Transcript Computational Biology

V8: Virus Structure and Assembly
At the simplest level, the function of the outer shells (CAPSID) of a virus particle
is to protect the fragile nucleic acid genome from:
Physical damage - Shearing by mechanical forces.
Chemical damage- UV irradiation (from sunlight) leading to chemical
modification.
Enzymatic damage - Nucleases derived from dead or leaky cells or deliberately
secreted by vertebrates as defence against infection.
The protein subunits in a virus capsid are multiply redundant, i.e. present in
many copies per particle. Damage to one or more subunits may render that
particular subunit non-functional, but does not destroy the infectivity of the whole
particle. Furthermore, the outer surface of the virus is responsible for
recognition of the host cell. Initially, this takes the form of binding of a specific
virus-attachment protein to a cellular receptor molecule. However, the
capsid also has a role to play in initiating infection by delivering the genome
from its protective shell in a form in which it can interact with the host cell.
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Virus Design
To form an infectious particle, a virus must overcome two fundamental problems:
(1) To assemble the particle utilizing only the information available from the
components which make up the particle itself (capsid + genome).
(2) Virus particles form regular geometric shapes, even though the proteins from
which they are made are irregularly shaped.
How do these simple organisms solve these difficulties? The information to answer
these problem lie in the rules of symmetry. In 1957, Fraenkel-Conrat &
Williams showed that when mixtures of purified tobacco mosaic virus (TMV)
RNA & coat protein were incubated together, virus particles formed. The
discovery that virus particles could form spontaneously from purified subunits
without any extraneous information indicated that the particle was in the free
energy minimum state & was therefore the favoured structure of the
components. This stability is an important feature of the virus particle.
Although some viruses are very fragile & are essentially unable to survive outside
the protected host cell environment, many are able to persist for long periods, in
some cases for years.
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Helical capsids
Tobacco mosaic virus (TMV) is representative of one of the two major
structural classes seen in viruses of all types, those with helical symmetry.
The simplest way to arrange multiple, identical
protein subunits is to use rotational symmetry
& to arrange the irregularly shaped proteins
around the circumference of a circle to form a
disc.
Multiple discs can then be stacked on top of one
another to form a cylinder, with the virus
genome coated by the protein shell or
contained in the hollow centre of the cylinder.
Closer examination of the TMV particle by X-ray
crystallography reveals that the structure of
the capsid actually consists of a helix rather
than a pile of stacked disks.
A helix can be defined mathematically by two
parameters:
amplitude (diameter) & pitch (the distance
covered by each complete turn of the helix)
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Helical capsids
Helices are rather simple structures formed by stacking repeated components
with a constant relationship (amplitude & pitch) to one another - note that if
this simple constraint is broken a spiral forms rather than a helix unsuitable for containing a virus genome.
The fact that helical symmetry
is a useful way of arranging a
single protein subunit to form a
particle is confirmed by the
large number of different types
of virus which have evolved
with this capsid arrangement.
TMV particles are rigid, rod-like structures, but some helical
viruses demonstrate considerable flexibility & longer helical
virus particles are often seen to be curved or bent. Flexibility is
important attribute since long helical particles are subject to
damage from shear forces & the ability to bend reduces the
chance of breakage.
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Icosahedral (isometric) capsids
An alternative way of building a virus capsid is to arrange protein subunits in the
form of a hollow quasi-spherical structure, enclosing the genome within.
The criteria for arranging subunits on the surface of a solid are more
complex than those for building a helix. In the 1950s, Brenner & Horne
developed sophisticated techniques which enabled them to use electron
microscopy to reveal many of the fine details of the structure of virus
particles.
One of the most useful techniques proved to be
the use of electron-dense dyes such as
phosphotungstic acid or uranyl acetate to
examine virus particles by negative staining.
The small metal ions in such dyes are able to
penetrate the minute crevices between the
protein subunits in a viral capsid to reveal
the fine structure of the particle.
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Icosahedral viruses
Francis Crick & James Watson (1956), were the first to suggest that virus capsids
are composed of numerous identical protein sub-units arranged either in
helical or cubic (=icosahedral) symmetry.
In order to construct a capsid from repeated subunits, a virus must 'know the
rules' which dictate how these are arranged. For an icosahedron, the rules
are based on the rotational symmetry of the solid, which is known as 2-3-5
symmetry:
An axis of two-fold rotational symmetry
through the centre of each edge
An axis of three-fold rotational symmetry
through the centre of each face
An axis of five-fold rotational symmetry
through the centre of each corner
(vertex)
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Icosahedral viruses
The simplest icosahedral capsids are built up by using 3 identical subunits to form
each triangular face, thereby requiring 60 identical subunits to form a complete
capsid.
