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Small angle X-ray scattering studies on adenovirus type 2 hexon
233
Biochimica et Biophysica Acta, 535 (1978) 233--240 © Elsevier/North-Holland Biomedical Press
BBA 37974
SMALL ANGLE X-RAY SCATTERING STUDIES ON ADENOVIRUS TYPE 2 HEXON
JOHANN BERGER, ROGER M. BURNETT, RICHARD M. FRANKLIN and MARKUS GRUTTER *
Department of Structure Biology, Biocenter, University of Basel, Klingelbergstrasse 70, CH-4056 Basel (Switzerland) (Received January 26th, 1978) (Revised manuscript received May 8th, 1978)
Summary Adenovirus type 2 hexons have been studied in solution by small angle X-ray scattering, and the following molecular parameters determined: radius of gyration (Rg)= 4.9 nm, molecular weight (M)= 31{~000, invariant volume (Vinv) = 630 nm 3, maximal distance (/)max) = 14.5--15.5 nm. A diffraction pattern was obtained up to an angular increment of h = 2.5 nm -1. Various models for the hexon have been explored by calculating the diffraction pattern from the Debye formula for 1200 spheres arranged to define the scattering volume of each model. Models were first built according to electron micrographic results. Later, preliminary results of a crystallographic study were used for model building. The experimental pattern and the pattern resulting from the model determined by crystallographic methods were compared and showed good agreement.
Introduction The hexon, the major structural subunit of the adenovirus virion, has been studied by various physical methods [1--3]. The radius of gyration has been determined by small angle X-ray scattering [3], but no shape information could be obtained in this earlier study due to the low concentration of the sample. From initial electron microscopic studies a hollow cylindrically shaped molecule was proposed [4]. An ultrastructural study of the adenovirus type 5 hexon by Nermut [5] led to a more detailed model and a crystallographic analysis of the type 2 hexon to a resolution of 2.9 A is now under way (Burnett, R.M., Griitter, M., Marcovic, Z. and White, J., unpublished). The purpose of this * Present address: Institute o f Molecular Biology, Univers/ty of Oregon, Eugene, Oreg. 9 7 4 0 3 , U.S.A.
234
study has been not only to determine the overall shape of hexon from its low angle diffraction pattern, but also to compare the results with the outline of the molecule recently available from crystallographic analysis. Materials and Methods
Specimen. Adenovirus type 2 hexon was prepared according to the method of Griitter and Franklin [ 2]. The protein was homogeneous by analytical ultracentrifugation and the sedimentation coefficient agreed with the published value [2]. The solution was dialyzed against 0.1 M phosphate buffer, pH 7.1, and concentrated by ultrafiltration to a concentration of 16 mg/ml. At higher concentrations hexons tend to aggregate (Griitter, M., unpublished observations). X-ray measurements were made with a Kratky camera using a highly stabilized X-ray generator (Philips PW 1130) with a copper tube (50 kV, 35 mA). An entrance slit of 125 pm and a counter slit of 300 pm were used; the sampledetector distance was 22 cm. The protein solutions were all measured in the same quartz capillary (diameter about 0.1 cm, irradiated volume about 40 pl) and measurements were made at 4°C. The scattered intensity was recorded with a proportional counter with pulse height discriminator which was adjusted to the copper Ka and I ~ lines. The a m o u n t of Kfl radiation was determined separately using a 30 pm Ni-filter which absorbs the K~ line almost completely. The spectra were recorded automatically using a programmable step scanning device. The scattering from hexon solutions at four protein concentrations ranging from 7 to 16 mg/ml was measured at 110 angles, ranging from h = 0.09 to 3.6 nm -1 (h = 4~/X • sin0, X = wavelength of the copper Ks line = 0.154 nm, 20 = scattering angle). The scattering at each angle was measured with a time constant of 200 s. One complete measurement of the whole angular range t o o k about 5 h. This procedure was automatically repeated six times at each concentration. The number of counts per point was between 2 • l 0 s and 1 • 106. The background was determined by measuring the scattered intensity of the buffer; again, the procedure was repeated six times. Since the slope of the Gaussian part of the pattern increased strongly as a function of time (see Results and Fig. 1) only the inner parts of curves measured in the first hour were used for deconvolution. Smearing caused by the line-shaped primary beam and the Kfl line was deconvoluted iteratively [6] and also by means of an indirect Fourier transformation of the distance distribution function [7]. Identical results were obtained by the two methods of desmearing. Model calculations. All model Calculations were performed with a computer program w h i c h calculated the theoretical diffraction pattern from a model consisting of identical spherical subunits. The Debye formula was used to describe this model. Results
Radius of gyration The strong increase of the innermost part of the diffraction pattern as a
235
function of time has already been mentioned. Fig. 1 shows a Guinier plot of this region. The dependence on time of the intensities extrapolated to zero angle was almost linear up to about 15 h. The time-dependent inner part could also be obtained simply by linear extrapolation of the intensities at zero angle to zero time. All curves measured at one concentration were identical in the angular range starting with h = 0.25 nm -~. This indicates that the substructure of the hexons remained the same. At each concentration, the innermost part of the curve measured in the first hour was taken with the average of the outer parts and used for deconvolution. Electron micrographs were made of samples subjected to the X-ray beam and negatively stained with uranyl acetate. These showed aggregated molecules forming clusters of different sizes with no particular arrangement. The radius of gyration Rg obtained by the Guinier plot and extrapolated to zero concentration was 4.9 ±0.2 nm. The value from the previous X-ray study [3] was 4.7 nm and is within our error range. In the case of rodlike particles the radius of gyration of the cross-section can be determined by multiplying the scattering intensity by the scattering angle and making the Guinier approximation. The radius of gyration of the cross-section was found to be 3.1 nm and agreed with that of Tejg-Jensen et al. [3]. The determination of the radius of gyration of the cross-section for proteins in small angle X-ray scattering is, however, a questionable method. More or less straight lines in the Guinier plot often lead to a wrong interpretation of the diffraction pattern. We feel t h a t the value of the cross-section for hexon is without significance.
