Roi Asor1,1, Daniel Khaykelson1,1, Orly Ben-Nun-Shaul2, Ariella Oppenheim2, Uri Raviv1,1. 1. Institute of Chemistry and Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel. 2. Department of Haematology, The Hebrew University-Hadassah Medical School, Ein Karem, Jerusalem 91120, Israel.
Abstract
Multivalent ions affect the structure and organization of virus nanoparticles. Wild-type simian virus 40 (wt SV40) is a nonenveloped virus belonging to the polyomavirus family, whose external diameter is 48.4 nm. Calcium ions and disulfide bonds are involved in the stabilization of its capsid and are playing a role in its assembly and disassembly pathways. Using solution small-angle X-ray scattering (SAXS), we found that the volume of wt SV40 swelled by about 17% when both of its calcium ions were chelated by ethylene glycol-bis(2-aminoethylether)-N,N,N',N'-tetraacetic acid and its disulfide bonds were reduced by dithiothreitol. By applying osmotic stress, the swelling could be reversed. DNA-containing virus-like particles behaved in a similar way. The results provide insight into the structural role of calcium ions and disulfide bonds in holding the capsid proteins in compact conformation.
Multivalent ions affect the structure and organization of virus nanoparticles. Wild-type simian virus 40 (wt SV40) is a nonenveloped virus belonging to the polyomavirus family, whose external diameter is 48.4 nm. Calcium ions and disulfide bonds are involved in the stabilization of its capsid and are playing a role in its assembly and disassembly pathways. Using solution small-angle X-ray scattering (SAXS), we found that the volume of wt SV40 swelled by about 17% when both of its calcium ions were chelated by ethylene glycol-bis(2-aminoethylether)-N,N,N',N'-tetraacetic acid and its disulfide bonds were reduced by dithiothreitol. By applying osmotic stress, the swelling could be reversed. DNA-containing virus-like particles behaved in a similar way. The results provide insight into the structural role of calcium ions and disulfide bonds in holding the capsid proteins in compact conformation.
Viruses are evolved examples of self-assembled
structures that
are functional and sophisticated biological machines. Virus nanoparticles,
empty virus-like particles (VLPs), or polymer-containing VLPs (PC-VLPs)
may be fabricated into functional materials or nanostructure devices,
serve as protein nanocapsules, nanocarriers for metallic nanoparticles,
drug or gene delivery, biosensors, or as nanoreactors for catalysis.[1−9] The surfaces of virus nanoparticles present a complex, nonuniform
pattern of charged, polar, and hydrophobic residues, which can be
tuned by pH.[10]Wild-type simian virus
40 (wt SV40) is a spherical nonenveloped
virus belonging to the polyomavirus family, with an external diameter
of 48.4 nm.[11] Its capsid proteins encapsidate
a circular double-stranded (ds) DNA genome of 5243 base pairs that
is compacted by histone octamers to form a minichromosome-like structure
confined within the capsid. SV40 can be used for gene delivery and
is known to be capable of infecting nondividing cells, a major limitation
of many retroviral vectors used for gene transfer.[12]The capsid structure of wt SV40, resolved by cryo-TEM[13] and crystallography,[14,15] is an icosahedron with triangulation, T, number
7 (T = 7).[16] The capsid
is built of three different viral encoded proteins (VPs); VP1, VP2,
and VP3. Immediately following translation, five VP1 monomers assemble
through interdigitating β-strands, to form a tightly bound pentamer
(VP15),[14,17] which serves as the basic subunit
of the capsid. 72 VP1 pentamers, arranged in a T =
7d icosahedral symmetry, are forming the outer capsid
shell. A molecule of VP2 or VP3 per VP15 is located in
the internal part of the capsid and connects the capsid to the chromatin
core. VP1 pentamers occupy two different positions in the capsid shell;
12 pentamers, located at the 12 vertices of the icosahedral structure
are forming pentavalent centers, in which each pentamer is surrounded
by five other pentamers. The other 60 pentamers occupy hexavalent
positions, in which a single pentamer is surrounded by six pentamers.The crystal structures of the wt SV40 capsid[14,15] and other polyoma viruses revealed that the arrangement in a T = 7 icosahedral structure is facilitated by nonequivalent
contacts between adjacent VP1 pentamers. The different contacts, α,
α′, α″, β, β′, and γ
are facilitated by flexible carboxy (C) terminal arms that extend
from the jelly roll β-barrel VP1 cores. The flexible arms (66
amino acid long) are extended from each VP1 monomer and inserted into
a neighboring pentamer. The flexibility of the interactions between
identical pentamers enables the icosahedral symmetry of the capsid.