A few simple virus particles are constructed in this way, e.g. bacteriophage ØX174:
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Examples of icosahedral viruses
In most cases, analysis reveals that icosahedral virus capsids contain more than
60 subunits, for the reasons of genetic economy given above.
The capsids of picornaviruses provide a good illustration of the construction of
icosahedral virus particles (e.g. polioviruses, foot-and-mouth disease virus,
rhinoviruses).
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Enveloped viruses
'Naked' virus particles, i.e. those in which the capsid
proteins are exposed to the external
environment are produced from infected cells at
the end of the replicative cycle when the cell
dies, breaks down & lyses, releasing the virions
which have been built up internally.
This simple strategy has drawbacks. In some
circumstances it is wasteful, resulting in the
premature death of the cell.
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Enveloped viruses
Many viruses have devised strategies to exit the
infected cell without its total destruction.
This presents a difficulty in that all living cells are
covered by a membrane composed of a lipid
bilayer. The viability of the cell depends on
the integrity of this membrane.
Viruses leaving the cell must therefore allow this
membrane to remain intact & this is
achieved by extrusion (budding) of the
particle through the membrane, during which
process the particle becomes coated in a
lipid envelope derived from the host cell
membrane & with a similar composition:
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Enveloped viruses
The structure underlying the envelope may be based on helical or icosahedral
symmetry & may be formed before or as the virus leaves the cell.
In the majority of cases, enveloped viruses use cellular membranes as sites
allowing them to direct assembly. The formation of the particle inside the
cell, maturation & release are in many cases a continuous process.
The site of assembly varies for different viruses. Not all enveloped viruses bud
from the cell surface membrane, many viruses use cytoplasmic membranes
such as the golgi complex, others such as herpesviruses which replicate in
the nucleus may utilize the nuclear membrane.
In these cases, the virus is usually extruded into some form of vacuole, in which it
is transported to the cell surface & subsequently released.
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Envelope Proteins
Envelope: If the virus particle became covered in a smooth, unbroken lipid bilayer,
this would be its undoing. Such a coating is effectively inert, & though effective
as a protective layer preventing desiccation of or enzymatic damage to the
particle, would not permit recognition of receptor molecules on the host cell.
Therefore, viruses modify their lipid envelopes by the synthesis of several
classes of proteins which are associated in one of three ways with the
envelope:
Matrix Proteins: These are internal virion proteins whose function is
effectively to link the internal nucleocapsid assembly
Glycoproteins: These are transmembrane proteins, anchored to the
membrane by a hydrophobic domain & can be subdivided into two types, by
their function:
External Glycoproteins - Anchored in the envelope by a single
transmembrane domain. Most of the structure of the protein is on the outside
of the membrane, with a relatively short internal tail. Often individual
monomers associate to form the 'spikes' visible on the surface of many
enveloped viruses in the electron microscope. Such proteins are the major
antigens of enveloped viruses.
Transport Channels - This class of proteins contains multiple hydrophobic
transmembrane domains, forming a protein-lined channel through the
envelope, which enables the virus to alter the permeability of the membrane,
e.g. ion-channels.
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Complex virus structures
The majority of viruses can be fitted into one of the three structural classes:
helical symmetry,
icosahedral symmetry or
enveloped viruses based on either of these two.
However, there are many viruses whose structure is more complex.
In these cases, although the general principles of symmetry already described
are often used to build part of the virus shell, the larger & more complex
viruses cannot be simply defined by a mathematical equation as can a
simple helix or icosahedron.
Because of the complexity of some of these viruses, they have defied attempts to
determine detailed atomic structures using the techniques described earlier.
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Pox viruses
An example of such a group & the problems of
complexity is shown by the members of the
poxvirus family.
These viruses have oval or 'brick-shaped' particles
200 - 400 nm long. In fact, these particles are so
large that they were first observed using high
resolution optical microscopes in 1886 &
thought at that time to be 'the spores of
micrococci'.
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Pox viruses
The external surface of the virion is ridged
in parallel rows, sometimes arranged
helically. The particles are extremely
complex & have been shown to
contain more than 100 different
proteins.
