACT: The formation of crystals of the quasi-spherical tomato bushy stunt virus (TBSV, family Tombusviridae) was investigated to understand how identical cubic crystals with a dodecahedral habit grow in the presence of two chemically different precipitants, ammonium sulfate and polyethylene glycol (PEG). Two-dimensional solubility phase diagrams were established to identify the zones in which the virus crystallizes or precipitates. In the presence of the salt the solubility of the virus decreases when temperature increases. The reverse occurs in the presence of PEG. Virions stored during several years as crystals or as amorphous precipitates readily solubilize upon dilution and recrystallize under appropriate conditions like freshly purified ones. Light scattering measurements confirm that both crystallizing agents promote attractive interactions between viral particles. On a molar basis PEG8000 is about 70-fold more effective than ammonium sulfate in insolubilizing TBSV. In the presence of each precipitant, heterogeneous nucleation takes places in a precipitate and crystal growth proceeds via an Ostwald ripening mechanism. The growth rate is controlled by the dissolution of the precipitate. Crystals with the largest dimensions always grow at apparently low supersaturation. 1. Introduction Phase diagrams have rarely been applied to investigate the crystallization of biological macromolecules like proteins, nucleic acids, or large assemblies such as ribosomes and viruses. This is astonishing for several reasons. First, to be amenable to crystallization, all these particles require the presence of a chemical compound (e.g., a salt, an alcohol, an organic polymer, or a mixture of them) termed precipitating or crystallizing agent (precipitant, crystallizant) that lowers their solubility.1,2 As a consequence, the crystallization of biomolecules is influenced by a much greater number of variables than that of small molecules. On the other hand, many biological particles can be isolated in mg quantities and their crystallographic structures have been determined at near-to-atomic resolution. For instance, even though several icosahedral plant viruses can be purified in gram amounts, brome grass mosaic virus (BMV) is the only one for which a phase diagram has been established.3 Here we report on the crystallogenesis of the virus responsible for the stunting and bushy growth of tomato plants (TBSV, genus Tombusvirus, family Tombusviridae) (Figure 1). The extensive structural and biological knowledge of TBSV is in strong contrast with the scarce information that is available about its crystal growth. For this reason, we have measured the solubility of the virus and mapped its crystallization space in the presence of two chemically different precipitants, ammonium sulfate and polyethylene glycol (PEG). To identify the nucleation and precipitations zones, we have prepared two-dimensional phase diagrams at 4 and 20 °C. Three crystal polymorphs could be located in the morphodroms and a relationship established between the salt and PEG concentrations at which virus solubility is identical. Further, the effects of temperature on virus solubility have been studied in the presence of both precipitants. Throughout all analyses the integrity and stability of the crystallized or precipitated virions was assessed by electron * Corresponding author. Phone: 333 8841 7008. Fax: 333 8860 2218. E-mail: [email protected]. † Architecture et Re´activite´ de l’ARN. ‡ Immunochimie des Peptides et des Virus. § Deceased.

Figure 1. Effect of TBSV on the growth of the nightshade Datura stramonium and electron micrograph of infectious viral particles. (a) Six-week-old and 30 cm high uninfected control plant (on the left) and plant whose two first leaves were infected artificially 3 weeks after germination (on the right). (b) Electron micrograph of negatively stained virions (scale bar is 100 nm long).

microscopy and dissolution/recrystallization assays. The association of the viral particles in various precipitant solutions has also been compared using light scattering techniques. The experimental results on TBSV are discussed in terms of precipitant effectiveness and crystallization mechanism and compared to those of BMV. 2. Experimental Section 2.1. Virus and Chemicals. TBSV was propagated in Datura stramonium plants (family Solanaceae) maintained at 25 °C with 14 h illumination. Fifty 3-week-old plants were infected manually by rubbing leaves with paper tissue soaked with sterile water containing 0.2 mg mL-1 virus and silicon carbide (Carborandum) powder. The infected leaves were collected 3 weeks later and ground in a Warring blender after the addition of a small volume of 20 mM sodium acetate solution adjusted at pH 5.8. This extract was filtered over cloth to remove the larger debris and the soluble proteins of the supernatant were precipitated by adding concentrated acetic acid upon stirring until the pH reached 4.8 at 20 °C. Precipitation was complete after 3 h at 4 °C and the insoluble material was removed by a 15 min centrifugation at 12500 rpm in a Jouan JA16 rotor. Subsequently, the virus was sedimented during a 1.5 h-long ultracentrifugation at 45 000 rpm in a Beckman Ti50.2 rotor. The virus pellet was suspended passively

10.1021/cg700722b CCC: $40.75  2008 American Chemical Society Published on Web 03/22/2008

TBSV Crystallization/Solubility Diagrams Table 1. Structural and Physical Chemical Properties of TBSV genome composition total dry Mr capsid triangulation number geometry protein subunit Mr no. of subunit copies total dry Mr viriona total dry Mr A260 nm/280 nmb E260 nmc dn/dcd Vje pIf D0g particle diameter crystallographich in solution dhi A2j