The C-arms contain an α-helix (amino acids 301–312) segment.
α- and β-contact interactions are predominantly hydrophobic
and occur between the helices (three in the α contact and two
in the β contact) of the monomers, taking part in the interaction.
γ interaction is a tight hydrophobic interaction between adjacent
surfaces of two monomers of neighboring pentamers. The different bonding
between adjacent pentamers is facilitated through different conformations
of a conserved pentapeptide hinge, KNPYP, through proline isomerization.[18]Calcium ions (Ca2+) and disulfide
bonds are involved
in the stabilization of the wt SV40 capsid and are playing a role
in its assembly and disassembly pathways.[12,19−22] Disulfide bonds are formed in VP1 in vivo and lead to folding of
the VP1 monomers and to the formation of stable pentamers, the capsid
building blocks.[17] Additional disulfide
bonds, between cys104, of adjacent pentamers, stabilize the assembled
particle.[14] β–β′
and α contacts include disulfide bonds, whereas the γ
contacts are unlikely to form disulfide bonds. The crystal structure
of SV40[14] reveals two potential calcium
ions binding sites, anchored between glutamic acid residues. The ions
lock the invading C terminal arm of one pentamer to its neighbor and
stabilize the α and β inter-pentamer interactions.[23] Mutating the glutamic acid residues to arginines
and lysines and mutants of the cysteine residues led to capsids that
were unstable to various degrees and affected viral entry and infection.[17,19,20]Ca2+ ions appear
to play an important role in the immune
evasion by SV40. Following recognition of the GM1 monogangliside[24,25] and additional receptors[26,27] on the cell surface,
SV40 enters the cell by endocytosis and is translocated to the endoplasmic
reticulum (ER) via the endosomic pathway. Unlike other viruses that
undergo conformational changes at the late, acidic endosomes, SV40
is stabilized at acidic pH, perhaps as the glutamic acid and other
basic residues at the calcium binding sites become protonated. Therefore,
unlike other viruses, SV40 reaches the ER intact, unexposed to the
lysosomal and proteosomal degradation, and does not display VP1 antigens
at the cell surface. Acid stability, most likely, underlies its immune
evasion.Between 6 and 8 h post infection, the infecting virus
undergoes
disassembly in the ER, releasing its genetic material that is transported
to the nucleus.[27] The release of Ca2+ ions, presumably via ER Ca2+ homeostasis, is
a key factor in SV40 disassembly.[20,28]VLPs
are formed spontaneously in vivo, in the nuclei of insect
cells.[12] Capsid formation in vitro requires
the addition of a charged polymer scaffold. We therefore term these
particles PC-VLPs. The size, shape, and symmetry of the resulting
capsid are dictated by the size and rigidity of the polyion scaffold.[29]T = 1 particles form within
several milliseconds when VP1 is mixed with 500-mer RNA.[30] When the circular ds-DNA of wt SV40 is used
for assembly, a T = 7 capsid is formed. The structure
of a T = 7 PC-VLP capsid is similar to that of wt
SV40 capsid. PC-VLPs provide a means to study the interactions between
the major capsid protein VP1, without the presence of VP2 and VP3.In this work we have used solution small angle X-ray scattering
(SAXS) to determine the structural changes in the capsid of wt SV40
and in T = 7 PC-VLPs encapsidating by SV40 DNA when
Ca2+ are chelated and disulfide bonds are reduced. SAXS
is a bulk method hence statistically reliable and highly sensitive
to small changes in the virus dimensions that would be too small to
visualize with other methods and under solution conditions. We found
that in the presence of both Ca2+ chelating and reducing
agents, the capsid of wt SV40 and PC-VLPs adopted a swollen conformation.
