A Hydrodynamic Study with Quasielastic Light Scattering and Sedimentation of Bacterial Elongation Factor EF-Tu Cuanosine=5’-DiphosphateComplex Under Nonassociating Conditions T O M SAM,’* CORNELIS PLEY,’ and MICHEL MANDEL’
Departments of ’Physical and Macromolecular Chemistry and ’Biochemistry, Corlaeus Laboratories, Leiden University, P. 0. Box 9502, 2300 RA Leiden, The Netherlands
SYNOPSIS
The hydrodynamics of the bacterial elongation factor EF-Tu have been studied in the presence of its ligand guanosine-5’-diphosphate( GDP ) by sedimentation in the ultracentrifuge and quasielastic light scattering. Sedimentation studies have made it possible to establish experimental conditions under which only negligible aggregation of the protein occurs (neutral pH, concentration < 3 mg/mL) . Analysis of the light intensity autocorrelation functions under these conditions revealed two independent scattering species with cm2 C1.The material with the lower and 0.04 X diffusion coefficients of 0.71 X diffusion coefficient, i.e., the aggregates, represented less than 1%of the total number of EF-Tu particles. The other 99% diffused as monomeric molecules with a molar mass corresponding to the value calculated from the known primary structure of the protein. The hydrodynamic parameters derived from the experimental data suggest that EF-Tu GDP in solution is close to a spherical particle.
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INTRODUCTION The soluble polypeptide elongation factor EF-Tu from Escherichia coli is a multifunctional protein involved in protein biosynthesis, viral RNA replication,’ and regulation of its own e x p r e ~ s i o nIt . ~ is the most abundant protein in the growing bacterial cell.4 Only a limited number of hydrodynamic studies have been devoted to EF-Tu, and most of our current knowledge of the shape and the dimensions of EF-Tu has been obtained from x-ray diffraction studies on crystals of (mildly trypsinized) EFT u guanosine-5’diphosphate ( G D P ) . From small-angle x-ray scattering results of EFT u - GDP by Sjoberg and Elias,’ the authors con0 1990 John Wiley & Sons, Inc. CCC 0006-3525/90/3-40299-10 $04.00 Biopolymers, Vol. 30, 299-308 (1990) * Present address: Pharmaceutical R&D Laboratories, Organon International, AKZO Pharma P. 0. Box 20,5340 BH Oss, The Netherlands.
cluded that the protein in solution can be modeled as a prolate ellipsoid of revolution with dimensions 6.25 X 1.94 X 1.94 nm or a n oblate ellipsoid of revolution of dimensions 4.08 X 4.08 X 1.18 nm. Smallangle neutron scattering of EF-Tu * GDP and EFT u - G T P by Antonsson et al.’ revealed for both complexes the same molar mass of 53,000 3,000 g/mol and comparable radii of gyration, i.e., 2.36 k 0.03 and 2.04 +- 0.04 nm, respectively. The higher molar mass, compared to the value of‘ 41,600 expected from the known primary s t r u c t u , “’ was attributed to the presence of 22% of EF-Tu dimers. Other small-angle neutron scattering experiments on EF-Tu. G T P solutions by Osterberg et al.” yielded a molar mass of 44,700 ? 3,000 and a radius of gyration of 2.28 nm. In the approximation of a uniform spherical distribution of scattering densities over the whole particle, these radii of gyration correspond to radii with values of 3.05 nm for EFT u - G D P and 3.10 nm for E F - T U - G T P ,o~r to a radius with a value of 3.64 nm for EF-Tu * GTP.” The x-ray diffraction studies c m crystals yielded a
*
299
300
SAM, PLEY, AND MANDEL
model, not completely resolved however, with dimensions of 7.4 X 5.0 X 4.5 nm for mildly trypsinized EF-Tu GDP. This is close to an ellipsoid of revolution with a ratio of the longer to the shorter axis of a / b = 1.54. A model for intact EF-Tu, which was obtained by image processing of electron micrographs of cylindrically aggregated EF-Tu GDP molecules, had comparable dimensions of 7.5 X 5.0 x 4.5 nm." The aim of the present study was to determine the hydrodynamic parameters of monomeric EFTu GDP in solution. Therefore conditions had to be established under which minimal aggregation takes place. For that purpose sedimentation experiments as function of the nature and concentration (total ionic strength) of various buffers with different characteristic pH values and as function of the protein concentration have been performed. Under conditions where the tendency of EF-Tu GDP to aggregate has been found to be minimal, complementary information on the hydrodynamic properties of EF-Tu GDP in its monomeric state has been obtained by quasielastic light scattering.
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MATERIALS A N D METHODS Isolation of EF-TU Elongation factor EF-Tu was prepared from E. coli (bacteria) as described before.13 The purity of the protein preparation was checked by SDS polyacrylamide gel electrophoresis. Protein concentration was determined spectrophotometrically using an absorption coefficient for EF-Tu GDP of 0.68 t 0.02 L/g.I4 The activity of EF-Tu was determined with the GDP exchange assay.I5 GDP was obtained from Boehringer, [ 3H]GDP was from Amersham. All other chemicals were of analytical quality.
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have been determined at constant temperature and at several scattering angles between 30" and 90". The measured normalized autocorrelation function in the case of a mixture of several small particles without significant interactions can be written as
g " ' ( i t ) = A { C ~ ~ e x p [ - I ' , . i t ] } ~ + B(1) j
Here I?, is the correlation rate for particle of type j and w, is its relative contribution to the scattering intensity, t is the sampling time, and i is the number of the channel (which runs from 1 to 96). A is an apparatus determined constant and B is the baseline with a theoretical value of unity. The diffusion coefficient D, of a particle of species j is given by rj.q - 2 , with q the length of the scattering vector q = (47rn/ Xo)sin(O/2),X o the wavelength of the light in vacuum, n the refractive index of the solution, and 0 the scattering angle. Correlation data have been fitted to Eq. ( 1)by a nonlinear least-squares procedure to obtain values for Dj. These fits had to meet three criteria to be considered satisfactory: a statistical quality factor close to unity ( a value of Q larger than 0.7 is generally found to be acceptable), no systematic deviations in the residue's plot, and only small deviations (of the order of 1%or less) of B from the theoretical baseline values of 1.0. The performance of the QLS equipment has been tested with solutions of monodisperse turnip yellow mosaic virus (TYMV B1 particles). The radius of this spherical particle has been determined with electron microscopy and x-ray diffraction to be 14.5 nm.16917The correlation data obtained from QLS could be fitted to a single exponential function [ j = 1 in Eq. ( 1) 1, which yielded an angle-independent diffusion coefficient, demonstrating the proper alignment and adjustment of the equipment. From the diffusion coefficient the equivalent hydrodynamic radius RH can be calculated according to the Stokes-Einstein relation:
light Scattering
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Samples of EF-Tu GDP solutions were filtered through a combination of 0.22- and 0.45-pm polycarbonate filters (Nucleopore) in an Amicon ultrafiltration apparatus (type 8 MC) to remove dust from the solutions. The intensity autocorrelation function of the scattered light was measured with Malvern Photocorrelation Spectrometer 4300 incorporating the Malvern Digital Correlator type K 7023/2 (with 96 channels). The light source was an argon ion laser (Spectra Physics model 165) operating at 514.5 nm. Intensity correlation functions
This yielded a value for TYMV of RH = (14.64 f 0.09) nm (for four experiments) in good agreement with the electron microscopy and x-ray diffraction results.
