8. lecture ss 20005optimization, energy landscapes, protein folding1 v8: virus structure and...

8. Lecture SS 20005

Optimization, Energy Landscapes, Protein Folding 1

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.http://www-micro.msb.le.ac.uk/109/structure.html

8. Lecture SS 20005


Virus DesignTo 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. http://www-micro.msb.le.ac.uk/109/structure.html

8. Lecture SS 20005


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.

http://www-micro.msb.le.ac.uk/109/structure.html

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)

8. Lecture SS 20005


Helical capsidsHelices 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.

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.

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.


8. Lecture SS 20005


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.

8. Lecture SS 20005


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)


8. Lecture SS 20005


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:


8. Lecture SS 20005


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).


8. Lecture SS 20005


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.


8. Lecture SS 20005


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:


8. Lecture SS 20005


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.


8. Lecture SS 20005


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. http://www-micro.msb.le.ac.uk/109/structure.html

8. Lecture SS 20005


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.


8. Lecture SS 20005


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'.


8. Lecture SS 20005


Pox virusesThe 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 & cross-

reacting 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

poxvirus particles, mostly concerned

with nucleic acid metabolism/genome

replication.


8. Lecture SS 20005


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.


8. Lecture SS 20005


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.


8. Lecture SS 20005


Icosahedral Geometry

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 quasi-

equivalence 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.


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.

8. Lecture SS 20005


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.

8. Lecture SS 20005


Icosahedral Symmetry of a viral capsid

Zandi et al., PNAS 101, 15556 (2004)

(a) Cryo-TEM reconstruction of CCMV. (b) Arrangement of subunits on a

truncated icosahedron; A, B, and C

denote the three symmetry

nonequivalent sites.

8. Lecture SS 20005


Why do viruses adopt icosahedral symmetry?

Zandi et al., PNAS 101, 15556 (2004)

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.

8. Lecture SS 20005


Monte Carlo simulations

Zandi et al., PNAS 101, 15556 (2004)

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.

8. Lecture SS 20005


Two different morphological units

Zandi et al., PNAS 101, 15556 (2004)

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).

8. Lecture SS 20005



Zandi et al., PNAS 101, 15556 (2004)

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.

8. Lecture SS 20005



Zandi et al., PNAS 101, 15556 (2004)

Energy per capsomer for E = 0 (black

curve) and |E / o | large compared to one

(dotted curve).

Note favorable numbersof particles.

8. Lecture SS 20005



Zandi et al., PNAS 101, 15556 (2004)

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.

8. Lecture SS 20005


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)

8. Lecture SS 20005


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 capsidbursts 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 mechanism for genome release.

Mechanical properties of capsids

Zandi et al., PNAS 101, 15556 (2004)

8. Lecture SS 20005


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 T-

structures 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.

Mechanical properties of capsids

Zandi et al., PNAS 101, 15556 (2004)

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