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Biochimica et Biophysica Ac

Regular paper

Divalent ion-dependent swelling of Tomato Bushy Stunt Virus:

A multi-approach study

R. Aramayoa, C. Merigouxb, E. Larquet a, P. Bronc, J. Perezd,

C. Dumase, P. Vachetteb, N. Boisset a,*

aInstitut de Mineralogie et de Physique de la Matiere Condensee, Universite Pierre et Marie Curie UMR7590 CNRS P7 IPGP,

Case Postale 115-75252 Paris Cedex 05, FrancebIBBMC, CNRS UMR 8619 Universite Paris-sud, Batiment 430, F-91405 Orsay Cedex, France

cUniversite Rennes I, UMR 6026 CNRS, Campus de Beaulieu, 35042 Rennes, FrancedSynchrotron SOLEIL, l’Orme des Merisiers, Saint-Aubin-BP 48, 91192 Gif-sur-Yvette Cedex, France

eCentre de Biochimie Structurale, CNRS UMR 5048, INSERM UMR 554, 29 rue de Navacelles, 34090 Montpellier, France

Received 3 March 2005; received in revised form 13 May 2005; accepted 19 May 2005

Available online 15 June 2005

This paper is dedicated to the memory of Dr. Jean Witz, initiator of the project, who died in 2003

Abstract

Time-resolved small-angle X-ray and neutron scattering (SAXS and SANS) in solution were used to study the swelling reaction of TBSV

upon chelation of its constituent calcium at mildly basic pH. SAXS intensities comprise contribution from the protein capsid and the RNA

moiety, while neutron scattering, recorded in 72% D2O, is essentially due to the protein capsid. Cryo-electron micrographs of compact and

swollen virus were used to produce 3D reconstructions of the initial and final conformations of the virus at a resolution of 13 A and 19 A,

respectively. While compact particles appear to be very homogeneous in size, solutions of swollen particles exhibit some size heterogeneity.

A procedure has been developed to compute the SAXS pattern from the 3D reconstruction for comparison with experimental data. Cryo-

electron microscopy thereby provides an invaluable starting (and ending) point for the analysis of the time-resolved swelling process using

the scattering data.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Icosahedral plant virus; Calcium ion; Structural transition; Time-resolved small-angle X-ray and neutron scattering; Cryo-electron microscopy; 3D

reconstruction

1. Introduction transitions of very complex supramolecular assemblies are

At various stages of their life cycle, icosahedral viruses

undergo large conformational changes, from assembly and

maturation to cell entry and decapsidation. These structural

0304-4165/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.bbagen.2005.05.020

Abbreviations: TBSV, Tomato Bushy Stunt Virus; cryo-EM, cryo-

electron microscopy; TEM, transmission electron microscopy; EDTA,

ethylene diamine tetracetic acid; SAXS, small-angle X-ray scattering; TR-

SAXS, time-resolved small-angle X-ray scattering; SANS, small-angle

neutron scattering; TR-SANS, time-resolved small-angle neutron scatter-

ing; FSC, Fourier shell correlation; CTF, contrast transfer function

* Corresponding author.

E-mail address: [email protected] (N. Boisset).

the focus of many biochemical and biophysical studies,

since a better understanding of their molecular basis can

offer, beyond the knowledge of crucial processes, a means

of blocking the replication cycle of the virus. Since 1978

and the first virus structure solved by X-ray crystallography,

several tens of structures have been determined of even very

large objects. However, the structure determination entirely

relies on the icosahedral symmetry, and all parts of the

virion which do not obey the symmetry are lost. This spatial

disorder often affects the RNA moiety and internal parts of

the viral capsid interacting with RNA. Furthermore, large

conformational changes are rarely amenable to crystallo-

graphic investigation.

ta 1724 (2005) 345 – 354

R. Aramayo et al. / Biochimica et Biophysica Acta 1724 (2005) 345–354346

Recently, remarkable progresses were made in the

understanding of a few processes of viral maturation, using

a variety of approaches [1]. We present here progresses

made in the study of an apparently very simple process, but

deceptively so, the divalent ion-dependent swelling of a

small plant virus, Tomato Bushy Stunt Virus (TBSV). We

use a combination of cryo-electron microscopy and scatter-

ing methods together with the results of landmark crystallo-

graphic studies performed in the early 1980s to study the

transition both structurally and kinetically.