Sedimentation Sedimentation velocity experiments have been carried out at 6 or 20°C with a Spinco model E ultracentrifuge ( Beckmann ) equipped with Schlieren
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
optics and an ultraviolet scanning system. Rotor speeds were about 40,000 rev/min; the actual average rotor speed was measured during each experiment. Sedimentation coefficients have been calculated from a least-squares fit of the logarithm of the distance of the boundary or peak position to the axis of rotation vs time. Sedimentation and diffusion coefficients have been reduced to standard conditions (2O.O"C and water as sedimentation solvent) with solvent viscosities having been determined with an Ubbelohde viscosimeter. Density measurements have been performed with a Digital Precision Density Meter DMA 02c (Anton Paar KG, Graz, Austria). The employed buffer system was always 10 m M Tris HC1 pH 7.5, 10 m M Mg acetate, 1 m M EDTA, 0.01 m M GDP, 1 m M NaN3 (to be called universal buffer) with a density of (1.00431 0.00002) g/mL at 20"C, unless stated otherwise. Note that an excess of Mg2+is needed in the buffer to stabilize the complex between EF-Tu and GDP whereas the EDTA prevents the interference of other divalent cations. In case of monodisperse material the Svedberg equation relates the apparent molar mass Ma to the experimentally determined sedimentation and diffusion coefficient, i.e., S and D , respectively.
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301
RESULTS AND DISCUSSION In order to obtain information about the dimensions of monomeric EF-Tu particles in solution, conditions had to be determined at which EF-Tu has a minimal association tendency. Information on the aggregational state of a macromolecule can be obtained from velocity sedimentation or QLS diffusion measurements. An advantage of the former as compared to the latter is that velocity sedimentation is a separation technique as well. Occurrence of more than one boundary or Schlieren peak is direct evidence for the existence of associates, whereas quasielastic light scattering measurements can only give this kind of information after the mathematical analysis of the light intensity autocorrelation function. It must be emphasized, however, that the absence of more than one boundary in velocity sedimentation is not an absolute proof for the nonexistence of aggregates since the resolution between boundaries may be poor (e.g., between boundaries of monomers and dimers) or the establishment of the dynamic equilibrium between the different aggregational states may be sufficiently fast to result in one common boundary. Sedimentation Experiments
Here the subscript zero refers to infinite dilution, while uq and d stand for the partial specific volume of the particles and the density of the solvent, respectively. Equilibrium sedimentation at low concentration has also been performed using the meniscus depletion method." The advantage of this method is that only relative concentrations need to be known for the evaluation of the equilibrium sedimentation profiles. For monodisperse particles in dilute solutions the integrated form of the fundamental sedimentation equilibrium equation 6 C / C o = w 2 . d r 2 - ( 1- u z . d ) . M / 2 . R T
(4)
may be used. Here w is the velocity of the ultracentrifuge rotor, 6C the equilibrium concentration at radius r , dr' the difference between r 2 and the square of the radius of the reference point, and Cothe uniform solute concentration before the sedimentation experiment. For globular proteins u2 is practically pressure independent and therefore a constant in the cell at sedimentation equilibrium. Thus the apparent molar mass Ma = M ( 1 - uz d ) may be determined from the equilibrium profile.
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e
Sedimentation velocity experiments of EF-Tu * GDP solutions have been performed as function of the protein concentration, different pH values and temperatures, and at high and low total ionic strength of the buffer solutions. The values of S20,w, although not very accurate, nevertheless indicate that sedimentation is almost invariant with respect to an increase in the total ionic strength of an acetate buffer ( p H = 6.5) from 0.13 to 0.60 M , to a lowering of the pH from 7.5 (universal buffer at total ionic strength 0.14 M ) to 6.5 (acetate buffer at total ionic strength 0.13 M ) or to a decrease in temperature from 20 to 6°C in universal buffer (see Figure 1 ) , other conditions remaining constant. Values of S20,w thus obtained still slightly depend on protein concentration. The values extrapolated to C == 0 have been found to be identical within standard deviations for all the different experimental conditions mentioned. Therefore a linear least-squares fit of all the S20,w values vs concentration has been performed, giving an intercept of 3.51 f 0.06 S and a slope of (1.0 f 0.8) X lO-'S- L - g - ' ( n = 1 9 ) . The fact that no decrease but a moderate increase in S value with protein concentration is found suggests that there is a weak association reaction between the EFTu GDP molecules.
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SAM, PLEY, AND MANDEL
4-
3-
0
Figure 1. The concentration dependence of the sedimentation coefficients of EFTuaGDP. Sedimentation in universal buffer ( p H = 7.5, I = 0.14M) a t 20.0"C ( 0 )or a t 6.0"C ( 0 ) Sedimentation . in Na acetate buffer ( p H = 6.5) a t 20.0"C a t I = 0.13M ( A ) or a t I = 0.60M (0). The ionic strength of the latter buffer system was achieved by addition of KCI.
The dependence of S20,won the total ionic strength of the universal buffer for EF-Tu GDP has been studied in more detail a t two fixed protein concentrations. A t p H = 7.5 and a concentration of C,, = 1
mg/mL, no ionic strength dependence of the sedimentation coefficient has been detected (Figure 2 ) . The differences in the S20,w values corresponding to various values of pH or concentration are probably
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I
I
I
I
I
100
I
I
1
2 00 ionic
1
300
It-7-J
600
strength / m M
Figure 2. The ionic strength dependence of the sedimentation coefficient of EF-Tu * GDP. Sedimentation conditions: (0) 20 mMTris buffer ( p H = 7.5), 2O.O0C,protein concentration 1.0 mg/mL; (0) 20 m M Tris buffer ( p H = 7.5) containing 22% ( w / w ) of glycerol, 6.0°C, protein concentration 11.4 mg/mL; ( A ) 20 m M HEPES buffer ( p H = 6.5), 2O.O0C, protein concentration 7.0 mg/mL. Ionic strength has been increased by addition of KCl.
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
1
experiments with H E P E S buffer at pH = 6.5 was a second, fast-sedimenting boundary detected. At an ionic strength of 0.185 M the slowly sedimenting material has a S20,w value of 3.54 -+ 0.01 S, in good agreement with the value found in the universal buffer a t low protein concentrations. About 10% of the material sedimented with a S20,a value of 8.5 -+ 0.3 S . Taking the former to correspond to EFT u * GDP monomers, the particles corresponding to the fast-sedimenting peak may be estimated to represent trimers or tetramers assuming, for the sake of fixing the order of magnitude, that the proteins are more or less spherical particles for which S is proportional to M2" and that up remains constant. The sedimentation of EF-Tu GDP was also more thoroughly studied as function of pH of the sedimenting medium. A t a concentration of 1 mg/mL of protein a boundary corresponding to a S20,w value of approximately 3.5 S was found for all the pH values studied (see Figure 3 and Table I ) . A t the acidic side, fast-sedimenting material was also present. For instance, at pH = 4.08,80% of the protein sediments a t 25 S, which is roughly equivalent to a molar mass of about lo6 g/mol. At p H = 5.07, where the solution was highly turbid, only 10% of all the molecules sediment a t 3.5 S. The remainder is present as a precipitate. At a concentration of 10 mg/mL of EFT u * GDP the S20,w value increases rapidly with decreasing p H from its 3.5 value a t p H = 7.5 up to 4.3 a t pH = 6.0, thus indicating again strong interactions between protein molecules under these conditions. Note that analysis of the GDP exchange of EF-Tu in assay buffer ( p H = 7.4) directly after the sedimentation experiment demonstrated that no appreciable (irreversible) denaturation of EF-Tu had taken place in experiments in which the pH has been lowered from p H = 7.5 to 6.0 (see Table 11).
