- Email: [email protected]
Structure of the top a-t component of alfalfa mosaic virus a non-icosahedral virion
J. Mol. Biol. (1983) 171, 139-155
Structure of the Top a-t Component of Alfalfa Mosaic Virus A Non-icosahedral Virion STEPHEN CUSACK
European Molecular Biology Laboratory, Grenoble Outstation c/o ILL, 156X, 38042 Grenoble Cedex, France GERT T. OOSTERGETEL, PETER C. J . KRIJGSMAN AND JAN E. MELLEMA
Department of Biochemistry, University of Leiden Wassenaarseweg 64, 2333 A L Leiden, The Netherlands (Received 7 February 1983, and in revised form 4 August 1983) Neutron-scattering in combination with quasi-elastic light-scattering and electron microscopy was used to derive a model for the capsid structure of the Top a-t component of alfalfa mosaic virus (AMV-Ta-t). In the electron microscope, AMV-Ta-t appears as an irregular ellipsoidal particle with apparent dimensions 275(__+31) A x 225( _ 22) A. Assuming that the particles are monodisperse, model calculations show that the neutron-scattering data are best explained by an oblate ellipsoidal shape for the virion with external dimensions 284 A x 284 A × 216 A. Based on this result, and in combination with the known composition of the virion, it is suggested that the capsid structure could be based on a deltahedron with 52 pointgroup symmetry and comprising 120 subunits. Such a model would imply a greater deviation from equivalent subunit interactions than normally necessary in icosahedral capsids. The neutron and photon correlation data, however, do not allow us to rule out the possibility that Top a-t is a slightly polydisperse preparation of irregular prolate shapes with mean dimensions 312 A x 232 A × 232 A. Both possibilities support the concept of alfalfa mosaic virus coat protein being capable of a wide range of intersubunit interactions, this flexibility resulting in considerable polymorphism in capsid structures.
1. I n t r o d u c t i o n Alfalfa mosaic virus is a p l a n t virus whose genome is composed of four distinct, single-stranded R N A molecules each p a c k a g e d in s e p a r a t e protein capsids whose size is roughly proportional to the molecular weight of the R N A enclosed (Heijtink et al., 1977). We h a v e previously studied the largest particle, the b o t t o m c o m p o n e n t AMV-Bt, which has an overall length of a b o u t 600 A and is cylindrical with rounded caps (Cusack et al., 1981). Three other components, denoted AMV-M, AMV-Tb and AMV-Ta-b, have a similar shape to AMV-B b u t lengths of 430 A, 350 A and 310 A, respectively. The protein capsids of all these c o m p o n e n t s can well be understood within the t h e o r y of quasi-equivalence proposed b y Caspar t Abbreviations used: AMV, alfalfa mosaic virus; D, deuterium. 139 0022-2836/83/340139-17 $03.00]0 © 1983 Academic Press Inc. (London} Ltd.
140
S. CUSACK E T A L .
& Klug (1962), the cylindrical part being based on a hexagonal lattice of axial repeat about 84 A (and containing 36 protein subunits per repeat distance) and the rounded ends being half-icosahedra (Mellema, 1975; Cremers et al., 1981). The possible number of subunits forming such a structure is given by the formula 6 0 + 1 8 n , (n-- 0, l, 2 . . . ) . A fifth component of AMV, denoted AMV-Ta-t, does not fit into the above pattern. Although AMV-Ta-t and AMV-Ta-b co-sediment in the ultracentrifuge and have the same electrophoretic mobility, they can be separated on the basis of their different solubility in the presence of magnesium ions (Heijtink & Jaspars, 1976). AMV-Ta-t is soluble, whereas AMV-Ta-b precipitates. Although some minor RNA species have been detected in these particles, the majority of both AMV-Ta-t and AMV-Ta-b virions appear to contain two molecules of RNA-4 (Heijtink & Jaspars, 1976). On the electron microscope grid, AMV-Ta-b is cylindrical with rounded caps, whereas AMV-Ta-t appears ellipsoidal (Fig. 1). From measurements of total particle weight combined with estimates of the RNA content it has been deduced that there are about 132 subunits in the capsid of AMV-Ta-b and 120 in the case of AMV-Ta-t (Heijtink et al., 1977). The former value fits the above formula (when n = 4), whereas the latter does not. The above observations give rise to two interesting questions. Firstly, what is the structure of the capsid of AMV-Ta-t if it is neither icosahedral nor cylindrical?
FIG. 1. Electron micrograph of a negatively stained preparation of AMV-Ta-t. Magnification 120,000 x.
T O P a-t C O M P O N E N T
OF A L F A L F A
MOSAIC VIRUS
141
Secondly, is the R N A organized differently in AMV-Ta-t as compared to the bacilliform components? W e have used neutron-scattering, electron microscopy and a number of other physical techniques to try and answer these questions. 2. M a t e r i a l s
and Methods
(a) Virus culture, isolation and purification AMV strain 425 was grown and isolated as described by Van Vloten-Doting & Jaspars (1972) and the Ta-t component separated from the bacilliform components by precipitating the latter with magnesium ions according to Heijtink & Jaspars (1976). The preparation was then purified by one cycle of sucrose density-gradient centrifugation in a zonal rotor. Concentrations of purified virus were determined spectroscopically using ~260,m~'lmg/m___ l 4"69 (Heijtink et al., 1977). (b) Preparative electrophoresis The purified Ta-t preparation was separated into components 13 and 14 (Bol & LakKaaschoek, 1974) by preparative eleetrophoresis in 3 ~ (w/v) polyacrylamide gels (Loenig, 1967): 0.2 mg of purified Ta-t was applied to a gel of 14 cm length and 0.6 cm diameter and electrophoresis was carried out for 66 h at 4°C and 75 V (4 mA/gel). After scanning the gel at 260 nm using a Zeiss PMQ2 spectrophotometer with a ZK4 gel scanner, the appropriate slices were cut from the gel. The nueleoproteins were eluted from the gel slices by homogenizing in 0-5 ml of P E N buffer (0-01 M-sodium phosphate, 0"001 M-EDTA, 0.001 Msodium azide, pH 7"0) followed by shaking overnight and removal of the gel residues by centrifugation. The resultant components were examined in the electron microscope. (c) Analytical ultracentrifuqation The purified Ta-t preparation was analysed in a Beckman Spinco model E ultracentrifuge, using an AN/F Ti rotor at 29,600 revs/min at 12°C, the virus concentration being 6"3 mg/ml. (d) Photon correlation spectroscopy Translational diffusion constants were measured by the technique of photon correlation using an apparatus similar to that described by Zulauf (1977). Measurements were made at scattering angles of 30 °, 90 ° and 153.2 °, and the correlation functions analysed using the moment expansion method (Brown et al., 1975).
(e) Neutron-scattering Purified virus samples were dialysed against P E N buffer containing D20 proportions of 0, 45, 56, 74 and 100°/o. Using these samples, small-angle neutron-scattering measurements were made using instrument D11 at the Institut Laue-Langevin, Grenoble (Ibel, 1976). The following experimental conditions were used:
Concentration
Wavelength
Sample-detector distance
Collimation
2-7 3-10 40 40
10.00 9-85 9-85 4.58
9"79 10"53 2.53 2.53
10 10 5 10
(mg/ml)
(A)
(m)
(m)
S. CUSACK E T A L .
142
Data collected on the 64 cm x 64 cm detector were circularly averaged and normalized by monitor count and then treated in the following way to correct for background and detector response. A normalized detector response was obtained according to: ~,, [In(q) -- Talec(q) -- (1 -- Ta)Icd(q) ] D(q) = B , [numerator] . . . . . 8 . . . . . q
(1)
where the sum is over all buffer spectra Is(q) with suitably good counting statistics (usually the 0%o and 45% buffers), Icd(q) is the electronic background, IEc(q) the empty cell spectrum and Ta the transmission of the buffer relative to the empty cell. q is 4g/)~ sin (0/2), where 0 is the scattering angle and 2 is the wavelength. I t is here assumed that the scattering due to the buffers is flat (i.e. independent of q) and given by (May et al., 1982):
V I . ( q ) - Tflec
c. = L
4,+g
.... , ..... . - i-:-
(2)
where g = g()., ~/oD20) and ~b is the incident flux. In the case of pure incoherent scattering, g = 1 and this is to a very good approximation true for pure H20 at ), = 10 A, thus enabling the flux to be derived, g becomes less than 1 for buffers with high D20 content and even for H20 at shorter wavelengths (Jacrot & Zaccai, 1981; May et al., 1982). Values of ca for each %oD20 buffer were then used to correct the sample scattering curves (and put them on an absolute scale) according to:
l [ ! s ( q ) - TslEc(q)--(1- Ts)Icd(q ) l~°rr(q) = cTsd~dNA L D(q)
c . ( 1 - Ts)gs] (1 - TB)g B ]"
(3)
Here Is(q) is the measured sample spectrum, c is the sample concentration, d the sample cell thickness, N A Avogadro's number and T s the sample transmission. In eqn (3) it is assumed that the fiat background measured with the sample scattering is given in analogy with eqn (2) by:
4~,gs (4)
Cs = l -- Ts
In this way the extra incoherent scattering due to unexchanged protons in the sample compared to the corresponding buffer can be corrected for. This effect is proportional to the volume fraction occupied by the virus in the solution and thus is important only for the high concentration samples. Except at high D20 contents, g is a slowly varying function of the transmission and so gs/gs ~ 1 (May et al., 1982). The advantage of this method of analysis is that shorter measuring times may be used for the buffers (except those used for the detector response) as only a single cB value is required from them. The corrected neutron-scattering curve for AMV-Ta-t in 100%o D20 is shown in Fig. 2 as an example. At sufficiently small scattering angles, and for a monodisperse solution without interparticle interactions, the corrected scattering curve is given by the well-known Guinier approximation: i~.rr(q) = 1(0) exp ( _ ~ . ~ ) '
(5)
where R 8 is the radius of gyration and I(0), the intensity at zero angle, is given by:
i,o,= M
B
~
2
(6)
TOP a-t COMPONENT OF A L F A L F A MOSAIC VIRUS
*n
143
I
.J 0
--I
-2
-5
0"00
0"04
0208
OJ'2
0:'6
0"20
q(I/RI
Fro. 2. N e u t r o n - s c a t t e r i n g curve f r o m A M V - T a - t in 100% D 2 0 . T h e curve is c o n s t r u c t e d by
combining the data sets obtained at a sample to detector distance of 10.53 m, 2-53 m and 2.53 m and a wavelength of 9.85 A, 9.85 A and 4,.58 A, respectively.
