J. Mol. Biol. (1990) 213, 187-195
Diagnostic of Precipitant for Biomacromolecule Crystallization by Quasi-elastic Light-scattering V. Mikol 1, E. Hirsch 2 and R. Gieg61 ~Laboratoire de Biochimie Institut de Biologie Moldculaire et Cellulaire du C N R S , 15 rue Rend Descartes F-67084 Strasbourg Cedex, France and 2Laboratoire de Spectromdtrie et d'Imagerie Ultrasonores Institut Le Bel, 4, rue Blaise Pascal Universitd Louis Pasteur, F-67070 Strasbourg Cedex, France
(Received 1 June 1989; accepted 19 December 1989) The translational diffusion coefficient D25,w of hen egg-white lysozyme and concanavalin A from the jack bean is measured in various precipitating agent solutions as a function of salt and protein concentration using quasi-elastic light-scattering. With some precipitants, in undersaturated protein solutions, a protein or salt concentration dependence of the diffision coefficient of the scatterers is observed. It can be correlated with the inability of the protein to crystallize in this precipitant once the solution is supersaturated. These variations of D2s,w are interpreted in terms of non-specific interactions and/or aggregation that prevent the protein from making appropriate contacts to form a crystal. With other precipitants known to lead to crystallization, no significant variation of the diffusion coefficient with increasing concentration was observed, indicating that under such conditions up to saturation the proteins remain essentially monodisperse. Application of this technique to find crystallization conditions of other proteins is discussed.
1. I n t r o d u c t i o n
As crystallization limits the number of biological macromolecule structures accessible by X-ray crystallography, there is a growing need to better understand biomacromolecule crystallization (Gieg6 et al., 1988; Gieg6 & Mikol, 1989). Little is known about the mechanism that yields protein crystals, and the interactions involved in the formation of such crystals remain poorly understood, although addressed by Langmuir as early as 1938. Since protein crystals are highly ordered threedimensional arrangements of macromolecules, it could have been expected that they are maintained through multiple direct interactions. But X-ray crystallography has revealed that lattice contacts consist in most cases of few weak proteinprotein interactions (van der Waals and hydrogen bonds) and numerous water-mediated hydrogen bonds, which seem to play the major role in maintaining the crystal lattice structure. On the other • hand, amorphous precipitation or a more appro0022-2836/90/090187-09 $03.00/0
priate term from colloid chemistry, flocculation, results from non-specific van der Waals attraction (e.g. see Hiemenz, 1986). Consequently, in an optimal protein crystallization experiment, the specific conditions of pH, temperature and precipitating agent that prevent the macromolecules in undersaturated solutions from interacting, through nonspecific contacts, will also promote the formation of crystals once supersaturation is established. In order to favour crystal growth, the macromolecule should be pure from a biological point of view (Gieg6 et al., 1986) and the protein should retain its native state up to its solubility limit; e.g. no interaction and/or aggregation should have taken place before the solution is supersaturated. So far, the crystallization of a new molecule relies on "trialand-error" methods and remains unpredictable. Although crystallization of macromolecules s e e m s not to be fundamentally different from that of small molecules (Rosenberger, 1986), very few rational guidelines are likely to provide methods for successful assays. Carter & Carter (1979) have 187
© 1990 Academic Press Limited
188
V. M i k o l et al.
proposed a statistical approach to reduce the n u m b e r of conditions to be tried. Since the method is based upon optical microscopic examination, it is useless if no crystals or crystal-like forms are obtained, because one cannot unambiguously evaluate and distinguish between a m o r p h o u s and crystalline precipitates. A very interesting approach to address this problem rationally was suggested by the pioneering work of K a m et al. (1978). These authors introduced a theoretical model of the crystallization process for understanding nucleation. I t allows the aggregation state of a supersaturated protein solution to be probed with light-scattering. Crystallization is described as a co-operative step-by-step addition of monomers, whereas a m o r p h o u s precipitation is a non-co-operative polymerization process. This approach requires the analysis of the distribution of species within s u p e r s a t u r a t e d protein solutions, which is e x t r e m e l y difficult to address experimentally. According to this thorough theoretical model, in solutions leading to crystallization, an a b r u p t change in aggregate size is predicted, whereas a nearly linear variation is expected for precipitating solutions. Although the conclusions of this latter model have not been generalized to m a n y other systems (Baldwin et al., 1986; Carter el al., 1988), it was one of the first m a j o r results concerning the understanding of protein nucleation. The goal of the present work is more limited, in the sense t h a t it is not intended to address protein crystallization from a f u n d a m e n t a l point of view. I t deals specifically with the d e v e l o p m e n t of a diagnostic method, based on the use of light-scattering for rationally choosing good solvent conditions for crystallization assays. To define and validate the method, hen egg-white lysozyme and concanavalin A from the jack bean were chosen as model protein systems to investigate the behaviour of a protein in u n d e r s a t u r a t e d solutions leading either toward crystallization or to a m o r p h o u s precipitation. Quasi-elastic light-scattering was used as a probe, since it is a sensitive technique for the detection of variations of size and interaction in macromolecule solutions (for a review, see e.g. Berne & Pecora, 1976; Bloomfield, 1981; Schurr & Schmitz, 1986). Hen egg-white lysozyme is known to crystallize easily in sodium chloride solutions, whereas experiments with a m m o n i u m sulphate solutions have been unsuccessful (e.g. see R i e s - K a u t t & Ducruix, 1989). Conversely, concanavalin A is shown to crystallize readily in a m m o n i u m sulphate solutions. Accordingly, the effect of a m m o nium sulphate t h a t favours different situations in both systems has been analysed in this study. Similarly, concanavalin A was studied under conditions t h a t lead to a m o r p h o u s precipitation. Quasi-elastic light-scattering provides information a b o u t the different behaviour of the solutions, and proves to be able to predict the evolution (amorphous precipitation or crystallization) of the solutions analysed when they become supersaturated.
2. Materials and Methods (a) Macromolecules and chemicals Grade I, 3 x crystallized chicken egg-white lysozyme (14,000Da) and type IV jack bean concanavalin A (27,000 Da) were purchased from Sigma. Lysozyme was dissolved in 40 mM-sodium acetate buffer (pH 4"6) and concanavalin A either in 50mM-Tris-acetate or in 10 mM-sodium cacodylate buffer at pH as indicated. Both proteins were used without further purification. The solutions were sterilized by filtration through Millipore 0"45/am membranes. Their concentrations were determined spectrophotometrically at 280 nm with E l%(w/v)= 26-3 for lysozyme at pH 4"6 and E 1°0 (w/,)= 13 for concanavalin A at pH 6"0. The volume fraction ~b was computed a~
dp = [ I + (I -- c)'?'wl(Jl:pro,] - I,
(I )
where vw and Vp,otare the partial specific vohlmes of water and protein, respectively, and c is the concentration of protein (in % (w/v)). The partial specific volumes of lysozyme, concanavalin A and water were taken as 0"703ml/g (Sophianopoulos et al.. 1962), 0"730ml/g (Sumner et al., 1938) and l'0 ml/g, respectively. Each light-scattering measurement corresponds to a specific preparation. Spermine was obtained from Sigma and all salts for the crystallization assays were from Merck. (b) Lighl-scatterinff Before carrying out a series of measurements, protein solutions (I to 45 mg/m[) were centrifuged for l0 rain at I 1,000 revs/min (8000 g). Portions (80/al) of each solution (1001d) were pipetted to clarify them from dust and to leave any particulate matter in the unused 20 #l. They were then placed in the scattering cells. A scattering cell was made out of a high-quality glass tube with an inner diameter of 4 mm and has a length of 42 mm. Once filled, the scattering cells were transferred to plastic buckets and again before the scattering experiments centrifuged in an R-18 rotor in a J-21 Beckmann centrifuge for at least 60 min at 5000 revs/min. A more detailed description of the experimental set-up has been given (Candau & Zana, 1981). Samples were introduced at the centre of a cylindrical glass cell that was filled with distilled water. The cell temperature was controlled at 25( +_0"l )°C by a circulating bath. and was fixed on a goniometer so that the sample tube could be positioned on its rotation axis. An argon-ion laser (Spectra Physics 2000) provided a green light beam (4880 A) with 600 mW laser power, which was focused on the centre of the cell. The scattered light was then collected by a photomultiplier (EMI 90-30). A digital autocorrelator (Brookheaven Instruments, BI 30) yielded the photon count autocorrelation function, with 64 channels. The output of the autocorrelator was then fed to a microcomputer for data analysis. The autocorrelation function was analysed using the cumulant method (Koppel, 1972) to yield the average decay rate < F > and the variance v. The latter parameter is a measure of the width of the distribution of decay rates and hence provides information about the polydispersity of the system and is given by: v = ( < F 2 > - < F > 2 ) / < F > 2. (2) For nearly spherical particles (see below), if the variance v is less than 0"06, it indicates a rather small size distribution of the particles (Israelachvili et al., 1976). In the case of monodisperse particles, the translational diffusion
Diagnostic for Protein Crystallization coefficient 1), is given by the 1st reduced cumulant < F > /2K 2. The magnitude of the scattering wave vector K is given by:
K = [4nn sin(O/2)]/~,
(3)
where 0 is the scattering angle, 2 is the wavelength of the incident light in vacuum and n is the refractive index of the scattering medium. Since initial measurements of the diffusion coefficient showed no variation as a function of the scattering angle, within experimental errors, all further experiments were carried out at a fixed scattering angle of 90 °. If the macromolecule is assumed to have a spherical shape, its radius can be computed at infinite dilution using the Stokes-Einstein equation, which relates the hydrodynamic radius Rh to the diffusion coefficient D~:
Rh = kT /6n~lD,,
(4)
where k is the Boltzmann's constant, r/is the viscosity of the solvent and T is absolute temperature. Experimental error is within 3%, and measurements were reproducible whatever the time-lag between the preparation of the solution and the light-scattering experiments. Diffusion coefficients were corrected tbr the viscosity of water at 25°C. Viscosity measurements of the different solvents (buffer plus precipitating agent) were performed using a temperature-controlled capillary standard viscometer.