\
r
0
N v)
-
i
6
8
PH Figure 3. Sedimentation of the slowly sedimenting fraction of E F - T u . GDP as function of pH at 20.0"C a n d a t an ionic strength of 0.14M. Total protein concentration: ( 0 )1.0 m g / m L a n d ( A ) 10.0 mg/mL.
significant, however. They reflect a small concentration dependence and, additionally, may be caused by the correction of the sedimentation coefficient to standard conditions. Even at high protein concentrations the sedimentation appeared to be independent of the total buffer ionic strength. Moreover, sedimentation of EF-Tu GDP in the universal buffer ( p H = 7.5) always occurred as one single boundary or Schlieren peak irrespective of the protein concentration or the concentration of added KCl. Only in one out of five single, nonreplicated
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Table I Sedimentation Behavior of the EF-Tu GDP ( 1 . 0 mg/mL) at 2 0 . 0 " C at Various pH Values" Slowly Sedimenting
E 7 - 7 ' ~GDP . PH
Buffer
4.1 5.1 5.9 7.0 8.0
Acetate Acetate Acetate Phosphate Tris Tris
9.0
Turbidity of t h e Sample
+ +++ + -
303
Fast-Sedimenting E F - T U* G D P
Fraction
S2O.W
Fraction
s,,,u
0.2 0.1 0.9 1.0 1.0 1.0
3.4 ? 0.5 3.:3 t 0.20 3.39 2 0.04 3.63 2 0.02 3.35 k 0.07 3.13 +- 0.13
0.8 0.9 0.1 0.0 0.0
25
-
0.0
-
I, 1,
-
"Buffers of 20 mM ionic strength had been supplemented with 10 mM MgC12, 100 m M KCI, 1 mM D T E , 0.01 mM GDF, and small amounts of acid to adjust the pH. No measurements possible because of precipitated material in the rotor cell.
304
SAM, PLEY, AND MANDEL
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Table I1 Sedimentation Behavior of EF-Tu GDP (10 mg/mL) at 20.0°C at Various pH Values, and the Corresponding GDP Exchange Properties Slowly Sedimenting EF-TU* GDP Turbidity of the Sample
PH
Buffer
6.0 6.5 7.0 7.5
Acetate Acetate Tris Tris
Fraction
sz0.w
GDP Exchange Activity (%)
0.90 0.95 1.oo 1.00
4.28 f 0.05 3.78 f 0.01 3.54 f 0.01 3.60 f 0.03
94 79 85 71
+ +
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Tu GDP corresponding to 4.3 X lo4,4.5 X lo4, and 4.6 X lo4 g/mol, respectively. From the inaccuracy on Ma and a relative error on up of at least 5%, the inaccuracy of M may be estimated to be on the order 5 X lo3 g/mol. All these M values are in good agreement with the molar mass of monomeric EF-Tu, which has been calculated as M = 4.36 X lo4 g/mol from the known primary structure of the protein." This seems to confirm that under these conditions (pH = 7.5 and C = 1 mg/mL) the protein is essentially present as monomeric particles.
Equilibrium sedimentation at 30,000 rpm and 21.7"C of EF-Tu * GDP of concentration C = 1mg/ mL in the universal buffer yielded sedimentation profiles that are in agreement with monodisperse solutions (Figure 4). Nonlinear least-squares fitting to the sedimentation data yielded a value of Ma = (1.20 0.01) X lo4 g/mol. Values of uz reported in the literature are 0.716 L/kg, derived from sedimentation data,19and 0.728 L/kg,' or 0.734 L/kg,20 used in small-angle x-ray scattering. Using these values we find from Ma the molar mass of EF_+
1.5
I
7
/
I
I
E
?
I
m
I
F
'LO$
d
3
I-
I
I
I
_1
I
0
0.5
6.97
P
/
/
d
10
7.0 5
7.00 distance
to
7.10 the
7.15
rotor centre
/cm
Figure 4. Equilibrium sedimentation of E F - T u - G D P at 21.7OC in universal buffer at 30,000 rpm.The broken line represents the theoretical sedimentation profile of monodisperse EF-Tu. GDP using a partial specific volume of 0.721 L/kg and M = 4.32 X lo4 g/mol.
305
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
Conversely, accepting this calculated value of the molar mass one can derive from Maa value u2 = 0.721 2 0.003 L/kg, which may be compared to the average of the three literature values, i.e., 0.726 k 0.009 (0.009 representing the standard deviation of the values with respect t o the mean). T h e observed weak concentration dependence of the sedimentation rate may indicate the presence of associated EF-Tu molecules a t higher concentrations, possibly in line with the presence of 22% of dimers in the EF-Tu preparations studied by Antonsson e t al.'
Quasielastic light Scattering Experiments T h e quasielastic light scattering experiments have been performed with EF-Tu GDP in universal buffer ( p H = 7.5) and a t concentrations C < 3 mg/ mL in order t o minimize association effects. Fitting single exponentials [ j = 1 in Eq. ( l ) ]to the experimentally obtained intensity correlation data gave a diffbsion coefficient for EF-Tu of 0.58 X cm2 s '. However, the quality of the fit was rather poor ( 4 = 0.32), as can be seen from the corresponding
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residues plot (Figure 5 a ) . The quality of the fit improved after fitting the data t o a correlation function for two independent scattering species [ j = 2 in Eq. ( 1) ; (Figure 5b). This yielded two diffusion coefficients with values 0.84 X and 0.05 X cm2 s-l, respectively. Although the deviations of the experimental points with respect t o the fitted curve are very small (less than 0.8%) , the mere fact that these small deviations show a systematic trend in the residues plot indicates that the fit is not altogether satisfactory. T h e correlation function of the buffer without protein showed a contribution to the first two to five channels of the photon correlator. This could either be due to free GDP or t o a n imperfection of the correlator a t the very short time end. Because it is very difficult to correct for this spurious effect, the data from the first five channels have subsequently been omitted from the fitting procedure. This did not improve the fit in the case of one single exponential (Figure 5c) but gave a definitely random distribution of smaller residues in case t,he squared double-exponential equation was used ( Figure 5 d ) . Thus a n autocorrelation function for two indepen-
-0.51 J do W 0
0
0
*0.5j,
0.0
___-__--__---
-0.5-1
d
0 I
V
I
I
I
I
V
I
I
0
20
,
,
40
,
I
,
60
CHANNEL NUMBER
Figure 5 . Residual plots showing the deviations of the experimental QLS data with respect to the fitted correlation functions. ( a ) Single exponential fit (96 channels), with Q = 0.32; ( b ) squared double exponential fit (96 channels), Q = 0.89; ( c ) single exponential fit (91 channels), Q = 0.26; ( d ) squared double exponential fit (91 channels), Q = 1.02.