4800 nucleotide-long monopartite RNA ∼1.67 × 106 T)3 icosahedron (i.e., 20 faces, 12 vertices) ∼40000 180 arranged in 60 capsomers of 3 subunits ∼7.2 × 106 ∼8.8 × 106 (∼83% protein) 1.6 5.0 mg mL-1 cm-1 0.2 mL g-1 0.71 mL g-1 4.1 1.12 × 107 cm2 s-1 33 nm 37 nm 7 × 10-4 mL mol g-2

a The removal of calcium ions bound to TBSV induced the reversible swelling of the capsid.4,5 b Maximal ratio of the absorbances at 260 and 280 nm for pure virus. c Extinction coefficient at 260 nm. d Increment of refraction index per concentration unit. e Partial specific volume.6 f Isoelectric point.7 g Translational diffusion coefficient extrapolated at zero concentration derived from DLS measurements performed on virus in 0.1 M sodium acetate solution at pH 4.5 and at 20 °C. h See refs 8 and 9. i Hydrodynamic diameter deduced from diffusion coefficient assuming that particles are hard spheres. j Second virial coefficient corresponding to the slope of the plot of scattered intensity (measured by SLS) versus virus concentration. Experimental conditions as under (g).

overnight in 20 mM sodium acetate at pH 6.0 and the last debris were removed by 10 min centrifugation at 5000 rpm in an Avanti rotor 7.5. The pure TBSV was then ultracentrifuged a second time, suspended in thrice distilled and sterile water, and filtered on a Millex membrane with a pore diameter of 0.22 µm (Millipore) prior to storage at 4 °C. The concentration of TBSV solutions was determined from its absorbance at 260 nm. A purification starting from 500 g fresh leaves yielded about 500 mg virus particles. The structural and physical chemical properties of the virions in such preparations are summarized in Table 1. Precipitant stock solutions, i.e., 3.5 M ammonium sulfate (Cat. No. HR2–541, and) and 50% m/v or 6.25 mM PEG-8000 (Mr 7000–9000, Cat. No. HR2–535) were purchased from Hampton Research (Aliso Viejo, CA). All other chemicals were of ACS grade. 2.2. Crystallization Assays. TBSV was crystallized in vitro by a variety of methods: batch, vapor diffusion, dialysis, and counterdiffusion.10 Phase diagrams at 4 and 20 °C were established by batch crystallization in the presence of 20 mM sodium acetate adjusted at pH 4.7 ( 0.2 and either ammonium sulfate or polyethylene glycol (PEG-8000). Assays were set up in 0.5 mL translucent Thermowell tubes (Cat. No. 6530, Corning Inc.). Stocks solutions consisted in (i) 120 mg mL-1 TBSV, (ii) 0.2 or 2.0 M ammonium sulfate and (iii) 4 or 40% (m/v) or 5 to 50 mM PEG-8000 in water and contained 20 mM sodium acetate pH 4.7 and 3 mM sodium azide. Buffer and precipitant solutions were always mixed first and the virus was added to this mixture. After mixing the pH measured with a Beckman Φ 100 ISFET pH meter equipped with a microprobe, was 4.7 ( 0.2 at 20 °C. The sample tubes were wrapped in a double layer of Parafilm foil and stored in thermally insulated containers (Electrolux, Luxembourg) placed at either 20 ( 1 °C or 4 ( 1 °C. All samples were kept undisturbed for the duration of the experiment. To monitor the crystallization process, 5 to 10 µl drops of crystallization medium were equilibrated by vapor diffusion against 200-500 µL reservoirs inside modular VDX plates.11 Other experiments were prepared inside X-ray capillary glass tubes either in batch mode or by counter diffusion. The outcome of crystallization was examined between crossed polarizers at a magnification of 20–50× using an Olympus model SZH binocular microscope. Precipitates were inspected for microcrystals using a Nikon Labophot-2 microscope (magnification range 40–400×) equipped for observation in polarized light or with dark field or phase contrast. 2.3. Solubility Measurements. Soluble virions were separated from crystallized or precipitated ones by filtration on a membrane with a