Here M r is the particle molecular weight, B / M is the scattering length per unit molecular weight of the particle, ~ is the particle partial specific volume and bs is the solvent scattering length density. Guinier plots of In (I(q)) against q2 enable both Rg and I(0) to be derived. In general: (]A (q)[2)spherical . . . . .
/~orr(q) =
ge,
(7)
where the angular dependence is given by the spherical average of the modulus squared of the scattering amplitude A (q). The latter is related by Fourier transformation to the excess scattering length density in the particle b(r)-bs: A(q) = S (b(r)-bs) e iq'r d3r.
(8)
v
An automatic least-squares technique (using a modified version of the program described by Schneider et al. (1978)) was used to fit homogeneous shell models representing the particle scattering length density distribution to the corrected spectra at each D20 contrast. As discussed by Cusack et al. (1981), the effect of instrumental smearing can be taken into account during this procedure. The most satisfactory models used were ellipsoids of revolution. The scattered intensity for a homogeneous ellipsoid of revolution with axial ratio u is given by: 1
I(q) = I(0) S dz gb2[qRx/l +z2(u - 1)], 0
where: ¢(x)=
3(s-inx-xc°sx) x3
(9)
144
S. CUSACK ET AL.
and the corresponding radius of gyration is: R~ = R ~ 5 . It should be noted that for an ellipsoidal shell model in which the shells are of uniform thickness (as used here), the axial ratios of the internal shells differ from that of the external shape. (f) Electron microscopy
For electron microscopy, AMV was fixed at 4°C overnight by dialysis against PEN buffer containing l~o (v/v) formaldehyde and negatively stained with 1% (w/v) uranyl acetate on normal carbon films.
3. Results (a) Analytical ultracentri fugat ion The virus preparation showed only one peak in the schlieren pattern upon sedimentation in the ultracentrifuge (Fig. 3). The calculated sedimentation coefficient S~O.w was 65.4S, which is in good agreement with the value of 66.0(+_0.9) S measured by Heijtink et al. (1977). (b) Photon correlation The translational diffusion constant D~0.w and the corresponding hydrodynamic radius R H = kaT/6u~lD~o.w was found to be independent of scattering angle (Table 1). The value of (1.52__0.02)× l0 -~ cm~/s for D~o.w is essentially the same as measured previously (Oostergetel et al., 1981). Also given in Table 1 are the values of the normalized second moment
FIo. 3. Schlieren patterns of AMV-Ta-t; lower: purified preparation used for neutron-scattering, photon correlation spectroscopy, electron microscopy and electrophoresis; upper: preparation containing Ta-t and TO-t. Sedimentation is from right to left. The photograph was taken ~25 min after reaching a speed of 29,600 revs/min.
T O P a-t C O M P O N E N T
OF ALFALFA
MOSAIC
VIRUS
145
TABLE 1
The diffusion constant D~o' w, normalized second moment #2 and hydrodynamic radius Ru of A M V Ta-t at three different scattering angles Scattering D,o w angle (°) (x 10- 7 s/cm 2) 30 90 153.2
~2
R H (A)
1.57+0.04 --0.14+0.07 136+4 1.52+.0.02 --0"01+0"02 140+2 1.52+0.02 0-02+0-01 140+2
#2 = ( ( D 2 ) - ( D ) 2 ) / ( D ) 2, which can be derived using the moment expansion method of data analysis (Brown et al., 1975). ~2 has a value of at most a few percent (except at the scattering angle of 30 ° , where the measurements are less reliable). This is generally assumed to be compatible with a monodisperse solution (within the statistical accuracy of the measurements) although not sufficient evidence to prove that it is. (c) Electron microscopy As shown in Figure l, AMV-Ta-t appears in the electron microscope as an irregular ellipsoidal particle with apparent dimensions 275( + 31)A × 225( + 22)A. Figure 4 gives the distribution of the lengths and the widths of the projected shapes. This virus preparation, after purification by sucrose density-gradient centrifugation, still contains the two electrophoretic components 13 and 14 (Fig. 5). After separation of these two components by preparative electrophoresis, no difference in the distribution of the projected shape could be detected by electron microscopy when plotted in a way similar to that shown in Figure 4. It should be remarked that in the absence of any artifacts introduced by the microscopy, the different projections possible of an oblate ellipsoid of revolution would produce a vertical line (constant length) in the plot of Figure 4, whereas those of a prolate ellipsoid would produce a horizontal line (constant width). The results correspond to neither of these ideal cases. This could be due to shrinkage or flattening artifacts resulting from sample preparation for the electron microscope and/or because the sample is actually polydisperse. In the latter case, a number of possibilities could be envisaged but not distinguished; for example, a shape distribution (particles of constant volume but with a distribution of axial ratios) or a size distribution (particles of the same axial ratio, but different sizes). (d) Neutron-scattering (i) Low-angle regime Guinier plots of the low-angle data show a strong dependence on concentration of the radius of gyration and extrapolated intensity at zero angle I(0). Radii of gyration typically increased by 10% on decreasing the concentration from 7 mg/ml to 1-7 mg/ml. This effect is attributable to strong electrostatic
146
S. C U S A C K E T A L . 500
/
-
/
/
250 a~
K
,~,
/
II I
200
/ x
, = == ~ ' ~ , , , ~ x x x~x x
x
~
xx
x
x
x ~
/
x
/
x
~
x
/
~x
,=, x
* ,= ,=,
w
x
x ~xxxxK
xxxx x
x
x
x
x xx
x
x x
x
. x
x
x
/ /
150-1
l
I
0
IO
20
50 3020-
IO-
0 r
,
i
1
,
,
I
150
I
i
I
I
!
400
Length ( ~ ) Fro. 4. Distribution of the largest and smallest dimension of Ta-t particles as measured from a n electron micrograph of a negatively stained preparation. Each cross represents a measured particle. Histograms of the larger and smaller diameters are placed along the horizontal and vertical axis, respectively.
interparticle interactions that are not adequately screened in the low ionic strength buffer used. Insufficient data were collected to allow a reliable extrapolation to zero concentration, and so R 8 and I(0) were derived from the fitting of models to the higher angle data (see below).
=e 0 tO O4
0
0 .ID
Migration
>
FIG. 5. Densil~ogram of a polyacrylamide gel showing the composition of the AMV-Ta-t preparation. The ratio of component 13 to component 14 is about 3 : 1. A small amount of component 15 is present.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
147
(ii) Particle shape and dimensions The ultracentrifuge and photon correlation results are consistent with the preparations being monodisperse although, as mentioned above, electron micrographs of the virions are suggestive of a more polydisperse sample and there are known to be two electrophoretic components present. In the following analysis of the neutron data we first explore the assumption that the particles are indeed identical. The possibility of polydispersity will be discussed subsequently. With the assumption of monodispersity, it is obvious from the lack of multiple pronounced maxima in the scattering curve of Figure 2 that the particles are not spherical. Furthermore, prolate ellipsoidal shapes with axial ratios in the range suggested by the electron microscopy results also have maxima that are too pronounced (see Fig. 8 and section (d)(iv), below). Oblate ellipsoids, on the other hand, can have much less distinct scattering curves. Calculations based on oblate ellipsoids of revolution enable the central and first subsidiary maximum (i.e. up to q = 0.06A -1) to be fitted very well, and also give the correct position of the second subsidiary maximum (see Fig. 6). The agreement could be improved and extended to q ~ 0-08 /k -~ by letting the third axis of the ellipsoid vary. However, it is doubtful whether this additional shape parameter is of real physical significance as, firstly, the information given by the model fits on the forward scattering, the radius of gyration and the internal structure (see below) were very similar for ellipsoids of revolution or general ellipsoids and, secondly, neither shape could satisfactorily fit the data beyond q ~ 0.09/~- 1. Related to this latter point is the occurrence of a maximum in the scattered intensity at about q = 0.16A -1 observable in both 0% and 100% D20. A marked peak in this 5 432I
~
-J
o
lllllllll
-I -2
-4-5 0.00
o-'o2
0.~4
o-'06
o-'os
o.lo
q (~,-~) FIo. 6. Fits to the neutron-scattering data of Ta-t in 0% (O), 45% (@), 56% (O), 74% (r-I) and 100% D20 (1). The model used was an oblate ellipsoid of revolution containing 3 shells. The semiaxes of the model are 142 A x 142 A x 108 A and the 2 internal shell boundaries have semi-axes of
134Ax134AxlOOAand87 Ax87 Ax53A.