1.C
0
i
I
5
10 h 2 × 102
Fig. 1. Guiniex plot of a smeared (convoluted) pattern of adenovirus type 2 hexon (concentration c = I0 m g / m l ) . T h e increase o f t h e s l o p e s o f t h e c u r v e s f r o m t h e b o t t o m t o t h e t o p i n d i c a t e s an a g g r e g a t i o n o f the h e x o n s in t h e X - r a y b e a m s i n c e the radius o f g y r a t i o n is d i r e c t l y r e l a t e d t o the s l o p e , T h e t i m e differe n c e b e t w e e n t h e i n d i v i d u a l c u r v e s is 5 h p e r c u r v e . T h e c u r v e at t i m e z e r o is at the b o t t o m o f the figure. = s m e a r e d i n t e n s i t y , h = 41r/~ • s i n S , 2~ = s c a t t e r i n g a n g l e , ~ = w a v e l e n g t h o f C u K a = 0 . 1 5 4 n m .
236
Molecular weight The molecular weight was calculated to be 310 000 using a partial specific volume of 0.738 cm3/g [2] and an absolute intensity at zero angle calculated by means of a calibrated polyethylene platelet [8]. JSrnvall and coworkers [9] have determined the molecular weight of one subunit to be 100 000 by several biochemical methods such as calculation of the molecular weight from the amino acid composition plus the number of unique cysteines (determined by sequence analysis of the cysteine-containing peptides), exclusion chromatography in guanidine hydrochloride, titration of accessible thiol groups, and peptide mapping. Since there are three identical subunits in the hexon, their value agrees with that obtained in this study. Both determinations give values somewhat lower than the earlier determination of 360 000 in this laboratory
[2]. Invariant volume The invariant Q, defined as
Q =;
I(h) h2dh
o
by Porod [ 10], is inversely related to the hydrated volume. In the angular range where the standard deviation of each measurement was lower than 5% (roughly three quarters of the measured range), Q was determined graphically following Simpson's rule. Since the integral is to infinite angle, the contribution of the high angle intensities is considerable. These values were therefore estimated assuming a decrease in intensity with h-4, according to Porod [ 10]. The volume was calculated to be 630 + 60 nm 3.
Maximal distance A Fourier inversion of the angular distribution of the intensity yields the function p(r), called the distance distribution function. Fig. 2 shows a plot of p(r) versus r. It was obtained by means of an indirect Fourier transformation [ 7] making the assumption, based on earlier models, that there are no distances within the molecule greater than 17.0 nm. The value of r at which p(r) passes through zero, represents the greatest distance Dma x within the molecule. Dma x was calculated to be 15.0 + 0.5 nm. The error range was obtained by Fourier inversion of the diffraction pattern at four different concentrations with the innermost part extrapolated to zero concentration. The square of the radius of gyration is also given by half the normalized second m o m e n t of p(r). Rg calculated in this way was 4.8 nm. This determination of Rg is independent of that calculated from the Guinier approximation.