,
80
,
0 1 1
306
SAM, PLEY, AND MANDEL
dent scattering species could be fitted satisfactorily t o the QLS data of the EF-Tu solution under the conditions mentioned. T h e fast correlation rate rl = 1/ T (~1) was found t o be independent of the sampling time and linearly dependent on the square of the scattering vector with the linear least-squares fit passing through the origin within experimental error (Figure 6 a ) . T h e values of the slow correlation rate r2= 1 / ~ ~ ( appeared 2 ) t o be more sensitive t o variations in the sampling time with a subsequent decrease in the accuracy of the diffusion coefficient determined therefrom. T h e following values for the diffusion of EF-Tu have been obtained from a linear least-squares fit of ria s function of q2: D20,,( 1) = (0.71 k 0.02) X lo6 cm2 s-l and D 2 0 , w ( 2 = ) (0.04 -+ 0.01) X cm2 s-'. In Figure 6b values of D20,w( i ) obtained from the individual correlation functions ( D = r / q 2 )are , plotted as function of the quality factor Q of the nonlinear least-squares fit and compared to the diffusion coefficients obtained directly from the least-squares lines represented in Figure 6a. It can be seen that the individual values corresponding to 0.9 < Q < 1.1 are in perfect agreement with the values quoted
c
above. This plot also demonstrates that better results have been obtained for the fast diffusion coefficient than for the slow one. The weight factors w1 and w2 giving the respective contributions to the scattered field correlation functions of the fast (smaller particles) and slow (larger particles) diffusion coefficient have been found to be approximately 0.7 and 0.3, respectively. As the intensity of the scattered light is proportional to the mass of the scattering particles, w1 and w2 represent mass fractions. From the value of D ( 2 ) a n average molar mass of the order of lo8 g/mol may be evaluated for the slowly moving particles. Thus it can be estimated that under the experimental conditions used more than 99% of the EF-Tu molecules (number fraction) should move with the higher diffusion ( 1) . T h e conclusion about the prescoefficient DZo,+, ence of only minute amounts of associated EF-Tu in universal buffer a t 25°C and low protein concentrations as derived from the light scattering experiments is in agreement with the findings from velocity and equilibrium sedimentation. From D20,w( 1) and the corresponding value of the sedimentation coefficient S!O,wr the apparent molar
I
lul
LO
30 c
v)
8
i
0
i:
n
0
t>
1 2 0 c
-0
10
0
Figure 6. ( a ) The scattering vector amplitude ( 9 )and sampling time dependence of the evaluated correlation times T ~ 1) ( and T ~ 2 () for EF-Tu. GDP (2.7 mg/mL) in universal buffer. The sampling times (in microseconds) were (with closed symbols referring to the left, open symbols to the right scale) as follows: scattering angle of 90": 2.0 (0,0 )and 1.0 ( A , A, H); scattering angle of 75": 2.7 (0, O ) , 1.2 ( A , A), and 0.2 (0, H);scattering angle a ) ; scattering angle of 30": 25.0 (0,0 ) and 7.5 of 60": 4.0 (0,O ) , 1.6 ( A , A), and 0.7 (0, (0, H).( b ) Correspondence between the quality parameters Q and the diffusion coefficients D obtained from the fitting of the correlation function. The solid lines represent the diffusion coefficients as determined from the least-squares lines and the dashed lines represent the upper and lower limits of the corresponding standard deviations.
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
mass of EF-Tu can be calculated using Eq. (3). This yields a value of Ma = (1.2 k 0.3) X lo4 g/mol, in perfect agreement with the value found from equilibrium sedimentation. As pointed out above, there are very good reasons to assume that this value corresponds to proteins in the monomeric form. The hydrodynamic radius that can be calculated from the diffusion coefficient of the monomeric particles D20,w ( 1) with the help of the Stokes-Einstein Eq. ( 2 ) corresponds to RH = 3.02 f 0.09 nm. If we assume the protein to be a rigid sphere, with a radius R corresponding to RH, the corresponding radius of gyration R G can be calculated using the relation
RG = ( g ) 1 / 2 R(spheres) 2
(5)
This hypothetical radius of gyration is found to have a value of 2.34 f 0.07 nm, which is in good agreement with the radius of gyration obtained from small-angle neutron scattering, i.e., 2.36 k 0.03 nm9 or 2.28 nm.” This suggests that EF-Tu GDP moves as a hydrodynamic particle with a nearly spherical shape. More detailed information about the protein in solution is difficult to obtain. It is well known that from the diffusion coefficient alone (or even in combination with other hydrodynamic quantities) no unambiguous knowledge about the shape and dimensions of the particles can be derived,21not in the least because of the difficulty in establishing the amount of solvent that moves with the protein molecule in the hydrodynamic experiment ( solvation layers or solvent trapped inside the molecule). Furthermorc>,only ellipsoid of revolution can be treated in a quantitative way, with the ratio of the shorter to the longer axis x = b / a determining the Perrin factor F.’2 The latter can be deduced from the ratio of the measured diffusion coefficient to the hypothetical diffusion coefficient D‘for a spherical particle with the same volume as the real one. Thus for a prolate ellipsoid of revolution one has
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Here U M is the volume of the protein containing a1 gram of solvent per gram dry protein, represents the partial specific volume of the pure solvent, taken to be 1.0 L/kg, and N A is Avogadro’s constant. Introducing into Eqs. ( 6 ) - ( 8 ) the values M = 4.32 X l o 4 g/mol and u2 = 0.721 L/kg (derived from the
307
former, see the sedimentation experiments) we may calculate F and x for any value of al. Thus in case 6’ = 0, we find F = 1.31 f 0.04, which corresponds to a ratio a / b = l / x N 5.9. This is much larger than found for the model of EF-Tu GDP derived from small-angle x-ray scattering’ for which the Perrin factor would be F = 0.31. We can also estimate other values for a and a / b making different choices for al. Should one assume, e.g., the hydrodynamic particle to drag along 1.35 gram water per gram dry protein, it could be represented by a prolate ellipsoid of semiaxes 6 X 1.5 X 1.5 nm ( a / b = 3.9), which comes close to the prolate ellipsoid deduced from smallangle x-ray scattering of EF-Tu-GDP.’ For an amount of water 6’ = 0.50, corresponding to the water content of the EF-Tu GDP in the crystalline state, the representative prolate ellipsoid of revolution would have semiaxes 5.4 X 2 X 2 nm. Both values of d1 are not unreasonable in view of the values estimated for other globular proteins.23The values of a1 derived for different proteins or for a given protein from various properties, thermodynamic or hydrodynamic, should not necessarily coincide, however.23Therefore such a detailed description of the hydrodynamic particle given above remains highly speculative. The safest conclusion to be drawn from this hydrodynamic study of monomeric EFTu GDP still remains that in solution this protein diffuses as a particle with a shape close to a sphere.
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REFERENCES 1. Kaziro, Y. ( 1978) Biochim. Biophys. Actu 505, 95127. 2. Blumenthal, L. & Carmichael, G. G. ( 1979)Ann. Rev. Biochem. 48, 325-548. 3. Bosch, L., Kraal, B., van der Meide, P. H., Duisterwinkel, F. J. & van Noort, J. M. ( 1983) Progr. Nucleic Acid Res. Mol. Biol. 30, 91-126, 4. Lake, J. A. (1976) J. Mol. Biol. 105, 131-159. 5. Morikawa, K., La Cour, T. F. M., Nyborg, J., Rasmussen, K. M., Miller, D. L. & Clark, B. F. C. (1978) J . Mol. Biol. 125, 325-338. 6. Kabsch, W., Gast, W. N., Schulz, G. E. & Lebermann, R. (1977) J . Mol. Biol. 117,999-1012. 7. Jurnak, F., McPherson, A., Wang, A. H. & Rich, A. (1980) J . Biol. Chem. 255,6751-6757. 8. Sjoberg, B. & Elias, P. ( 1978) Biochim. Biophys. Actu 519,507-512. 9. Antonsson, B., Lebermann, R., Jacrot, B. & Zaccai, G. (1986) Biochemistry 25, 3655-3659. 10. Arai, K., Clark, B. F. C., Duffy, L., Jones. M. D., Ka-
ziro, y., Laursen, R. A., L’Italien, J., Miller, D. L., Nagarkatti, S., Nakamura, S., Nielsen, K . M., Peter-
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11. 12. 13. 14. 15. 16.
17.