148
S. C U S A C K E T A L .
position has been observed from all AMV virions so far studied (Cusack et dl., 1981; Oostergetel et al., 1983) and corresponds to the intersubunit interference arising from the capsid surface lattice. Clearly no homogeneous shell model can be expected to reproduce the measured intensity to this resolution. The external dimensions of the ellipsoid of revolution best fitting the data are 284/~ x 284 A x 216 A, corresponding to an axial ratio of 0-76. These dimensions could be changed by up to 3% without significantly affecting the quality of the fits. However, all models (ellipsoid of revolution or general ellipsoid, two or three shells) led to very similar results for the total volume of the particle envelope (9.0_+0.2) x l06 A 3 and the forward scattered intensity and radius of gyration as a function of contrast. These values are tabulated below. D20 (%)
(~g)
1(0) (10-23 cm2/daiton)
0 45 56 74 I00
104.5__+ 1 46 ___+5 113-0 __+1 108.5__+0.5 107.4 + 0 . 5
360"0--+3 0.43 + 0-03 12.0__+0"5 124-3__+0-5 460.0 + 3
18-97 0-66 --3"5 --11-15 -- 21.45
A plot of I(0) against the fraction of D20 gives an excellent straight line with matchpoint 46-8(_+0-5)O/o D20. According to equation (6), I(0) can be calculated from the composition and partial specific volume of the particle. Assuming that AMV-Ta-t contains 15-6°/o (Heijtink et al., 1977) by weight RNA (scattering length/unit mass (3.25 +0.92x) × 10-14 cm/dalton, where x is the fraction of D20 ) and 84-4% protein (scattering length/unit mass (2.32 + 1-45x) × 10-14 cm/dalton, calculated from the sequence (Van Beynum et al., 1977) and assuming 10% nonexchangeability of the "exchangable" protons) and a partial specific volume of 0.703 cm3/g (Heijtink et al., 1977), the calculated matchpoint is 46.2~/o D20, in good agreement with that observed. The particle weight deduced from these results is 3"67(_+0.05) x 106 Mr. This is about 3% higher than that determined by hydrodynamic methods (Oostergetel et al., 1981). A Stuhrmann plot of the radii of gyration again shows a good straight line, demonstrating the consistency of the data. The radius of gyration at infinite contrast is 106.0( _+0.1)/~ and the negative slope indicates that denser material (RNA) is in the interior. (iii) Internal structure The shell model-fitting method in principle allows one to deduce information about the internal structure of particles in cases where the scattering length density is compartmentalized into more or less distinct regions (Chauvin et al., 1978; Schneider et al., 1978; Cusack et al., 1981; Timmins & Jacrot, 1983). In the present case, the procedure is limited by the inability to obtain good fits beyond about q -- 0-06 A-1 without the introduction of an unjustifiably large number of parameters. A set of consistent model fits to five contrasts is shown in Figure 6 and the linearity with contrast of the excess scattering length density found in each shell is demonstrated in Figure 7. The semi-axes of the oblate ellipsoidal model are
TOP a-t COMPONENT
g-
OF ALFALFA
MOSAIC VIRUS
149
3
I
E u I o v
-i-
--2-
o~
{D
-3
o.o
o:2
i
o14
0.6
o18
1.0
Fraction D20
Fro. 7. The variation of scattering length density with contrast derived from the model fits shown in Fig. 4. ( 0 ) Inner region; ( , ) intermediate shell; (A) outer shell.
142 A x 142 A x 108 A, and the two internal shell boundaries have semi-axes 134 A x 134 A x 100 A and 87 A x 87 A x 53 A. The inner region has a match-point of 69.7(± 1.3)% D20, suggesting that it is pure RNA. The central shell has a match-point of 43.5(±0.8)~/o D20 and is therefore mainly protein but with a small percentage of RNA. The thin outer shell, which has a match-point of 50-0(± 1"0)~/o D20, was introduced to take account of the fact that when the external dimensions of the particle were allowed to float in the fitting procedure, they were consistently less in the case of the 56% data. This same situation arose in the analysis of the neutron scattering data of the VRU strain of AMV (Oostergetel et al., 1983, accompanying paper) and is interpreted there as indicating a higher proportion of hydrophilic residues (80%) to hydrophobic residues (20~o) in the external region of the protein. There, as here, the alternative explanation that there is RNA penetrating to the surface leads to a too high content of RNA in the particle, whereas the interpretation of the scattering density distribution given above leads to an RNA content of 16.5%, in close agreement with that quoted by Heijtink et al. (1977). It should be remarked that, although the model just described gives the best fit to the data, almost as good results are obtained by different decompositions of the internal structure (while maintaining the same external dimensions). The overall conclusion is that protein extends about 55 A in from the surface of the particle and that a small percentage of the RNA interpenetrates into internal regions of the protein capsid. (iv) Polydispersity I f we now consider the possibility of polydispersity in the sample, the analysis of the neutron data is more difficult as we do not know the nature of the polydispersity (e.g. whether due to shape or size, with a continuous or discrete
S. CUSACK ET AL.
150
_1
0.00
I
I
I
I
0.02
0-04
0"06
0.08
O. I0
q(I/~l Fro. 8. In both curves the crosses are the experimentally measured neutron data for Top a-t in 100% D20. The lines are calculated curves for a prolate ellipsoid of revolution of dimensions 312 A x 232 A x 232 A, (top) with normal wavelength smearing (A)./).= 0.09), (bottom) with increased wavelength smearing (A2/). -- 0.18).
distribution). Small-angle scattering is very sensitive to polydispersity but its effect is to smear scattering curves in a similar way to t h a t arising from a wavelength distribution of the incident beam (Glatter, 1980). Thus, in the modelfitting procedure for analysing the neutron d a t a from D11, the wavelength spread is normally fixed with A;t/2 (FWHM¢) = 0.09. I f this p a r a m e t e r is free to v a r y in the least-squares fitting process, polydispersity effects can be simulated. Using this method, the neutron-scattering curves were re-analysed using the mean dimensions from electron microscopy as a starting point for refinement, b u t assuming t h a t they corresponded to a prolate ellipsoid of revolution and allowing the possibility of polydispersity. As shown, for example, in Figure 8, fits comparable in quality to those of Figure 6 can be obtained with a prolate shape of mean dimensions 232 A × 232 A × 312 A (slightly larger than the electron microscopy values) provided t h a t A~/2 was increased to 0.18 (FWHM). Assuming t h a t the polydispersity was due to only size, not shape, and had a Gaussian form, this would correspond to a fractional standard deviation (ar/R) of 0.065, which is to be compared with the corresponding value of about 0-1 according to electron microscopy. Thus, this possibility would be consistent with the electron microscopy measurements, allowing for some shrinkage and distortion in the sample preparation. Since for a size distribution of identically shaped particles the
t (FWHM), Full width at half maximum.
T O P a-t C O M P O N E N T
OF A L F A L F A
MOSAIC V I R U S
151
normalized second m o m e n t of the diffusion constant is given by/~2 = (aR/R) z, the value of 0.004 for /~2 implied by this distribution is also compatible with the photon correlation results. Of course, it is not possible to deduce the nature of the polydispersity (whether size, shape, continuous or discrete) from the neutron data. The argument given above serves only to show that the photon correlation results do not rule out a narrow distribution which, however, is detectable by small-angle scattering. 4. Discussion
It has long been recognized that preparations of AMV strain 425 nucleoproteins contain four major and at least 13 minor electrophoretic components (Bol & LakKaashoek, 1974), and that a further splitting of some of these components can be made on the basis of solubility in the presence of magnesium (Heijtink & Jaspars, 1976). These authors pointed out that magnesium seems to preferentially precipitate bacilliform particles, that is those with 60+ 18n protein monomers in their capsids. Thus, they were able to identify Ta-b (i.e. magnesium-insoluble components 13 and 14) with the capsid consisting of 132 subunits (n = 4) and TO-b (magnesium-insoluble component 15) with the 114 subunit capsid (n = 3). The magnesium-soluble components 13 and 14 (constituting Ta-t) were recognized to be anomalous in their number of subunits (about 120), but apart from describing them as irregularly spheroidal no attempt was made to propose a capsid structure for these particles. The results of the present study unfortunately do not resolve the question as to whether Ta-t particles have a unique capsid structure or not, although in the latter case the polydispersity must be small to be compatible with all the data. Successful crystallization of Ta-t particles may be the only way to resolve this problem. The assumption of monodispersity leads to the possibility that Ta-t has an oblate ellipsoidal shape, whereas allowance of some polydispersity implies that prolate shapes cannot be ruled out. In the following discussion we consider the problem from another viewpoint by asking what kind of capsid structures can be built out of about 120 subunits? Hitherto all simple virus capsids have been found to conform to either helical or icosahedral designs (or a combination of both, as in the case of the bacilliform particles of AMV). The reason for this is that these symmetries allow structures to be built from identical subunits that minimize the deviations from equivalent subunit interactions. Assuming that intersubunit interactions are predominant, these structures are likely to be of the lowest energy (Caspar & Klug, 1962). If we no longer restrict attention to isometric (i.e. spherical) capsids, then a variety of deltahedra (i.e. polyhedra with triangular faces) of lower symmetry than icosahedral are conceivable, some of which could account for the irregularly spheroidal particles of AMV. Starting from the observation that AMV protein is able to form bacilliform surface lattices with both five- and sixfold vertices and three subunits per triangular face (i.e. one dimer per edge), we ask what other lattices are possible if we preserve these characteristics but relax the need for ieosahedral or helical