Small isometric viruses possess an icosahedrally sym-

metric capsid comprising one or a few distinct protein

subunits encapsulating a molecule of nucleic acid [2]. For

recent reviews, see [3,4]. The crystal structure of many of

these viruses shows at the interface between subunits the

presence of divalent cations, mostly Ca2+ [5,6] but also

Mg2+ [7], which appear to play a critical role in virion

stability. Actually, conformational changes of these viruses

have been observed upon changes of pH and chelation of

divalent ions, resulting in a swollen form of the virion, long

before the first virus crystallographic structure was known

[8,9]. They were later observed by crystallography and

electron microscopy [6,10]. These conformational transi-

tions probably correspond to early stages of the virion

uncoating for RNA release in the infected cell.

The swelling of TBSV has been extensively investigated

by analytical centrifugation, fluorescence spectroscopy,

small-angle neutron and X-ray scattering, and biochemical

techniques [10,11]. TBSV was the first virus whose three-

dimensional structure was crystallographically determined

at a resolution of 2.9 A [12]. Following the determination of

the native conformation, the structure of swollen TBSV was

obtained at a resolution of 8 A [10]. The TBSV particle

consists of a single stranded RNA of Mr 1.5�106 Da inside

an icosahedral T=3 capsid made of 180 subunits of Mr

40,500 Da arranged in three different packing environments

(A, B, and C: A-type subunits pack around the fivefold axes,

whereas B- and C-type subunits alternate around the

threefold axes). Each subunit comprises two domains

connected via a hinge. The S-domains (170 residues) build

the spherical shell, while the P-domains (115 residues)

associate into 90 dimers (30 C–C and 60 A–B dimers),

radially projecting at the outer surface of the capsid. In the

expansion process, the domains appear to undergo rigid

body movements, preserving many subunit interactions but

leading to the formation of an opening at quasi-threefold

axes [10]. The N-terminal parts of the coat protein referred

to as the R-domain, amounting to ca. 25% of the chain,

which interacts through many basic residues with RNA as

well as the entire RNA, are invisible in electron density

maps of either compact or swollen virions, because they are

not icosahedrally ordered [13]. Low resolution neutron

diffraction studies of single crystals of compact virion

showed that most of the missing protein fraction is found in

an inner shell, while RNA lies between those two shells,

preferentially located below the 30 C–C dimers [14].

Finally, the overall radial distributions of RNA and protein

are conserved, with all radii increasing by ca. 22 A [11].

However, no information was available regarding the ki-

netics of the transition and its molecular mechanism.

A preliminary time-resolved small-angle X-ray scattering

(TR-SAXS) study has been performed using the X-ray beam

of a bending magnet at LURE [15]. Data analysis showed

that a final EDTA concentration of about 40 mM was

required to saturate the system (i.e. to yield kinetics

independent from EDTA concentration) and that, following

an initial lag-phase, an intermediate conformation at least

was involved in the swelling transition. Model-dependent

characterization of the intermediate suggested that the

transition most likely involved a class of intermediate

conformations, which was, on average, more swollen with

time. However, the available flux severely limited the

quality of the data, with a useful resolution of about 80 A

and a time resolution of 2 s. Furthermore, the paucity of

structural information regarding the RNA distribution

hampered the structural interpretation of the scattering data.

Therefore, we have undertaken a coupled approach of the

problem, combining scattering methods and 3D cryo-EM.

TR-SAXS experiments, using the very high flux of un-

dulator SAXS beamline ID02 at ESRF (Grenoble, France),

provided high quality data at a nominal resolution of about

25 A. Time-resolved small-angle neutron scattering (TR-

SANS) experiments were also performed on the SANS

instrument D22 at ILL (Grenoble, France) in a 72% D2O

buffer so as to mask RNA contribution and monitor more

specifically the protein capsid swelling. Finally, cryo-

electron microscopy was used to characterize the compact

and swollen forms of the virus at a resolution of about 15 A.

The present report focuses on the tools developed to

implement this combination of approaches as applied to the

native, compact structure of the virus, a prerequisite for a

meaningful interpretation of time-resolved studies in struc-

tural terms. A procedure was established to calculate the

small-angle scattering pattern of the 3D reconstructions,

thereby providing the missing link between EM derived

reconstructions and SAXS data.

2. Materials and methods

2.1. Virus preparation

TBSV was propagated in Datura stramonium. Plant

proteins were removed from the sap by precipitation at pH

4.8, and the virus was purified by two cycles of high and

low speed centrifugations. Stock viral solutions were

conserved at 30 to 60 mg/ml, in 20 mM sodium acetate

buffer containing 0.01% sodium azide. Solutions were

filtered through 0.22 Am Millex filters and were dialyzed

for 24 h against at least three changes of appropriate buffer

before use. All chemicals used were of analytical grade:

EDTA (tetrasodium salt) was from Sigma Chemical Co (St

R. Aramayo et al. / Biochimica et Biophysica Acta 1724 (2005) 345–354 347

Louis, USA), all others from Merck (Darmstadt, Germany).