SAM, PLEY, AND MANDEL
sen, T. E., Takahashi, K. & Wade, M. (1980) Proc. Natl. Acad. Sci. USA 77,1326-1330. Osterberg, R., Elias, P., Kjems, J. & Bauer, R. ( 1986) J . Biomol. Struct. Dynam. 6, 1111-1120. Cremers, A. F. M., Sam, A. P., Bosch, L. & Mellema, J. E. (1981) J . Mol. Biol. 153,477-486. Sam, A. P., Pingoud, P. & Bosch, L. (1985) FEBS Lett. 1 8 5 , 51-56. Sam, A. P. ( 1983) Ph.D. thesis, Leiden University. Pingoud, A., Urbanke, C., Krause, G., Peters, F. & Maass, G. (1977) Eur. J . Biochem. 78,403-409. Finch, J. T. & Klug, A. (1966) J . Mol. Biol. 1 5 , 3 4 4 364. Klug, A., Longley, W. & Lebermann, R. (1966) J . Mol. Biol. 1 5 , 315-343.
18. Yphantis, D. A. (1964) Biochemistry 3 , 297-317. 19. Arai, K., Kawakita, M., Kaziro, Y., Kondo, T. & Ui, N. (1973) J . Biochem. 7 3 , 1095-1105. 20. Osterberg, R., Sjoberg, B., Ligaarden, R. & Elias, P. (1981) Eur. J . Biochem. 117,155-159. 21. Tanford, C. ( 1961 ) Physical Chemistry of Macromolecules, Wiley, New York. 22. Perrin, F. ( 1936) J . Phys. Radium 7 , 1. 23. Kuntz, I. D., Jr. & Kauzmann, W. (1974) in Advances in Protein Chemistry, Vol. 28, Anfinsen, C. B., Edsall, J. T. & Richards, F. M., Eds., Academic Press, New York, pp. 239-342.
Received June 23, 1989 Accepted January 22, 1990
Departments of ’Physical and Macromolecular Chemistry and ’Biochemistry, Corlaeus Laboratories, Leiden University, P. 0. Box 9502, 2300 RA Leiden, The Netherlands
SYNOPSIS
The hydrodynamics of the bacterial elongation factor EF-Tu have been studied in the presence of its ligand guanosine-5’-diphosphate( GDP ) by sedimentation in the ultracentrifuge and quasielastic light scattering. Sedimentation studies have made it possible to establish experimental conditions under which only negligible aggregation of the protein occurs (neutral pH, concentration < 3 mg/mL) . Analysis of the light intensity autocorrelation functions under these conditions revealed two independent scattering species with cm2 C1.The material with the lower and 0.04 X diffusion coefficients of 0.71 X diffusion coefficient, i.e., the aggregates, represented less than 1%of the total number of EF-Tu particles. The other 99% diffused as monomeric molecules with a molar mass corresponding to the value calculated from the known primary structure of the protein. The hydrodynamic parameters derived from the experimental data suggest that EF-Tu GDP in solution is close to a spherical particle.
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INTRODUCTION The soluble polypeptide elongation factor EF-Tu from Escherichia coli is a multifunctional protein involved in protein biosynthesis, viral RNA replication,’ and regulation of its own e x p r e ~ s i o nIt . ~ is the most abundant protein in the growing bacterial cell.4 Only a limited number of hydrodynamic studies have been devoted to EF-Tu, and most of our current knowledge of the shape and the dimensions of EF-Tu has been obtained from x-ray diffraction studies on crystals of (mildly trypsinized) EFT u guanosine-5’diphosphate ( G D P ) . From small-angle x-ray scattering results of EFT u - GDP by Sjoberg and Elias,’ the authors con0 1990 John Wiley & Sons, Inc. CCC 0006-3525/90/3-40299-10 $04.00 Biopolymers, Vol. 30, 299-308 (1990) * Present address: Pharmaceutical R&D Laboratories, Organon International, AKZO Pharma P. 0. Box 20,5340 BH Oss, The Netherlands.
cluded that the protein in solution can be modeled as a prolate ellipsoid of revolution with dimensions 6.25 X 1.94 X 1.94 nm or a n oblate ellipsoid of revolution of dimensions 4.08 X 4.08 X 1.18 nm. Smallangle neutron scattering of EF-Tu * GDP and EFT u - G T P by Antonsson et al.’ revealed for both complexes the same molar mass of 53,000 3,000 g/mol and comparable radii of gyration, i.e., 2.36 k 0.03 and 2.04 +- 0.04 nm, respectively. The higher molar mass, compared to the value of‘ 41,600 expected from the known primary s t r u c t u , “’ was attributed to the presence of 22% of EF-Tu dimers. Other small-angle neutron scattering experiments on EF-Tu. G T P solutions by Osterberg et al.” yielded a molar mass of 44,700 ? 3,000 and a radius of gyration of 2.28 nm. In the approximation of a uniform spherical distribution of scattering densities over the whole particle, these radii of gyration correspond to radii with values of 3.05 nm for EFT u - G D P and 3.10 nm for E F - T U - G T P ,o~r to a radius with a value of 3.64 nm for EF-Tu * GTP.” The x-ray diffraction studies c m crystals yielded a
*
299
300
SAM, PLEY, AND MANDEL
model, not completely resolved however, with dimensions of 7.4 X 5.0 X 4.5 nm for mildly trypsinized EF-Tu GDP. This is close to an ellipsoid of revolution with a ratio of the longer to the shorter axis of a / b = 1.54. A model for intact EF-Tu, which was obtained by image processing of electron micrographs of cylindrically aggregated EF-Tu GDP molecules, had comparable dimensions of 7.5 X 5.0 x 4.5 nm." The aim of the present study was to determine the hydrodynamic parameters of monomeric EFTu GDP in solution. Therefore conditions had to be established under which minimal aggregation takes place. For that purpose sedimentation experiments as function of the nature and concentration (total ionic strength) of various buffers with different characteristic pH values and as function of the protein concentration have been performed. Under conditions where the tendency of EF-Tu GDP to aggregate has been found to be minimal, complementary information on the hydrodynamic properties of EF-Tu GDP in its monomeric state has been obtained by quasielastic light scattering.
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MATERIALS A N D METHODS Isolation of EF-TU Elongation factor EF-Tu was prepared from E. coli (bacteria) as described before.13 The purity of the protein preparation was checked by SDS polyacrylamide gel electrophoresis. Protein concentration was determined spectrophotometrically using an absorption coefficient for EF-Tu GDP of 0.68 t 0.02 L/g.I4 The activity of EF-Tu was determined with the GDP exchange assay.I5 GDP was obtained from Boehringer, [ 3H]GDP was from Amersham. All other chemicals were of analytical quality.