Crystal Growth & Design, Vol. 8, No. 5, 2008 1523 0.22 µm pore diameter (Ultrafree, Millipore). Subsequently, the filtrate was centrifuged 10 min at 10 000 rpm. These steps were performed at the temperature of the crystallization to prevent the dissolution of the crystals or precipitates. The supernatant was diluted in water prior to absorbance measurement at 260 nm. 2.4. Light Scattering Measurements. Intensities of scattered light in static mode (static light scattering, SLS) and correlation times in dynamic mode (dynamic light scattering, DLS) were measured at 20 °C with a Zetasizer Nano S instrument (Malvern, U.K.).12 Samples were analyzed in 45 µL quartz cuvettes and toluene was used as a standard scatterer. All solvents were prepared with thrice-distilled water and filtered through Millex membranes (pore diameter 0.2 µm, Millipore) to eliminate dust particles. The scattered intensity was proportional to virus concentration in the range 0.01–0.1 mg mL-1. Second virial coefficients were derived from the slop of the Debye plot representing the residual intensity as a function of virus concentration. Mean particle diameter was obtained from the plot of size distribution by intensity. Corrections were applied for particle shape (assumed to be spherical), virion increment of refractive index (dn/ dc), solvent refractive index (measured at 20 °C with an Abbe refractometer) and viscosity measured at 20 °C with a 3.5 mL microUbbelohde capillary viscosimeter (Schott, Germany). 2.5. Electron Microscopy. Integrity and association of virus preparations and precipitates were examined at the microscopy facility of the Institut de Biologie Mole´culaire des Plantes (IBMP-CNRS, Strasbourg) after negative staining with uranyl acetate.13 Nickel grids coated with a polyvinyl formal (Formvar) film were covered with 2-20 µL of a virus suspension at 0.1–1 mg mL-1. The excess was blotted after 2 min and 5 µL of 2% (m/v) aqueous uranyl acetate solution at pH ∼ 4.5 added. After 10 s, the excess stain was eliminated by contact with a piece of filter paper and the grid was air-dried for 5 min at ambient temperature. Negatively stained air-dried virus samples were examined with a Hitachi H-600 transmission electron microscope operated at 75 kV. Micrographs were recorded with a Hamamatsu CCD Advantage HR camera. 2.6. X-ray Diffraction Analysis. TBSV crystals were characterized in-house with a Nonius diffractometer equipped with a Rigaku rotating copper anode (operated at 45 kV, 90 mA) and a DIP2000b MacScience image plate. Medium-sized crystals were mounted in Lindemann glass capillaries that were sealed with silicon grease. Set of diffraction images were collected at the crystallization temperature with an oscillation angle of 0.25°, an exposure time of 20 min, and a crystal-to-detector distance of 250 mm. The image plate was offset by an angle of 20° to determine the diffraction limit of the crystals. Reflections were indexed using the program DENZO from HKL package.14 Protein Data Bank accession code of the TBSV crystal morph I is 2tbv. 2.7. Solubilization of Precipitated and Crystalline Virus. Precipitated or crystalline material originating from phase diagrams was separated from soluble virions by centrifugation (30 min, 10000 rpm) at the temperature of crystallization. After complete dissolution of the pellets in ∼30 mL water, the suspensions were transferred in Spectra/ Por 2 dialysis tubing (Spectrum, Houston, TX) and dialyzed 3-times against 5 L of thrice-distilled water containing 3 mM sodium azide at intervals of 24 h. The resulting virus suspensions were then subjected to two cycles of low and high speed centrifugations as for purification. After every ultracentrifugation, the pellets were dissolved overnight in 25 mL of water containing sodium azide. 2.8. Miscellaneous. The volume fraction (in %) occupied by viral particles in solution was calculated using the relationship:

Fp ) 100{1 - [Vjs(1 - cv)/(cvVjv + Vjs(1 - cv))]}

(1)

in which cv is the virus concentration (in g/ml), Vjv the specific volume of the virus (Table 1), and Vjs the specific volume of the solvent (Vjs ) 1 mL g-1 for water). The virus volume fraction in crystals was estimated using the method of Li and Steitz.15 A crystal was successively transferred in three drops of a 100 µL reservoir solution to dilute contaminating soluble or precipitated material. During this time a known volume of water was introduced inside a glass capillary (with a slightly greater cross-section than that of the crystal) and the length of the liquid column was measured under a binocular microscope. The capillary was then emptied and dried, the crystal sucked inside it, and the excess of solution removed with a thin capillary. Reservoir solution was added at some distance of the crystal, and the length of the liquid column was measured

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Lorber and Witz

before and after it was moved over the crystal. The volume of the crystal was derived from three above measurements. The amount of virus contained in it was deduced from absorbance at 260 nm after the transfer of the content of the capillary and the dissolution of the crystal in a known volume of water.

3. Results TBSV was the first icosahedral virus that was crystallized.16 Its crystallographic structure model revealed the isometric architecture of its capsid and led to the discovery of the basic rules of the geometrical construction of regular viruses.8,9,18–21 3.1. TBSV Crystallization in Ammonium Sulfate vs PEG Solutions. The present analyses of the crystallization outcome after very long equilibration times were not intended to study liquid–liquid phase separation.22–25 Here, two small series of 50 batch crystallization assays with various concentrations of TBSV and ammonium sulfate or PEG-8000 C were first set up at 20 °C and 4° to define the ranges of virus and precipitant concentrations that produce crystals after an incubation time of 6 months. No crystal appeared in ammonium sulfate solutions kept at 20 °C but many assays that contained this salt or PEG and were stored at 4 °C became rapidly cloudy and produced crystals. In contrast, the aspect of others did not change over six months (result not shown). On the basis of these preliminary results, three 2D diagrams of 150 batch crystallization assays of 200 µL each were prepared. The maximal virus and precipitant concentrations imposed by those of the stock solutions were 70 mg mL-1 (8 µM) for TBSV (volume fraction 5.1%), 1.8 M ammonium sulfate and 20% (m/v) (25 mM) PEG-8000. In all 2.2 g pure TBSV were consumed to cover ranges of 19 salt and 21 PEG concentrations. After 36 months at constant temperature, a great proportion of the assays contained a white precipitate that had settled at the bottom of the tubes. In some of them, clear solution of variable height above it contained crystals. The pH of the samples (4.7 ( 0.2 at 20 °C) had not changed since the beginning of the experiments. As expected, nonbirefringent dodecahedral crystals (morph I) that measured more than 3 mm across, had formed in a number of assays containing ammonium sulfate (Figure 2). These crystals are the original cubic bodycentered crystals (space group I23, unit cell parameter a ) 383 Å, with 2 virions per unit cell) reported by Bawden and Pirie that served for structure determination.8,9,19,26 Similar crystals (morph II) were obtained in the presence PEG solutions at either 4 or 20 °C (Figures 2). Morph I and II have the same cubic unit cell (a ) 383 Å) and virus volume fraction (37% in morph I and 42% with SD 10% for n ) 8 in morph II, consistent with the presence of 2 virus particles per asymmetric unit). Their diffraction limit is better than 3.5 Å on a rotating anode. Finally, a third crystal form (morph III) that has a prismatic habit and is not birefringent was found in six assays at 4 °C that contained 10 to 20 mg mL-1 virus and 5-7% (m/v) PEG (Figure 2). This polymorph is extremely sensitive to temperature variation and could not be characterized by X-ray diffraction. 3.2. TBSV Solubility in the Presence of Ammonium Sulfate vs PEG. The solubility data in listed in Table 2 are plotted as solid squares in Figure 3. In some sample tubes containing ammonium sulfate at 4 °C, the height of the layer of settled precipitate increased with the salt concentration. In a semilogarithmic plot, the solubility curve divides in three parts: (i) below 0.6 M, the solubility of crystals varies quasilinearly; (ii) above 1.2 M, that of the precipitate is almost constant, and (iii) in between, that of crystals mixed with precipitate gradually decreases when salt concentration