Virus concentrations were measured by UV absorption

spectroscopy, using an extinction coefficient of A(260

nm)=5.2 cm2/mg [16].

2.2. Time-resolved X-ray scattering experiments

TR-SAXS patterns were recorded on instrument ID02

using the emission from an undulator at ESRF (Grenoble)

[17]. The sample to detector distance was 2.3 m, the

wavelength of the X-rays was k =0.995 A and data were

recorded over the angular range 0.02 A�1<Q <0.29 A�1

where Q =4ksinh/k (2h is the scattering angle). Mixing was

performed using a Biologic SFM3 stopped-flow mixer

described at http://www.biologic.info/rapid-kinetics/mixers.

html#mivers_7. Temperature was kept constant at 20 -C. A30 mg/ml solution of compact TBSV in 100 mM Tris–HCl,

5 mM CaCl2 buffer, pH 7.55 (Buffer A), was mixed with an

equal volume of Tris/EDTA buffer (100 mM Tris–HCl, 120

mM EDTA, pH 7.55). 110 frames of 0.1 s each were

collected at intervals following a geometrical series of

reason a =1.038 over a total time of 1518 s. Static patterns

of the compact and swollen viruses were recorded using 20

frames of 0.1 s each. The corresponding buffers were also

recorded and subtracted from the virus solution patterns

after proper scaling to the transmitted intensity. Scattering

curves were recorded using a CCD detector with X-ray

image intensifier [18].

2.3. Neutron scattering experiments

Neutron scattering patterns were recorded on the SANS

instrument D22 at the high flux reactor of ILL (Grenoble).

The sample–detector distance was 3.5 m, with a collimation

length of 8 m. The wavelength was 6 A with a 10%

bandwidth. All measurements were performed at 20 -C. A54 mg/ml TBSV solution was dialyzed for 3 days against

four changes of the appropriate 72% D2O buffer 100 mM

Tris–HCl, 5 mM CaCl2, pH 7.88 (pD 8.2). Mixing was

performed using a Biologic SF3 stopped-flow mixer in

which the measuring cell is a modified 1-mm path-length

Hellma quartz cell. Neutron scattering experiments were

performed in 72% D2O. The scattering pattern of the

compact virus used here was recorded after mixing the

above-mentioned solution with an equal volume (300 Aleach) of the dialysis buffer, together with buffer scattering,

using 8 frames of 100 s.

Data were processed using Grasp, a program written

by C. Dewhurst available at http://www.ill.fr/lss/grasp/

grasp_main.html, before averaging.

2.4. Modelling the missing N-terminal part of the capsid

protein

A contrast variation study of TBSV had been interpreted

in terms of a 3-layer model surrounding a central lumen

filled with solvent [16]. The agreement of the model with

our data recorded in 72% D2O was checked and found

satisfactory. We therefore used this model as a guide to

position the missing N-terminal residues. The position of

each residue was simply defined by that of its Ca atom, all

other atoms being located at the same point. This pseudo-

atomic model approximation was shown to leave the pattern

unchanged out to Q =0.13 A�1 (data not shown). The

position of each Ca was determined randomly under the

following constraints. First, two successive Ca atoms were

separated by 3.8 A. Second, the distribution of residues

among the three layers was translated in geometrical

constraints imposed to the reconstructed chains. The thick-

ness of the ‘‘RNA’’ layer is such that at least 9 residues are

required to cross it entirely. Since 9 residues yield a volume

fraction occupied by the protein already larger than that

predicted by the three-layer model of Chauvin et al. [16], we

kept the residue number fixed at this minimal value. This 9-

residue-long stretch was then systematically moved along

the crystallographically invisible part of the sequence. For

each position, we first estimated the scattering length

density associated with the protein moiety in each layer

by taking into account the actual contribution from each

residue.

Once all three chains were modelled, the whole capsid

was generated using icosahedral symmetry operators before

computing the scattering pattern using CRYSON software

[19,20]. We established that the precise position of each

residue had less impact on the scattering pattern than the

location of the 9-residue-long stretch along the sequence.