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have been determined at constant temperature and at several scattering angles between 30" and 90". The measured normalized autocorrelation function in the case of a mixture of several small particles without significant interactions can be written as
g " ' ( i t ) = A { C ~ ~ e x p [ - I ' , . i t ] } ~ + B(1) j
Here I?, is the correlation rate for particle of type j and w, is its relative contribution to the scattering intensity, t is the sampling time, and i is the number of the channel (which runs from 1 to 96). A is an apparatus determined constant and B is the baseline with a theoretical value of unity. The diffusion coefficient D, of a particle of species j is given by rj.q - 2 , with q the length of the scattering vector q = (47rn/ Xo)sin(O/2),X o the wavelength of the light in vacuum, n the refractive index of the solution, and 0 the scattering angle. Correlation data have been fitted to Eq. ( 1)by a nonlinear least-squares procedure to obtain values for Dj. These fits had to meet three criteria to be considered satisfactory: a statistical quality factor close to unity ( a value of Q larger than 0.7 is generally found to be acceptable), no systematic deviations in the residue's plot, and only small deviations (of the order of 1%or less) of B from the theoretical baseline values of 1.0. The performance of the QLS equipment has been tested with solutions of monodisperse turnip yellow mosaic virus (TYMV B1 particles). The radius of this spherical particle has been determined with electron microscopy and x-ray diffraction to be 14.5 nm.16917The correlation data obtained from QLS could be fitted to a single exponential function [ j = 1 in Eq. ( 1) 1, which yielded an angle-independent diffusion coefficient, demonstrating the proper alignment and adjustment of the equipment. From the diffusion coefficient the equivalent hydrodynamic radius RH can be calculated according to the Stokes-Einstein relation:
light Scattering
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Samples of EF-Tu GDP solutions were filtered through a combination of 0.22- and 0.45-pm polycarbonate filters (Nucleopore) in an Amicon ultrafiltration apparatus (type 8 MC) to remove dust from the solutions. The intensity autocorrelation function of the scattered light was measured with Malvern Photocorrelation Spectrometer 4300 incorporating the Malvern Digital Correlator type K 7023/2 (with 96 channels). The light source was an argon ion laser (Spectra Physics model 165) operating at 514.5 nm. Intensity correlation functions
This yielded a value for TYMV of RH = (14.64 f 0.09) nm (for four experiments) in good agreement with the electron microscopy and x-ray diffraction results.
Sedimentation Sedimentation velocity experiments have been carried out at 6 or 20°C with a Spinco model E ultracentrifuge ( Beckmann ) equipped with Schlieren
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
optics and an ultraviolet scanning system. Rotor speeds were about 40,000 rev/min; the actual average rotor speed was measured during each experiment. Sedimentation coefficients have been calculated from a least-squares fit of the logarithm of the distance of the boundary or peak position to the axis of rotation vs time. Sedimentation and diffusion coefficients have been reduced to standard conditions (2O.O"C and water as sedimentation solvent) with solvent viscosities having been determined with an Ubbelohde viscosimeter. Density measurements have been performed with a Digital Precision Density Meter DMA 02c (Anton Paar KG, Graz, Austria). The employed buffer system was always 10 m M Tris HC1 pH 7.5, 10 m M Mg acetate, 1 m M EDTA, 0.01 m M GDP, 1 m M NaN3 (to be called universal buffer) with a density of (1.00431 0.00002) g/mL at 20"C, unless stated otherwise. Note that an excess of Mg2+is needed in the buffer to stabilize the complex between EF-Tu and GDP whereas the EDTA prevents the interference of other divalent cations. In case of monodisperse material the Svedberg equation relates the apparent molar mass Ma to the experimentally determined sedimentation and diffusion coefficient, i.e., S and D , respectively.
+
301
RESULTS AND DISCUSSION In order to obtain information about the dimensions of monomeric EF-Tu particles in solution, conditions had to be determined at which EF-Tu has a minimal association tendency. Information on the aggregational state of a macromolecule can be obtained from velocity sedimentation or QLS diffusion measurements. An advantage of the former as compared to the latter is that velocity sedimentation is a separation technique as well. Occurrence of more than one boundary or Schlieren peak is direct evidence for the existence of associates, whereas quasielastic light scattering measurements can only give this kind of information after the mathematical analysis of the light intensity autocorrelation function. It must be emphasized, however, that the absence of more than one boundary in velocity sedimentation is not an absolute proof for the nonexistence of aggregates since the resolution between boundaries may be poor (e.g., between boundaries of monomers and dimers) or the establishment of the dynamic equilibrium between the different aggregational states may be sufficiently fast to result in one common boundary. Sedimentation Experiments
Here the subscript zero refers to infinite dilution, while uq and d stand for the partial specific volume of the particles and the density of the solvent, respectively. Equilibrium sedimentation at low concentration has also been performed using the meniscus depletion method." The advantage of this method is that only relative concentrations need to be known for the evaluation of the equilibrium sedimentation profiles. For monodisperse particles in dilute solutions the integrated form of the fundamental sedimentation equilibrium equation 6 C / C o = w 2 . d r 2 - ( 1- u z . d ) . M / 2 . R T
(4)
may be used. Here w is the velocity of the ultracentrifuge rotor, 6C the equilibrium concentration at radius r , dr' the difference between r 2 and the square of the radius of the reference point, and Cothe uniform solute concentration before the sedimentation experiment. For globular proteins u2 is practically pressure independent and therefore a constant in the cell at sedimentation equilibrium. Thus the apparent molar mass Ma = M ( 1 - uz d ) may be determined from the equilibrium profile.
-
e
Sedimentation velocity experiments of EF-Tu * GDP solutions have been performed as function of the protein concentration, different pH values and temperatures, and at high and low total ionic strength of the buffer solutions. The values of S20,w, although not very accurate, nevertheless indicate that sedimentation is almost invariant with respect to an increase in the total ionic strength of an acetate buffer ( p H = 6.5) from 0.13 to 0.60 M , to a lowering of the pH from 7.5 (universal buffer at total ionic strength 0.14 M ) to 6.5 (acetate buffer at total ionic strength 0.13 M ) or to a decrease in temperature from 20 to 6°C in universal buffer (see Figure 1 ) , other conditions remaining constant. Values of S20,w thus obtained still slightly depend on protein concentration. The values extrapolated to C == 0 have been found to be identical within standard deviations for all the different experimental conditions mentioned. Therefore a linear least-squares fit of all the S20,w values vs concentration has been performed, giving an intercept of 3.51 f 0.06 S and a slope of (1.0 f 0.8) X lO-'S- L - g - ' ( n = 1 9 ) . The fact that no decrease but a moderate increase in S value with protein concentration is found suggests that there is a weak association reaction between the EFTu GDP molecules.
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302
SAM, PLEY, AND MANDEL
4-
3-
0
Figure 1. The concentration dependence of the sedimentation coefficients of EFTuaGDP. Sedimentation in universal buffer ( p H = 7.5, I = 0.14M) a t 20.0"C ( 0 )or a t 6.0"C ( 0 ) Sedimentation . in Na acetate buffer ( p H = 6.5) a t 20.0"C a t I = 0.13M ( A ) or a t I = 0.60M (0). The ionic strength of the latter buffer system was achieved by addition of KCI.
The dependence of S20,won the total ionic strength of the universal buffer for EF-Tu GDP has been studied in more detail a t two fixed protein concentrations. A t p H = 7.5 and a concentration of C,, = 1
mg/mL, no ionic strength dependence of the sedimentation coefficient has been detected (Figure 2 ) . The differences in the S20,w values corresponding to various values of pH or concentration are probably
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I
I
I
I
I
100
I
I
1
2 00 ionic
1
300
It-7-J
600
strength / m M
Figure 2. The ionic strength dependence of the sedimentation coefficient of EF-Tu * GDP. Sedimentation conditions: (0) 20 mMTris buffer ( p H = 7.5), 2O.O0C,protein concentration 1.0 mg/mL; (0) 20 m M Tris buffer ( p H = 7.5) containing 22% ( w / w ) of glycerol, 6.0°C, protein concentration 11.4 mg/mL; ( A ) 20 m M HEPES buffer ( p H = 6.5), 2O.O0C, protein concentration 7.0 mg/mL. Ionic strength has been increased by addition of KCl.