Figure 2. TBSV crystals grown in vitro in ammonium sulfate or PEG solutions. (a) Voluminous morph I crystals grown in a 50 mg/ml virus suspension containing 0.4 M ammonium sulfate at 4 °C. (b, c) Crystals of morph II with medium dimensions grown in the presence of 10–20 mg/ml virus in 6–8% (m/v) PEG at (b) 4 and (c) 20 °C. (d) Morph III crystals with greatest dimensions at 15 mg/mL virus in 6% (m/v) PEG at 4 °C. All scale bars are 1 mm. No crystal was birefringent between crossed polarizers. Table 2. Solubility of TBSV under various experimental conditions AmSO4a

PEG-8000a × C (M) I (M)c Sd,e at 4 °C 103M (% m/v) 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

5.4 5.1 4.8 4.5 4.2 3.9 3.6 3.3 3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6

0.02, P 0.03, P 0.03, P 0.03, P 0.03, P 0.03, P 0.04, P 0.04, P,C 0.05, P,C 0.07, P,C 0.13, P,C 0.32, C 0.57, C 2.4, C 9.5, C 35, C n.d.

25.00 (20) 23.75 (19) 22.50 (18) 21.25 (17) 20.00 (16) 18.75 (15) 17.50 (14) 16.25 (13) 15.00 (12) 13.75 (11) 12.50 (10) 11.25 (9) 10.00 (8) 8.75 (7) 7.50 (6) 6.25 (5) 5.00 (4)

S4d,e at 4 °C 0.02, P 0.02, P 0.02, P 0.03, P 0.03, P 0.03, P 0.03, P 0.03, P 0.03, P 0.03, P 0.04, P 0.15, P,C 1.0, C 2.5, C 7.0, C 31, C 65, C

S20,d,e at Rb 20 °C S20/S4 1.3, P 1.4, P 1.4, P 1.4, P 1.4, P 1.5, P 1.6, P 1.6, P 1.7, P 3.0, P,C 6.6, P,C 13, C 38, C 70, C n.d. n.d. n.d.

65 70 70 47 47 50 53 53 57 100 165 87 38 28 n.d. n.d. n.d.

a All precipitant solutions contained 20 mM sodium acetate adjusted at pH 4.5. b Quotient of the solubility in PEG-8000 solution at 20 °C and that at 4 °C. c Ionic strength I is equal to 3 times the salt concentration C. d Solubility in mg mL-1. e Crystal habit is indicated by a letter: (P) stands for precipitate and (C) for crystals. Errors on virus and precipitant concentrations are estimated to 10 and 5%, respectively. Abbreviation used: n.d., not determined.

increases. The linear parts intersect at ∼0.75 M. Morph I is accompanied by precipitate in the intervals from ∼0.8 to ∼1.2 M salt and ∼1 to ∼70 mg mL-1 virus. Solubility and supersolubility curves run parallel when precipitate replaces crystals at highest precipitant concentrations. DLS measurements reveal that the mean diameter of virus aggregates increases from ∼100 to >2000 nm between 0.8 and 1.2 M ammonium sulfate (Figure 4, top panel). In this salt, the A2 values exhibit strong fluctuations but no trend. The mean A2 is -0.0013 mL mol g-2 (SD ) 0.0014, n ) 12) for single

TBSV Crystallization/Solubility Diagrams

Crystal Growth & Design, Vol. 8, No. 5, 2008 1525

Figure 4. Aggregation of TBSV in ammonium sulfate and in PEG8000 solutions monitored by DLS at 20 °C. For each compound, the plot displays the variation of the mean particle diameter as a function of precipitant and virus concentration.