189
appropriate volumes of precipitating agent, buffer and protein to a volume of 100/A. The tubes were stored in a temperature-controlled water-bath (25(-t- 0"I)°C). After 8 weeks, portions of the supernatant were pipetted and centrifuged to sediment all crystalline or particle matters; their concentrations were then determined spectrophotometrically and defined as the solubility. (d) Crystallization Crystallization experiments were carried out in Linbro boxes (Flow Laboratory) using the hanging drop method (e.g. see Blundell & Johnson, 1976; MePherson, 1982). A volume of l ml of buffered reservoir solutions (Mikol el al., 1989a) at a higher concentration of precipitating agent were set in each well of the plate. A 5-pl volume of reservoir solution and 5 pl of protein solution were placed onto a silanized cover glass so that the initial volume of the drop was l0 pl (except for experiments with spermine, see Table 1). The cover glass with the droplet was placed over a reservoir solution and the chamber sealed with silicone grease. Crystallization experiments were followed over 8 weeks and are summarized in Table 1. Various salts, including NaCl, LiCl, KCI, MgSO a, CH3COONH 4, Na2SO 4, NH4NO 3, (NH4)2SO 4, K2SO 4, NH4CI and NaNO 3 were used as precipitants for concanavalin A crystallization.
3. Results and Discussion
(c) Solubility Crystallization or amorphous precipitation experiments for measurements of solubility were carried out by a batch method in sterile Eppendorf tubes by slowly adding
(a) Hydrodynamic properties of the proteins Q u a s i - e l a s t i c l i g h t - s c a t t e r i n g of m a c r o m o l e c u l e solutions can provide a straightforward way to
Table 1 Conditions of crystallization
Type
Salt concentration~ (~I)
pH
Protein species
Concentrationb (mg/ml)
NaCI (NH4)2SO,
9"68 2"0/2'5/3"0
4'6d 4"6d
Lysozyme Lysozyme*
20 20/30
NaNO 3 NH4N03 LiCI NaCl KCI NH4C1 CH3COONH4 Na2SO4 K2804 MgSO4 (NH4)2S04
0'10/0' 12 0"10/0'12 0.10/0.12 0-10]0"12 0-10]0'l 2 0"10]0"12 0-10/0"12 0"10/0"12 0"10/0-12 0"10/0"I2 l'0/l'2
6-0c 6-0~ 6.0~ 6-0~ 6-0~ 6-0" 6-0~ 6-0~ 6"0c 6-0" 6-0/6-5/7-~
Concanavalin A Concanavalin A Concanavalin A Concanavalin A Coneanavalin A Concanavalin A Concanavalin A Coneanavalin A Coneanavalin A Concanavalin A Coneanavalin A
7'5/l0 7'5/10 7'5/10 7'5/10 7'5110 7"5110 7-5]10 7"5]10 7"5/10 7"5]10 7"5/10
Spermine (tetrahydrochloride) Ethylene diammonium sulphate
0'04]0"05]0'06 0"08/0'1/0'12¢ 0'15/0'2
5"6]6'0 6"3/7"0c 6"0]6-5/7"0° 0'25/0-3
Coneanavalin A* Concanavalin A*
5"5]10 7'5/10
"The indicated concentration of salt is that of the reservoir, bThat of the protein is the initial protein concentration in the drop (all combinations of conditions were tested). CThedrops were not equilibrated against spermine solutions but sodium chloride solutions; concentrations are given below; accordingly the drops were made out of 5/~l of protein solutions and 5 #l of spermine solutions. The buffers werea 40 raM-sodium acetate, ~10 raM-sodium cacodylate and f50 mM-Tris-acetate. The asterisk (*) indicates conditions where amorphous precipitates are obtained; in other cases crystals are grown: the tetragonal form for lysozyme (e.g. see Ries-Kautt & Ducruix, 1989} and the orthorhombic form for concanavalin A with the morphology described by Mikol & Gieg6 (1989).
V. Mikol et al.
190 Table 2
Hydrodynamic properties of the proteins
Lysozyme + (40 raM-sodium) acetate, pH 4.6) 2% (w/v) NaCl 0"8 M-(NH4)~S04 l'0 M-(NH~)2SO4 Coneanavalin A + (50 mM-Trisacetate, pH 7"0) 1-0 M-(NH4)2S04 1.2 M-(NH4)2S04
D25.~ ( x 10~ cmZ/s)
Rh (A)
R~ (h)
10"3 11"4 I 1"5
21"2 19"0 19-1
17.2 17'2 17"2
5'7 5'7
38.4 38.4
37-2 37-2
Numerical values are obtained from extrapolations to infinite dilution (see Figs l and 2). Dzs.~ represents the diffusion coefficient corrected for the viscosity of water at 25°C and Rh the corresponding hydrodynamic radius. R~ is the radius of the macromoleculecomputed from X-ray data (the macromoleculeis assumed to be a sphere of the same volume as that derived from crystallographic structure without the hydration layer of the macromolecule).
obtain the translational diffusion coefficient of the scatterers and hence information about their hydrodynamic properties. T a b l e 2 presents the d a t a obtained with lysozyme and concanavalin A. From X - r a y analysis (Phillips, 1967), it was shown t h a t lysozyme consists of a compact structure, which can be a p p r o x i m a t e d as an ellipsoid, the dimensions of which are 45 A × 30 A x 30 (1 A=0-1 nm). I f the macromolecule is assumed to be a sphere of the same volume, its radius can be computed as 17.2 A, which agrees with the hydrodynamic radius obtained from the light-scattering experiments in ammonium sulphate solutions. However, in 2 % (w/v) sodium chloride, the agreement is apparently not as good. Nevertheless, it must be noticed first t h a t the radius computed from X-ray structure does not take into account the hydration of the macromolecule and t h a t the macromolecule does not retain a perfect spherical shape, and second, t h a t chloride ions are associated with lysozyme in the crystal structure. This m a y account for the larger size of the enzyme obser~/ed in sodium chloride solutions than in a m m o n i u m sulphate solutions. Moreover, it was determined by other studies (Dubin et al., 1971) t h a t the diffusion coefficient of lysozyme in aqueous solutions without chloride ions at p H 4.2 and 20 °C was 10-6 x l0 -~ em2/s (D2o,w), which is consistent with our values obtained in both salts at p H 4.6. X - r a y studies of concanavalin A crystals (Becker et al., 1975) revealed t h a t the lectin consists of a t e t r a m e r of identical protomers; each one is folded to form an ellipsoid dome 42 A in height with the greatest section 4 0 A x 3 9 A and the base 40 A x 25 A. At neutral p H and high ionic strength, the tetrameric structure is favoured and if it is
estimated as a sphere of the same volume, the corresponding h y d r o d y n a m i c radius can be computed as 37 A. This latter value agrees well with our d a t a obtained in ammonium sulphate (l'0 M and 1"2 M) at p H 7'0 where the extrapolated diffusion coefficient (D2s.w) can be estimated at 5.7x l0 -v cm2/s and accordingly the h y d r o d y n a m i c radius as 38-4 h . (b) Crystallization diagnostic Since sodium chloride solution leads lysozyme to crystallize, it was chosen as the crystallizing precipitant for this protein. A set of cells containing 2 % (w/v) sodium chloride at p H 4-6 and lysozyme at various concentrations ranging from 1 to 40 mg/ml (~b ranges from 0"07 ~/o to 2"8 %, which are low values from a physical-chemical point of view but correspond to high concentrations from a biological point of view). The cells were analysed using quasi-elastic light-scattering. Figure l(a) displays the translational diffusion coefficient to the scatterers as a function of the concentration of lysozyme. I t does not v a r y as a function of the protein concentration as long as the solution remains undersaturated. A small decrease in the diffusion coefficient can be observed as the protein concentration exceeds its solubility. Indeed, as the protein solution becomes supersaturated, interactions between macromolecules could take place and accordingly affect the observed h y d r o d y n a m i c properties of the macromolecules. This rapid decline observed near the saturation is in agreement with the theory outlined by K a m et al. (1978). Accordingly to their model, it reflects the presence of co-operative associations. Similarly, a set of experiments was carried out with solutions containing 20 mg lysozyme/ml ( ¢ = 1 " 4 % ) at p H 4 - 6 and different amounts of sodium chloride with concentrations ranging from 0"5% to 4 % (w/v). The diffusion coefficient of the scatterers, presented in Figure l(c), is shown to remain nearly constant. All preliminary crystallization experiments of concanavalin A in the salt solutions listed above yield crystals (see Table 1 ). The first series of lightscattering experiments with this protein was carried out in a m m o n i u m sulphate solutions, because this salt leads lysozyme to precipitation and concanavalin A to crystallization. A set of solutions containing a determined q u a n t i t y of a m m o n i u m sulphate (1"0 M) and different amounts of concanavalin A varying from 1 to 9 mg/ml ( ¢ = 0 " 0 7 % to 0-66%) yielded diffusion coefficients t h a t were roughly constant t h r o u g h o u t the investigated concentration range (Fig. l(b)). The same behaviour is observed when the solution contains 1"2 M-ammonium sulphate. No rapid decrease of the diffusion coefficient was observed in those precrystalline solutions near saturation. This discrepancy with the predictions resulting from the approach presented by K a m et al. (1978) might stem from two facts. First, such an a b r u p t change m a y occur at a higher concentration of protein and,
Diagnostic for Protein Crystallization II'6
Undersaturated soln
Supersoturoted
sob 0'15
E
% 8.8
0'10
x
cY
005
--e
•
6'0 0
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2'o
0'00
4'0
[Lysozyme] (mg/ml) (o)
6.5 •
•
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0"15
% 3-5
0"10
X 3
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.