Model calculation The scattering volume can be modeled by varying the spatial arrangement of spherical scattering bodies. The scattering from these centres may then be calculated efficiently using Debye's formula. All computations were performed with 1200 spheres of radius 0.5 nm, representing a reasonable compromise
237
o
~o~
/
°%
\
oo o o
o
°\ o
0%%
F i g . 2. P l o t o f t h e d i s t a n c e d i s t r i b u t i o n f u n c t i o n p(r) v e r s u s r. p(r) h a s b e e n o b t a i n e d b y a F o u r i e r i n v e r s i o n o f t h e a n g u l a r d i s t r i b u t i o n o f t h e i n t e n s i t y , p(r) is in a r b i t r a r y u n i t s . T h e v a l u e o f r at t h e p o i n t at w h i c h p(r) p a s s e s t h r o u g h z e r o r e p r e s e n t s t h e l o n g e s t d i m e n s i o n o f tile m o l e c u l e .
between computation time and the ability to fit a defined shape without error. This method gives great flexibility in modelling even the most complex shape. In all the work described below the scattering volume was assumed to be 630 nm 3. The first model was a hollow cylinder [4]. The height was 12.5 nm, the outer diameter 8.0 nm, and the inner diameter 1.0 nm. In Fig. 3 the theoretical pattern is compared with the experimental one. The radius of gyration of the model was 4.5 nm. The general features of both curves were the same with two subsidiary maxima in the angular range up to h = 2.5 nm -~, but the discrepancies between model and experimental data indicate that the dimensions and shape of the model were representative of hexon only to a first approximation.
.¢= H o~ 2
°
~
I
0
ooo
I
1
2 h [nm -1 ]
I
o
I
• h [nm -1 ]
2
F i g . 3. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n (ooo) a n d t h e t h e o r e t i c a l p a t t e r n o f a c y l i n d r i cal m o d e l p r o p o s e d o n t h e b a s i s o f u l t r a s t r u c t u r a l s t u d i e s b y P e t t e r s o n et al. [ 4 ] . H e i g h t = 1 2 . 5 n m , o u t e r d i a m e t e r : 8 . 0 n m , i n n e r d i a m e t e r = 1 . 0 n m . T h e r a d i u s o f g y r a t i o n R g o f t h i s m o d e l is 4.5 n m . M o s t o f t h e e x p e r i m e n t a l p o i n t s h a v e b e e n o m i t t e d . T h e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n at z e r o a n g l e h a s b e e n o b t a i n e d b y e x t r a p o l a t i n g t h e d e c o n v o l u t e d p a t t e r n in t h e O u i n i e r p l o t t o z e r o a n g l e . T h e c u r v e s h a v e b e e n n o r m a l i z e d t o 10 5 at z e r o a n g l e . F i g . 4. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n f r o m a h o l l o w c y l i n d e r c o n t a i n i n g s o m e m a t e r i a l in t h e c e n t r a l c a v i t y . H e i g h t = 1 3 . 0 n m , o u t e r d i a m e t e r = 9 . 0 n m , i n n e r d i a m e t e r = 1.5 r i m . R g f o r t h i s m o d e l is 4.9 n m .
238
Since at the time of our first calculations the crystallographic dimensions were n o t y e t available we tried to refine the first model to a shape whose theoretical diffraction pattern fits the experimental data. The simple model of a hollow cylinder was used since the use of a more complicated shape is unreasonable a priori. The best fit was obtained with a cylinder of height 13.0 nm, and o u ter and inner diameters of 9.0 and 1.5 nm. Fig. 4 shows a comparison between the experimental and theoretical curves. A channel t h r o u g h o u t the whole molecule shifts the second subsidiary m axi m um to a higher angle than that observed, whereas the pattern of a model in which some spheres are p u t into this channel fits the observed position of this second maximum. The radius of gyration calculated for this simple model was 4.9 nm. The model proposed by N e r m u t [5] is a conical triangular prism with a base of 8.5 × 9.8 nm and a top of about 7.5 nm in diameter. A fine central channel (1.0--1.5 nm) in the base dilates toward the t o p to a hole of a b o u t 2.5--3.5 nm diameter. The height of the model is 11.0 nm. Fig. 5 shows the theoretical diffraction pattern of this model compared with the experimental one. The dimensions of the model are t oo small. This is indicated by the radius of gyration o f 4.1 n m and the position of the first subsidiary maximum. Later in the study the overall molecular dimensions and shape were obtained from a electron density map at a resolution of 6/~. An idealized representation of the electron density is shown in Fig. 6. It is a conical body of height 11.1 nm with an hexagonal base of side 8.9 nm and an equi-triangular top of side 9.6 nm; two vertical edges run f r om adjacent corners of the base to an apex of the triangular top. There is no channel t h r o u g h o u t the molecule but there is a central hole o f diameter 1.0 nm and de pt h of 1.2 nm at the top, and a conical hole of diameter 3.5 nm at the base narrowing to a diameter of 1.0 nm at a depth of 5.0 nm. Fig. 7 shows how the electron density was modelled with spheres. Fig. 8 shows the theoretical pattern compared with the experimental
_~
%°°
°°%
2
0
Oooo °
1
2 h
[n~ I l
F i g . 5. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n o f a m o d e l c a l c u l a t e d a c c o r d i n g t o t h e u l t r a s t r u c t u r a l m o d e l o f t y p e 5 h e x o n b y N e r m u t [ 5 ] . R g o f t h e m o d e l is 4 . 1 nm. F i g . 6. model F i g . 7. shown
An idealized representation of hexon as seen in a 6 ~ electron density map. The dimensions of the are d e s c r i b e d in t h e t e x t . T h e w a y t h e m o d e l h a s b e e n b u i l t u p w i t h 1 2 0 0 s p h e r e s is s h o w n i n T h e c o m p a r i s o n o f t h e t h e o r e t i c a l d i f f r a c t i o n p a t t e r n o f t h i s m o d e l w i t h t h e e x p e r i m e n t a l curve i s in Fig. 8.