Figure 3. Crystallization/solubility diagrams and morphodroms of TBSV in ammonium sulfate or PEG solutions. The diagrams display experimental solubility data (solid squares), derived supersaturations (in Arabic numbers), and occurrence of the crystal morphs I, II, and III. Dotted lines superimposed on solubility data are guides to the eye. The zone where crystals nucleate is hatched horizontally and the one where a precipitate replaces the crystals is hatched vertically. At variance with the well-defined solubility curve, the boundary between nucleation and precipitation zones is actually not as sharp as drawn because of the supersaturation continuum.

particles (between 0.1 and 0.7 M salt) and for aggregates (at superior salt concentrations) (Figure 5). In the presence of PEG-8000 TBSV solubility curves at 4 and 20 °C are also biphasic (panels b and c in Figure 3). At 4 °C, the solubility of morph II and III varies linearly below 8% (m/v) or 10 mM PEG. That of precipitate deprived of crystals is almost invariable above 11% (m/v). In the intermediate region, the transition from one linear part to the other is abrupt. Solubility and supersolubility curves are well-separated at high precipitant concentrations at 4 °C. At 20 °C, the former is displaced toward higher precipitant concentrations and the slope of the part that corresponds to the nucleation zone is less steep. Morph II is found without precipitate in a small part of the diagram and morph III is absent (Figure 3c). Above 12% (m/v) PEG, nucleation and precipitation zones come so close to the solubility curve that the metastable zone almost disappears. The

Figure 5. Variation of the second virial coefficient of TBSV determined by SLS with the ammonium sulfate or PEG-8000 concentration. A2 was derived from the slope of the plot of the light intensity scattered in static mode at 20 °C versus virus concentration. Horizontal lines passing through A2 ) 0 do not indicate the mean of the experimental data.

width of the latter does not exceed 0.1 mg/mL (the semilog representation magnifies the difference between the graphs at 4 and 20 °C). In DLS, the mean diameter of the aggregates increases from 30 to 100 nm below 12% (m/v) PEG. Above this concentration, an additional population of aggregates appears with a mean diameter reaching 400-700 nm (Figure 4, bottom panel). Unlike in ammonium sulphate solutions, the A2 values do not vary very much. The mean A2 is -0.0002 mL mol g-2 (SD ) 0.0007, n ) 10) for unsaturated solutions (containing single virions between 0 and 9% m/v or 0 and 11 mM PEG-8000) and for supersaturated virus solutions containing aggregates (Figure 5).

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3.3. Properties of TBSV Recovered from Crystals and Precipitates. Crystalline and precipitated TBSV that has been in contact with ammonium sulfate or PEG-8000 at 4 or 20 °C for 5 years readily dissolves in water or buffer solution. Precipitates that formed under various conditions were inspected visually in polarized light or phase contrast. At magnifications of 200-400×, no microcrystals could be identified. Electron microscopy analyses confirmed that the virions had not been altered by precipitation (e.g., the proportion of empty capsids was not superior to that in the original preparations). The virus recovered from precipitates and from crystals (dissolved in water and repeatedly dialyzed and centrifuged at low and high speed to eliminate as much as possible salt or polymer) exhibits the same UV absorbance spectrum as the one kept in water for the same duration (result not shown). Within the limits of experimental error, the diffusion coefficients, mean particle diameters, and second virial coefficients were identical to those of controls. Regardless of the composition of the solution in which the crystals or precipitates had been stored, the virions crystallized and yielded crystals of morph I and II in the appropriate crystallization conditions (results not shown). 4. Discussion TBSV samples that are considered to be very pure according to the spectrophotometric criterion can yield macroscopic morph I crystals with facets easily recognizable by the unaided eye. At 4 °C, dodecahedral crystals similar to those in Figure 2a but with dimensions exceeding 4 × 4 × 4 mm3 can be grown in 500 µL virus suspension at 50 mg mL-1 containing concentrated ammonium sulfate. The edge of a TBSV crystal with such an exceptional volume is not made by more particles (with an ∼30 nm diameter) than the 1 mm-long edge of a crystal of a protein with a Mr ≈ 150 000 and 1 mm3 contains ∼3.5 × 1013 virions. These crystals belong to space group I23 (a ) 383 Å, 2 virions/ unit cell, Matthews coefficient ∼3.2 Å3 Da1- solvent content ∼63%). Morphs I grown in the presence of ammonium sulfate and morph II that grows in PEG-8000 solutions are isomorphs (panels b and c in Figure 2). Nonbirefringent crystals of morph III are also isometric and might be another habit for the same unit cell.27 4.1. Solubility and Cystallizability of TBSV. As reported by Bawden and Pirie,16 TBSV is less soluble at 20 °C than at 4 °C, i.e. its solubility variation is retrograde in the presence of ammonium sulfate. No crystal grows at the former temperature. At variance, the solubility variation is normal in the presence of PEG-8000; S20 °C can exceed S4 °C by a factor of 100 (Table 2). Moreover, in the presence of either compound the virus aggregates already at very low concentration and it becomes almost insoluble in concentrated precipitant solutions (S4 °C is only 0.02–0.03 mg mL-1). The higher solubility of TBSV of the crystalline phase with respect to the amorphous one, suggests that the first solid phase has a superior chemical potential. This differs from what was observed with calf rennin.28 In PEG solution, the metastable zone is very narrow at 20 °C (panels b and c in Figure 3). The solubility is the same in 0.5 M ammonium sulfate and in 7% (m/v) or 8.8 mM PEG-8000 (Table 2). In DLS, a transition between soluble and aggregated virions is detected at 1.0–1.1 M ammonium sulfate and 12–15% m/v or 15–19 mM PEG-8000 (Figure 4). The attractive interactions are stronger in ammonium sulfate than in PEG solutions (A2 ) -0.0013 vs -0.0002 mL mol g-2). A similar A2 value was found for BMV at pH 5 in 4-8% (m/v) PEG8000.29 At constant pH and temperature, the outcome of TBSV crystallization depends not only on the supersaturation σ (defined