152
S. CUSACK E T A L .
Q (a)
(b)
(c)
Fro. 9. Models of non-icosahedral structures visualized as projections along symmetry axes. (a) Model for a structure with 32 pointgroup symmetry, containing 108 subunits. (b) Model for a structure with 222 pointgroup symmetry, containing 120 subunits. (c) Model for a structure with 52 pointgroup symmetry, containing 120 subunits. s y m m e t r y ? Using Euler's t h e o r e m t , it is s t r a i g h t f o r w a r d to show t h a t deltahedra with 12 fivefold vertices (necessary for closure) and m sixfold vertices m u s t h a v e 60 + 6m subunits. The bacilliform structures clearly fit this f o r m u l a when ~n = 3n, their particularly being t h a t there are two groups of six linked fivefold vertices forming the two half icosahedra at the ends of the particle. Figure 9 shows three oblate structures built according to the less stringent rules just described. These can be described in t e r m s of the linking of the 12 fivefold vertices and the a p p r o x i m a t e axial ratios. (1) A structure with 32 p o i n t g r o u p s y m m e t r y of 108 subunits (m = 8), in which there are three groups of four fivefold vertices. The axial ratios are a p p r o x i m a t e l y 1 : 1:0-65. (2) A structure with 222 pointgroup s y m m e t r y of 120 subunits (m = 10), whose fivefold vertices are a r r a n g e d in four groups of three (or 2 groups of 6). Axial ratios 1 : 0 . 8 1 : 0 - 4 2 . (3) A structure with 52 pointgroup s y m m e t r y of 120 subunits, in which the fivefold vertices are grouped according to l, 5, 5, 1. Axial ratio 1 : 1 : 0.77. t Euler's theorem relates the number of edges (E), faces (F) and vertices (V) of a polyhedron according to F+ V = 2+E.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
153
We have not been able to build other regular structures of this kind in this size range (apart from the bacilliform structures with 96, 114 or 132 subunits). However, one can expand structure three into a 150-subunit model (m = 15: still with 52 pointgroup symmetry) by adding a ring of five sixfold vertices between the two rings of five fivefold vertices. The axial ratios of this nearly spherical, but oblate, structure are l : 1 : 0.90. If we accept the hypothesis of a unique and regular capsid structure for Ta-t, then model (3) is an obvious candidate for it. The experimental evidence for this identification is; firstly, the correspondence of the number of subunits (120); and secondly, that the size and axial ratio of Ta-t determined by neutron-scattering (assuming monodispersity) agree remarkably well with that of the model. The only other possibility in this size range is model (2), which cannot be ruled out as a minor component of Ta-t, but presumably will be less favoured, as its flatness would imply very large deviations from equivalence and considerable strain. We suggest that the 108-subunit model (1) is a possible structure for the capsid of TO-t (i.e. magnesium-soluble component 15), which could be present also in trace amounts in Ta-t preparations. This interpretation of the results would imply that the heterogeneity observed electrophoretically in Ta-t (75~/o component 13 and 25% component 14) is due principally to the possibility of encapsulating different combinations of RNA molecules within the same capsid (e.g. 2 x R N A - 4 , R N A - 4 + Z , or X in the case of Ta-t; Bol & Lak-Kaashoek, 1974). The fact that the size and shape distribution of components 13 and 14 of Ta-t are very similar (see Results section (c)) supports the idea that these components differ only in their RNA contents and not their capsid structures. Similarly, this heterogeneity would not be detectable in the photon correlation measurements, which are primarily sensitive to the external particle shape. The measured hydrodynamic radius of 140( _+2) A agrees fairly well with the value of 131 A calculated from the dimensions of the model derived by neutron-scattering. The very slight heterogeneity in the RNA content of Ta-t would not be sufficient to invalidate the assumption of monodispersity in the analysis of the neutron-scattering results and would also be difficult to detect in sedimentation experiments (although we find that the s value decreases with increasing proportion of component 14, depending on the exact fraction of Ta-t taken). If we now consider the alternative interpretation of the data, that Ta-t is a mixture of prolate shapes with mean size about 232 A x 232 A x 312 A, then firstly we note that, apart from the bacilliform structures with 114 or 132 subunits (which anyway would have diameters of only about 195 A), no other regular prolate structures with the required number of subunits can be built using the rules given above. Since the magnesium precipitation apparently specifically separates from total Ta preparations the bacilliform structures (Ta-b) and the spheroidal structures (Ta-t), this would imply that Ta-t consists of irregular capsid structures without symmetry. Deltahedra without symmetry apparently can be constructed; although of the required size, it is unlikely that there will be many possibilities because of constraints imposed by closure (Don Caspar, personal communication). A final possibility is that Ta-t capsids are composed of partially degraded protein, although there is no evidence that the quality of AMV
154
S. CUSACK ET AL.
coat protein obtained from Ta-t is lower than that from other components. In summary, we have shown that it is possible that there is a specific, if novel, structure for the Ta-t capsid. The alternative possibility, that a variety of structures exists, implies the possibility of forming non-symmetrical protein capsids that nevertheless are stable. In either case, the lower symmetry structures proposed here imply greater deviations from equivalent subunit interactions than are normally necessary in icosahedral structures. This is consistent with the concept of AMV coat protein being very flexible and prone to polymorphism, as already evidenced in its ability to form both icosahedral and cylindrical particles as well as different helical structures in the case of strain VRU (Cremers et al., 1981). The suggestion is that given the variety of possible protein-protein interactions apparently available, it is the protein-RNA interactions in combination with the particular conformation of the RNA being encapsulated that can in some cases determine the capsid shape. That the same capsid can contain different combinations of RNA of similar molecular weight is reasonable. What is more surprising is that the same combination of two RNA-4 molecules appears to be contained in two different capsids, Ta-t and Ta-b. A possible solution to this is that two RNA-4 molecules can combine with different degrees of inter- and intramolecular secondary structure. The resultant conformations could favour either the formation of capsids of the type Ta-t or Ta-b. Such an hypothesis could be tested by comparison of in situ crosslinked RNA from Ta-t and Ta-b. In suggesting that the protein penetrates deeper into the particle in the case of Ta-t than for bacilliform particles (Cusack et al., 1981; Oostergetel et al., 1983, accompanying paper), the neutron-scattering analysis would support the idea that the RNA was packed differently in the case of Ta-t. This might also help explain the different solubility with respect to magnesium. Finally, it is possible that the arguments developed here also apply to the structure of anomalous virions of other species. For example, the 150-subunit middle component of pea enation mosaic virus, recognized as unusual by Hull & Lane (1973), could very well be explained by the nearly spherical model with 5-fold symmetry described above. A similar situation could apply to the top component of tobacco streak virus (Ghabrial & Lister, 1974) and tulare mosaic virus (Lister & Saksena, 1976). This work was sponsored in part by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). The help of Dr M. Zulauf with the photon correlation measurements is gratefully acknowledged.
REFERENCES Bol, F. J. & Lak-Kaashoek, M. (1974). Virology, 60, 476-484. Brown, J. C., Pusey, P. N. & Dietz, R. (1975). J. Chem. Phys. 62, 1136-1144. Caspa.r, D. L. D. & Klug, A. (1962). Cold Spring Harbor Syrup. Quant. Biol. 27, 1-24. Chauvin, C., Witz, J. & Jacrot, B. (1978). J. Mol. Biol. 124, 641-651. Cremers, A. F. M., Oostergetel, G. T., Schilstra, M. J. & Mellema, J. E. (1981). J. Mol. Biol. 145, 545-561. Cusack, S., Miller, A., Krijgsman, P. C. J. & Mellema, J. E. (1981). J. Mol. Biol. 145, 525543.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
155
Ghabrial, S. A. & Lister, R. M. (1974). Virology, 57, 1-10. Glatter, O. (1980). J. Appl. Crystallogr. 13, 7-11. Heijtink, R. A. & Jaspars, E. M. J. (1976). Virology, 69, 75-80. Heijtink, R. A., Houwing, C. J. & Jaspars, E. M. J. (1977). Biochemistry, 16, 4684-4693. Hull, R. & Lane, L. C. (1973). Virology, 55, 1-13. Ibel, K. (1976). J. Appl. Crystallogr. 9, 630-643. Jacrot, B. & Zaccai, G. (1981). Biopolymers, 20, 2413-2426. Lister, R. M. & Saksena, K. N. (1976). Virology, 70, 440-450. Loenig, U. E. (1967). Biochem. J. 102, 251-257. May, R. P., Ibel, K. & Haas, J. (1982). J. Appl. Crystallogr. 15, 15-19. Mellema, J. E. (1975). J. Mol. Biol. 94, 643-648. Oostergetel, G. T., Krijgsman, P. C. J., Mellema, J. E., Cusack, S. & Miller, A. (1981). Virology, 109, 206-210. Oostergetel, G. T., Mellema, J. E. & Cusack, S. (1983). J. Mol. Biol. 171, 157-173. Schneider, D., Zulauf, M., Schafer, R. & Franklin, R. M. (1978). J. Mol. Biol. 124, 97-122. Timmins, P. & Jacrot, B. (1984), Neutron Scattering in Molecular Biology (Worcester, D. L., ed.), Elsevier/North Holland, Amsterdam, in the press. Van Beynum, G. M. A., De Graaf, J. M., Castel, A., Kraal, B. & Bosch, L. (1977). Eur. J. Biochem. 72, 63-78. Van VIoten-Doting, L. & Jaspars, E. M. J. (1972). Virology, 48, 699-708. Zulauf, M. (1977). J. Mol. Biol. 114, 259-266.