239 (]
Fig. 7. T o p (a) a n d b o t t o m (b) of the m o d e l o f t h e h e x o n s h o w n in Fig. 6. T h e s p h e r e s h a v e a r a d i u s o f 0.5 n m . 18 l a y e r s c o n s i s t i n g of a t o t a l of 1 2 0 0 s p h e r e s h a v e b e e n u s e d t o b u i l d u p t h e w h o l e m o d e l . See the text for the dimensions.
H
2 oo
0
o
I
I
1
2 h [nm"1 ]
Fig. 8. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e of h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n c a l c u l a t e d a c c o r d i n g t o t h e prelimina.ry c r y s t a l l o g r a p h i c results. Rg f o r t h e m o d e l is 4.6 n m .
one. The radius of gyration is 4.6 nm and the position of the first and second subsidiary maxima agree very well. Deviations exist mainly in the height of the maxima. Discussion The radius of gyration calculated by the Guinier approximation is 4.9 -+ 0.2 nm. We estimate that the error which could be caused by the deconvolution procedure as not greater than -+0.1 nm. The radius of gyration of our model (4.6 nm) falls at the lowest extremity of this range. Although the value of the radius of gyration of the cross-section agrees with the cross-section of the model at half the height, we think that the determination of such a parameter is not possible by small angle Xiray scattering. We decided to fit to the deconvoluted pattern and n o t to convolute the theoretical pattern for the following reasons: it is necessary to have a deconvoluted diffraction pattern to calculate the radius of gyration and the zero intensity and, furthermore, the deconvolution of our diffraction pattern was not difficult numerically, as would have been the deconvolution of a sphere. Although the model of the electron density was idealized by us, details of shape would n o t alter the diffraction pattern very much in the angular range we
240 studied, although a diffraction pattern calculated with the weighted atomic coordinates would very likely have lower subsidiary maxima, at the same positions, and fit the experimental curve in these parts just as well. We think that this study illustrates the advantages and disadvantages of low angle X-ray scattering as a method to determine molecular shape. Without the crystallographic information it would have been impossible to determine the exact shape of the hexon, b u t low angle X-ray scattering could distinguish between models proposed from electron microscopy. In particular, the method is very powerful in excluding models. A height lower than 11.0 nm and the possibility of the larger cavity being placed at the triangular end may both be excluded. The results indicate that the X-ray scattering from hexons in solution is consistent with their having a shape similar to that in the crystal. We have used models derived from adenovirus type 5 hexon as well as crystallographic data on adenovirus type 2 hexon to fit the low angle X-ray scattering curves. Since these types represent different serotypes, we must ask if there are any fundamental structural differences between hexon from type 5 and type 2 adenovirus. The limited comparative information available says no. The amino acid compositions are almost identical [11] and selected diffraction patterns of the two types of hexon are practically indistinguishable [ 12]. Acknowledgments We are very grateful to Mr. Ariel Lustig for the analytical ultracentrifuge runs. This work was supported by grants numbers 3.674.75 and 3.265.74 of the Swiss National Science Foundation. References 1 Franklin, R.M., Petterson, U.. ~kervall, K., Strandberg, B. and Philipson, L. (1971) J. Mol. Biol. 57, 383--395 2 Griitter, M. and Franklin, R.M. (1974) J. MoL Biol. 89, 163--178 3 Tejg-Jensen, B.° Furngreen, B., Lindqvist° I. and Philipson, L. (1972) Monatsh. Chem. 103. 1730-1736 4 Petterson, U., Philipson, L. and H6glund, S. (1967) Virology 33, 575--590 5 Nermut, M.V. (1975) Virology 65. 480--495 6 Glatter, O. (1974) J. Appl. Crystallogr. 7. 147--153 7 Glatter° O. (1977) J. Appl. CrystaUogr. 10, 415--421 8 Kratky, O., Pilz, I. and Schmitz, P.J. (1966) J. C o l l o i d I n t e r f a c e Sci. 21° 24--34 9 JSrnvall, H.° Petterson, U. and Philipson, L. (1974) Eur. J. Biochem. 48, 179--192 10 Porod, G. (1951) KoUoid-Z. 124, 83--114 11 Petterson, U. (1971) Virology 4 3 , 1 2 3 - - 1 3 6 12 Cornick, G., Sigler° P.B. and Ginsberg, H.S. (1971) J. Mol. Biol. 57, 397--401
Biochimica et Biophysica Acta, 535 (1978) 233--240 © Elsevier/North-Holland Biomedical Press
BBA 37974
SMALL ANGLE X-RAY SCATTERING STUDIES ON ADENOVIRUS TYPE 2 HEXON
JOHANN BERGER, ROGER M. BURNETT, RICHARD M. FRANKLIN and MARKUS GRUTTER *
Department of Structure Biology, Biocenter, University of Basel, Klingelbergstrasse 70, CH-4056 Basel (Switzerland) (Received January 26th, 1978) (Revised manuscript received May 8th, 1978)
Summary Adenovirus type 2 hexons have been studied in solution by small angle X-ray scattering, and the following molecular parameters determined: radius of gyration (Rg)= 4.9 nm, molecular weight (M)= 31{~000, invariant volume (Vinv) = 630 nm 3, maximal distance (/)max) = 14.5--15.5 nm. A diffraction pattern was obtained up to an angular increment of h = 2.5 nm -1. Various models for the hexon have been explored by calculating the diffraction pattern from the Debye formula for 1200 spheres arranged to define the scattering volume of each model. Models were first built according to electron micrographic results. Later, preliminary results of a crystallographic study were used for model building. The experimental pattern and the pattern resulting from the model determined by crystallographic methods were compared and showed good agreement.