Antigenically, poxviruses are very complex,
inducing both specific & crossreacting antibodies - hence ability to
vaccinate against one disease with
another virus (i.e. the use of vaccinia
virus to immunize against smallpox
(variola) virus).
Poxviruses & a number of other complex
viruses also emphasise the true
complexity of some virus - there are at
least ten enzymes present in
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poxvirus particles, mostly concerned
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with nucleic acid metabolism/genome
Summary
1. To protect the genome
2. To deliver the genome to the appropriate site in the host cell so that it can
be replicated.
3. A number of repeated structural motifs found in many different virus
groups are evident. The most obvious is the division of many virus
structures into those based on helical or icosahedral symmetry.
4. Virus particles are not inert. Many are armed with a variety of enzymes
which carry out a range of complex reactions, most frequently
concerned with the replication of the genome.
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Icosahedral Viruses
Half of all virus families share icosahedral geometry, even though they may
have nothing else in common

speculation that there may be a physical advantage to icosahedral
geometries.
Why is it interesting to understand these laws?

One may be able to develop strategies to fight viruses.

One could build self-assembling nano-particles from proteins with
special desired properties.
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Icosahedral Geometry
An icosahedron is 20-sided solid,
where each facet has threefold
symmetry (Fig. 1A).
To build an icosahedron out of
protein, each face must be made of
at least three proteins, because an
individual protein cannot have
intrinsic threefold symmetry.
In an icosahedron, the proteins are related by exact two-, three-, and fivefold symmetry axes.
It turns out that few spherical viruses are built of 60 subunits, but most viruses are built
of T multiples of 60, where the T (for triangulation) number indicates the number of
subunits within each of the 60 icosahedral asymmetric units. The term quasiequivalence indicates that the subunits are in distinct but quasi-equivalent
environments. In this manner, some subunits are arranged around icosahedral fivefold
axes and others are arranged as hexamers.
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Icosahedral Geometry
Quasi-equivalence is readily apparent in
a virus structure by the presence of
pentameric and hexameric
groupings of subunits, the
capsomers (Fig. 1B).
A selection of cryoelectron microscopy
image reconstructions demonstrating
different T numbers:
polio (T=1), small hepatitis B virus (HBV)
capsid (T=3), large HBV capsid (T=4),
bacteriophage HK97 (T=7), and herpes
simplex virus (T=16).
An icosahedral facet is highlighted on
selected images.
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Icosahedral Symmetry of a viral capsid
(a) Cryo-TEM reconstruction of CCMV.
(b) Arrangement of subunits on a
truncated icosahedron; A, B, and C
denote the three symmetry
nonequivalent sites.
Zandi et al., PNAS 101, 15556 (2004)
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Why do viruses adopt icosahedral symmetry?
Derive model for equilibrium viral structures that retains the essential features of the process
and results in the predominance of icosahedral CK structures as well as the existence of
other structures observed in vitro that do not fall into this classification.
Start from the observation that, despite the wide range of amino acid sequences and folding
structures of viral coat proteins, capsid proteins spontaneously self-assemble into a
common viral architecture.
The actual kinetic pathways and intermediates involved are quite varied [e.g., CCMV
assembles from dimers, Polyoma from pentameric capsomers, and HK97 from pentamers
and hexamers] but the equilibrium structures of viral capsids are invariably made up of the
same units (e.g., pentamers andor hexamers).
This finding suggests that, although the interaction potential between subunits is asymmetric
and species-specific, capsomers interact through a more isotropic and generic interaction
potential. The focus of the present work is not on the kinetics process of the assembly but
rather on understanding the optimal equilibrium structures.
Zandi et al., PNAS 101, 15556 (2004)
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Monte Carlo simulations
Based on the ideas noted above we consider a minimal model for the equilibrium
structure of molecular shells in which we do not attempt to describe individual
subunits but instead focus on the capsomers.
The effective capsomer-capsomer potential V(r) is assumed to depend only on
the separation r between the capsomer centers and captures the essential
ingredients of their interaction: a short-range repulsion, representing subunit
conformational rigidity, plus a longer-range attraction, corresponding to the
driving force (e.g., hydrophobic interaction) for capsomer aggregation.
The capsomer-capsomer binding energy 0 is taken to be 15 kT, a typical value
reported from atomistic calculations of subunit binding energies.
Zandi et al., PNAS 101, 15556 (2004)
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Two different morphological units
Another essential feature of viral capsids is the existence of two different
morphological units (pentamers and hexamers).