Lorber and Witz

as the quotient of initial virus concentration on solubility) but also on the relative concentrations of virus and precipitant.30,31 A very low supersaturation (2 e σ e 3) is sufficient to trigger the nucleation and sustain crystal growth (Figure 3) but the same σ induces precipitation at higher precipitant concentration. While crystallization occurs at 2 e σ e 400 in the presence of ammonium sulfate at 4 °C, the crystals reach the greatest dimensions at low salt concentrations and 2 e σ e 50. In the presence of PEG, the useful supersaturation range goes from 2 to 20 at 4 °C and from 2 to only 10 at 20 °C. At 4 °C, the biggest crystals grow at lowest PEG concentrations when 2 e σ e 15. At 20 °C and similar supersaturations, slightly higher precipitant concentrations are needed. In PEG solution, crystallization yields crystals deprived of precipitate at 2 e σ e 5. At high PEG concentrations, the virus precipitates at lower supersaturation (2 e σ e 3) at 20 °C than at 4 °C (7 e σ e 50) or than in salt solution at 4 °C (13 e σ e 30). Above supersaturation values are derived from solubilities measured a posteriori (i.e., once crystals have formed) and are correct only if the crystallization medium is homogeneous. Because TBSV virions partition between a soluble phase and a sparingly soluble precipitate before crystallization starts, the experimentally determined supersaturations are apparent values. In reality, at the highest virus concentration (70 mg mL-1, virus volume fraction ≈5%) the precipitate occupies only ∼1/20th of the volume of the solution. This means that the precipitate formed in PEG solution, heterogeneous nucleation occurs at a local supersaturation of not 2 but at least σ ) 2 × 20 or 40. 4.2. Mechanisms of Virus Insolubilization. Because the protein capsid is the only part of the virus that is in contact with the solvent and interacts with other capsids inside crystals, the mechanisms of protein crystallization and precipitation apply. Obviously, salts and nonionic polymers insolubilize the virions by distinct mechanisms. Neutral salts like ammonium sulfate at high concentration salt-out proteins by establishing preferential interactions. Their ions shield the surface charges of the macromolecules.32 When a soluble protein is transferred to a crystalline or aggregated phase, the precipitant is excluded from some parts of the surface of the molecule. Protein association is promoted as soon as attractive potentials dominate over repulsive ones.33 Protein solubility has been related to the second virial coefficient of the solution.24 Since the virus has an isoelectric point of ∼4.1, its net charge is close to zero and its solubility minimal at pH 4.5. Two situations can be distinguished. Either repulsive interactions are weaker because of the screening of charges by salt ions or attractive ones are stronger because of a different hydration scheme or of the occurrence of hydrophobic contacts.34 Ammonium sulfate is not only involved in ionic bonds but it also stabilizes hydrophobic contacts during the crystallization of specific protein/nucleic acid complexes.35 Our DLS measurements confirm that this salt is an efficient precipitant even at low virus concentrations (Figure 4). The extremely low solubilities measured here (Table 2 and Figure 2a) are presumably a consequence of the conjugated influence of the proximity of solvent pH and virus pI and of the effectiveness of ammonium and sulfate ions.34 In the case of BMV, sodium acetate and sodium nitrate decrease the repulsive interactions between particles.3 The propensity of isometric virions to assemble in 2D and 3D arrays in the presence of a low concentration of PEG has been described.13,36 TBSV readily crystallizes in the presence of PEGs with a variety of chain lengths at acidic to neutral pH (Lorber and Witz, unpublished results). For many macro-

TBSV Crystallization/Solubility Diagrams

Crystal Growth & Design, Vol. 8, No. 5, 2008 1527

Figure 6. TBSV solubility equivalence between ammonium sulfate and PEG-8000 at 4 °C. Plot of PEG-8000 concentration versus ammonium sulfate concentration in which the solubility of TBSV is the same in the presence 20 mM Na acetate at pH 4.5 and at 4 °C. Data derived directly or by interpolation from the solubilities of samples that contained only crystals. The equation of the regression line (R ) 0.95) is y ) 10 x + 2 where x is the salt molarity. The line intersects with the y axis at 2% (m/v) PEG instead of zero because the solution is not ideal. Departure from ideality is shown by the dashed line. TBSV has the same solubility in the presence of 0.5 M ammonium sulfate solution and of 7% (m/v) or 8.8 mM PEG-8000. Table 3. Solubility Constants of TBSVa ammonium sulfate T (°C) β β′ Ks Ks′ K s″

4 3.1 3.1 5.3 1.8 5.8

PEG-8000 4 3.8 391 6.0

20 4.4 292 6.7

a

The constants were determined using the solubility values measured on virus samples that contained crystals but no precipitate (see Table 2). The logarithm of the solubility of many proteins varies linearly with the precipitant concentration C46 such as log S ) β – KsC, where S is the solubility, Ks the salting-out constant (given by the slope of the graph), and β the logarithm of solubility at C ) 0 (corresponding to the intercept with the ordinate). In the case of salts, C can be replaced by the ionic strength I so that log S ) β′ – K′sI.47 The salting-out constant K″s was derived from plot of log S ) β″ – K″s log C.28,48 S is expressed in g per 1000 g water and C in molarity. The ionic strength of ammonium sulfate is equal to three times the molar concentration.