Introduction The hexon, the major structural subunit of the adenovirus virion, has been studied by various physical methods [1--3]. The radius of gyration has been determined by small angle X-ray scattering [3], but no shape information could be obtained in this earlier study due to the low concentration of the sample. From initial electron microscopic studies a hollow cylindrically shaped molecule was proposed [4]. An ultrastructural study of the adenovirus type 5 hexon by Nermut [5] led to a more detailed model and a crystallographic analysis of the type 2 hexon to a resolution of 2.9 A is now under way (Burnett, R.M., Griitter, M., Marcovic, Z. and White, J., unpublished). The purpose of this * Present address: Institute o f Molecular Biology, Univers/ty of Oregon, Eugene, Oreg. 9 7 4 0 3 , U.S.A.
234
study has been not only to determine the overall shape of hexon from its low angle diffraction pattern, but also to compare the results with the outline of the molecule recently available from crystallographic analysis. Materials and Methods
Specimen. Adenovirus type 2 hexon was prepared according to the method of Griitter and Franklin [ 2]. The protein was homogeneous by analytical ultracentrifugation and the sedimentation coefficient agreed with the published value [2]. The solution was dialyzed against 0.1 M phosphate buffer, pH 7.1, and concentrated by ultrafiltration to a concentration of 16 mg/ml. At higher concentrations hexons tend to aggregate (Griitter, M., unpublished observations). X-ray measurements were made with a Kratky camera using a highly stabilized X-ray generator (Philips PW 1130) with a copper tube (50 kV, 35 mA). An entrance slit of 125 pm and a counter slit of 300 pm were used; the sampledetector distance was 22 cm. The protein solutions were all measured in the same quartz capillary (diameter about 0.1 cm, irradiated volume about 40 pl) and measurements were made at 4°C. The scattered intensity was recorded with a proportional counter with pulse height discriminator which was adjusted to the copper Ka and I ~ lines. The a m o u n t of Kfl radiation was determined separately using a 30 pm Ni-filter which absorbs the K~ line almost completely. The spectra were recorded automatically using a programmable step scanning device. The scattering from hexon solutions at four protein concentrations ranging from 7 to 16 mg/ml was measured at 110 angles, ranging from h = 0.09 to 3.6 nm -1 (h = 4~/X • sin0, X = wavelength of the copper Ks line = 0.154 nm, 20 = scattering angle). The scattering at each angle was measured with a time constant of 200 s. One complete measurement of the whole angular range t o o k about 5 h. This procedure was automatically repeated six times at each concentration. The number of counts per point was between 2 • l 0 s and 1 • 106. The background was determined by measuring the scattered intensity of the buffer; again, the procedure was repeated six times. Since the slope of the Gaussian part of the pattern increased strongly as a function of time (see Results and Fig. 1) only the inner parts of curves measured in the first hour were used for deconvolution. Smearing caused by the line-shaped primary beam and the Kfl line was deconvoluted iteratively [6] and also by means of an indirect Fourier transformation of the distance distribution function [7]. Identical results were obtained by the two methods of desmearing. Model calculations. All model Calculations were performed with a computer program w h i c h calculated the theoretical diffraction pattern from a model consisting of identical spherical subunits. The Debye formula was used to describe this model. Results
Radius of gyration The strong increase of the innermost part of the diffraction pattern as a
235
function of time has already been mentioned. Fig. 1 shows a Guinier plot of this region. The dependence on time of the intensities extrapolated to zero angle was almost linear up to about 15 h. The time-dependent inner part could also be obtained simply by linear extrapolation of the intensities at zero angle to zero time. All curves measured at one concentration were identical in the angular range starting with h = 0.25 nm -~. This indicates that the substructure of the hexons remained the same. At each concentration, the innermost part of the curve measured in the first hour was taken with the average of the outer parts and used for deconvolution. Electron micrographs were made of samples subjected to the X-ray beam and negatively stained with uranyl acetate. These showed aggregated molecules forming clusters of different sizes with no particular arrangement. The radius of gyration Rg obtained by the Guinier plot and extrapolated to zero concentration was 4.9 ±0.2 nm. The value from the previous X-ray study [3] was 4.7 nm and is within our error range. In the case of rodlike particles the radius of gyration of the cross-section can be determined by multiplying the scattering intensity by the scattering angle and making the Guinier approximation. The radius of gyration of the cross-section was found to be 3.1 nm and agreed with that of Tejg-Jensen et al. [3]. The determination of the radius of gyration of the cross-section for proteins in small angle X-ray scattering is, however, a questionable method. More or less straight lines in the Guinier plot often lead to a wrong interpretation of the diffraction pattern. We feel t h a t the value of the cross-section for hexon is without significance.