Edited by A. Klug
Structure of the Top a-t Component of Alfalfa Mosaic Virus A Non-icosahedral Virion STEPHEN CUSACK
European Molecular Biology Laboratory, Grenoble Outstation c/o ILL, 156X, 38042 Grenoble Cedex, France GERT T. OOSTERGETEL, PETER C. J . KRIJGSMAN AND JAN E. MELLEMA
Department of Biochemistry, University of Leiden Wassenaarseweg 64, 2333 A L Leiden, The Netherlands (Received 7 February 1983, and in revised form 4 August 1983) Neutron-scattering in combination with quasi-elastic light-scattering and electron microscopy was used to derive a model for the capsid structure of the Top a-t component of alfalfa mosaic virus (AMV-Ta-t). In the electron microscope, AMV-Ta-t appears as an irregular ellipsoidal particle with apparent dimensions 275(__+31) A x 225( _ 22) A. Assuming that the particles are monodisperse, model calculations show that the neutron-scattering data are best explained by an oblate ellipsoidal shape for the virion with external dimensions 284 A x 284 A × 216 A. Based on this result, and in combination with the known composition of the virion, it is suggested that the capsid structure could be based on a deltahedron with 52 pointgroup symmetry and comprising 120 subunits. Such a model would imply a greater deviation from equivalent subunit interactions than normally necessary in icosahedral capsids. The neutron and photon correlation data, however, do not allow us to rule out the possibility that Top a-t is a slightly polydisperse preparation of irregular prolate shapes with mean dimensions 312 A x 232 A × 232 A. Both possibilities support the concept of alfalfa mosaic virus coat protein being capable of a wide range of intersubunit interactions, this flexibility resulting in considerable polymorphism in capsid structures.
1. I n t r o d u c t i o n Alfalfa mosaic virus is a p l a n t virus whose genome is composed of four distinct, single-stranded R N A molecules each p a c k a g e d in s e p a r a t e protein capsids whose size is roughly proportional to the molecular weight of the R N A enclosed (Heijtink et al., 1977). We h a v e previously studied the largest particle, the b o t t o m c o m p o n e n t AMV-Bt, which has an overall length of a b o u t 600 A and is cylindrical with rounded caps (Cusack et al., 1981). Three other components, denoted AMV-M, AMV-Tb and AMV-Ta-b, have a similar shape to AMV-B b u t lengths of 430 A, 350 A and 310 A, respectively. The protein capsids of all these c o m p o n e n t s can well be understood within the t h e o r y of quasi-equivalence proposed b y Caspar t Abbreviations used: AMV, alfalfa mosaic virus; D, deuterium. 139 0022-2836/83/340139-17 $03.00]0 © 1983 Academic Press Inc. (London} Ltd.
140
S. CUSACK E T A L .
& Klug (1962), the cylindrical part being based on a hexagonal lattice of axial repeat about 84 A (and containing 36 protein subunits per repeat distance) and the rounded ends being half-icosahedra (Mellema, 1975; Cremers et al., 1981). The possible number of subunits forming such a structure is given by the formula 6 0 + 1 8 n , (n-- 0, l, 2 . . . ) . A fifth component of AMV, denoted AMV-Ta-t, does not fit into the above pattern. Although AMV-Ta-t and AMV-Ta-b co-sediment in the ultracentrifuge and have the same electrophoretic mobility, they can be separated on the basis of their different solubility in the presence of magnesium ions (Heijtink & Jaspars, 1976). AMV-Ta-t is soluble, whereas AMV-Ta-b precipitates. Although some minor RNA species have been detected in these particles, the majority of both AMV-Ta-t and AMV-Ta-b virions appear to contain two molecules of RNA-4 (Heijtink & Jaspars, 1976). On the electron microscope grid, AMV-Ta-b is cylindrical with rounded caps, whereas AMV-Ta-t appears ellipsoidal (Fig. 1). From measurements of total particle weight combined with estimates of the RNA content it has been deduced that there are about 132 subunits in the capsid of AMV-Ta-b and 120 in the case of AMV-Ta-t (Heijtink et al., 1977). The former value fits the above formula (when n = 4), whereas the latter does not. The above observations give rise to two interesting questions. Firstly, what is the structure of the capsid of AMV-Ta-t if it is neither icosahedral nor cylindrical?
FIG. 1. Electron micrograph of a negatively stained preparation of AMV-Ta-t. Magnification 120,000 x.
T O P a-t C O M P O N E N T
OF A L F A L F A
MOSAIC VIRUS
141
Secondly, is the R N A organized differently in AMV-Ta-t as compared to the bacilliform components? W e have used neutron-scattering, electron microscopy and a number of other physical techniques to try and answer these questions. 2. M a t e r i a l s
and Methods
(a) Virus culture, isolation and purification AMV strain 425 was grown and isolated as described by Van Vloten-Doting & Jaspars (1972) and the Ta-t component separated from the bacilliform components by precipitating the latter with magnesium ions according to Heijtink & Jaspars (1976). The preparation was then purified by one cycle of sucrose density-gradient centrifugation in a zonal rotor. Concentrations of purified virus were determined spectroscopically using ~260,m~'lmg/m___ l 4"69 (Heijtink et al., 1977). (b) Preparative electrophoresis The purified Ta-t preparation was separated into components 13 and 14 (Bol & LakKaaschoek, 1974) by preparative eleetrophoresis in 3 ~ (w/v) polyacrylamide gels (Loenig, 1967): 0.2 mg of purified Ta-t was applied to a gel of 14 cm length and 0.6 cm diameter and electrophoresis was carried out for 66 h at 4°C and 75 V (4 mA/gel). After scanning the gel at 260 nm using a Zeiss PMQ2 spectrophotometer with a ZK4 gel scanner, the appropriate slices were cut from the gel. The nueleoproteins were eluted from the gel slices by homogenizing in 0-5 ml of P E N buffer (0-01 M-sodium phosphate, 0"001 M-EDTA, 0.001 Msodium azide, pH 7"0) followed by shaking overnight and removal of the gel residues by centrifugation. The resultant components were examined in the electron microscope. (c) Analytical ultracentrifuqation The purified Ta-t preparation was analysed in a Beckman Spinco model E ultracentrifuge, using an AN/F Ti rotor at 29,600 revs/min at 12°C, the virus concentration being 6"3 mg/ml. (d) Photon correlation spectroscopy Translational diffusion constants were measured by the technique of photon correlation using an apparatus similar to that described by Zulauf (1977). Measurements were made at scattering angles of 30 °, 90 ° and 153.2 °, and the correlation functions analysed using the moment expansion method (Brown et al., 1975).
(e) Neutron-scattering Purified virus samples were dialysed against P E N buffer containing D20 proportions of 0, 45, 56, 74 and 100°/o. Using these samples, small-angle neutron-scattering measurements were made using instrument D11 at the Institut Laue-Langevin, Grenoble (Ibel, 1976). The following experimental conditions were used:
Concentration
Wavelength
Sample-detector distance
Collimation
2-7 3-10 40 40
10.00 9-85 9-85 4.58
9"79 10"53 2.53 2.53
10 10 5 10
(mg/ml)
(A)
(m)
(m)
S. CUSACK E T A L .
142
Data collected on the 64 cm x 64 cm detector were circularly averaged and normalized by monitor count and then treated in the following way to correct for background and detector response. A normalized detector response was obtained according to: ~,, [In(q) -- Talec(q) -- (1 -- Ta)Icd(q) ] D(q) = B , [numerator] . . . . . 8 . . . . . q
(1)
where the sum is over all buffer spectra Is(q) with suitably good counting statistics (usually the 0%o and 45% buffers), Icd(q) is the electronic background, IEc(q) the empty cell spectrum and Ta the transmission of the buffer relative to the empty cell. q is 4g/)~ sin (0/2), where 0 is the scattering angle and 2 is the wavelength. I t is here assumed that the scattering due to the buffers is flat (i.e. independent of q) and given by (May et al., 1982):
V I . ( q ) - Tflec
c. = L
4,+g
.... , ..... . - i-:-
(2)
where g = g()., ~/oD20) and ~b is the incident flux. In the case of pure incoherent scattering, g = 1 and this is to a very good approximation true for pure H20 at ), = 10 A, thus enabling the flux to be derived, g becomes less than 1 for buffers with high D20 content and even for H20 at shorter wavelengths (Jacrot & Zaccai, 1981; May et al., 1982). Values of ca for each %oD20 buffer were then used to correct the sample scattering curves (and put them on an absolute scale) according to:
l [ ! s ( q ) - TslEc(q)--(1- Ts)Icd(q ) l~°rr(q) = cTsd~dNA L D(q)
c . ( 1 - Ts)gs] (1 - TB)g B ]"
(3)
Here Is(q) is the measured sample spectrum, c is the sample concentration, d the sample cell thickness, N A Avogadro's number and T s the sample transmission. In eqn (3) it is assumed that the fiat background measured with the sample scattering is given in analogy with eqn (2) by:
4~,gs (4)
Cs = l -- Ts
In this way the extra incoherent scattering due to unexchanged protons in the sample compared to the corresponding buffer can be corrected for. This effect is proportional to the volume fraction occupied by the virus in the solution and thus is important only for the high concentration samples. Except at high D20 contents, g is a slowly varying function of the transmission and so gs/gs ~ 1 (May et al., 1982). The advantage of this method of analysis is that shorter measuring times may be used for the buffers (except those used for the detector response) as only a single cB value is required from them. The corrected neutron-scattering curve for AMV-Ta-t in 100%o D20 is shown in Fig. 2 as an example. At sufficiently small scattering angles, and for a monodisperse solution without interparticle interactions, the corrected scattering curve is given by the well-known Guinier approximation: i~.rr(q) = 1(0) exp ( _ ~ . ~ ) '
(5)
where R 8 is the radius of gyration and I(0), the intensity at zero angle, is given by:
i,o,= M
B
~
2
(6)
TOP a-t COMPONENT OF A L F A L F A MOSAIC VIRUS
*n
143
I
.J 0
--I
-2
-5
0"00
0"04
0208
OJ'2
0:'6
0"20
q(I/RI
Fro. 2. N e u t r o n - s c a t t e r i n g curve f r o m A M V - T a - t in 100% D 2 0 . T h e curve is c o n s t r u c t e d by
combining the data sets obtained at a sample to detector distance of 10.53 m, 2-53 m and 2.53 m and a wavelength of 9.85 A, 9.85 A and 4,.58 A, respectively.