molecules these linear and neutral polymers are as effective precipitating and crystallizing agents as salts.37,38 The relationship describing protein solubility in the presence of inorganic salts is applicable to them.39 PEGs render proteins insoluble by steric exclusion and by decreasing the repulsive protein– protein interactions via the addition of an attractive potential that was quantified in the case of urate oxidase.33,40–42 At the right concentration, PEG with an adequate chain length occupies such a great volume in solution that it creates depletion zones around protein molecules.43 As a consequence of this crowding or depletion attraction, the latter come so close together that their solvation shells overlap.44 With BMV an increase in PEG concentration diminishes repulsive interactions and enhanced attraction between virions results in precipitation. For this virus PEG and salt operate in synergy.3 Finally, the solubility of dodecahedral TBSV crystals is the same in the presence of 7% (m/v) or 8.8 mM PEG-8000 and of 500 mM ammonium sulfate. In Figure 6, in the plot drawn with the solubility data of virus samples that contained exclusively crystalline material, a departure from linearity means that PEG solutions containing TBSV like pure PEG solutions are nonideal.45 The effectiveness of both precipitants in insolubilizing the virus is mirrored by the “salting-out” constants (see Table 3 for definitions and values). At 4 °C, it is 74-fold greater in polymer (Ks ) 391) than in salt solution (Ks ) 5.3) meaning

Figure 7. Growth kinetics of a TBSV crystal in a precipitate in vitro. The crystal is in a 20 µL drop containing 50 mg/mL virus, 8% (m/v) PEG-8000, and 20 mM sodium acetate pH 4.5 at 20 °C. Nucleation was triggered by vapor diffusion and supersaturation did not exceed 2 (see gray area in Figure 3c). All pictures were taken at the same magnification but not in exactly the same orientation. The time scale in days is not linear. A clear halo around the crystal indicates that it grows at the expenses of insoluble material.

that the polymer is more effective than the salt on a molar basis (albeit the effectiveness of both is equivalent on a weight basis). In PEG solution, it is lower at 20 °C (Ks ) 292) than at 4 °C (Ks ) 391). For ammonium sulfate K′s is only equal to a third of Ks because the ionic strength is equals three times the molar concentration. As to K″s, it is close in salt (5.8 at 4 °C) and PEG (6.0 at 4 °C and 6.7 at 20 °C) solutions and varies only a little with temperature in the range 2-10 found for proteins.48 Together with the strong “salting-out” effectiveness of highmolecular weight PEGs, Ks values that are much greater than those of sodium sulfate have already been reported.28 4.3. Heterogeneous Nucleation within Precipitates. Although salts and nonionic polymers insolubilize the virions in different ways, crystallization proceeds via a common mechanism. A striking feature of TBSV crystallization is that a same crystal morph can be produced in the presence of two chemically different precipitants. The bonds involved in the packing forces are not the same in both precipitants but the common point is that the virus precipitates above a critical supersaturation and that crystals appear after some time inside the insoluble phase. In solution, heterogeneous nucleation occurs at preferential sites like on microscopic nucleants where the energy barrier that must be overcome is substantially lower than that required to perform homogeneous nucleation in the bulk.49 We have never seen TBSV grow directly from solutions that contained no precipitate. The low solubility of the virus in the presence of a precipitating agent is favorable to heterogeneous nucleation in a limited supersaturation range (see Figure 3). Once a proportion of the virus particles has become insoluble and settled, this virus-rich solid phase coexists with the virus-poor solution. The precipitated virions simultaneously provide the nucleants for heterogeneous nucleation and a local supersaturation that is more than an order of magnitude superior to that in the initial solution (see section 4.1). Both contribute to increase the nucleation rate. A striking feature is that this happens only in a given interval of precipitant concentrations. Beyond, the precipitate is stable and no nucleation occurs although the virions have not been irreversibly damaged. This means that the relative proportions of virus particles and precipitant molecules plays an important role too. Figure 3 shows that at a same supersaturation (for instance 25 in salt solution or 10 in PEG solution at 4 °C, or 5 at 20 °C) crystals are only produced below given precipitant concentrations. To the best of our knowledge, this phenomenon seems not to have been reported for proteins. 4.4. Crystal Growth by Ostwald Ripening. Clear halos visible around the growing crystals are an indication that the precipitate dissolves while crystals grow. At the end of this process frequently only few or a single crystal are left that can reach a volume of a few cubic millimeter when sufficient