By applying external osmotic pressure to the virus particles, the
swollen conformation shrunk back to its original size. Similarly the,
SV40-PC-VLPs capsid can be stabilized upon adding Ca2+ ions
to the assembly solution. Understanding these interactions and their
influence on the wt SV40 structure and stability provides insights
into the assembly and disassembly of wt SV40, which, in vivo, takes
place in the nucleus and ER, respectively, and provides unique means
to improve the design of PC-VLPs-based assembly systems.
Results and Discussion
To better understand the interactions between VP1 pentamers, we
studied the effect of calcium and disulfide bonds on the structure
of wt SV40 and PC-VLPs. We performed SAXS measurements from wt SV40
and PC-VLPs in saline solution with and without the calcium chelating
agent ethylene glycol-bis(2-aminoethylether)-N,N,N′,N′-tetraacetic
acid (EGTA) and the disulfide bond reducing agent dithiothreitol (DTT).Figure A shows
that EGTA by itself did not significantly change the scattering curve.
This result suggests that negligible structural changes occurred when
Ca2+ ions were bound to the virus or detached from it.
When only DTT was added, the minima of the scattering curve slightly
shifted toward lower scattering angles, indicating that the dimensions
of the virus slightly increased.
Figure 1
Azimuthally integrated background-subtracted
SAXS intensity curves
from 3 mg/mL wt SV40. Measurements were performed using our in-house
SAXS setup in different solution conditions. The scattering intensity
is plotted as a function of q, which is the magnitude
of the scattering vector. (A) Saline solution, saline solution with
30 mM DTT, and saline solution with 40 mM EGTA. (B) Saline solution
(as in A) and saline solution with both 40 mM EGTA and 30 mM DTT.
Azimuthally integrated background-subtracted
SAXS intensity curves
from 3 mg/mL wt SV40. Measurements were performed using our in-house
SAXS setup in different solution conditions. The scattering intensity
is plotted as a function of q, which is the magnitude
of the scattering vector. (A) Saline solution, saline solution with
30 mM DTT, and saline solution with 40 mM EGTA. (B) Saline solution
(as in A) and saline solution with both 40 mM EGTA and 30 mM DTT.When both EGTA and DTT were added
to the saline solution (Figure B), the minima clearly
shifted to lower scattering angles. The results suggest that the combined
effect of Ca2+ release and reduction of disulfide bonds
led to a significant swelling of wt SV40 and that the two elements
depend on one another, in agreement with earlier reports.[19,20,31] This observation suggests that
either disulfide bonds or Ca2+ bonds were sufficient to
keep the capsid close to its original dimensions. When both types
of bonds were simultaneously removed, the association between pentamers
was sufficiently weaker, hence capsid swelling was achievable.The results of Figure B where then repeated with higher concentrations of EGTA and
DTT (Figure ). To
analyze the data in Figure , we calibrated lower resolution models of concentric spherical
shells against the atomic model of the capsid, taken from protein
data bank (PDB) entry 1SVA.[32] We used our home-developed[33] state-of-the-art scattering data analysis software
D+ (https://scholars.huji.ac.il/uriraviv/software/d-software), to compute the expected solution scattering curve from the atomic
model of the capsid (Figure A). We then fitted the result to a geometric model of concentric
spherical shells with a radial electron density profile, given by
a sum of hyperbolic tangents (Figure B), generated as explained in our earlier papers.[34,35] Similar analysis was repeated for a swollen capsid (Figure C,D). Figure compares the scattering curves from the
two atomic models: the capsid of wt SV40 (Figure A) and the swollen SV40 capsid (Figure C).
Figure 2
Azimuthally integrated
background-subtracted SAXS intensity curves
from 1 mg/mL wt SV40 in saline solution (A,B) and in saline solution
with both 50 mM EGTA and 50 mM DTT (C,D). The data (blue symbols)
were fitted to models (red curves) of concentric spherical shells
with radial electron density profiles as shown in (B,D). The cartoons
show the electron density profile of the fitted models. The water
electron density, capsid wall thicknesses, the outer radii, and the
polydispersities of the outer radii are indicated in the figure. The
central part of the electron density (shown in blue in the cartoons)
corresponds to the electron density of the minichromosome of wt SV40.[35] Models were convolved with an instrument Gaussian
resolution function whose standard deviation, σ, was 0.01 nm–1.