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0"~
-~
0
.
0"05
~.
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0'00
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[eonconsvoUnhi (mg/m0 (b)
16 0'15
2 m
0"10 ="
•
X
,B o
0"05 0
0
4
0
second, this does not seem to be a general rule. Indeed, in the case of the water-sucrose system, no rapid decrease of the diffusion coefficient was detected in the supersaturated region with increasing concentration (English & Dole, 1950). A second set of solutions containing concanavalin A at a constant concentration at p H 6"0 but t h a t of ammonium sulphate varying from 0-2 to 1"0 ~ were analysed. The results, presented in Figure l(d), show no significant variations of D t with increasing salt concentration. Similar results were obtained with sodium nitrate as the precipitating agent (see Table 3). In all these experiments, the variance v is less than 0"06, which indicates t h a t the proteins are essentially monodisperse under the solvent conditions used. (c) Amorphous precipitation diagnostic
•
a-
191
Crystallization experiments with lysozyme remained unsuccessful in ammonium sulphate solutions (Table 1). Thus, this salt was elected as the amorphous precipitant for lysozyme and, accordingly, the h y d r o d y n a m i c properties of the protein analysed. Figure 2(a) shows d a t a obtained at p H 4"6 with lysozyme at various concentrations and ammonium sulphate at 0"8 M or 1"0 M. The data, however, display a different trend: as the protein concentration is increased, the diffusion coefficient decreases rather linearly (hence, similarly, the a p p a r e n t h y d r o d y n a m i c radius is shown to increase). These gradual variations are indeed predicted by the approach of K a m et al. (1978). The lysozyme concentration was maintained constant at 20 mg/ml (¢=1.4°/o) t h r o u g h o u t the n e x t series of experiments and the a m m o n i u m sulphate concentration was screened from 40mM to 1"4M. The results, displayed in Figure 2(b), show t h a t D2s.w remains essentially constant as the salt concentration increases. This behaviour could appear unexpected but is probably accounted for by the rather low concentration of lysozyme used with respect to its
0
S
0"00
0 [Noel] (% ,w/v)
(c)
6.5 m
i
i
I
l
B
015
eo ~-°x3-5
/
3 -0- - -
0
"D
_9_
0
0
01_
0'10 0"05
0 0
0"50. 0
o15 [Ammonium sulphote] (M) (d)
S
~Io
0"00
Figure 1. Crystallization diagnostic. (a) Variations of the diffusion coefficient of lysozyme (D25,w) ( I ) and the variance v (O) as a function of protein concentration in 2% (w/v) NaCl. The continuous and broken lines show the fit of the diffusion coefficient and the variance, respectively. (b) Variations of the diffusion coefficient of concanavalin A (D2s.,~) as a function of protein concentration in 50 mM-Tris-acetate (pH 7"0), 1"0 M-ammonium sulphate (m) and 1"2 M-ammonium sulphate ([-]); S' and S" indicate the solubility of the protein in 1-0 and 1"2 M-ammonium sulphate, respectively. The variance v is indicated for 1"0 M ( 0 ) and 1"2 M (O)- (c) Variations of the diffusion coefficient of lysozyme (D2s.w) (m) and the variance v (O) as a function of salt concentration for 20 mg lysozyme/ml, in 40 mM-sodium acetate (pH 4"6); S indicates the solubility of the protein. (d) Variations of D2s,w of concanavalin A ( 1 ) and the variance v (O) at 11 mg/ml as a function of ammonium sulphate concentration in 50 mM-Tris-acetate (pH 6"0).
V. Mikol et al.
192
Table 3
Diagnostic of crystallization with the hydrodynamic properties of the proteins System
[Salt]~ ~
[Protein]T ~
Crystallization (C) Precipitation(P)
Lysozyme + NaCl
(NH4hS04
D2s.. = cst v~0"06 D2a.w=CSt v~0'06
Dzs.w = cst v~0"06 D25,~1 v~0"06
C
Dzs,~=cst v~0"06 D25..=cst v~0"~
Dzs.w=CSt v~0"06 D25.w=CSt v~0"06
C
P
Concanavalin A +
(NH4)2SO4 NaNOa Ethylene diammonium sulphate Spermine
D2s,w,~
Dzs.wJ.
v:>0"l
v_>0'l
Dzs.~,~ vT
--
C
P e
aThe arrows indicate either an increase (T) or a decrease (~) of the concentration, and how it affects the hydrodynamic properties of the proteins. Experimental conditions are as described for Figs 1 and 2. cst, constant.
solubility. In all these experiments, the variance v is less than 0"06. Since it can be estimated that the lysozyme molecule bears about eight net positive charges at pH 4"6 and at low ionic strength (40 raM-sodium acetate), repulsive electrostatic interactions take place and can account for the high value of the diffusion coefficient observed in Figures l(c) and 2(b). From this first series of experiments, one can conclude, according to the decrease of the translational diffusion coefficient with ammonium sulphate, that aggregation and/or interaction between macromolecules takes place as the protein concentration is increased and can be correlated with the absence of success in crystallizing lysozyme in ammonium sulphate solutions. Another set of experiments with concanavalin A were then carried out with ethylene diammonium sulphate without knowing whether the lectin can be crystallized with this precipitating agent. At a low concentration of protein (5"5mg/ml) no specific variation of D25.w (and of P~) as a function of the salt concentration is observed (Fig. 2(c)) but, with a higher protein concentration of protein (11 mg/ml), a decrease of D, and an increase of the variance v of the fit of the autocorrelation function is observed: v is greater than 0"07 for most experiments, which indicates that the protein solution is not monodisperse. Furthermore, there is experimental evidence that the particle distribution is rather large in these solutions. Indeed, with sample times ranging from 1 #s to 40/~s, the shape of the autocorrelation function varies continuously and the variance v remains greater than 0"25, as illustrated by Figure 3. Even though the data could not be analysed accurately, the variations of the shape of
the autocorrelation function show the existence of a particle distribution with minimal and maximum size values approximately within the ratio 1:40. This suggests that aggregation takes place. Accordingly, the system is composed of small individual protein molecules coexisting with a continuous distribution of aggregates of individual particles. Consequently, the existence of these aggregates can account for the amorphous precipitation of this system when supersaturated. This conclusion agrees well with unsuccessful crystallization experiments with ethylene diammonium sulphate as the precipitating agent. Other measurements with concanavalin A were made with a polyamine salt (spermine) as the precipitant. The results, shown in Figure 2(d), indicate that the polydispersity and the size of the macromolecule increase as the salt concentration increases. Again, no crystals can be obtained with this precipitating agent, only an amorphous precipitate. In the case of concanavalin A, there is evidence that real aggregation takes place with ethylene diammonium sulphate or spermine, whereas interactions are more likely to occur with lysozyme in ammonium sulphate solutions. Indeed, (1) the index of polydispersity of lysozyme solution remains rather low and does not permit the existence of a particle distribution to be established and (2) variations of the diffusion coefficient occur only with an increase of the protein concentration. Table3 summarizes the whole set of measurements obtained in various precipitants, whether they lead to crystallization or to amorphous precipitation. It emphazises that conditions that lead to crystallization favour a free state for the macromolecule in the
Diagnostic for Protein Crystallization
193
11.6
0.4 "
S"
5" 0.15 o
~_o8-8
0"10 ~"
%
0"2
~,
x
"-_,
-
o
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e.ol
:.