To account for the intrinsic differences between capsomer units we assume that
they can adopt two internal states: P(entamer) and H(examer). The potential has
the same form for interactions between different capsomer types except that the
equilibrium spacing [the minimum of V(r)] includes the geometrical size
difference between pentamers and hexamers of the same edge length (size ratio
0.85).
The energy difference E between a P and an H capsomer, which reflects
differences between individual contact interactions and folding conformations of
pentamer and hexamer proteins, enters as a Boltzmann factor eE/kT that provides
the relative thermal probability for a noninteracting unit to be in the P state.
For each fixed total number of capsomers N, the number NP of P units (and
hence the number NH = N - NP of H units) is permitted to vary and was not fixed
to be 12 (as in the CK construction).
Zandi et al., PNAS 101, 15556 (2004)
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Monte Carlo simulations
We carry out Monte Carlo simulations in which N interacting capsomers are allowed to
range over a spherical surface while switching between P and H states, thus exploring all
possible geometries and conformations. In this way we obtain the optimal structure for a
given number N of capsomers and a given capsid radius R.
We have used Metropolis Monte Carlo (MC) simulation with 105 equilibration steps and 105
production steps. An elementary MC step consisted of either an attempt to move a
randomly chosen disk over the surface of a sphere in a random direction or an attempt to
change its size.
The ratio of MC attempts of moving a disk versus switching the size of a disk was set to
10. However, we tested different ratios and the result was robust, independent of the ratio.
The finite-temperature internal energy E(R) is evaluated for each of a range of equilibrated
sphere radii R and then minimized with respect to R, leading to a special radius R* for
each N. We tested different forms for V(r) and found the conclusions discussed below to
be robust.
Zandi et al., PNAS 101, 15556 (2004)
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Monte Carlo simulations
Note favorable numbers
of particles.
Energy per capsomer for E = 0 (black
curve) and |E / o | large compared to one
(dotted curve).
Zandi et al., PNAS 101, 15556 (2004)
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Icosahedral Symmetry of a viral capsid
Minimum energy structures produced by Monte Carlo simulation, with P-state
capsomers shown in black. (a) The P and H states here have the same energies.
The resulting N=12, 32, 42, and 72 structures correspond to T=1, T=3, T=4, and
T=7 C-K icosahedra.
(b) Minimum energy structures for |E / o | >> 1, i.e., only one size of capsomer.
The N = 24 and 48 structures have octahedral symmetry, and N = 32 is
icosahedral, whereas N = 72 is highly degenerate, fluctuating over structures with
different symmetry, including T = 7.
Zandi et al., PNAS 101, 15556 (2004)
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Icosahedral Symmetry of a viral capsid
Stability around the minimum 72.
N = 71 has essentially the same structure as N = 72, but a structural defect.
N = 73 has many surface defects.
Zandi et al., PNAS 101, 15556 (2004)
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Mechanical properties of capsids
Our minimal model for capsid structure posits an explicit potential for capsomer
interactions, which provides us with a tool to study the mechanical and genome
release properties of viral capsids. To address the effect of strain on capsid structure,
we repeated our E0 simulations at each of successive fixed capsid radii in excess of
the optimal radius R*. For fixed N 32 (T = 3) and NP = 12, the capsid
bursts dramatically when RR* exceeds a critical value (1.107), in the form of a large
crack stretching across the capsid surface. The bursting of the capsid is one of
several possible gene release scenarios. Just before this point is reached the capsid
is uniformly swollen (see Fig. 6a), with all interstitial holes grown larger in size
compared to those in the optimized R R* structure (see N = 32 in Fig. 3a). The
appearance of these pores constitutes another mechanismZandi
foretgenome
release.
al., PNAS 101,
15556 (2004)
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Mechanical properties of capsids
Finally, when we allow the number of capsomers to change during swelling, we find
that the bursting scenario competes with still another mechanism, decapsidation; at
a critical radius 1.107 R* the capsid energy can be reduced by ejecting one of
the 12 pentamers, followed by a decrease in capsid size.
These phenomena have been observed, for instance, for the Tymoviruses and a
series of Flock House virus mutants. The fact that the minimal model reproduces
realistic release mechanisms, in addition to accounting for both the predominant Tstructures and the exceptional nonicosahedral structures, suggests that it can be
applied as well to studying the mechanical properties of capsids and serve as a
guide for the design of artificial viruses.
Zandi et al., PNAS 101, 15556 (2004)
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