Figure 3
Calibration of geometric
capsid models by comparing with the computed
scattering curves from atomic models. (A) Atomic model (blue symbols,
wine color cartoon), based on PDB entry 1SVA.[32] The geometric
centers of pentamers in the PDB was at a radius of 21.3 nm for the
vertices and 21.1 nm for the edges. We assumed a hydration layer with
an electron density of 364 e/nm3 and thickness of 0.2 nm.
The red curve and red cartoon show the best fitted concentric shell
model (B). The electron density profile of the concentric shell models,
shown in (A). (C) Atomic model of a swollen capsid in which the geometric
centers were multiplied by a factor of 1.1 (blue symbol, wine color
cartoon) and the best fitted concentric shell model (red curve and
red cartoon). (D) The electron density profile of the concentric shell
models, shown in (C). The wall thicknesses and outer radii used in
the geometric models (red curves) are indicated in the figure.
Figure 4
Effect of capsid outer radius. Comparing the
scattering curves
from the two atomic models in Figure . The outer radii of each model are indicated in the
figure. The inset shows the higher q-range on an
expanded scale.
Azimuthally integrated
background-subtracted SAXS intensity curves
from 1 mg/mL wt SV40 in saline solution (A,B) and in saline solution
with both 50 mM EGTA and 50 mM DTT (C,D). The data (blue symbols)
were fitted to models (red curves) of concentric spherical shells
with radial electron density profiles as shown in (B,D). The cartoons
show the electron density profile of the fitted models. The water
electron density, capsid wall thicknesses, the outer radii, and the
polydispersities of the outer radii are indicated in the figure. The
central part of the electron density (shown in blue in the cartoons)
corresponds to the electron density of the minichromosome of wt SV40.[35] Models were convolved with an instrument Gaussian
resolution function whose standard deviation, σ, was 0.01 nm–1.Calibration of geometric
capsid models by comparing with the computed
scattering curves from atomic models. (A) Atomic model (blue symbols,
wine color cartoon), based on PDB entry 1SVA.[32] The geometric
centers of pentamers in the PDB was at a radius of 21.3 nm for the
vertices and 21.1 nm for the edges. We assumed a hydration layer with
an electron density of 364 e/nm3 and thickness of 0.2 nm.
The red curve and red cartoon show the best fitted concentric shell
model (B). The electron density profile of the concentric shell models,
shown in (A). (C) Atomic model of a swollen capsid in which the geometric
centers were multiplied by a factor of 1.1 (blue symbol, wine color
cartoon) and the best fitted concentric shell model (red curve and
red cartoon). (D) The electron density profile of the concentric shell
models, shown in (C). The wall thicknesses and outer radii used in
the geometric models (red curves) are indicated in the figure.Effect of capsid outer radius. Comparing the
scattering curves
from the two atomic models in Figure . The outer radii of each model are indicated in the
figure. The inset shows the higher q-range on an
expanded scale.On the basis of the calibration
in Figure , the data
in Figure were fitted
to a model of concentric spherical
shells with a radial electron density profile, given by a sum of hyperbolic
tangents (Figure C),
generated as explained in our earlier papers.[34,35] The polydispersity of the outer radii was taken into account as
explained.[36] The analysis showed that the
radius of wt SV40 increased from 24.2 ± 0.2 to 25.5 ± 1.2
nm. The increased polydispersity suggests that the particles could
have also slightly changed their shape. The ∼5% increase in
the capsid radius led to ∼11% increase in the surface area
and ∼17% increase in volume. The spacing between the centers
of adjacent pentamers in wt SV40 varies between 8.5 and 10.3 nm.[14,35] The swelling of the particles in the presence of 50 mM DTT and 50
mM EGTA suggests that on average, the distances between pentamers
increased by ∼0.5 nm. We attribute this ability to maintain
the capsid structure while increasing the distance between subunits,
in about 0.5 nm, to the important role of the flexible C arms in increasing
the stability of the capsid, by effectively increasing the range of
inter-pentamers interaction.The inner core electron density
of 371 e/nm3 corresponds
to the density of the minichromosome. When the particle swelled, the
density was supposed to decrease down to 364 e/nm3, whereas
the actual value was 366 e/nm3. In the future, it will
be interesting to perform in situ time-resolved SAXS experiments to
elucidate how viral particles are swelling as they are mixed with
chelating and/or reducing agents.To isolate the interactions
between VP1 pentamers, we studied the
effect of Ca2+ ions on the structure of PC-VLPs. A solution
of soluble VP1 pentamers were prepared by performing dialysis of purified
empty VP1 capsids (see Materials and Methods) against 1 mM DTT and 1 mM ethylenediaminetetraacetic acid (EDTA).