The configuration in which residues 1–24 are located in the

inner (third) layer (50 A–80 A radii), residues 25–33 within

the ‘‘RNA-rich’’ (second) layer and residues 34–387 in the

outermost layer was found to yield the best agreement with

the experimental data. In a subsequent step, various

configurations of the residues within their ascribed layer

were explored but no real optimisation procedure has been

implemented as yet. Finally, the models yielding the best

agreement were checked for the presence of major steric

conflicts with symmetry-related chains, in which case the

model was eliminated.

2.5. Cryo-electron microscopy

Compact TBSV was diluted in sodium acetate 20 mM

buffer, pH 5.9, MgCl2 50 mM, CaCl2 10 mM, while swollen

TBSV form was obtained after an overnight dialysis in

Tris–HCl 100 mM buffer, pH 7.5, EDTA 20 mM. For cryo-

electron microscopy, virus solutions were diluted to a

concentration of 1 mg/ml and deposited on 400 mesh holey

carbon-coated grids. After blotting with filter paper, the

grids were frozen by rapid plunging in liquid ethane and

were mounted and inserted in the microscope using a

nitrogen cooled side entry Gatan 626 cryoholder. Observa-

tions were carried out at a temperature of �180 -C in a

JEOL 2010F electron microscope equipped with a CRP

http:\\www.biologic.info\rapid-kinetics\mixers.html#mivers_7

http:\\www.ill.fr\lss\grasp\grasp_main.html

Fig. 1. TR-SAXS patterns of TBSV during swelling. The virus solution was

mixed with an equal volume of an EDTA-containing buffer. The final

EDTA concentration was 60 mM. Colors change gradually from the

compact virus pattern (blue) to the swollen virus pattern (red).


objective lens (Cs: 2.0 mm, Cc: 2.1 mm, focal length: 2.8

mm), using an accelerating voltage of 200 kV, with the

following illumination conditions: alpha 2, spot 2, 120 Amcondenser aperture and 70 Am objective aperture. Images

were recorded, using the MDS minimum electron dose

system (10 electrons per A2), with a magnification of

�50,000 on Kodak films So163. For each field, two images

were recorded using two different defocus values, one close

to focus for high resolution data recording and one further

from focus for a good visualization of particles.

2.6. Image processing and three-dimensional

reconstructions

Electron micrographs were digitised with a Nikon

Coolscan 8000ED at 10 Am/pixel, corresponding to a

nominal pixel size of 2 A. Data were processed as described

in [21]. Briefly, images were corrected for contrast transfer

effects, and focal pairs of images were combined using the

SUMPS and CTFMIX programs [21]. Particle origins and

orientations were determined and refined using the model-

based orientation determination method [22]. The TBSV

reconstruction was determined using as starting model the

structure of TBSV [12] computed at 40 A resolution. In the

case of swollen TBSV particles, the starting model was our

three-dimensional reconstruction of TBSV computed at 40

A resolution, rescaled to match with the main population of

particles having the bigger diameter (ca. 36 nm), and

scooped out in order to only include the outermost layer.

Density maps were calculated by Fourier–Bessel formalism

originally described by Crowther [23] and implemented in

the EM3DR program of Baker and Cheng [22]. Resolution

was estimated using Fourier Shell Correlation (FSC)

criterion with a cutting level of 0.5 (FSC0.5) [24,25]. We

determined 3D reconstructions of the compact and swollen

TBSV at 13 A and 19 A, respectively. For docking atomic

coordinates 2tbv from Protein Data Bank on EM volumes,

the Situs software [26] was used to fit 15 copies of trimers

ABC (one quarter of the total capsid) on the total compact

3D cryoEM volume. Then, the best fit found by Situs was

kept, and the whole capsid architecture was generated by

applying icosahedral symmetries on additional copies of the

aligned substructure. For surface representations of aligned

architectures, the aligned PDB volume was converted into

SPIDER format and was low-pass filtered to 13 A

resolution. A threshold density corresponding to the half

dynamic range was then applied to compute surface

representations of this filtered volume. Similarly, threshold

densities of EM volumes were chosen to give the best fit

with this reference volume.

2.7. Calculation of scattering patterns from EM

reconstructions

The simulation procedure to calculate scattering patterns

from cryo-EM 3D reconstructions was implemented using

SFALL, FFT, MAPROT, MAPMASK programs from the

CCP4 suite [27] and MAPMAN program [28]. It was

applied to the compact and swollen forms of TBSV virus

cryo-EM density maps.