'
0
oo5 n
2'0
~
o
0'00
4'o
'
o
,
,
3'0
,
45
0-0
Sample time (p~s)
[Lysozyme] (mg/ml) (o)
Figure 3. Particle distribution in a concanavalin A solution. Variations of the diffusion coefficient, D25,, ( 1 ) and the variance v (I-l) as a function of the sample time in a concanavalin A solution at 10mg/ml containing l0 raM-sodium cacodylate buffer (pH 7-0) in 170 raM-ethylene diammonium sulphate.
16
0"15
2
E
o
vc
u n d e r s a t u r a t e d state, while conditions t h a t do not yield crystals favour interactions or aggregations.
0'10
x 3= u3
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--
~
0
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o -
o
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005 4. Concluding
0
S
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[Ammonium sulphate] ( M) (b)
•
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[Spermine] (m~)
ca)
This s t u d y d e m o n s t r a t e s the correlation of the concentration dependence of the translational diffusion coefficient of lysozyme in the u n d e r s a t u r a t e d region with its ability to crystallize, as suggested by K a m et al. (1978) in the s u p e r s a t u r a t e d region with the help of a theoretical model. When variations of the diffusion coefficient are observed, the system will lead to a m o r p h o u s precipitation once supersaturated, whereas when no variations are noticed in u n d e r s a t u r a t e d solutions, the s y s t e m will lead to crystallization once supersaturated. Similarly, in the case of concanavalin A, when variations of the diffusion coefficient are observed in a salt solution in the u n d e r s a t u r a t e d region, it can be correlated with unsuccessful crystallization trials. Thus, to be crystallized, lysozyme and concanavalin A are required not to be implied in interactions or aggregations in
0"00
26o
6,5 0
Remarks
26o
0-0
"
Figure 2. Amorphous precipitation diagnostic. (a) Variations of the diffusion coefficient of lysozyme (D25.w) as a function of protein concentration in 40 mM-sodium acetate (pH 4-6) and ammonium sulphate at 0"SM ( 1 ) and l'0M (FT); S' and S" indicate the solubility in 0"8 and 1"0 M-ammonium sulphate. The variance v is indicated for 0"8 M ( 0 ) and 1'0 M (O). (b) Variations of D25,w ( I ) and the variance v (O) with ammonium sulphate concentration in 20 mg lysozyme/ml, 40 mM-sodium acetate (pH 4"6). (c) Variations of the diffusion coefficient of concanavalin A (D2s,w) as a function of salt concentration (ethylene diammonium sulphate) in l0 mM-sodium cacodylate buffer (pH 7"0) and eoneanavalin A at 5"5 mg/ml ( 1 ) and l l mg/ml (Fl). The variance v is indicated for the solutions containing 11 mg coneanavalin A/ml (O). (d) Variations of the diffusion coefficient, D2s.w (D) and the variance v ( 0 ) as a function of spermine concentration in 10 mM-sodium cacodylate (pH 6"0) and 5"7 mg concanavalin A/ml.
194
V. Mikol et al.
undersaturated solutions. If this latter condition is not fulfilled (it will affect the hydrodynamic properties of the macromolecule), the systems will lead to amorphous precipitates once supersaturated and the protein molecules will not be able to re-order themselves and to interact through appropriate contacts to form crystals. Note t h a t the two extreme cases, crystallization or amorphous precipitation were investigated in this work. However, a biological macromolecule crystallizing solution often contains a mixture of precipitate and crystals. Moreover, crystals often appear to be surrounded by a precipitate-depleted zone. In such systems, two distinct precipitates can occur. First, a gel-like precipitate (or flocculate) in which the individual units retain their identity but lose their kinetic independence. This latter precipitate is induced by precipitating agents promoting the formation of non-specific contacts. This is probably the case for ammonium sulphate with lysozyme or for spermine and ethylene diammonium sulphate with concanavalin A. Second, a crystal-like precipitate can be formed, as can be observed in supersaturated solutions of lysozyme in sodium chloride (although crystallites cannot be distinguished by optical inspection, such precipitates are sometimes glittering under polarized light, 'in contrast to amorphous precipitates, which appear opalescent). This crystal-like precipitation is due to kinetics parameter and cannot be predicted from the quasi-elastic light-scattering experiments, which only reflect the nature of potential interactions between macromolecules. The conclusions arising from this work with the two proteins, lysozyme and concanavalin A as models can probably be generalized to other macromolecules. Light-scattering measurements could become a diagnostic technique to discriminate between solvents (precipitating agent plus buffer) leading to crystallization or amorphous precipitation. This approach could permit a rational and significant reduction of the number of parameters to be assayed in a crystallization screening. It should be noted t h a t this information on the ability to crystallize a protein can be gathered in a much shorter time than waiting for the outcome of crystallization trials. Due to the great advances made in recombinant DNA techniques, m a n y proteins can be produced in sufficient amounts to carry out such preliminary rational diagnostic experiments. This implies the preparation of milligrams of protein devoted to such measurements. Furthermore, all the biological material needed for these assays can be recovered through dialysis procedures and used for further quasi-elastic light-scattering experiments or crystallization assays. From a practical point of view, it is advised t h a t in order to diagnose a precipitant, two series of experiments should be done; the first at constant protein concentration and varying salt concentration and the second at constant salt concentration and varying protein concentration. The method has been used to investigate new crystallization conditions for yeast aspartyl-RNA synthetase (Mikol el at., 1990). Simi-
larly, the kinetics of crystallization was followed using quasi-elastic light-scattering and is described elsewhere (Mikoi et al., 1989b). The present diagnostic technique is likely to be applicable to undersaturated protein solutions containing organic precipitants (such as polyethylene glycol and 2methyl-2,4-pentanediol) provided the ionic strength remains high enough to screen electrostatic repulsive interactions. During reviewing of this paper, two contributions concerning the use of light-scattering on protein crystallization process were presented at the Third International Conference on Crystallization of Biological Macromolecules held in Washington, DC, 13 to 19 August, 1989 (Kadima el al., 1990, Pusey, 1989). We are indebted to S. Candau for advice and stimulating discussions. J. C. Thierry, who suggested to us the use of light-scattering in protein crystallization and M. Ruff are gratefully acknowledged for helpful discussions. This work was supported by grants from Centre National d'Etudes Spatiales (CNES) and Centre National de la Recherche Scientifique. V.M. was supported by a CNES fellowship.
References
Baldwin, E. T., Crumley, K. V. & Carter, C. W., Jr (1986). Biophys. J. 49, 47-48. Becket, J. W., Reeke, G. N., Jr, Wang, J. L., Cunningham,. B. A. & Edelman, G.M. (1975). J. Biol. Chem. 250, 1513-1524. Berne, B. J. & Pecora, R. (1976). Dynamic Light Scattering, Wiley, New York. Bloomfield, V. A. (1981). Annu. Rev. Biophys. Bioeng. 10, 421-450. Blundell, T. L. & Johnson, L. N. (1976). Protein Crystallography, Academic Press, New York. Candau, S. & Zana, R. (1981). J. Coll. Interf. Sci., 84, 206-219. Carter, C. W. & Carter, C. W., Jr (1979). J. Biol. Chem. 254, 12119-12223. Carter, C. W., Jr. Baldwin, E. T. & Frick, L. (1988). J. Crystal Growth, 90, 60-73. Dubin, S. B., Clark, N. A. & Benedek, G. B. (1971). J. Chem. Phys. 54, 5158-5164. English, A. C. & Dole, M. (1950). J. Amer. Chem. Soc. 72, 3261-3267. Gieg~, R. & Mikol, V. (1989). Trends Biotechnol. 7, 277-282. Gieg~, R., Dock, A. C., Kern, D., Lorber, B., Thierry, J.-C. & Moras, D. (1986). J. Crystal Growth, 75, 554-561. Gieg~, R., Ducruix, A., Fontecilla-Camps, J. C., Feigelson, R. S., Kern, R. & McPherson, A. (1988). J. Crystal Growth, 90, 1-370. Hiemenz, P. C. (1986). Principles of Colloid and Surface Chemistry, 2nd edit., Marcel Dekker, New York. Israelachvili, J. N., Mitchell, D. J. & Ninham, B. W. (1976). J. Chem. Soc. Faraday Trans. lI, 72, 1525-1568. K~iima, W., McPherson, A., Dunn, M. F. & Jurnak, F. (1990). Biophys. J. 57, 125-132. Kam, Z., Shore, H. B. & Feher, G. (1978). J. Mol. Biol. 123,539-555.