By mixing VP1 pentamers with wt 5.2 kpb circular ds-DNA, PC-VLPs with
a T = 7 symmetry were spontaneously assembled.[35] The assembly buffer did not contain Ca2+ ions and most likely the VP1 did not have disulfide bonds (see Materials and Methods). The assembly reaction was
triggered by binding of the VP1 pentamers to the circular ds-DNA rather
than VP1−VP1 interaction. This binding was facilitated by the
net positive charge of the VP1 pentamer side that is facing the capsid
lumen[14] and the net negative change on
the DNA. Both the DNA and VP1 pentamers were neutralized by monovalent
counterions. The association between the DNA and VP1 pentamers was
driven by the release of their counterions into the solution because
the DNA and VP1 could neutralize each other. When the counterions
were released, they gained solution entropy, which lowered the total
free energy.Figure shows that
without Ca2+ ions, the PC-VLP had an outer radius of 26.6
± 1.0 nm, which is about 2 nm larger than wt SV40. When 4 mM
CaCl2 was added to the solution, the radius of the PC-VLP
decreased to 25.3 nm, which is much closer to that of wt SV40. The
density profiles in Figure B,D, show thicker walls, suggesting that the DNA was still
forced against the wall, thus exerting internal pressure on the capsid
wall, which may explain the slightly larger radius, compared with
wt SV40. The compaction of the PC-VLP by the Ca2+ ions
was therefore, most likely, owing to strengthening of capsid protein−protein
interaction, rather than a decrease in the PC-VLP internal pressure.
In both particles, the inner cavity had electron density close to
bulk water, suggesting the particles were empty.
Figure 5
Azimuthally integrated
background-subtracted SAXS intensity curves
from PC-VLPs (blue symbols). 8.5 μM VP1 were mixed with the
wt circular 5.2 kbp ds-DNA in a molar ratio of 144:1 in saline solutions
containing 4 mM CaCl2 (A,B) and in saline solution (C,D).
The data were fitted to models of concentric spherical shells (red
curves and cartoons) with radial electron density profiles as shown
in (B,D). The wall thicknesses, outer radii, and outer radius polydispersities
are indicated in the figure. Models were convolved with an instrument
Gaussian resolution function whose standard deviation, σ, was
0.015 nm–1.
Azimuthally integrated
background-subtracted SAXS intensity curves
from PC-VLPs (blue symbols). 8.5 μM VP1 were mixed with the
wt circular 5.2 kbp ds-DNA in a molar ratio of 144:1 in saline solutions
containing 4 mM CaCl2 (A,B) and in saline solution (C,D).
The data were fitted to models of concentric spherical shells (red
curves and cartoons) with radial electron density profiles as shown
in (B,D). The wall thicknesses, outer radii, and outer radius polydispersities
are indicated in the figure. Models were convolved with an instrument
Gaussian resolution function whose standard deviation, σ, was
0.015 nm–1.To study the effect of moderate osmotic pressure, we put
26 μL
of 3 mg/mL wt SV40 solution in a quartz capillary. 4 μL of 40
wt % 20 kD poly(ethylene glycol) (PEG) solution in water were then
added to the virus solution. The added PEG solution led to precipitation
of the virus particles into a condensed phase at the bottom of the
capillary. The precipitant was formed owing to the moderate osmotic
pressure (of about 25 kPa), which was applied by the PEG solution.