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
1
experiments with H E P E S buffer at pH = 6.5 was a second, fast-sedimenting boundary detected. At an ionic strength of 0.185 M the slowly sedimenting material has a S20,w value of 3.54 -+ 0.01 S, in good agreement with the value found in the universal buffer a t low protein concentrations. About 10% of the material sedimented with a S20,a value of 8.5 -+ 0.3 S . Taking the former to correspond to EFT u * GDP monomers, the particles corresponding to the fast-sedimenting peak may be estimated to represent trimers or tetramers assuming, for the sake of fixing the order of magnitude, that the proteins are more or less spherical particles for which S is proportional to M2" and that up remains constant. The sedimentation of EF-Tu GDP was also more thoroughly studied as function of pH of the sedimenting medium. A t a concentration of 1 mg/mL of protein a boundary corresponding to a S20,w value of approximately 3.5 S was found for all the pH values studied (see Figure 3 and Table I ) . A t the acidic side, fast-sedimenting material was also present. For instance, at pH = 4.08,80% of the protein sediments a t 25 S, which is roughly equivalent to a molar mass of about lo6 g/mol. At p H = 5.07, where the solution was highly turbid, only 10% of all the molecules sediment a t 3.5 S. The remainder is present as a precipitate. At a concentration of 10 mg/mL of EFT u * GDP the S20,w value increases rapidly with decreasing p H from its 3.5 value a t p H = 7.5 up to 4.3 a t pH = 6.0, thus indicating again strong interactions between protein molecules under these conditions. Note that analysis of the GDP exchange of EF-Tu in assay buffer ( p H = 7.4) directly after the sedimentation experiment demonstrated that no appreciable (irreversible) denaturation of EF-Tu had taken place in experiments in which the pH has been lowered from p H = 7.5 to 6.0 (see Table 11).
\
r
0
N v)
-
i
6
8
PH Figure 3. Sedimentation of the slowly sedimenting fraction of E F - T u . GDP as function of pH at 20.0"C a n d a t an ionic strength of 0.14M. Total protein concentration: ( 0 )1.0 m g / m L a n d ( A ) 10.0 mg/mL.
significant, however. They reflect a small concentration dependence and, additionally, may be caused by the correction of the sedimentation coefficient to standard conditions. Even at high protein concentrations the sedimentation appeared to be independent of the total buffer ionic strength. Moreover, sedimentation of EF-Tu GDP in the universal buffer ( p H = 7.5) always occurred as one single boundary or Schlieren peak irrespective of the protein concentration or the concentration of added KCl. Only in one out of five single, nonreplicated
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Table I Sedimentation Behavior of the EF-Tu GDP ( 1 . 0 mg/mL) at 2 0 . 0 " C at Various pH Values" Slowly Sedimenting
E 7 - 7 ' ~GDP . PH
Buffer
4.1 5.1 5.9 7.0 8.0
Acetate Acetate Acetate Phosphate Tris Tris
9.0
Turbidity of t h e Sample
+ +++ + -
303
Fast-Sedimenting E F - T U* G D P
Fraction
S2O.W
Fraction
s,,,u
0.2 0.1 0.9 1.0 1.0 1.0
3.4 ? 0.5 3.:3 t 0.20 3.39 2 0.04 3.63 2 0.02 3.35 k 0.07 3.13 +- 0.13
0.8 0.9 0.1 0.0 0.0
25
-
0.0
-
I, 1,
-
"Buffers of 20 mM ionic strength had been supplemented with 10 mM MgC12, 100 m M KCI, 1 mM D T E , 0.01 mM GDF, and small amounts of acid to adjust the pH. No measurements possible because of precipitated material in the rotor cell.
304
SAM, PLEY, AND MANDEL
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Table I1 Sedimentation Behavior of EF-Tu GDP (10 mg/mL) at 20.0°C at Various pH Values, and the Corresponding GDP Exchange Properties Slowly Sedimenting EF-TU* GDP Turbidity of the Sample
PH
Buffer
6.0 6.5 7.0 7.5
Acetate Acetate Tris Tris
Fraction
sz0.w
GDP Exchange Activity (%)
0.90 0.95 1.oo 1.00
4.28 f 0.05 3.78 f 0.01 3.54 f 0.01 3.60 f 0.03
94 79 85 71
+ +
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Tu GDP corresponding to 4.3 X lo4,4.5 X lo4, and 4.6 X lo4 g/mol, respectively. From the inaccuracy on Ma and a relative error on up of at least 5%, the inaccuracy of M may be estimated to be on the order 5 X lo3 g/mol. All these M values are in good agreement with the molar mass of monomeric EF-Tu, which has been calculated as M = 4.36 X lo4 g/mol from the known primary structure of the protein." This seems to confirm that under these conditions (pH = 7.5 and C = 1 mg/mL) the protein is essentially present as monomeric particles.
Equilibrium sedimentation at 30,000 rpm and 21.7"C of EF-Tu * GDP of concentration C = 1mg/ mL in the universal buffer yielded sedimentation profiles that are in agreement with monodisperse solutions (Figure 4). Nonlinear least-squares fitting to the sedimentation data yielded a value of Ma = (1.20 0.01) X lo4 g/mol. Values of uz reported in the literature are 0.716 L/kg, derived from sedimentation data,19and 0.728 L/kg,' or 0.734 L/kg,20 used in small-angle x-ray scattering. Using these values we find from Ma the molar mass of EF_+
1.5
I
7
/
I
I
E
?
I
m
I
F
'LO$
d
3
I-
I
I
I
_1
I
0
0.5
6.97
P
/
/
d
10
7.0 5
7.00 distance
to
7.10 the
7.15
rotor centre
/cm
Figure 4. Equilibrium sedimentation of E F - T u - G D P at 21.7OC in universal buffer at 30,000 rpm.The broken line represents the theoretical sedimentation profile of monodisperse EF-Tu. GDP using a partial specific volume of 0.721 L/kg and M = 4.32 X lo4 g/mol.
305
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
Conversely, accepting this calculated value of the molar mass one can derive from Maa value u2 = 0.721 2 0.003 L/kg, which may be compared to the average of the three literature values, i.e., 0.726 k 0.009 (0.009 representing the standard deviation of the values with respect t o the mean). T h e observed weak concentration dependence of the sedimentation rate may indicate the presence of associated EF-Tu molecules a t higher concentrations, possibly in line with the presence of 22% of dimers in the EF-Tu preparations studied by Antonsson e t al.'
Quasielastic light Scattering Experiments T h e quasielastic light scattering experiments have been performed with EF-Tu GDP in universal buffer ( p H = 7.5) and a t concentrations C < 3 mg/ mL in order t o minimize association effects. Fitting single exponentials [ j = 1 in Eq. ( l ) ]to the experimentally obtained intensity correlation data gave a diffbsion coefficient for EF-Tu of 0.58 X cm2 s '. However, the quality of the fit was rather poor ( 4 = 0.32), as can be seen from the corresponding
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residues plot (Figure 5 a ) . The quality of the fit improved after fitting the data t o a correlation function for two independent scattering species [ j = 2 in Eq. ( 1) ; (Figure 5b). This yielded two diffusion coefficients with values 0.84 X and 0.05 X cm2 s-l, respectively. Although the deviations of the experimental points with respect t o the fitted curve are very small (less than 0.8%) , the mere fact that these small deviations show a systematic trend in the residues plot indicates that the fit is not altogether satisfactory. T h e correlation function of the buffer without protein showed a contribution to the first two to five channels of the photon correlator. This could either be due to free GDP or t o a n imperfection of the correlator a t the very short time end. Because it is very difficult to correct for this spurious effect, the data from the first five channels have subsequently been omitted from the fitting procedure. This did not improve the fit in the case of one single exponential (Figure 5c) but gave a definitely random distribution of smaller residues in case t,he squared double-exponential equation was used ( Figure 5 d ) . Thus a n autocorrelation function for two indepen-
-0.51 J do W 0
0
0
*0.5j,
0.0
___-__--__---
-0.5-1
d
0 I
V
I
I
I
I
V
I
I
0
20
,
,
40
,
I
,
60
CHANNEL NUMBER
Figure 5 . Residual plots showing the deviations of the experimental QLS data with respect to the fitted correlation functions. ( a ) Single exponential fit (96 channels), with Q = 0.32; ( b ) squared double exponential fit (96 channels), Q = 0.89; ( c ) single exponential fit (91 channels), Q = 0.26; ( d ) squared double exponential fit (91 channels), Q = 1.02.