Diagnostic for Protein Crystallization Koppel, D. E. (1972). J. Chem. Phys. 57, 4814-4820. Langmuir, I. (1938). J. Chem. Phys. 5, 873-896. McPherson, A. (1982). Preparation and Analysis of Protein Crystals, Wiley, New York. Mikol, V. & Gieg6, R. (1989). J. Crystal Growth, 97, 324-332. Mikol, V., Rodeau, J.-L. & Gieg~, R. (1989a). J, Appl. CrystaUogr. 22, 155-161. Mikol, V., Hirsch, E. & Gieg~, R. (1989b). FEBS Letters, 258, 63-66. Mikol, V., Vincendou, P., Eriani, G., Hirsch, E. & Gieg~, R. (1990). J. Crystal Growth, in the press. Phillips, D. C. (1967). Proc. Nat. Acad. 8ci., U.S.A. 57, 484-495.
195
Pusey, M. L. (1989). Abstr. L19 Third Int. Conf. Crystallization Biol. Macronwl. (Ward, K.B. & Gilliland, G. L., eds), p. 33, Washington, DC, U.S.A. Ries-Kautt, M. M. & Ducruix, A. F. (1989). J. Biol. Chem. 264, 745-748. Rosenberger, F. (1986). J. Crystal Growth, 75, 618-636. Schurr, J. M. & Schmitz, K. S. (1986). Annu. Rev. Phys. Chem. 37, 271-305. Sophianopoulos, A. J., Rhodes, C. K., Holcomb, D. N. & Van Holde, K. E. (1962). J. Biol. Chem. 237, 1107-1112. Sumner, J. B., Gralen, N. & Eriksson-Quensel, I.-B. (1938). J. Biol. Chem. 125, 45-48.
Edited by W. A. Hendrickson
Diagnostic of Precipitant for Biomacromolecule Crystallization by Quasi-elastic Light-scattering V. Mikol 1, E. Hirsch 2 and R. Gieg61 ~Laboratoire de Biochimie Institut de Biologie Moldculaire et Cellulaire du C N R S , 15 rue Rend Descartes F-67084 Strasbourg Cedex, France and 2Laboratoire de Spectromdtrie et d'Imagerie Ultrasonores Institut Le Bel, 4, rue Blaise Pascal Universitd Louis Pasteur, F-67070 Strasbourg Cedex, France
(Received 1 June 1989; accepted 19 December 1989) The translational diffusion coefficient D25,w of hen egg-white lysozyme and concanavalin A from the jack bean is measured in various precipitating agent solutions as a function of salt and protein concentration using quasi-elastic light-scattering. With some precipitants, in undersaturated protein solutions, a protein or salt concentration dependence of the diffision coefficient of the scatterers is observed. It can be correlated with the inability of the protein to crystallize in this precipitant once the solution is supersaturated. These variations of D2s,w are interpreted in terms of non-specific interactions and/or aggregation that prevent the protein from making appropriate contacts to form a crystal. With other precipitants known to lead to crystallization, no significant variation of the diffusion coefficient with increasing concentration was observed, indicating that under such conditions up to saturation the proteins remain essentially monodisperse. Application of this technique to find crystallization conditions of other proteins is discussed.
1. I n t r o d u c t i o n
As crystallization limits the number of biological macromolecule structures accessible by X-ray crystallography, there is a growing need to better understand biomacromolecule crystallization (Gieg6 et al., 1988; Gieg6 & Mikol, 1989). Little is known about the mechanism that yields protein crystals, and the interactions involved in the formation of such crystals remain poorly understood, although addressed by Langmuir as early as 1938. Since protein crystals are highly ordered threedimensional arrangements of macromolecules, it could have been expected that they are maintained through multiple direct interactions. But X-ray crystallography has revealed that lattice contacts consist in most cases of few weak proteinprotein interactions (van der Waals and hydrogen bonds) and numerous water-mediated hydrogen bonds, which seem to play the major role in maintaining the crystal lattice structure. On the other • hand, amorphous precipitation or a more appro0022-2836/90/090187-09 $03.00/0
priate term from colloid chemistry, flocculation, results from non-specific van der Waals attraction (e.g. see Hiemenz, 1986). Consequently, in an optimal protein crystallization experiment, the specific conditions of pH, temperature and precipitating agent that prevent the macromolecules in undersaturated solutions from interacting, through nonspecific contacts, will also promote the formation of crystals once supersaturation is established. In order to favour crystal growth, the macromolecule should be pure from a biological point of view (Gieg6 et al., 1986) and the protein should retain its native state up to its solubility limit; e.g. no interaction and/or aggregation should have taken place before the solution is supersaturated. So far, the crystallization of a new molecule relies on "trialand-error" methods and remains unpredictable. Although crystallization of macromolecules s e e m s not to be fundamentally different from that of small molecules (Rosenberger, 1986), very few rational guidelines are likely to provide methods for successful assays. Carter & Carter (1979) have 187
© 1990 Academic Press Limited
188
V. M i k o l et al.
proposed a statistical approach to reduce the n u m b e r of conditions to be tried. Since the method is based upon optical microscopic examination, it is useless if no crystals or crystal-like forms are obtained, because one cannot unambiguously evaluate and distinguish between a m o r p h o u s and crystalline precipitates. A very interesting approach to address this problem rationally was suggested by the pioneering work of K a m et al. (1978). These authors introduced a theoretical model of the crystallization process for understanding nucleation. I t allows the aggregation state of a supersaturated protein solution to be probed with light-scattering. Crystallization is described as a co-operative step-by-step addition of monomers, whereas a m o r p h o u s precipitation is a non-co-operative polymerization process. This approach requires the analysis of the distribution of species within s u p e r s a t u r a t e d protein solutions, which is e x t r e m e l y difficult to address experimentally. According to this thorough theoretical model, in solutions leading to crystallization, an a b r u p t change in aggregate size is predicted, whereas a nearly linear variation is expected for precipitating solutions. Although the conclusions of this latter model have not been generalized to m a n y other systems (Baldwin et al., 1986; Carter el al., 1988), it was one of the first m a j o r results concerning the understanding of protein nucleation. The goal of the present work is more limited, in the sense t h a t it is not intended to address protein crystallization from a f u n d a m e n t a l point of view. I t deals specifically with the d e v e l o p m e n t of a diagnostic method, based on the use of light-scattering for rationally choosing good solvent conditions for crystallization assays. To define and validate the method, hen egg-white lysozyme and concanavalin A from the jack bean were chosen as model protein systems to investigate the behaviour of a protein in u n d e r s a t u r a t e d solutions leading either toward crystallization or to a m o r p h o u s precipitation. Quasi-elastic light-scattering was used as a probe, since it is a sensitive technique for the detection of variations of size and interaction in macromolecule solutions (for a review, see e.g. Berne & Pecora, 1976; Bloomfield, 1981; Schurr & Schmitz, 1986). Hen egg-white lysozyme is known to crystallize easily in sodium chloride solutions, whereas experiments with a m m o n i u m sulphate solutions have been unsuccessful (e.g. see R i e s - K a u t t & Ducruix, 1989). Conversely, concanavalin A is shown to crystallize readily in a m m o n i u m sulphate solutions. Accordingly, the effect of a m m o nium sulphate t h a t favours different situations in both systems has been analysed in this study. Similarly, concanavalin A was studied under conditions t h a t lead to a m o r p h o u s precipitation. Quasi-elastic light-scattering provides information a b o u t the different behaviour of the solutions, and proves to be able to predict the evolution (amorphous precipitation or crystallization) of the solutions analysed when they become supersaturated.