3. Results and discussion

3.1. SAXS measurements

Fig. 1 shows X-ray scattering patterns recorded at

different times after mixing the virus solution in buffer A

with an equal volume of a 120 mM EDTA buffer. The very

high flux available on undulator beamline ID02 allowed

data collection over 0.1 s after a single shot (mixing) with

excellent statistics out to 0.22 A�1. The expected inward

shift of scattering patterns associated with swelling is

observed together with the two crossing points at

Q =0.0374 A�1 and Q =0.0575 A�1 reported by Perez

[15], but seen here with the greatest accuracy. Such high

quality data are both a boon and an impediment for

subsequent interpretation since no simplistic model will

account for the observed scattering pattern within exper-

imental uncertainty.

The system is complex since, beyond intrinsic complex-

ity of any structural transition, the virus comprises protein

and RNA moieties, both contributing to scattering patterns.

Qualitative information regarding the RNA location is

available from contrast variation in low-resolution neutron

crystallography [14], but there is no structure or even

reliable density distribution. Modelling RNA structure and

location in the capsid is therefore very difficult. Further-

more, even protein distribution is only partially known,

since the crystal structure left undetermined the location of

the 66 (C-chain) or 100 (A- and B-chain) N-terminal

residues [12]. To overcome these limitations, we used a

Fig. 3. Model of the completed trimer of coat protein in the compact virus.

Chain A: blue; chain B: violet; chain C: green. The crystal structure is

shown in ribbon representation while balls are used to display the modelled

N-terminal ends.


multi-technique approach. Cryo-EM study of native com-

pact virus provided precious information on RNA distribu-

tion within the capsid, while SANS simplified somewhat the

system. Indeed, taking advantage of the very different

scattering length of H2O and D2O, it is possible, by using

appropriate mixtures of normal and heavy water, to mask

protein or RNA moiety [29].

3.2. SANS measurements

Recording SANS data of TBSV in 72% D2O essentially

provided scattering from the protein fraction. Using

CRYSON software, we calculated the scattering pattern of

the part of the protein capsid solved by crystallography

(PDB entry 2tbv). The comparison between the experimen-

tal (black curve) and the calculated (blue curve) scattering

patterns is shown in Fig. 2. The minima and maxima are at

similar positions but the overall dynamic of the calculated

curve is larger, with intensities being much weaker at large

angles. This discrepancy is likely due to the contribution of

the missing part of the protein, thought to interact with RNA

through more than 10 positively charged residues in the N-

terminal part while also forming a second, smaller layer

below the RNA-containing layer at radii between 80 and 50

A. We therefore undertook to model this missing part in the

three chains of the asymmetric unit A, B and C so as to fit

the scattering pattern while satisfying several constraints as

exposed in the Material and methods section. The scattering

pattern of one of the best models is shown in Fig. 2 (red

curve) with the model displayed in Fig. 3. The agreement is

significantly better though not perfect, leaving room for

further improvement.

3.3. Cryo-electron microscopy and 3D reconstruction

For cryo-electron microscopy, two samples were pre-

pared with a TBSV concentration of 1 mg/ml. First,

Fig. 2. Comparison of the experimental SANS pattern of compact TBSV in

72% D2O with calculated curves from models. The blue curve is obtained

using the crystal structure (PDB file 2tbv). The red curve corresponds to the

coat protein trimer in which the missing N-terminal parts have been

modelled as shown in Fig. 3.

compact TBSV was diluted in a sodium acetate 20 mM,

pH 5.9 buffer, with MgCl2 50 mM and CaCl2 10 mM. These

salts were added to the buffer to prevent the natural

tendency of the virus to form bidimensional patches, and

to get large amounts of isolated particles in all possible

orientations within the ice layer. Second, swollen TBSV was

obtained from a stock TBSV solution in a sodium acetate 20

mM, pH 5.9, buffer after one night of dialysis against Tris–

HCl 100 mM, pH 7.5, buffer with EDTA 20 mM. For both

samples, selected fields were exposed twice to the electron

beam under low dose conditions, using defocus values

ranging from 1500 to 2000 nm for the first exposure, and

from 2500 to 3500 nm for the second exposure. In its

compact conformation, the TBSV appears as black particles

of homogeneous size (Fig. 4a), and 2500 particles were

extracted from five digitised micrographs. Conversely, the

swollen form of the virus exhibits a central hollow white

area and particles display some size heterogeneity (Fig. 4b).