The PEG was excluded from the particles and led to depletion attraction
between them.[37,38]Figure shows that the minima in the scattering
curve shifted to higher scattering angles. This result suggests (see Figure ) that the osmotic
pressure also decreased the capsid dimensions, owing to transport
of water molecules from the inner volume of the virus toward the PEG
solution, at which their chemical potential was lower. Water removal
forced the capsid proteins to get closer to one another, and the virus
adopted a tighter conformation. Larger structural changes were not
observed under the rather moderate osmotic stress used in this study.
Figure 6
Azimuthally
integrated background-subtracted SAXS intensity curves
from 3 mg/mL wt SV40 with 5 wt % 20 kD PEG. Measurements were performed
using our in-house SAXS setup in saline solution, and in saline solution
with both 40 mM EGTA and 30 mM DTT (A). In (B), we compare the measured
scattering intensities in saline solution with and without added PEG.
Azimuthally
integrated background-subtracted SAXS intensity curves
from 3 mg/mL wt SV40 with 5 wt % 20 kD PEG. Measurements were performed
using our in-house SAXS setup in saline solution, and in saline solution
with both 40 mM EGTA and 30 mM DTT (A). In (B), we compare the measured
scattering intensities in saline solution with and without added PEG.Addition of EGTA and DTT lead
to swelling of the capsid (Figure ). We attribute the
swelling to weakening of the interaction between pentamers either
by reduction of the disulfide bonds or by the release of Ca2+ ions. The swollen structure, enabled to explore a wider range of
conformational space. Figure shows that applying osmotic stress to wt SV40 in the swollen
conformation, recouped the structure of native wt SV40 under similar
osmotic stress. Upon addition of PEG, a precipitate formed, suggesting
that the density of virus particles increased, consistent with the
observed structure-factor peaks at the lower q-range.
The behavior at the higher q-range is consistent
with a small decrease of the outer capsid radius (see Figure ).We note that the concentration
of chelating and reducing agents
in vivo are at least an order of magnitude lower than used here. When
we dialyzed wt SV40 particles against solutions with 2 mM DTT and
2 mM EGTA, similar results were obtained. At 5 mM concentrations,
it has been recently shown that DTT makes DNA-containing VLPs less
resistant to mechanical stress and prone to damage, whereas EDTA induces
a marked softening of the particles.[39]
Conclusions
In this paper, we showed that both calcium ions and disulfide bonds
stabilized the structure of wt SV40 and PC-VLPs. When only calcium
ions were removed, the structure of wt SV40 remained nearly unchanged.
Reducing disulfide bonds led to a slight swelling of wt SV40. When
both calcium ions were chelated and disulfide bonds were reduced,
the volume of wt SV40 increased by about 17% and the spacing between
pentamers increased by about 5% (or 0.5 nm). The swelling of the virus
could be reversed by applying osmotic pressure using PEG solution.
PC-VLPs formed by mixing VP1 and the wt circular ds-DNA showed similar
behavior. The volume changes were attributed to the interactions between
the capsid proteins rather than to the internal pressure in the particles.
Materials
and Methods
Samples Preparation for SAXS Measurements
wt SV40 was
purified as explained in our earlier paper.[11] The control wt SV40 sample was measured in saline (0.9 wt % NaCl).
The other samples were either mixed with EGTA and DTT and/or 20 kD
PEG solutions. The samples were then equilibrated at ambient room
temperature for about an hour, before they were transferred to the
measurement cell.Virus-like particles were formed by a disassembly-reassembly
protocol in a similar way to our earlier study.[30] Purified empty VP1 capsids were dialyzed twice against
two disassembly buffers. The first buffer contained 50 mM NaCl, 20
mM Tris at pH 8.9, 5 mM EDTA, and 2 mM DTT. In the second dialysis,
the disassembly buffer contained 50 mM NaCl, 20 mM Tris at pH 8.9,
2 mM EDTA and 2 mM DTT. Hence, the resulting VP1 pentamers did not
contain Ca2+ or disulfide bonds.VP1 pentamers solution
at concentration of 17 μM was mixed
at a volume ratio of 1:1 with a solution containing the wt SV40 circular
ds-DNA at a concentration of 0.12 μM with and without 4 mM CaCl2. The final solution of the assembled particles contained
150 mM NaCl, 1 mM, EDTA, 1 mM DTT, and 0 or 4 mM CaCl2.