2. Materials and Methods (a) Macromolecules and chemicals Grade I, 3 x crystallized chicken egg-white lysozyme (14,000Da) and type IV jack bean concanavalin A (27,000 Da) were purchased from Sigma. Lysozyme was dissolved in 40 mM-sodium acetate buffer (pH 4"6) and concanavalin A either in 50mM-Tris-acetate or in 10 mM-sodium cacodylate buffer at pH as indicated. Both proteins were used without further purification. The solutions were sterilized by filtration through Millipore 0"45/am membranes. Their concentrations were determined spectrophotometrically at 280 nm with E l%(w/v)= 26-3 for lysozyme at pH 4"6 and E 1°0 (w/,)= 13 for concanavalin A at pH 6"0. The volume fraction ~b was computed a~
dp = [ I + (I -- c)'?'wl(Jl:pro,] - I,
(I )
where vw and Vp,otare the partial specific vohlmes of water and protein, respectively, and c is the concentration of protein (in % (w/v)). The partial specific volumes of lysozyme, concanavalin A and water were taken as 0"703ml/g (Sophianopoulos et al.. 1962), 0"730ml/g (Sumner et al., 1938) and l'0 ml/g, respectively. Each light-scattering measurement corresponds to a specific preparation. Spermine was obtained from Sigma and all salts for the crystallization assays were from Merck. (b) Lighl-scatterinff Before carrying out a series of measurements, protein solutions (I to 45 mg/m[) were centrifuged for l0 rain at I 1,000 revs/min (8000 g). Portions (80/al) of each solution (1001d) were pipetted to clarify them from dust and to leave any particulate matter in the unused 20 #l. They were then placed in the scattering cells. A scattering cell was made out of a high-quality glass tube with an inner diameter of 4 mm and has a length of 42 mm. Once filled, the scattering cells were transferred to plastic buckets and again before the scattering experiments centrifuged in an R-18 rotor in a J-21 Beckmann centrifuge for at least 60 min at 5000 revs/min. A more detailed description of the experimental set-up has been given (Candau & Zana, 1981). Samples were introduced at the centre of a cylindrical glass cell that was filled with distilled water. The cell temperature was controlled at 25( +_0"l )°C by a circulating bath. and was fixed on a goniometer so that the sample tube could be positioned on its rotation axis. An argon-ion laser (Spectra Physics 2000) provided a green light beam (4880 A) with 600 mW laser power, which was focused on the centre of the cell. The scattered light was then collected by a photomultiplier (EMI 90-30). A digital autocorrelator (Brookheaven Instruments, BI 30) yielded the photon count autocorrelation function, with 64 channels. The output of the autocorrelator was then fed to a microcomputer for data analysis. The autocorrelation function was analysed using the cumulant method (Koppel, 1972) to yield the average decay rate < F > and the variance v. The latter parameter is a measure of the width of the distribution of decay rates and hence provides information about the polydispersity of the system and is given by: v = ( < F 2 > - < F > 2 ) / < F > 2. (2) For nearly spherical particles (see below), if the variance v is less than 0"06, it indicates a rather small size distribution of the particles (Israelachvili et al., 1976). In the case of monodisperse particles, the translational diffusion
Diagnostic for Protein Crystallization coefficient 1), is given by the 1st reduced cumulant < F > /2K 2. The magnitude of the scattering wave vector K is given by:
K = [4nn sin(O/2)]/~,
(3)
where 0 is the scattering angle, 2 is the wavelength of the incident light in vacuum and n is the refractive index of the scattering medium. Since initial measurements of the diffusion coefficient showed no variation as a function of the scattering angle, within experimental errors, all further experiments were carried out at a fixed scattering angle of 90 °. If the macromolecule is assumed to have a spherical shape, its radius can be computed at infinite dilution using the Stokes-Einstein equation, which relates the hydrodynamic radius Rh to the diffusion coefficient D~:
Rh = kT /6n~lD,,
(4)
where k is the Boltzmann's constant, r/is the viscosity of the solvent and T is absolute temperature. Experimental error is within 3%, and measurements were reproducible whatever the time-lag between the preparation of the solution and the light-scattering experiments. Diffusion coefficients were corrected tbr the viscosity of water at 25°C. Viscosity measurements of the different solvents (buffer plus precipitating agent) were performed using a temperature-controlled capillary standard viscometer.
189
appropriate volumes of precipitating agent, buffer and protein to a volume of 100/A. The tubes were stored in a temperature-controlled water-bath (25(-t- 0"I)°C). After 8 weeks, portions of the supernatant were pipetted and centrifuged to sediment all crystalline or particle matters; their concentrations were then determined spectrophotometrically and defined as the solubility. (d) Crystallization Crystallization experiments were carried out in Linbro boxes (Flow Laboratory) using the hanging drop method (e.g. see Blundell & Johnson, 1976; MePherson, 1982). A volume of l ml of buffered reservoir solutions (Mikol el al., 1989a) at a higher concentration of precipitating agent were set in each well of the plate. A 5-pl volume of reservoir solution and 5 pl of protein solution were placed onto a silanized cover glass so that the initial volume of the drop was l0 pl (except for experiments with spermine, see Table 1). The cover glass with the droplet was placed over a reservoir solution and the chamber sealed with silicone grease. Crystallization experiments were followed over 8 weeks and are summarized in Table 1. Various salts, including NaCl, LiCl, KCI, MgSO a, CH3COONH 4, Na2SO 4, NH4NO 3, (NH4)2SO 4, K2SO 4, NH4CI and NaNO 3 were used as precipitants for concanavalin A crystallization.
3. Results and Discussion
(c) Solubility Crystallization or amorphous precipitation experiments for measurements of solubility were carried out by a batch method in sterile Eppendorf tubes by slowly adding
(a) Hydrodynamic properties of the proteins Q u a s i - e l a s t i c l i g h t - s c a t t e r i n g of m a c r o m o l e c u l e solutions can provide a straightforward way to
Table 1 Conditions of crystallization
Type
Salt concentration~ (~I)
pH
Protein species
Concentrationb (mg/ml)
NaCI (NH4)2SO,
9"68 2"0/2'5/3"0
4'6d 4"6d
Lysozyme Lysozyme*
20 20/30
NaNO 3 NH4N03 LiCI NaCl KCI NH4C1 CH3COONH4 Na2SO4 K2804 MgSO4 (NH4)2S04
0'10/0' 12 0"10/0'12 0.10/0.12 0-10]0"12 0-10]0'l 2 0"10]0"12 0-10/0"12 0"10/0"12 0"10/0-12 0"10/0"I2 l'0/l'2
6-0c 6-0~ 6.0~ 6-0~ 6-0~ 6-0" 6-0~ 6-0~ 6"0c 6-0" 6-0/6-5/7-~
Concanavalin A Concanavalin A Concanavalin A Concanavalin A Coneanavalin A Concanavalin A Concanavalin A Coneanavalin A Coneanavalin A Concanavalin A Coneanavalin A
7'5/l0 7'5/10 7'5/10 7'5/10 7'5110 7"5110 7-5]10 7"5]10 7"5/10 7"5]10 7"5/10
Spermine (tetrahydrochloride) Ethylene diammonium sulphate
0'04]0"05]0'06 0"08/0'1/0'12¢ 0'15/0'2
5"6]6'0 6"3/7"0c 6"0]6-5/7"0° 0'25/0-3
Coneanavalin A* Concanavalin A*
5"5]10 7'5/10
"The indicated concentration of salt is that of the reservoir, bThat of the protein is the initial protein concentration in the drop (all combinations of conditions were tested). CThedrops were not equilibrated against spermine solutions but sodium chloride solutions; concentrations are given below; accordingly the drops were made out of 5/~l of protein solutions and 5 #l of spermine solutions. The buffers werea 40 raM-sodium acetate, ~10 raM-sodium cacodylate and f50 mM-Tris-acetate. The asterisk (*) indicates conditions where amorphous precipitates are obtained; in other cases crystals are grown: the tetragonal form for lysozyme (e.g. see Ries-Kautt & Ducruix, 1989} and the orthorhombic form for concanavalin A with the morphology described by Mikol & Gieg6 (1989).
V. Mikol et al.
190 Table 2
Hydrodynamic properties of the proteins
Lysozyme + (40 raM-sodium) acetate, pH 4.6) 2% (w/v) NaCl 0"8 M-(NH4)~S04 l'0 M-(NH~)2SO4 Coneanavalin A + (50 mM-Trisacetate, pH 7"0) 1-0 M-(NH4)2S04 1.2 M-(NH4)2S04
D25.~ ( x 10~ cmZ/s)
Rh (A)
R~ (h)
10"3 11"4 I 1"5
21"2 19"0 19-1
17.2 17'2 17"2
5'7 5'7
38.4 38.4
37-2 37-2
Numerical values are obtained from extrapolations to infinite dilution (see Figs l and 2). Dzs.~ represents the diffusion coefficient corrected for the viscosity of water at 25°C and Rh the corresponding hydrodynamic radius. R~ is the radius of the macromoleculecomputed from X-ray data (the macromoleculeis assumed to be a sphere of the same volume as that derived from crystallographic structure without the hydration layer of the macromolecule).