1.C
0
i
I
5
10 h 2 × 102
Fig. 1. Guiniex plot of a smeared (convoluted) pattern of adenovirus type 2 hexon (concentration c = I0 m g / m l ) . T h e increase o f t h e s l o p e s o f t h e c u r v e s f r o m t h e b o t t o m t o t h e t o p i n d i c a t e s an a g g r e g a t i o n o f the h e x o n s in t h e X - r a y b e a m s i n c e the radius o f g y r a t i o n is d i r e c t l y r e l a t e d t o the s l o p e , T h e t i m e differe n c e b e t w e e n t h e i n d i v i d u a l c u r v e s is 5 h p e r c u r v e . T h e c u r v e at t i m e z e r o is at the b o t t o m o f the figure. = s m e a r e d i n t e n s i t y , h = 41r/~ • s i n S , 2~ = s c a t t e r i n g a n g l e , ~ = w a v e l e n g t h o f C u K a = 0 . 1 5 4 n m .
236
Molecular weight The molecular weight was calculated to be 310 000 using a partial specific volume of 0.738 cm3/g [2] and an absolute intensity at zero angle calculated by means of a calibrated polyethylene platelet [8]. JSrnvall and coworkers [9] have determined the molecular weight of one subunit to be 100 000 by several biochemical methods such as calculation of the molecular weight from the amino acid composition plus the number of unique cysteines (determined by sequence analysis of the cysteine-containing peptides), exclusion chromatography in guanidine hydrochloride, titration of accessible thiol groups, and peptide mapping. Since there are three identical subunits in the hexon, their value agrees with that obtained in this study. Both determinations give values somewhat lower than the earlier determination of 360 000 in this laboratory
[2]. Invariant volume The invariant Q, defined as
Q =;
I(h) h2dh
o
by Porod [ 10], is inversely related to the hydrated volume. In the angular range where the standard deviation of each measurement was lower than 5% (roughly three quarters of the measured range), Q was determined graphically following Simpson's rule. Since the integral is to infinite angle, the contribution of the high angle intensities is considerable. These values were therefore estimated assuming a decrease in intensity with h-4, according to Porod [ 10]. The volume was calculated to be 630 + 60 nm 3.
Maximal distance A Fourier inversion of the angular distribution of the intensity yields the function p(r), called the distance distribution function. Fig. 2 shows a plot of p(r) versus r. It was obtained by means of an indirect Fourier transformation [ 7] making the assumption, based on earlier models, that there are no distances within the molecule greater than 17.0 nm. The value of r at which p(r) passes through zero, represents the greatest distance Dma x within the molecule. Dma x was calculated to be 15.0 + 0.5 nm. The error range was obtained by Fourier inversion of the diffraction pattern at four different concentrations with the innermost part extrapolated to zero concentration. The square of the radius of gyration is also given by half the normalized second m o m e n t of p(r). Rg calculated in this way was 4.8 nm. This determination of Rg is independent of that calculated from the Guinier approximation.