1528 Crystal Growth & Design, Vol. 8, No. 5, 2008

Lorber and Witz

material is available. The image sequence in Figure 7 summarizes this process. The same occurs when crystallization is performed in batch or by vapor diffusion, or by counterdiffusion in solution or in agarose gel.50 This phenomenon is known as Ostwald’s step rule and characterized by the formation of a preliminary metastable phase (here the precipitate) that is different from the stable phase (crystals).51 It has been described for several proteins, with largest crystals increasing their size at the expenses of smaller ones.52 To identify whether the crystal growth rate is limited by the rate at which individual virions arrive at the crystal’s surface or by that at which they are incorporated into its lattice, the rates of volume diffusion, and that of surface diffusion have been compared. In the first case, the variation in crystal radius with time is given by Fick’s law53

dr/dt ) DV(c - S)/δeff

(2)

where D is the volume diffusion coefficient, V the molar volume, δeff the effective diffusion length (i.e., the distance traveled by a virion moving across the crystallization drop), c the concentration of the solute, and S its solubility at the temperature of crystallization. In the second, the growth rate is derived from the Burton-Cabrera-Frank model according to which

dr/dt ) nsDsV(c/S - 1)/xs2

(3)

where ns is the number of adsorbed growth units per surface area unit, Ds the surface diffusion coefficient (considered to be equal to D in 3), V the molecular volume, and xs the surface diffusion distance.54,55 Assuming that the growth of the crystal in Figure 7 (which measured 0.8 mm across after 35 days or 840 h) was continuous, the rate was ∼2.6 × 10-11 cm/s-1 (2.6 × 10-3 Å or 0.9 µm h-1, i.e. ∼300 layers of virions added to the crystal surface per hour or 1 layer every 15 s). For growth controlled by volume diffusion, the numerical data are D ) 2.9 × 10-8 cm2 s-1 (i.e., 1.1 × 10-7 cm2 s-1 corrected for solvent viscosity that is 3.8fold the viscosity of water), V ) 1.6 × 107 cm3, c ) 50 mg mL-1 or 5.7 × 10-9 mol cm-3, S ) 38 mg mL-1 or 4.3 × 10-9 mol cm-3 (in the presence of 8% m/v PEG-8000 at 20 °C), δeff ) 0.2 cm (the distance traveled by a virion is the half of the diameter of a 20 µL drop or 2 mm). The resulting linear growth rate is 3.2 × 10-9 cm s-1 or 0.1 µm h-1 or 0.3 × 10-1 Å s-1. For growth controlled by surface diffusion, ns ) 4.6 × 10-14 (i.e., the inverse of half of the surface area of a virion with 100% of the sites occupied), Ds ) 2.9 × 10-8 cm2 s-1 (assumed to be equal to the above volume diffusion coefficient), V ) 2.6 × 10-17 cm3, and xs ) 1 × 10-6 cm2.55 Hence a growth rate of 1.1 × 10-26 cm s-1 or 4.0 × 10-27 µm h-1 or 1.1 × 10-18 Å s-1 is found. Thus, the above experimental data suggest that growth is controlled by volume diffusion. In other words, the dissolution of precipitated TBSV determines the rate at which crystals grow. Indeed, surface diffusion would not be rate limiting if we take into account the fact that an icosahedron has 20 times more possibilities to make packing contacts than any asymmetric particle, or that the surface diffusion distance is 100-fold greater or site occupancy 100-fold smaller. The same situation is observed with β-amylase and aspartyl-tRNA synthetase.52,55 A time-resolved SAXS study of BMV showed that solutions of pure PEG or of PEG and salt mixtures produce the same microcrystalline face-centered cubic virus crystals (a ) 391 Å), but that the latter do not grow from amorphous precipitate but from organized arrangements of particles.56 While TBSV

crystallization generally ends up with a few macroscopic crystals that of BMV terminates in less than 30 min with a great number of microcrystals less than 50 µm across.57 With TBSV the open question is if morph III is actually another packing than morph II or if it could result from it by conversion. 5. Conclusions The present study shows that TBSV crystallizes essentially at high virus and low precipitant concentrations and becomes almost totally insoluble in the opposite case. At low to moderate supersaturation well-shaped crystals with a volume of a few cubic millimeters can be produced by heterogeneous nucleation in an amorphous precipitate. These crystals grow by Ostwald ripening and their growth rate is limited by the dissolution of the insoluble material. For TBSV, polyethylene glycol is a more effective precipitant than ammonium sulfate on a molar basis. Differences between the solubility of the virus in salt and polymer solutions suggests that other chemical groups at the surface of the capsid are involved in the lattice contacts. Also the proportions of hydrogen bonds, Van der Waals forces, ionic interactions, and hydrophobic interactions participating protein– protein recognition presumably differ. Solubility diagrams are an irreplaceable tool for understanding the crystallization of proteins and other biological particles.58 Although large sample volumes have been used in the case of TBSV, 2D diagrams actually do not consume greater amounts of biological material than many assays done at random. They are easily applicable to investigate the effects of polymers and salts on the solubility of biomolecules and to control their crystallization, from laboratory to industrial scale.59–63 Acknowledgment. This article is dedicated to the memory of Jean and Marie-There`se Witz. The authors thank G. Bec and Ph. Dumas for their help with diffraction analyses, M. Ehrardt (I.B.M.P., Strasbourg) for expert assistance with electron microscopy analyses, and B. Michels (Laboratoire de Dynamique des Fluides Complexes, Strasbourg) for help with virus characterization. They are grateful to M. Rie`s-Kautt (Universite´ de Paris) and A. Marquette (ISIS, Strasbourg) for discussions and to R. Giege´ (UPR 9002, IBMC) for continued interest. Support from the Universite´ Louis Pasteur and French Ministry for Research (Grants ACI-BCMS 042358 and PIR-MME) is acknowledged.

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