Hence, twenty micrographs were necessary to collect a

significant amount of particles. After the digitisation of

micrographs, contrast transfer function (CTF) parameters

were estimated on their averaged power spectra, using

CTFZeros [21] and WEB softwares [30]. During particle

picking, two homologous image sets were extracted from

focal pairs and recombined after phase flipping using

CTFMIX [21]. The determination of Eulerian angles and

3D reconstructions were carried out in several refinement

Fig. 4. Cryo-electron microscopy of Tomato Bushy Stunt Virus in its compact (a) and swollen (b) conformations. (c) Surface representation of the 3D

reconstruction volume of the compact TBSV at 13 A resolution obtained from 2500 particles and using EM3DR. The volume is observed from outside and

from inside after removing the front half. (d) Fitting of the atomic coordinates from Protein Data Bank (2tbv) in cryo-EM 3D using Situs and Chimera

softwares. (e) Surface representation of the 3D reconstruction volume of the swollen TBSVat 19 A resolution obtained from 2500 particles and using EM3DR.

The volume is observed from outside and from inside after removing the front half. (f) Semi-transparent surface rendering of the swollen virus superposed with

the surface representation of the compact reconstruction volume (dark grey). The swelling from 32 nm to 36 nm is clearly visible between the two

conformations.


cycles using EMPFT and EM3DR softwares [22]. More

elaborate schemes are now available for CTF correction and

iterative computation of refined 3D reconstruction volumes.

However, we did not seek here subnanometric resolution of

the viral capsid, as TBSV is mostly composed of h-sheets,requiring a 4.5 A resolution to be correctly visualized [31].

The compact TBSV 3D reconstruction volume reached a

resolution of FSC0.5=1/13 A�1 within 6 cycles of centring

and angular assignment. The overall diameter of the particle

is equal to 32 nm (Fig. 4c left), and protruding domains of

capsid protein are well defined on the surface representa-

tions and seem in good agreement with atomic coordinates

from PDB (Fig. 4d). In a cutaway surface representation of

the back half virion, strong densities appear within the

reconstruction volume (Fig. 4c, right), that most likely

corresponds to the RNA molecule. The fact that this RNA

appears in the 3D reconstruction volume despite its lack of

icosahedric structure indicates that its location is constrained

within a given range of radii. This observation is in good

agreement with a model of radial distribution of RNAwithin

the central part of the viral capsid [16]. However, as we will

see in the next section, a spherical distribution of RNA is

not accurate enough to simulate SAXS data from cryo-EM.

The swollen TBSV 3D reconstruction volume reached a

resolution of only FSC0.5=1/19 A�1 within 8 cycles of

centring and angular assignment. The lower resolution of

this second 3D reconstruction volume is clearly visible in

the less defined structure of protruding domain on surface

representation of the capsid (Fig. 4e, left). This phenomenon

is most likely due to structural variations within the set of

swollen particles. This was confirmed using the approach of

White et al. describing the sorting of two sets of Hsp27

complexes, using multivariate statistical analysis (MSA)

[32]. Indeed, when subjecting the centered images of

swollen TBSV to MSA, the size heterogeneity was revealed

in one of the three first eigenvectors. Unfortunately, we did

not observe two or more defined classes of images, but a

continuous size variation among the image sets. Therefore,


the compact TBSV reference volume was interpolated to

produce the best fit with the largest image class of swollen

TBSV. All cryoEM images were then aligned on this

reference volume, but a selection of the largest ones was

carried out using their cross-correlation coefficient values

with this enlarged reference. The threshold cross-correlation

(CC) value used for this selection corresponds to (average

CC)� (2�r). A new reference volume was then computed

from this image subset and was used for further angular

refinements of the whole image population, and complete

cycles of alignment, sorting, and 3D reconstruction were

carried out iteratively. Three main differences are visible

when comparing this volume with the compact structure.

First, the overall diameter of the particle expanded from 32

nm for the compact to 36 nm for the swollen TBSV (Fig.

4f). Second, despite their less defined shape, a rotation of

the protruding capsid domains is visible around the 3-fold

axes (Fig. 4e, left), as already demonstrated by X-ray

crystallography [10]. Third, when considering inner parts of

the structure, RNA seems to have moved away from its

central position (Fig. 4e, right). This is even more visible on

radial density profiles computed from both volumes (Fig.

5a, asterisk and black dot).

Fig. 5. Radial plots of densities for the compact (dashed lines) and swollen

(continuous lines) structures of TBSV. (a) Curves obtained from exper-

imental cryo-EM 3D reconstruction volumes. (b) Curves obtained with the

scaling procedure using SAXS data. The swelling process is characterized

by the displacement (black arrows) of two peaks of radial densities to larger

radii. The inner presence (asterisk) or absence (black dot) of material,

presumably RNA, is also observed in these curves.