Model calculation The scattering volume can be modeled by varying the spatial arrangement of spherical scattering bodies. The scattering from these centres may then be calculated efficiently using Debye's formula. All computations were performed with 1200 spheres of radius 0.5 nm, representing a reasonable compromise
237
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F i g . 2. P l o t o f t h e d i s t a n c e d i s t r i b u t i o n f u n c t i o n p(r) v e r s u s r. p(r) h a s b e e n o b t a i n e d b y a F o u r i e r i n v e r s i o n o f t h e a n g u l a r d i s t r i b u t i o n o f t h e i n t e n s i t y , p(r) is in a r b i t r a r y u n i t s . T h e v a l u e o f r at t h e p o i n t at w h i c h p(r) p a s s e s t h r o u g h z e r o r e p r e s e n t s t h e l o n g e s t d i m e n s i o n o f tile m o l e c u l e .
between computation time and the ability to fit a defined shape without error. This method gives great flexibility in modelling even the most complex shape. In all the work described below the scattering volume was assumed to be 630 nm 3. The first model was a hollow cylinder [4]. The height was 12.5 nm, the outer diameter 8.0 nm, and the inner diameter 1.0 nm. In Fig. 3 the theoretical pattern is compared with the experimental one. The radius of gyration of the model was 4.5 nm. The general features of both curves were the same with two subsidiary maxima in the angular range up to h = 2.5 nm -~, but the discrepancies between model and experimental data indicate that the dimensions and shape of the model were representative of hexon only to a first approximation.
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F i g . 3. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n (ooo) a n d t h e t h e o r e t i c a l p a t t e r n o f a c y l i n d r i cal m o d e l p r o p o s e d o n t h e b a s i s o f u l t r a s t r u c t u r a l s t u d i e s b y P e t t e r s o n et al. [ 4 ] . H e i g h t = 1 2 . 5 n m , o u t e r d i a m e t e r : 8 . 0 n m , i n n e r d i a m e t e r = 1 . 0 n m . T h e r a d i u s o f g y r a t i o n R g o f t h i s m o d e l is 4.5 n m . M o s t o f t h e e x p e r i m e n t a l p o i n t s h a v e b e e n o m i t t e d . T h e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n at z e r o a n g l e h a s b e e n o b t a i n e d b y e x t r a p o l a t i n g t h e d e c o n v o l u t e d p a t t e r n in t h e O u i n i e r p l o t t o z e r o a n g l e . T h e c u r v e s h a v e b e e n n o r m a l i z e d t o 10 5 at z e r o a n g l e . F i g . 4. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n f r o m a h o l l o w c y l i n d e r c o n t a i n i n g s o m e m a t e r i a l in t h e c e n t r a l c a v i t y . H e i g h t = 1 3 . 0 n m , o u t e r d i a m e t e r = 9 . 0 n m , i n n e r d i a m e t e r = 1.5 r i m . R g f o r t h i s m o d e l is 4.9 n m .
238
Since at the time of our first calculations the crystallographic dimensions were n o t y e t available we tried to refine the first model to a shape whose theoretical diffraction pattern fits the experimental data. The simple model of a hollow cylinder was used since the use of a more complicated shape is unreasonable a priori. The best fit was obtained with a cylinder of height 13.0 nm, and o u ter and inner diameters of 9.0 and 1.5 nm. Fig. 4 shows a comparison between the experimental and theoretical curves. A channel t h r o u g h o u t the whole molecule shifts the second subsidiary m axi m um to a higher angle than that observed, whereas the pattern of a model in which some spheres are p u t into this channel fits the observed position of this second maximum. The radius of gyration calculated for this simple model was 4.9 nm. The model proposed by N e r m u t [5] is a conical triangular prism with a base of 8.5 × 9.8 nm and a top of about 7.5 nm in diameter. A fine central channel (1.0--1.5 nm) in the base dilates toward the t o p to a hole of a b o u t 2.5--3.5 nm diameter. The height of the model is 11.0 nm. Fig. 5 shows the theoretical diffraction pattern of this model compared with the experimental one. The dimensions of the model are t oo small. This is indicated by the radius of gyration o f 4.1 n m and the position of the first subsidiary maximum. Later in the study the overall molecular dimensions and shape were obtained from a electron density map at a resolution of 6/~. An idealized representation of the electron density is shown in Fig. 6. It is a conical body of height 11.1 nm with an hexagonal base of side 8.9 nm and an equi-triangular top of side 9.6 nm; two vertical edges run f r om adjacent corners of the base to an apex of the triangular top. There is no channel t h r o u g h o u t the molecule but there is a central hole o f diameter 1.0 nm and de pt h of 1.2 nm at the top, and a conical hole of diameter 3.5 nm at the base narrowing to a diameter of 1.0 nm at a depth of 5.0 nm. Fig. 7 shows how the electron density was modelled with spheres. Fig. 8 shows the theoretical pattern compared with the experimental
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F i g . 5. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e o f h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n o f a m o d e l c a l c u l a t e d a c c o r d i n g t o t h e u l t r a s t r u c t u r a l m o d e l o f t y p e 5 h e x o n b y N e r m u t [ 5 ] . R g o f t h e m o d e l is 4 . 1 nm. F i g . 6. model F i g . 7. shown
An idealized representation of hexon as seen in a 6 ~ electron density map. The dimensions of the are d e s c r i b e d in t h e t e x t . T h e w a y t h e m o d e l h a s b e e n b u i l t u p w i t h 1 2 0 0 s p h e r e s is s h o w n i n T h e c o m p a r i s o n o f t h e t h e o r e t i c a l d i f f r a c t i o n p a t t e r n o f t h i s m o d e l w i t h t h e e x p e r i m e n t a l curve i s in Fig. 8.