Here M r is the particle molecular weight, B / M is the scattering length per unit molecular weight of the particle, ~ is the particle partial specific volume and bs is the solvent scattering length density. Guinier plots of In (I(q)) against q2 enable both Rg and I(0) to be derived. In general: (]A (q)[2)spherical . . . . .
/~orr(q) =
ge,
(7)
where the angular dependence is given by the spherical average of the modulus squared of the scattering amplitude A (q). The latter is related by Fourier transformation to the excess scattering length density in the particle b(r)-bs: A(q) = S (b(r)-bs) e iq'r d3r.
(8)
v
An automatic least-squares technique (using a modified version of the program described by Schneider et al. (1978)) was used to fit homogeneous shell models representing the particle scattering length density distribution to the corrected spectra at each D20 contrast. As discussed by Cusack et al. (1981), the effect of instrumental smearing can be taken into account during this procedure. The most satisfactory models used were ellipsoids of revolution. The scattered intensity for a homogeneous ellipsoid of revolution with axial ratio u is given by: 1
I(q) = I(0) S dz gb2[qRx/l +z2(u - 1)], 0
where: ¢(x)=
3(s-inx-xc°sx) x3
(9)
144
S. CUSACK ET AL.
and the corresponding radius of gyration is: R~ = R ~ 5 . It should be noted that for an ellipsoidal shell model in which the shells are of uniform thickness (as used here), the axial ratios of the internal shells differ from that of the external shape. (f) Electron microscopy
For electron microscopy, AMV was fixed at 4°C overnight by dialysis against PEN buffer containing l~o (v/v) formaldehyde and negatively stained with 1% (w/v) uranyl acetate on normal carbon films.
3. Results (a) Analytical ultracentri fugat ion The virus preparation showed only one peak in the schlieren pattern upon sedimentation in the ultracentrifuge (Fig. 3). The calculated sedimentation coefficient S~O.w was 65.4S, which is in good agreement with the value of 66.0(+_0.9) S measured by Heijtink et al. (1977). (b) Photon correlation The translational diffusion constant D~0.w and the corresponding hydrodynamic radius R H = kaT/6u~lD~o.w was found to be independent of scattering angle (Table 1). The value of (1.52__0.02)× l0 -~ cm~/s for D~o.w is essentially the same as measured previously (Oostergetel et al., 1981). Also given in Table 1 are the values of the normalized second moment
FIo. 3. Schlieren patterns of AMV-Ta-t; lower: purified preparation used for neutron-scattering, photon correlation spectroscopy, electron microscopy and electrophoresis; upper: preparation containing Ta-t and TO-t. Sedimentation is from right to left. The photograph was taken ~25 min after reaching a speed of 29,600 revs/min.
T O P a-t C O M P O N E N T
OF ALFALFA
MOSAIC
VIRUS
145
TABLE 1
The diffusion constant D~o' w, normalized second moment #2 and hydrodynamic radius Ru of A M V Ta-t at three different scattering angles Scattering D,o w angle (°) (x 10- 7 s/cm 2) 30 90 153.2
~2
R H (A)
1.57+0.04 --0.14+0.07 136+4 1.52+.0.02 --0"01+0"02 140+2 1.52+0.02 0-02+0-01 140+2
#2 = ( ( D 2 ) - ( D ) 2 ) / ( D ) 2, which can be derived using the moment expansion method of data analysis (Brown et al., 1975). ~2 has a value of at most a few percent (except at the scattering angle of 30 ° , where the measurements are less reliable). This is generally assumed to be compatible with a monodisperse solution (within the statistical accuracy of the measurements) although not sufficient evidence to prove that it is. (c) Electron microscopy As shown in Figure l, AMV-Ta-t appears in the electron microscope as an irregular ellipsoidal particle with apparent dimensions 275( + 31)A × 225( + 22)A. Figure 4 gives the distribution of the lengths and the widths of the projected shapes. This virus preparation, after purification by sucrose density-gradient centrifugation, still contains the two electrophoretic components 13 and 14 (Fig. 5). After separation of these two components by preparative electrophoresis, no difference in the distribution of the projected shape could be detected by electron microscopy when plotted in a way similar to that shown in Figure 4. It should be remarked that in the absence of any artifacts introduced by the microscopy, the different projections possible of an oblate ellipsoid of revolution would produce a vertical line (constant length) in the plot of Figure 4, whereas those of a prolate ellipsoid would produce a horizontal line (constant width). The results correspond to neither of these ideal cases. This could be due to shrinkage or flattening artifacts resulting from sample preparation for the electron microscope and/or because the sample is actually polydisperse. In the latter case, a number of possibilities could be envisaged but not distinguished; for example, a shape distribution (particles of constant volume but with a distribution of axial ratios) or a size distribution (particles of the same axial ratio, but different sizes). (d) Neutron-scattering (i) Low-angle regime Guinier plots of the low-angle data show a strong dependence on concentration of the radius of gyration and extrapolated intensity at zero angle I(0). Radii of gyration typically increased by 10% on decreasing the concentration from 7 mg/ml to 1-7 mg/ml. This effect is attributable to strong electrostatic
146
S. C U S A C K E T A L . 500
/
-
/
/
250 a~
K
,~,
/
II I
200
/ x
, = == ~ ' ~ , , , ~ x x x~x x
x
~
xx
x
x
x ~
/
x
/
x
~
x
/
~x
,=, x
* ,= ,=,
w
x
x ~xxxxK
xxxx x
x
x
x
x xx
x
x x
x
. x
x
x
/ /
150-1
l
I
0
IO
20
50 3020-
IO-
0 r
,
i
1
,
,
I
150
I
i
I
I
!
400
Length ( ~ ) Fro. 4. Distribution of the largest and smallest dimension of Ta-t particles as measured from a n electron micrograph of a negatively stained preparation. Each cross represents a measured particle. Histograms of the larger and smaller diameters are placed along the horizontal and vertical axis, respectively.
interparticle interactions that are not adequately screened in the low ionic strength buffer used. Insufficient data were collected to allow a reliable extrapolation to zero concentration, and so R 8 and I(0) were derived from the fitting of models to the higher angle data (see below).
=e 0 tO O4
0
0 .ID
Migration
>
FIG. 5. Densil~ogram of a polyacrylamide gel showing the composition of the AMV-Ta-t preparation. The ratio of component 13 to component 14 is about 3 : 1. A small amount of component 15 is present.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
147
(ii) Particle shape and dimensions The ultracentrifuge and photon correlation results are consistent with the preparations being monodisperse although, as mentioned above, electron micrographs of the virions are suggestive of a more polydisperse sample and there are known to be two electrophoretic components present. In the following analysis of the neutron data we first explore the assumption that the particles are indeed identical. The possibility of polydispersity will be discussed subsequently. With the assumption of monodispersity, it is obvious from the lack of multiple pronounced maxima in the scattering curve of Figure 2 that the particles are not spherical. Furthermore, prolate ellipsoidal shapes with axial ratios in the range suggested by the electron microscopy results also have maxima that are too pronounced (see Fig. 8 and section (d)(iv), below). Oblate ellipsoids, on the other hand, can have much less distinct scattering curves. Calculations based on oblate ellipsoids of revolution enable the central and first subsidiary maximum (i.e. up to q = 0.06A -1) to be fitted very well, and also give the correct position of the second subsidiary maximum (see Fig. 6). The agreement could be improved and extended to q ~ 0-08 /k -~ by letting the third axis of the ellipsoid vary. However, it is doubtful whether this additional shape parameter is of real physical significance as, firstly, the information given by the model fits on the forward scattering, the radius of gyration and the internal structure (see below) were very similar for ellipsoids of revolution or general ellipsoids and, secondly, neither shape could satisfactorily fit the data beyond q ~ 0.09/~- 1. Related to this latter point is the occurrence of a maximum in the scattered intensity at about q = 0.16A -1 observable in both 0% and 100% D20. A marked peak in this 5 432I
~
-J
o
lllllllll
-I -2
-4-5 0.00
o-'o2
0.~4
o-'06
o-'os
o.lo
q (~,-~) FIo. 6. Fits to the neutron-scattering data of Ta-t in 0% (O), 45% (@), 56% (O), 74% (r-I) and 100% D20 (1). The model used was an oblate ellipsoid of revolution containing 3 shells. The semiaxes of the model are 142 A x 142 A x 108 A and the 2 internal shell boundaries have semi-axes of
134Ax134AxlOOAand87 Ax87 Ax53A.