3.4. Simulated SAXS data from cryo-EM reconstruction

The scattering intensity I(Q) from a diluted monodis-

perse solution of macromolecules is an isotropic function of

the scattering vector Q proportional to the spherical average

of squared structure factors F(Q) of the scattering particle.

F(Q) can be expressed as the Fourier transform of excess

scattering density of the particle relative to the solvent.

The following procedure was established to calculate the

small-angle scattering profile of a particle from its 3D cryo-

EM reconstruction map and to optimise the fit with

experimental SAXS data. Few methods were developed

for computing small-angle scattering spectra from atomic

models. They are founded on the classical Debye’s equation

or the more practicable and efficient multipole expansion

method [19,20]. In the case of electron-density maps, a

method based on Fourier transform of the density map [33]

is an appropriate and efficient approach to obtaining I(Q),

and we applied it here. In contrast to cryo-electron micro-

scopy, solution X-ray scattering provides absolute and

accurate measurements of structure factor amplitudes of

particles in their natural room temperature aqueous environ-

ment. Testing the compatibility and accuracy of cryo-EM

models with SAXS data is a prerequisite to the combination

of these methods for the analysis of TBSV time-resolved

swelling process.

Cryo-EM density 3D maps were sampled at 3 A intervals

on a cubic grid in the CCP4 map format [27]. After various

corrections described below, the maps were subjected to a

Fast Fourier Transform algorithm as implemented in SFALL

program [27]. The structure factors values generated in the

range up to 1/20 A�1 were averaged within thin spherical

shells. A sufficient number of Fourier coefficients are

needed within each shell to ensure appropriate averaging.

Consequently, the pseudo cubic unit cell containing the

virus particle had large parameters, typically 1200 A. This is

also necessary to ensure that no interparticle vector will

contribute to the calculated scattering intensity. The

simulated scattering curve was then compared to exper-

imental SAXS data recorded on the compact and swollen

forms of TBSV.

The scattering pattern calculated using the original

density map from cryo-EM (circles) is shown in Fig. 6,

together with the experimental curve (dashed line).

Although both curves exhibit similar features, with marked

minima and maxima, their positions are not identical and

their overall dynamical ranges are significantly different.

Given a 3D cryo-EM density map, the procedure optimises

the fit of the corresponding simulated scattering curve to the

SAXS data using various scaling factors applied to the three

shells of the density map and an optimal electron density

contrast between the particle and the bulk solvent. First, a

threshold parameter derived from the radial density profile

(Fig. 5a) was estimated to isolate the particle envelope from

the solvent region, so that the selected voxels delineate the

expected volume of the viral particle. During cryo-EM

Fig. 7. Comparison of the experimental X-ray scattering curve of swollen

TBSV (dashed line) with the scattering curve calculated from the cryo-EM

density map after the optimisation procedure (continuous line).

Fig. 8. Comparison of the experimental neutron scattering curve of compact

TBSV in 72% D2O (dashed line) with the scattering curve calculated from

the cryo-EM density map masking shell 2 (see text for details).

Fig. 6. Comparison of the experimental X-ray scattering curve of compact

TBSV (dashed line) with the scattering curve calculated from the cryo-EM

density map before (circles) and after (continuous line) optimisation (see

text for details).


reconstruction, the surrounding density was set to an

arbitrary value. To account for the true electron density

contrast of the SAXS experiment, a scale factor was applied

to the particle density and the average density in solvent

region was set to zero. For this purpose, the average density

of the outermost layer corresponding to the capsid was set to

0.1 electrons/A3, a standard contrast between protein and

bulk solvent. This density-scaling factor was applied to the

two inner layers and subjected to further optimisation to

rescale the relative inner density fluctuations of these shells

(Fig. 5b). A small but significant improvement in the fit

with SAXS data was also obtained when the density of the

center of the particle (radius up to 20–25 A) was flattened

and set to the solvent density. Such density fluctuations in

the innermost region were not observed in previous data

[14,16]. The EM image magnification calibration may be

inaccurate, so that the absolute scale of the reconstruction

has to be determined. A shrink factor of 0.98 was adjusted

to optimise the fit to the SAXS data, and the density of the

external capsomer shell in the scaled cryo-EM map was

compared by cross-correlation within the low-resolution

electron density map calculated from the crystal structure of

the virus.