obtain the translational diffusion coefficient of the scatterers and hence information about their hydrodynamic properties. T a b l e 2 presents the d a t a obtained with lysozyme and concanavalin A. From X - r a y analysis (Phillips, 1967), it was shown t h a t lysozyme consists of a compact structure, which can be a p p r o x i m a t e d as an ellipsoid, the dimensions of which are 45 A × 30 A x 30 (1 A=0-1 nm). I f the macromolecule is assumed to be a sphere of the same volume, its radius can be computed as 17.2 A, which agrees with the hydrodynamic radius obtained from the light-scattering experiments in ammonium sulphate solutions. However, in 2 % (w/v) sodium chloride, the agreement is apparently not as good. Nevertheless, it must be noticed first t h a t the radius computed from X-ray structure does not take into account the hydration of the macromolecule and t h a t the macromolecule does not retain a perfect spherical shape, and second, t h a t chloride ions are associated with lysozyme in the crystal structure. This m a y account for the larger size of the enzyme obser~/ed in sodium chloride solutions than in a m m o n i u m sulphate solutions. Moreover, it was determined by other studies (Dubin et al., 1971) t h a t the diffusion coefficient of lysozyme in aqueous solutions without chloride ions at p H 4.2 and 20 °C was 10-6 x l0 -~ em2/s (D2o,w), which is consistent with our values obtained in both salts at p H 4.6. X - r a y studies of concanavalin A crystals (Becker et al., 1975) revealed t h a t the lectin consists of a t e t r a m e r of identical protomers; each one is folded to form an ellipsoid dome 42 A in height with the greatest section 4 0 A x 3 9 A and the base 40 A x 25 A. At neutral p H and high ionic strength, the tetrameric structure is favoured and if it is
estimated as a sphere of the same volume, the corresponding h y d r o d y n a m i c radius can be computed as 37 A. This latter value agrees well with our d a t a obtained in ammonium sulphate (l'0 M and 1"2 M) at p H 7'0 where the extrapolated diffusion coefficient (D2s.w) can be estimated at 5.7x l0 -v cm2/s and accordingly the h y d r o d y n a m i c radius as 38-4 h . (b) Crystallization diagnostic Since sodium chloride solution leads lysozyme to crystallize, it was chosen as the crystallizing precipitant for this protein. A set of cells containing 2 % (w/v) sodium chloride at p H 4-6 and lysozyme at various concentrations ranging from 1 to 40 mg/ml (~b ranges from 0"07 ~/o to 2"8 %, which are low values from a physical-chemical point of view but correspond to high concentrations from a biological point of view). The cells were analysed using quasi-elastic light-scattering. Figure l(a) displays the translational diffusion coefficient to the scatterers as a function of the concentration of lysozyme. I t does not v a r y as a function of the protein concentration as long as the solution remains undersaturated. A small decrease in the diffusion coefficient can be observed as the protein concentration exceeds its solubility. Indeed, as the protein solution becomes supersaturated, interactions between macromolecules could take place and accordingly affect the observed h y d r o d y n a m i c properties of the macromolecules. This rapid decline observed near the saturation is in agreement with the theory outlined by K a m et al. (1978). Accordingly to their model, it reflects the presence of co-operative associations. Similarly, a set of experiments was carried out with solutions containing 20 mg lysozyme/ml ( ¢ = 1 " 4 % ) at p H 4 - 6 and different amounts of sodium chloride with concentrations ranging from 0"5% to 4 % (w/v). The diffusion coefficient of the scatterers, presented in Figure l(c), is shown to remain nearly constant. All preliminary crystallization experiments of concanavalin A in the salt solutions listed above yield crystals (see Table 1 ). The first series of lightscattering experiments with this protein was carried out in a m m o n i u m sulphate solutions, because this salt leads lysozyme to precipitation and concanavalin A to crystallization. A set of solutions containing a determined q u a n t i t y of a m m o n i u m sulphate (1"0 M) and different amounts of concanavalin A varying from 1 to 9 mg/ml ( ¢ = 0 " 0 7 % to 0-66%) yielded diffusion coefficients t h a t were roughly constant t h r o u g h o u t the investigated concentration range (Fig. l(b)). The same behaviour is observed when the solution contains 1"2 M-ammonium sulphate. No rapid decrease of the diffusion coefficient was observed in those precrystalline solutions near saturation. This discrepancy with the predictions resulting from the approach presented by K a m et al. (1978) might stem from two facts. First, such an a b r u p t change m a y occur at a higher concentration of protein and,
Diagnostic for Protein Crystallization II'6
Undersaturated soln
Supersoturoted
sob 0'15
E
% 8.8
0'10
x
cY
005
--e
•
6'0 0
S
2'o
0'00
4'0
[Lysozyme] (mg/ml) (o)
6.5 •
•
!
a
n
•
~
•
0"15
% 3-5
0"10
X 3
•
--
O----$
O----O
.
.
•
-.
.
O
0"~
-~
0
.
0"05
~.
--0 O
0'00
h
0
[eonconsvoUnhi (mg/m0 (b)
16 0'15
2 m
0"10 ="
•
X
,B o
0"05 0
0
4
0
second, this does not seem to be a general rule. Indeed, in the case of the water-sucrose system, no rapid decrease of the diffusion coefficient was detected in the supersaturated region with increasing concentration (English & Dole, 1950). A second set of solutions containing concanavalin A at a constant concentration at p H 6"0 but t h a t of ammonium sulphate varying from 0-2 to 1"0 ~ were analysed. The results, presented in Figure l(d), show no significant variations of D t with increasing salt concentration. Similar results were obtained with sodium nitrate as the precipitating agent (see Table 3). In all these experiments, the variance v is less than 0"06, which indicates t h a t the proteins are essentially monodisperse under the solvent conditions used. (c) Amorphous precipitation diagnostic
•
a-
191
Crystallization experiments with lysozyme remained unsuccessful in ammonium sulphate solutions (Table 1). Thus, this salt was elected as the amorphous precipitant for lysozyme and, accordingly, the h y d r o d y n a m i c properties of the protein analysed. Figure 2(a) shows d a t a obtained at p H 4"6 with lysozyme at various concentrations and ammonium sulphate at 0"8 M or 1"0 M. The data, however, display a different trend: as the protein concentration is increased, the diffusion coefficient decreases rather linearly (hence, similarly, the a p p a r e n t h y d r o d y n a m i c radius is shown to increase). These gradual variations are indeed predicted by the approach of K a m et al. (1978). The lysozyme concentration was maintained constant at 20 mg/ml (¢=1.4°/o) t h r o u g h o u t the n e x t series of experiments and the a m m o n i u m sulphate concentration was screened from 40mM to 1"4M. The results, displayed in Figure 2(b), show t h a t D2s.w remains essentially constant as the salt concentration increases. This behaviour could appear unexpected but is probably accounted for by the rather low concentration of lysozyme used with respect to its
0
S
0"00
0 [Noel] (% ,w/v)
(c)
6.5 m
i
i
I
l
B
015
eo ~-°x3-5
/
3 -0- - -
0
"D
_9_
0
0
01_
0'10 0"05
0 0
0"50. 0
o15 [Ammonium sulphote] (M) (d)
S
~Io
0"00
Figure 1. Crystallization diagnostic. (a) Variations of the diffusion coefficient of lysozyme (D25,w) ( I ) and the variance v (O) as a function of protein concentration in 2% (w/v) NaCl. The continuous and broken lines show the fit of the diffusion coefficient and the variance, respectively. (b) Variations of the diffusion coefficient of concanavalin A (D2s.,~) as a function of protein concentration in 50 mM-Tris-acetate (pH 7"0), 1"0 M-ammonium sulphate (m) and 1"2 M-ammonium sulphate ([-]); S' and S" indicate the solubility of the protein in 1-0 and 1"2 M-ammonium sulphate, respectively. The variance v is indicated for 1"0 M ( 0 ) and 1"2 M (O)- (c) Variations of the diffusion coefficient of lysozyme (D2s.w) (m) and the variance v (O) as a function of salt concentration for 20 mg lysozyme/ml, in 40 mM-sodium acetate (pH 4"6); S indicates the solubility of the protein. (d) Variations of D2s,w of concanavalin A ( 1 ) and the variance v (O) at 11 mg/ml as a function of ammonium sulphate concentration in 50 mM-Tris-acetate (pH 6"0).
V. Mikol et al.
192
Table 3
Diagnostic of crystallization with the hydrodynamic properties of the proteins System
[Salt]~ ~
[Protein]T ~
Crystallization (C) Precipitation(P)
Lysozyme + NaCl
(NH4hS04
D2s.. = cst v~0"06 D2a.w=CSt v~0'06
Dzs.w = cst v~0"06 D25,~1 v~0"06
C
Dzs,~=cst v~0"06 D25..=cst v~0"~
Dzs.w=CSt v~0"06 D25.w=CSt v~0"06
C
P
Concanavalin A +
(NH4)2SO4 NaNOa Ethylene diammonium sulphate Spermine
D2s,w,~
Dzs.wJ.
v:>0"l
v_>0'l
Dzs.~,~ vT
--
C
P e
aThe arrows indicate either an increase (T) or a decrease (~) of the concentration, and how it affects the hydrodynamic properties of the proteins. Experimental conditions are as described for Figs 1 and 2. cst, constant.
solubility. In all these experiments, the variance v is less than 0"06. Since it can be estimated that the lysozyme molecule bears about eight net positive charges at pH 4"6 and at low ionic strength (40 raM-sodium acetate), repulsive electrostatic interactions take place and can account for the high value of the diffusion coefficient observed in Figures l(c) and 2(b). From this first series of experiments, one can conclude, according to the decrease of the translational diffusion coefficient with ammonium sulphate, that aggregation and/or interaction between macromolecules takes place as the protein concentration is increased and can be correlated with the absence of success in crystallizing lysozyme in ammonium sulphate solutions. Another set of experiments with concanavalin A were then carried out with ethylene diammonium sulphate without knowing whether the lectin can be crystallized with this precipitating agent. At a low concentration of protein (5"5mg/ml) no specific variation of D25.w (and of P~) as a function of the salt concentration is observed (Fig. 2(c)) but, with a higher protein concentration of protein (11 mg/ml), a decrease of D, and an increase of the variance v of the fit of the autocorrelation function is observed: v is greater than 0"07 for most experiments, which indicates that the protein solution is not monodisperse. Furthermore, there is experimental evidence that the particle distribution is rather large in these solutions. Indeed, with sample times ranging from 1 #s to 40/~s, the shape of the autocorrelation function varies continuously and the variance v remains greater than 0"25, as illustrated by Figure 3. Even though the data could not be analysed accurately, the variations of the shape of
the autocorrelation function show the existence of a particle distribution with minimal and maximum size values approximately within the ratio 1:40. This suggests that aggregation takes place. Accordingly, the system is composed of small individual protein molecules coexisting with a continuous distribution of aggregates of individual particles. Consequently, the existence of these aggregates can account for the amorphous precipitation of this system when supersaturated. This conclusion agrees well with unsuccessful crystallization experiments with ethylene diammonium sulphate as the precipitating agent. Other measurements with concanavalin A were made with a polyamine salt (spermine) as the precipitant. The results, shown in Figure 2(d), indicate that the polydispersity and the size of the macromolecule increase as the salt concentration increases. Again, no crystals can be obtained with this precipitating agent, only an amorphous precipitate. In the case of concanavalin A, there is evidence that real aggregation takes place with ethylene diammonium sulphate or spermine, whereas interactions are more likely to occur with lysozyme in ammonium sulphate solutions. Indeed, (1) the index of polydispersity of lysozyme solution remains rather low and does not permit the existence of a particle distribution to be established and (2) variations of the diffusion coefficient occur only with an increase of the protein concentration. Table3 summarizes the whole set of measurements obtained in various precipitants, whether they lead to crystallization or to amorphous precipitation. It emphazises that conditions that lead to crystallization favour a free state for the macromolecule in the
Diagnostic for Protein Crystallization
193
11.6
0.4 "
S"
5" 0.15 o
~_o8-8
0"10 ~"
%
0"2
~,
x
"-_,
-
o
•
e.ol
:.