148
S. C U S A C K E T A L .
position has been observed from all AMV virions so far studied (Cusack et dl., 1981; Oostergetel et al., 1983) and corresponds to the intersubunit interference arising from the capsid surface lattice. Clearly no homogeneous shell model can be expected to reproduce the measured intensity to this resolution. The external dimensions of the ellipsoid of revolution best fitting the data are 284/~ x 284 A x 216 A, corresponding to an axial ratio of 0-76. These dimensions could be changed by up to 3% without significantly affecting the quality of the fits. However, all models (ellipsoid of revolution or general ellipsoid, two or three shells) led to very similar results for the total volume of the particle envelope (9.0_+0.2) x l06 A 3 and the forward scattered intensity and radius of gyration as a function of contrast. These values are tabulated below. D20 (%)
(~g)
1(0) (10-23 cm2/daiton)
0 45 56 74 I00
104.5__+ 1 46 ___+5 113-0 __+1 108.5__+0.5 107.4 + 0 . 5
360"0--+3 0.43 + 0-03 12.0__+0"5 124-3__+0-5 460.0 + 3
18-97 0-66 --3"5 --11-15 -- 21.45
A plot of I(0) against the fraction of D20 gives an excellent straight line with matchpoint 46-8(_+0-5)O/o D20. According to equation (6), I(0) can be calculated from the composition and partial specific volume of the particle. Assuming that AMV-Ta-t contains 15-6°/o (Heijtink et al., 1977) by weight RNA (scattering length/unit mass (3.25 +0.92x) × 10-14 cm/dalton, where x is the fraction of D20 ) and 84-4% protein (scattering length/unit mass (2.32 + 1-45x) × 10-14 cm/dalton, calculated from the sequence (Van Beynum et al., 1977) and assuming 10% nonexchangeability of the "exchangable" protons) and a partial specific volume of 0.703 cm3/g (Heijtink et al., 1977), the calculated matchpoint is 46.2~/o D20, in good agreement with that observed. The particle weight deduced from these results is 3"67(_+0.05) x 106 Mr. This is about 3% higher than that determined by hydrodynamic methods (Oostergetel et al., 1981). A Stuhrmann plot of the radii of gyration again shows a good straight line, demonstrating the consistency of the data. The radius of gyration at infinite contrast is 106.0( _+0.1)/~ and the negative slope indicates that denser material (RNA) is in the interior. (iii) Internal structure The shell model-fitting method in principle allows one to deduce information about the internal structure of particles in cases where the scattering length density is compartmentalized into more or less distinct regions (Chauvin et al., 1978; Schneider et al., 1978; Cusack et al., 1981; Timmins & Jacrot, 1983). In the present case, the procedure is limited by the inability to obtain good fits beyond about q -- 0-06 A-1 without the introduction of an unjustifiably large number of parameters. A set of consistent model fits to five contrasts is shown in Figure 6 and the linearity with contrast of the excess scattering length density found in each shell is demonstrated in Figure 7. The semi-axes of the oblate ellipsoidal model are
TOP a-t COMPONENT
g-
OF ALFALFA
MOSAIC VIRUS
149
3
I
E u I o v
-i-
--2-
o~
{D
-3
o.o
o:2
i
o14
0.6
o18
1.0
Fraction D20
Fro. 7. The variation of scattering length density with contrast derived from the model fits shown in Fig. 4. ( 0 ) Inner region; ( , ) intermediate shell; (A) outer shell.
142 A x 142 A x 108 A, and the two internal shell boundaries have semi-axes 134 A x 134 A x 100 A and 87 A x 87 A x 53 A. The inner region has a match-point of 69.7(± 1.3)% D20, suggesting that it is pure RNA. The central shell has a match-point of 43.5(±0.8)~/o D20 and is therefore mainly protein but with a small percentage of RNA. The thin outer shell, which has a match-point of 50-0(± 1"0)~/o D20, was introduced to take account of the fact that when the external dimensions of the particle were allowed to float in the fitting procedure, they were consistently less in the case of the 56% data. This same situation arose in the analysis of the neutron scattering data of the VRU strain of AMV (Oostergetel et al., 1983, accompanying paper) and is interpreted there as indicating a higher proportion of hydrophilic residues (80%) to hydrophobic residues (20~o) in the external region of the protein. There, as here, the alternative explanation that there is RNA penetrating to the surface leads to a too high content of RNA in the particle, whereas the interpretation of the scattering density distribution given above leads to an RNA content of 16.5%, in close agreement with that quoted by Heijtink et al. (1977). It should be remarked that, although the model just described gives the best fit to the data, almost as good results are obtained by different decompositions of the internal structure (while maintaining the same external dimensions). The overall conclusion is that protein extends about 55 A in from the surface of the particle and that a small percentage of the RNA interpenetrates into internal regions of the protein capsid. (iv) Polydispersity I f we now consider the possibility of polydispersity in the sample, the analysis of the neutron data is more difficult as we do not know the nature of the polydispersity (e.g. whether due to shape or size, with a continuous or discrete
S. CUSACK ET AL.
150
_1
0.00
I
I
I
I
0.02
0-04
0"06
0.08
O. I0
q(I/~l Fro. 8. In both curves the crosses are the experimentally measured neutron data for Top a-t in 100% D20. The lines are calculated curves for a prolate ellipsoid of revolution of dimensions 312 A x 232 A x 232 A, (top) with normal wavelength smearing (A)./).= 0.09), (bottom) with increased wavelength smearing (A2/). -- 0.18).
distribution). Small-angle scattering is very sensitive to polydispersity but its effect is to smear scattering curves in a similar way to t h a t arising from a wavelength distribution of the incident beam (Glatter, 1980). Thus, in the modelfitting procedure for analysing the neutron d a t a from D11, the wavelength spread is normally fixed with A;t/2 (FWHM¢) = 0.09. I f this p a r a m e t e r is free to v a r y in the least-squares fitting process, polydispersity effects can be simulated. Using this method, the neutron-scattering curves were re-analysed using the mean dimensions from electron microscopy as a starting point for refinement, b u t assuming t h a t they corresponded to a prolate ellipsoid of revolution and allowing the possibility of polydispersity. As shown, for example, in Figure 8, fits comparable in quality to those of Figure 6 can be obtained with a prolate shape of mean dimensions 232 A × 232 A × 312 A (slightly larger than the electron microscopy values) provided t h a t A~/2 was increased to 0.18 (FWHM). Assuming t h a t the polydispersity was due to only size, not shape, and had a Gaussian form, this would correspond to a fractional standard deviation (ar/R) of 0.065, which is to be compared with the corresponding value of about 0-1 according to electron microscopy. Thus, this possibility would be consistent with the electron microscopy measurements, allowing for some shrinkage and distortion in the sample preparation. Since for a size distribution of identically shaped particles the
t (FWHM), Full width at half maximum.
T O P a-t C O M P O N E N T
OF A L F A L F A
MOSAIC V I R U S
151
normalized second m o m e n t of the diffusion constant is given by/~2 = (aR/R) z, the value of 0.004 for /~2 implied by this distribution is also compatible with the photon correlation results. Of course, it is not possible to deduce the nature of the polydispersity (whether size, shape, continuous or discrete) from the neutron data. The argument given above serves only to show that the photon correlation results do not rule out a narrow distribution which, however, is detectable by small-angle scattering. 4. Discussion
It has long been recognized that preparations of AMV strain 425 nucleoproteins contain four major and at least 13 minor electrophoretic components (Bol & LakKaashoek, 1974), and that a further splitting of some of these components can be made on the basis of solubility in the presence of magnesium (Heijtink & Jaspars, 1976). These authors pointed out that magnesium seems to preferentially precipitate bacilliform particles, that is those with 60+ 18n protein monomers in their capsids. Thus, they were able to identify Ta-b (i.e. magnesium-insoluble components 13 and 14) with the capsid consisting of 132 subunits (n = 4) and TO-b (magnesium-insoluble component 15) with the 114 subunit capsid (n = 3). The magnesium-soluble components 13 and 14 (constituting Ta-t) were recognized to be anomalous in their number of subunits (about 120), but apart from describing them as irregularly spheroidal no attempt was made to propose a capsid structure for these particles. The results of the present study unfortunately do not resolve the question as to whether Ta-t particles have a unique capsid structure or not, although in the latter case the polydispersity must be small to be compatible with all the data. Successful crystallization of Ta-t particles may be the only way to resolve this problem. The assumption of monodispersity leads to the possibility that Ta-t has an oblate ellipsoidal shape, whereas allowance of some polydispersity implies that prolate shapes cannot be ruled out. In the following discussion we consider the problem from another viewpoint by asking what kind of capsid structures can be built out of about 120 subunits? Hitherto all simple virus capsids have been found to conform to either helical or icosahedral designs (or a combination of both, as in the case of the bacilliform particles of AMV). The reason for this is that these symmetries allow structures to be built from identical subunits that minimize the deviations from equivalent subunit interactions. Assuming that intersubunit interactions are predominant, these structures are likely to be of the lowest energy (Caspar & Klug, 1962). If we no longer restrict attention to isometric (i.e. spherical) capsids, then a variety of deltahedra (i.e. polyhedra with triangular faces) of lower symmetry than icosahedral are conceivable, some of which could account for the irregularly spheroidal particles of AMV. Starting from the observation that AMV protein is able to form bacilliform surface lattices with both five- and sixfold vertices and three subunits per triangular face (i.e. one dimer per edge), we ask what other lattices are possible if we preserve these characteristics but relax the need for ieosahedral or helical