The choice of these scaling parameters was made by a

trial and error approach to optimise the fit with the first three

minima–maxima in the experimental scattering curve and

reduce the overall dynamical range difference (Fig. 6, black

line). The same magnification and density scaling factors

were used for the cryo-EM density map of the compact (Fig.

6) and swollen (Fig. 7) forms of TBSV. The contribution of

the contrast of the hydration layer [20] has not been

explicitly introduced in this preliminary procedure and has

probably a marginal contribution in resolution ranges used

here.

The procedure performs remarkably well on both the

compact and swollen forms of the TBSV particle, as judged

by the good fit, up to Q =0.18 A�1 (Figs. 6 and 7). Even in

the outermost parts of the pattern, all modulations are

closely in phase with the experimental ones, in spite of a

higher general level of intensity for the latter. This small

discrepancy between the computed and experimental

scattering curves can easily be corrected here using an

attenuation B-factor of 400 A2. The power spectrum of

reconstructed cryo-EM particles is affected by a spatial

frequency-dependent attenuation of amplitudes, the enve-

lope decay function, attributed to partial electron beam

coherence, microscope and specimen instabilities. Previous

studies indicated that such amplitude corrections were

clearly improved by using X-ray solution scattering data

[34–36].

Similar observations are made when comparing the

experimental SANS pattern in 72% D2O with the calculated

scattering pattern from the external protein layer together

with the thin third layer from the cryo-EM reconstruction

(Fig. 8).

3.5. Incorporating SAXS constraints in an optimal 3D

reconstruction procedure

One of the key steps in processing cryo-EM images is the

correction of the instrumental factors that affect the

maximum resolution achievable and generate inappropriate

weighting of amplitudes and distortions of the 3D single


reconstruction. As previously underlined [36,37], SAXS is a

unique tool to estimate the CTF and envelope decay

functions. An analogous strategy was used by other groups

to correct the amplitude scale factors and improve the

interpretability of cryo-EM 3D reconstruction maps [34,35].

Our results on TBSV demonstrate that a typical cryo-EM

reconstruction and solution X-ray scattering data yield

comparable structure factor profiles. We show that an

appropriate weighting of density fluctuations inside the

particle and an optimal scaling easily derived from this

procedure lead to a significant improvement of the fit

between these data. In macromolecular crystallography,

idealization in direct space is routinely used to improve the

phases of structure factors and relies on properties of the

electron density map: positivity, compact support, point-

group or axial symmetry, histogram matching depending on

the nature of the component (RNA, protein), and proper

solvent–particle contrast. The simultaneous application of

real and reciprocal space constraints using SAXS data

emerges as a tool to attenuate structural distortion problems

and improve the quality and compatibility of cryo-EM

density maps with X-ray data [26].

4. Conclusion

We have reported here our current progresses in the study

of an apparently simple divalent ion-dependent swelling

process of TBSV. Even at the present stage of the work, the

potential of mutual improvement of various approaches

clearly appears. While cryo-electron microscopy provides

very useful 3D reconstruction of particles, the inner

fluctuations of density are not as reliable as the volume

information and can be improved when taking into account

information from scattering methods directly obtained in

solution. Less prone to experimental artefacts, SAXS and

SANS suffer from limitations in the structural interpretation

and greatly benefit from external information from cryo-

EM, 3D models of course, but also information on particle

homogeneity in size (as in the case of the swollen form of

the virus). Coupling those two low-to-medium resolution

methods with the high-resolution results of crystallographic

studies further enhances the quality of the structural

interpretation of both cryo-EM reconstructions and scatter-

ing data. This multi-pronged approach advocated in a recent

review [38] is an obligate path to try and elucidate the nature

and mechanism of the conformational transitions that

viruses, these complex supramolecular assemblies, undergo

at key stages of their life cycle such as decapsidation or

maturation.

Acknowledgements

This work was partly supported by European Commis-

sion (NoE ‘‘3D-EM’’ contract No. LSHG-CT-2004-

502828). We acknowledge the European Synchrotron

Radiation Facility for the provision of synchrotron radiation

facilities and we would like to thank S. Finet and T.

Narayanan (ESRF) for assistance in using beamline ID02.

Similarly, we acknowledge the Laue-Langevin Institute for

the provision of neutron scattering facilities. And we are

grateful to I. Grillo, P. Timmins (ILL) and D. Durand

(IBBMC) for their help with the TR-SANS measurements

on D22. We are grateful to Region Ile-de-France for

convention SESAME 1999 E 1298 for the support to

cryoelectron microscope JEOL 2010F installed at the

Pasteur Institute.

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