SAXS Measurement Setup and Data Reduction
SAXS measurements
of the wt SV40 presented in Figures and 6 were performed in our
in-house setup, described in our earlier paper.[40] A background measurement was taken before the sample using
the same capillary. SAXS results presented in Figure were performed using the flow cell setup
in the SWING beamline at Soleil Synchrotron (GIF-sur-YVETTE)[41] and in the P12 beamline of the EMBL located
at the PETRA III storage ring (DESY, Hamburg).[42] The PC-VLPs were measured in the flow-cell setup at ID02
beamline in ESRF (Grenoble).[43] All measurements
were taken at room temperature and buffer background measurements
were taken before and after each virus sample. Data reduction was
performed as explained in ref (11). The averaged background signals were then subtracted from
the averaged samples signals.
Extracting the Radius of
Virus Particles
The scattering
intensity from noninteracting N virus particles is
given by, I(q) = NIvirus(q), where Ivirus(q) is the scattering intensity of a single soluble virus given bywhere the form factor, FF, is the Fourier
transform of the electron density contrast of the virus with respect
to the solvent, Δρ(r⃗). q⃗ is the elastic momentum transfer vector. The brackets
⟨ ⟩ represent average over time and virus orientations
in the solution. At low resolution, the virus particle can be approximately
considered as spherical. This assumption holds up to a resolution
at which the inter-pentamer correlations contribute significantly
to the scattering intensity as was previously shown.[11,35] In order to determine the change in the outer radius of the particles
at different chemical environments, the lower q range
of the resulting 1D data, was analyzed using the X+ (https://scholars.huji.ac.il/uriraviv/software/x) software developed in our lab[34,36,44] and our recent[33,45] state-of-the-art analysis
software D+. The analysis with X+ was done with a model of concentric
spheres with a radial electron density profile that was constructed
from a sum of hyperbolic tangents as explained in our earlier papers.[34,35] The model was then fitted to the scattering data by adjusting the
thickness and electron density of each layer, and three layers or
less were needed to obtained the best fit.Using our home developed
software D+, we computed the scattering from the atomic model of the
capsid, based on protein data bank entry 1SVA.[32] By comparing
the resulting scattering curve of the atomic model with that of a
concentric sphere model with a radial electron density profile (Figure ), we calibrated
the electron density and thickness of the capsid wall. The calculation
was performed with the outer wall radius of the capsid crystal structure,
24.4 nm (Figure A,B),
and a swollen capsid with an outer wall radius of 26.4 nm (Figure C,D). The calibration
reduced the number of free parameters in the concentric shell model.
Authors: Chao Chen; Marie-Christine Daniel; Zachary T Quinkert; Mrinmoy De; Barry Stein; Valorie D Bowman; Paul R Chipman; Vincent M Rotello; C Cheng Kao; Bogdan Dragnea Journal: Nano Lett Date: 2006-04 Impact factor: 11.189
Authors: Lina Loo; Richard H Guenther; Veronica R Basnayake; Steven A Lommel; Stefan Franzen Journal: J Am Chem Soc Date: 2006-04-12 Impact factor: 15.419
Authors: Billy Tsai; Joanna M Gilbert; Thilo Stehle; Wayne Lencer; Thomas L Benjamin; Tom A Rapoport Journal: EMBO J Date: 2003-09-01 Impact factor: 11.598
Authors: Peggy P Li; Akira Naknanishi; Mary A Tran; Ken-Ichiro Ishizu; Masaaki Kawano; Martin Phillips; Hiroshi Handa; Robert C Liddington; Harumi Kasamatsu Journal: J Virol Date: 2003-07 Impact factor: 5.103
Authors: Roi Asor; Lisa Selzer; Christopher John Schlicksup; Zhongchao Zhao; Adam Zlotnick; Uri Raviv Journal: ACS Nano Date: 2019-06-25 Impact factor: 15.881