,
80
,
0 1 1
306
SAM, PLEY, AND MANDEL
dent scattering species could be fitted satisfactorily t o the QLS data of the EF-Tu solution under the conditions mentioned. T h e fast correlation rate rl = 1/ T (~1) was found t o be independent of the sampling time and linearly dependent on the square of the scattering vector with the linear least-squares fit passing through the origin within experimental error (Figure 6 a ) . T h e values of the slow correlation rate r2= 1 / ~ ~ ( appeared 2 ) t o be more sensitive t o variations in the sampling time with a subsequent decrease in the accuracy of the diffusion coefficient determined therefrom. T h e following values for the diffusion of EF-Tu have been obtained from a linear least-squares fit of ria s function of q2: D20,,( 1) = (0.71 k 0.02) X lo6 cm2 s-l and D 2 0 , w ( 2 = ) (0.04 -+ 0.01) X cm2 s-'. In Figure 6b values of D20,w( i ) obtained from the individual correlation functions ( D = r / q 2 )are , plotted as function of the quality factor Q of the nonlinear least-squares fit and compared to the diffusion coefficients obtained directly from the least-squares lines represented in Figure 6a. It can be seen that the individual values corresponding to 0.9 < Q < 1.1 are in perfect agreement with the values quoted
c
above. This plot also demonstrates that better results have been obtained for the fast diffusion coefficient than for the slow one. The weight factors w1 and w2 giving the respective contributions to the scattered field correlation functions of the fast (smaller particles) and slow (larger particles) diffusion coefficient have been found to be approximately 0.7 and 0.3, respectively. As the intensity of the scattered light is proportional to the mass of the scattering particles, w1 and w2 represent mass fractions. From the value of D ( 2 ) a n average molar mass of the order of lo8 g/mol may be evaluated for the slowly moving particles. Thus it can be estimated that under the experimental conditions used more than 99% of the EF-Tu molecules (number fraction) should move with the higher diffusion ( 1) . T h e conclusion about the prescoefficient DZo,+, ence of only minute amounts of associated EF-Tu in universal buffer a t 25°C and low protein concentrations as derived from the light scattering experiments is in agreement with the findings from velocity and equilibrium sedimentation. From D20,w( 1) and the corresponding value of the sedimentation coefficient S!O,wr the apparent molar
I
lul
LO
30 c
v)
8
i
0
i:
n
0
t>
1 2 0 c
-0
10
0
Figure 6. ( a ) The scattering vector amplitude ( 9 )and sampling time dependence of the evaluated correlation times T ~ 1) ( and T ~ 2 () for EF-Tu. GDP (2.7 mg/mL) in universal buffer. The sampling times (in microseconds) were (with closed symbols referring to the left, open symbols to the right scale) as follows: scattering angle of 90": 2.0 (0,0 )and 1.0 ( A , A, H); scattering angle of 75": 2.7 (0, O ) , 1.2 ( A , A), and 0.2 (0, H);scattering angle a ) ; scattering angle of 30": 25.0 (0,0 ) and 7.5 of 60": 4.0 (0,O ) , 1.6 ( A , A), and 0.7 (0, (0, H).( b ) Correspondence between the quality parameters Q and the diffusion coefficients D obtained from the fitting of the correlation function. The solid lines represent the diffusion coefficients as determined from the least-squares lines and the dashed lines represent the upper and lower limits of the corresponding standard deviations.
QUASIELASTIC LIGHT SCATTERING AND SEDIMENTATION
mass of EF-Tu can be calculated using Eq. (3). This yields a value of Ma = (1.2 k 0.3) X lo4 g/mol, in perfect agreement with the value found from equilibrium sedimentation. As pointed out above, there are very good reasons to assume that this value corresponds to proteins in the monomeric form. The hydrodynamic radius that can be calculated from the diffusion coefficient of the monomeric particles D20,w ( 1) with the help of the Stokes-Einstein Eq. ( 2 ) corresponds to RH = 3.02 f 0.09 nm. If we assume the protein to be a rigid sphere, with a radius R corresponding to RH, the corresponding radius of gyration R G can be calculated using the relation
RG = ( g ) 1 / 2 R(spheres) 2
(5)
This hypothetical radius of gyration is found to have a value of 2.34 f 0.07 nm, which is in good agreement with the radius of gyration obtained from small-angle neutron scattering, i.e., 2.36 k 0.03 nm9 or 2.28 nm.” This suggests that EF-Tu GDP moves as a hydrodynamic particle with a nearly spherical shape. More detailed information about the protein in solution is difficult to obtain. It is well known that from the diffusion coefficient alone (or even in combination with other hydrodynamic quantities) no unambiguous knowledge about the shape and dimensions of the particles can be derived,21not in the least because of the difficulty in establishing the amount of solvent that moves with the protein molecule in the hydrodynamic experiment ( solvation layers or solvent trapped inside the molecule). Furthermorc>,only ellipsoid of revolution can be treated in a quantitative way, with the ratio of the shorter to the longer axis x = b / a determining the Perrin factor F.’2 The latter can be deduced from the ratio of the measured diffusion coefficient to the hypothetical diffusion coefficient D‘for a spherical particle with the same volume as the real one. Thus for a prolate ellipsoid of revolution one has
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Here U M is the volume of the protein containing a1 gram of solvent per gram dry protein, represents the partial specific volume of the pure solvent, taken to be 1.0 L/kg, and N A is Avogadro’s constant. Introducing into Eqs. ( 6 ) - ( 8 ) the values M = 4.32 X l o 4 g/mol and u2 = 0.721 L/kg (derived from the
307
former, see the sedimentation experiments) we may calculate F and x for any value of al. Thus in case 6’ = 0, we find F = 1.31 f 0.04, which corresponds to a ratio a / b = l / x N 5.9. This is much larger than found for the model of EF-Tu GDP derived from small-angle x-ray scattering’ for which the Perrin factor would be F = 0.31. We can also estimate other values for a and a / b making different choices for al. Should one assume, e.g., the hydrodynamic particle to drag along 1.35 gram water per gram dry protein, it could be represented by a prolate ellipsoid of semiaxes 6 X 1.5 X 1.5 nm ( a / b = 3.9), which comes close to the prolate ellipsoid deduced from smallangle x-ray scattering of EF-Tu-GDP.’ For an amount of water 6’ = 0.50, corresponding to the water content of the EF-Tu GDP in the crystalline state, the representative prolate ellipsoid of revolution would have semiaxes 5.4 X 2 X 2 nm. Both values of d1 are not unreasonable in view of the values estimated for other globular proteins.23The values of a1 derived for different proteins or for a given protein from various properties, thermodynamic or hydrodynamic, should not necessarily coincide, however.23Therefore such a detailed description of the hydrodynamic particle given above remains highly speculative. The safest conclusion to be drawn from this hydrodynamic study of monomeric EFTu GDP still remains that in solution this protein diffuses as a particle with a shape close to a sphere.
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Received June 23, 1989 Accepted January 22, 1990