152
S. CUSACK E T A L .
Q (a)
(b)
(c)
Fro. 9. Models of non-icosahedral structures visualized as projections along symmetry axes. (a) Model for a structure with 32 pointgroup symmetry, containing 108 subunits. (b) Model for a structure with 222 pointgroup symmetry, containing 120 subunits. (c) Model for a structure with 52 pointgroup symmetry, containing 120 subunits. s y m m e t r y ? Using Euler's t h e o r e m t , it is s t r a i g h t f o r w a r d to show t h a t deltahedra with 12 fivefold vertices (necessary for closure) and m sixfold vertices m u s t h a v e 60 + 6m subunits. The bacilliform structures clearly fit this f o r m u l a when ~n = 3n, their particularly being t h a t there are two groups of six linked fivefold vertices forming the two half icosahedra at the ends of the particle. Figure 9 shows three oblate structures built according to the less stringent rules just described. These can be described in t e r m s of the linking of the 12 fivefold vertices and the a p p r o x i m a t e axial ratios. (1) A structure with 32 p o i n t g r o u p s y m m e t r y of 108 subunits (m = 8), in which there are three groups of four fivefold vertices. The axial ratios are a p p r o x i m a t e l y 1 : 1:0-65. (2) A structure with 222 pointgroup s y m m e t r y of 120 subunits (m = 10), whose fivefold vertices are a r r a n g e d in four groups of three (or 2 groups of 6). Axial ratios 1 : 0 . 8 1 : 0 - 4 2 . (3) A structure with 52 pointgroup s y m m e t r y of 120 subunits, in which the fivefold vertices are grouped according to l, 5, 5, 1. Axial ratio 1 : 1 : 0.77. t Euler's theorem relates the number of edges (E), faces (F) and vertices (V) of a polyhedron according to F+ V = 2+E.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
153
We have not been able to build other regular structures of this kind in this size range (apart from the bacilliform structures with 96, 114 or 132 subunits). However, one can expand structure three into a 150-subunit model (m = 15: still with 52 pointgroup symmetry) by adding a ring of five sixfold vertices between the two rings of five fivefold vertices. The axial ratios of this nearly spherical, but oblate, structure are l : 1 : 0.90. If we accept the hypothesis of a unique and regular capsid structure for Ta-t, then model (3) is an obvious candidate for it. The experimental evidence for this identification is; firstly, the correspondence of the number of subunits (120); and secondly, that the size and axial ratio of Ta-t determined by neutron-scattering (assuming monodispersity) agree remarkably well with that of the model. The only other possibility in this size range is model (2), which cannot be ruled out as a minor component of Ta-t, but presumably will be less favoured, as its flatness would imply very large deviations from equivalence and considerable strain. We suggest that the 108-subunit model (1) is a possible structure for the capsid of TO-t (i.e. magnesium-soluble component 15), which could be present also in trace amounts in Ta-t preparations. This interpretation of the results would imply that the heterogeneity observed electrophoretically in Ta-t (75~/o component 13 and 25% component 14) is due principally to the possibility of encapsulating different combinations of RNA molecules within the same capsid (e.g. 2 x R N A - 4 , R N A - 4 + Z , or X in the case of Ta-t; Bol & Lak-Kaashoek, 1974). The fact that the size and shape distribution of components 13 and 14 of Ta-t are very similar (see Results section (c)) supports the idea that these components differ only in their RNA contents and not their capsid structures. Similarly, this heterogeneity would not be detectable in the photon correlation measurements, which are primarily sensitive to the external particle shape. The measured hydrodynamic radius of 140( _+2) A agrees fairly well with the value of 131 A calculated from the dimensions of the model derived by neutron-scattering. The very slight heterogeneity in the RNA content of Ta-t would not be sufficient to invalidate the assumption of monodispersity in the analysis of the neutron-scattering results and would also be difficult to detect in sedimentation experiments (although we find that the s value decreases with increasing proportion of component 14, depending on the exact fraction of Ta-t taken). If we now consider the alternative interpretation of the data, that Ta-t is a mixture of prolate shapes with mean size about 232 A x 232 A x 312 A, then firstly we note that, apart from the bacilliform structures with 114 or 132 subunits (which anyway would have diameters of only about 195 A), no other regular prolate structures with the required number of subunits can be built using the rules given above. Since the magnesium precipitation apparently specifically separates from total Ta preparations the bacilliform structures (Ta-b) and the spheroidal structures (Ta-t), this would imply that Ta-t consists of irregular capsid structures without symmetry. Deltahedra without symmetry apparently can be constructed; although of the required size, it is unlikely that there will be many possibilities because of constraints imposed by closure (Don Caspar, personal communication). A final possibility is that Ta-t capsids are composed of partially degraded protein, although there is no evidence that the quality of AMV
154
S. CUSACK ET AL.
coat protein obtained from Ta-t is lower than that from other components. In summary, we have shown that it is possible that there is a specific, if novel, structure for the Ta-t capsid. The alternative possibility, that a variety of structures exists, implies the possibility of forming non-symmetrical protein capsids that nevertheless are stable. In either case, the lower symmetry structures proposed here imply greater deviations from equivalent subunit interactions than are normally necessary in icosahedral structures. This is consistent with the concept of AMV coat protein being very flexible and prone to polymorphism, as already evidenced in its ability to form both icosahedral and cylindrical particles as well as different helical structures in the case of strain VRU (Cremers et al., 1981). The suggestion is that given the variety of possible protein-protein interactions apparently available, it is the protein-RNA interactions in combination with the particular conformation of the RNA being encapsulated that can in some cases determine the capsid shape. That the same capsid can contain different combinations of RNA of similar molecular weight is reasonable. What is more surprising is that the same combination of two RNA-4 molecules appears to be contained in two different capsids, Ta-t and Ta-b. A possible solution to this is that two RNA-4 molecules can combine with different degrees of inter- and intramolecular secondary structure. The resultant conformations could favour either the formation of capsids of the type Ta-t or Ta-b. Such an hypothesis could be tested by comparison of in situ crosslinked RNA from Ta-t and Ta-b. In suggesting that the protein penetrates deeper into the particle in the case of Ta-t than for bacilliform particles (Cusack et al., 1981; Oostergetel et al., 1983, accompanying paper), the neutron-scattering analysis would support the idea that the RNA was packed differently in the case of Ta-t. This might also help explain the different solubility with respect to magnesium. Finally, it is possible that the arguments developed here also apply to the structure of anomalous virions of other species. For example, the 150-subunit middle component of pea enation mosaic virus, recognized as unusual by Hull & Lane (1973), could very well be explained by the nearly spherical model with 5-fold symmetry described above. A similar situation could apply to the top component of tobacco streak virus (Ghabrial & Lister, 1974) and tulare mosaic virus (Lister & Saksena, 1976). This work was sponsored in part by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). The help of Dr M. Zulauf with the photon correlation measurements is gratefully acknowledged.
REFERENCES Bol, F. J. & Lak-Kaashoek, M. (1974). Virology, 60, 476-484. Brown, J. C., Pusey, P. N. & Dietz, R. (1975). J. Chem. Phys. 62, 1136-1144. Caspa.r, D. L. D. & Klug, A. (1962). Cold Spring Harbor Syrup. Quant. Biol. 27, 1-24. Chauvin, C., Witz, J. & Jacrot, B. (1978). J. Mol. Biol. 124, 641-651. Cremers, A. F. M., Oostergetel, G. T., Schilstra, M. J. & Mellema, J. E. (1981). J. Mol. Biol. 145, 545-561. Cusack, S., Miller, A., Krijgsman, P. C. J. & Mellema, J. E. (1981). J. Mol. Biol. 145, 525543.
TOP a-t COMPONENT OF ALFALFA MOSAIC VIRUS
155
Ghabrial, S. A. & Lister, R. M. (1974). Virology, 57, 1-10. Glatter, O. (1980). J. Appl. Crystallogr. 13, 7-11. Heijtink, R. A. & Jaspars, E. M. J. (1976). Virology, 69, 75-80. Heijtink, R. A., Houwing, C. J. & Jaspars, E. M. J. (1977). Biochemistry, 16, 4684-4693. Hull, R. & Lane, L. C. (1973). Virology, 55, 1-13. Ibel, K. (1976). J. Appl. Crystallogr. 9, 630-643. Jacrot, B. & Zaccai, G. (1981). Biopolymers, 20, 2413-2426. Lister, R. M. & Saksena, K. N. (1976). Virology, 70, 440-450. Loenig, U. E. (1967). Biochem. J. 102, 251-257. May, R. P., Ibel, K. & Haas, J. (1982). J. Appl. Crystallogr. 15, 15-19. Mellema, J. E. (1975). J. Mol. Biol. 94, 643-648. Oostergetel, G. T., Krijgsman, P. C. J., Mellema, J. E., Cusack, S. & Miller, A. (1981). Virology, 109, 206-210. Oostergetel, G. T., Mellema, J. E. & Cusack, S. (1983). J. Mol. Biol. 171, 157-173. Schneider, D., Zulauf, M., Schafer, R. & Franklin, R. M. (1978). J. Mol. Biol. 124, 97-122. Timmins, P. & Jacrot, B. (1984), Neutron Scattering in Molecular Biology (Worcester, D. L., ed.), Elsevier/North Holland, Amsterdam, in the press. Van Beynum, G. M. A., De Graaf, J. M., Castel, A., Kraal, B. & Bosch, L. (1977). Eur. J. Biochem. 72, 63-78. Van VIoten-Doting, L. & Jaspars, E. M. J. (1972). Virology, 48, 699-708. Zulauf, M. (1977). J. Mol. Biol. 114, 259-266.
Edited by A. Klug