239 (]
Fig. 7. T o p (a) a n d b o t t o m (b) of the m o d e l o f t h e h e x o n s h o w n in Fig. 6. T h e s p h e r e s h a v e a r a d i u s o f 0.5 n m . 18 l a y e r s c o n s i s t i n g of a t o t a l of 1 2 0 0 s p h e r e s h a v e b e e n u s e d t o b u i l d u p t h e w h o l e m o d e l . See the text for the dimensions.
H
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0
o
I
I
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2 h [nm"1 ]
Fig. 8. C o m p a r i s o n b e t w e e n t h e s c a t t e r i n g c u r v e of h e x o n ( o o o ) a n d t h e t h e o r e t i c a l p a t t e r n c a l c u l a t e d a c c o r d i n g t o t h e prelimina.ry c r y s t a l l o g r a p h i c results. Rg f o r t h e m o d e l is 4.6 n m .
one. The radius of gyration is 4.6 nm and the position of the first and second subsidiary maxima agree very well. Deviations exist mainly in the height of the maxima. Discussion The radius of gyration calculated by the Guinier approximation is 4.9 -+ 0.2 nm. We estimate that the error which could be caused by the deconvolution procedure as not greater than -+0.1 nm. The radius of gyration of our model (4.6 nm) falls at the lowest extremity of this range. Although the value of the radius of gyration of the cross-section agrees with the cross-section of the model at half the height, we think that the determination of such a parameter is not possible by small angle Xiray scattering. We decided to fit to the deconvoluted pattern and n o t to convolute the theoretical pattern for the following reasons: it is necessary to have a deconvoluted diffraction pattern to calculate the radius of gyration and the zero intensity and, furthermore, the deconvolution of our diffraction pattern was not difficult numerically, as would have been the deconvolution of a sphere. Although the model of the electron density was idealized by us, details of shape would n o t alter the diffraction pattern very much in the angular range we
240 studied, although a diffraction pattern calculated with the weighted atomic coordinates would very likely have lower subsidiary maxima, at the same positions, and fit the experimental curve in these parts just as well. We think that this study illustrates the advantages and disadvantages of low angle X-ray scattering as a method to determine molecular shape. Without the crystallographic information it would have been impossible to determine the exact shape of the hexon, b u t low angle X-ray scattering could distinguish between models proposed from electron microscopy. In particular, the method is very powerful in excluding models. A height lower than 11.0 nm and the possibility of the larger cavity being placed at the triangular end may both be excluded. The results indicate that the X-ray scattering from hexons in solution is consistent with their having a shape similar to that in the crystal. We have used models derived from adenovirus type 5 hexon as well as crystallographic data on adenovirus type 2 hexon to fit the low angle X-ray scattering curves. Since these types represent different serotypes, we must ask if there are any fundamental structural differences between hexon from type 5 and type 2 adenovirus. The limited comparative information available says no. The amino acid compositions are almost identical [11] and selected diffraction patterns of the two types of hexon are practically indistinguishable [ 12]. Acknowledgments We are very grateful to Mr. Ariel Lustig for the analytical ultracentrifuge runs. This work was supported by grants numbers 3.674.75 and 3.265.74 of the Swiss National Science Foundation. References 1 Franklin, R.M., Petterson, U.. ~kervall, K., Strandberg, B. and Philipson, L. (1971) J. Mol. Biol. 57, 383--395 2 Griitter, M. and Franklin, R.M. (1974) J. MoL Biol. 89, 163--178 3 Tejg-Jensen, B.° Furngreen, B., Lindqvist° I. and Philipson, L. (1972) Monatsh. Chem. 103. 1730-1736 4 Petterson, U., Philipson, L. and H6glund, S. (1967) Virology 33, 575--590 5 Nermut, M.V. (1975) Virology 65. 480--495 6 Glatter, O. (1974) J. Appl. Crystallogr. 7. 147--153 7 Glatter° O. (1977) J. Appl. CrystaUogr. 10, 415--421 8 Kratky, O., Pilz, I. and Schmitz, P.J. (1966) J. C o l l o i d I n t e r f a c e Sci. 21° 24--34 9 JSrnvall, H.° Petterson, U. and Philipson, L. (1974) Eur. J. Biochem. 48, 179--192 10 Porod, G. (1951) KoUoid-Z. 124, 83--114 11 Petterson, U. (1971) Virology 4 3 , 1 2 3 - - 1 3 6 12 Cornick, G., Sigler° P.B. and Ginsberg, H.S. (1971) J. Mol. Biol. 57, 397--401