'
0
oo5 n
2'0
~
o
0'00
4'o
'
o
,
,
3'0
,
45
0-0
Sample time (p~s)
[Lysozyme] (mg/ml) (o)
Figure 3. Particle distribution in a concanavalin A solution. Variations of the diffusion coefficient, D25,, ( 1 ) and the variance v (I-l) as a function of the sample time in a concanavalin A solution at 10mg/ml containing l0 raM-sodium cacodylate buffer (pH 7-0) in 170 raM-ethylene diammonium sulphate.
16
0"15
2
E
o
vc
u n d e r s a t u r a t e d state, while conditions t h a t do not yield crystals favour interactions or aggregations.
0'10
x 3= u3
b --
--
-0-
--
~
0
_o._L
o -
o
0
005 4. Concluding
0
S
i
'
'C~O0
[Ammonium sulphate] ( M) (b)
•
m
•
"G
,,
•
0
. .i
I"
I I"
0
0"15
0
%
0"10 ~.
x
o/
o []
' [Salt] (mM) (C)
....
0'05
o
...........
ti 0
0
0
0-2
l
0
0
E o
~
4.C
0"1
c~ II
1'5
0
'
'
[Spermine] (m~)
ca)
This s t u d y d e m o n s t r a t e s the correlation of the concentration dependence of the translational diffusion coefficient of lysozyme in the u n d e r s a t u r a t e d region with its ability to crystallize, as suggested by K a m et al. (1978) in the s u p e r s a t u r a t e d region with the help of a theoretical model. When variations of the diffusion coefficient are observed, the system will lead to a m o r p h o u s precipitation once supersaturated, whereas when no variations are noticed in u n d e r s a t u r a t e d solutions, the s y s t e m will lead to crystallization once supersaturated. Similarly, in the case of concanavalin A, when variations of the diffusion coefficient are observed in a salt solution in the u n d e r s a t u r a t e d region, it can be correlated with unsuccessful crystallization trials. Thus, to be crystallized, lysozyme and concanavalin A are required not to be implied in interactions or aggregations in
0"00
26o
6,5 0
Remarks
26o
0-0
"
Figure 2. Amorphous precipitation diagnostic. (a) Variations of the diffusion coefficient of lysozyme (D25.w) as a function of protein concentration in 40 mM-sodium acetate (pH 4-6) and ammonium sulphate at 0"SM ( 1 ) and l'0M (FT); S' and S" indicate the solubility in 0"8 and 1"0 M-ammonium sulphate. The variance v is indicated for 0"8 M ( 0 ) and 1'0 M (O). (b) Variations of D25,w ( I ) and the variance v (O) with ammonium sulphate concentration in 20 mg lysozyme/ml, 40 mM-sodium acetate (pH 4"6). (c) Variations of the diffusion coefficient of concanavalin A (D2s,w) as a function of salt concentration (ethylene diammonium sulphate) in l0 mM-sodium cacodylate buffer (pH 7"0) and eoneanavalin A at 5"5 mg/ml ( 1 ) and l l mg/ml (Fl). The variance v is indicated for the solutions containing 11 mg coneanavalin A/ml (O). (d) Variations of the diffusion coefficient, D2s.w (D) and the variance v ( 0 ) as a function of spermine concentration in 10 mM-sodium cacodylate (pH 6"0) and 5"7 mg concanavalin A/ml.
194
V. Mikol et al.
undersaturated solutions. If this latter condition is not fulfilled (it will affect the hydrodynamic properties of the macromolecule), the systems will lead to amorphous precipitates once supersaturated and the protein molecules will not be able to re-order themselves and to interact through appropriate contacts to form crystals. Note t h a t the two extreme cases, crystallization or amorphous precipitation were investigated in this work. However, a biological macromolecule crystallizing solution often contains a mixture of precipitate and crystals. Moreover, crystals often appear to be surrounded by a precipitate-depleted zone. In such systems, two distinct precipitates can occur. First, a gel-like precipitate (or flocculate) in which the individual units retain their identity but lose their kinetic independence. This latter precipitate is induced by precipitating agents promoting the formation of non-specific contacts. This is probably the case for ammonium sulphate with lysozyme or for spermine and ethylene diammonium sulphate with concanavalin A. Second, a crystal-like precipitate can be formed, as can be observed in supersaturated solutions of lysozyme in sodium chloride (although crystallites cannot be distinguished by optical inspection, such precipitates are sometimes glittering under polarized light, 'in contrast to amorphous precipitates, which appear opalescent). This crystal-like precipitation is due to kinetics parameter and cannot be predicted from the quasi-elastic light-scattering experiments, which only reflect the nature of potential interactions between macromolecules. The conclusions arising from this work with the two proteins, lysozyme and concanavalin A as models can probably be generalized to other macromolecules. Light-scattering measurements could become a diagnostic technique to discriminate between solvents (precipitating agent plus buffer) leading to crystallization or amorphous precipitation. This approach could permit a rational and significant reduction of the number of parameters to be assayed in a crystallization screening. It should be noted t h a t this information on the ability to crystallize a protein can be gathered in a much shorter time than waiting for the outcome of crystallization trials. Due to the great advances made in recombinant DNA techniques, m a n y proteins can be produced in sufficient amounts to carry out such preliminary rational diagnostic experiments. This implies the preparation of milligrams of protein devoted to such measurements. Furthermore, all the biological material needed for these assays can be recovered through dialysis procedures and used for further quasi-elastic light-scattering experiments or crystallization assays. From a practical point of view, it is advised t h a t in order to diagnose a precipitant, two series of experiments should be done; the first at constant protein concentration and varying salt concentration and the second at constant salt concentration and varying protein concentration. The method has been used to investigate new crystallization conditions for yeast aspartyl-RNA synthetase (Mikol el at., 1990). Simi-
larly, the kinetics of crystallization was followed using quasi-elastic light-scattering and is described elsewhere (Mikoi et al., 1989b). The present diagnostic technique is likely to be applicable to undersaturated protein solutions containing organic precipitants (such as polyethylene glycol and 2methyl-2,4-pentanediol) provided the ionic strength remains high enough to screen electrostatic repulsive interactions. During reviewing of this paper, two contributions concerning the use of light-scattering on protein crystallization process were presented at the Third International Conference on Crystallization of Biological Macromolecules held in Washington, DC, 13 to 19 August, 1989 (Kadima el al., 1990, Pusey, 1989). We are indebted to S. Candau for advice and stimulating discussions. J. C. Thierry, who suggested to us the use of light-scattering in protein crystallization and M. Ruff are gratefully acknowledged for helpful discussions. This work was supported by grants from Centre National d'Etudes Spatiales (CNES) and Centre National de la Recherche Scientifique. V.M. was supported by a CNES fellowship.
References
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195
Pusey, M. L. (1989). Abstr. L19 Third Int. Conf. Crystallization Biol. Macronwl. (Ward, K.B. & Gilliland, G. L., eds), p. 33, Washington, DC, U.S.A. Ries-Kautt, M. M. & Ducruix, A. F. (1989). J. Biol. Chem. 264, 745-748. Rosenberger, F. (1986). J. Crystal Growth, 75, 618-636. Schurr, J. M. & Schmitz, K. S. (1986). Annu. Rev. Phys. Chem. 37, 271-305. Sophianopoulos, A. J., Rhodes, C. K., Holcomb, D. N. & Van Holde, K. E. (1962). J. Biol. Chem. 237, 1107-1112. Sumner, J. B., Gralen, N. & Eriksson-Quensel, I.-B. (1938). J. Biol. Chem. 125, 45-48.
Edited by W. A. Hendrickson
