Biomedical Engineering Reference
In-Depth Information
viruses adopt a particular configuration from the range of possible shapes and sizes
(see Fig.
1
).
Attempts to explain this faceting or buckling phenomena have been made using
simplified models. Using the discrete canonical capsid model, we identified that
viruses belonging to the
class 2
(h>k>0) morphological group can undergo
buckling transitions (See discussion in Sect.
3
). The virus structures in this group,
which includes HK97 (T
D
7), have a degree of freedom associated with the
hexamer configurations [
36
]. This is in contrast to the structures in
class 1
and
class
3
which we believe to consist of rigid hexamers, with zero degrees of freedom.
This degree of freedom in the
class 2
hexamers was identified through our analysis
of endo angle constraints (see Sect.
3
), and we find two distinct stable states that
the hexamer can sample. The two available hexamer configurations are a
pucker in
and
pucker out
state, corresponding to the faceted and rounded conformation of the
capsid, respectively. An alternative explanation to the buckling phenomena has been
put forth using purely continuum elastic theory of thin shells, proposed by Lidmar,
Mirny, and Nelson (LMN) [
41
]. According to the LMN theory, the equilibrium
configuration of the capsid is governed by a minimization of the elastic energy of
the shell. As the elastic energy is dependent on the elastic properties of the shell,
shape changes will arise in response to modulation of these properties. While both
of these models have offered reasonable explanations for the buckling transition
of virus caspids, neither work has incorporated molecular detail into their models.
Recently, we have attempted to bridge the discrete and the continuum description
of the virus capsid buckling transition by developing a multiscale approach which
relates atomic level equilibrium fluctuations to the macroscopic elastic properties of
the system [
85
,
86
].
In the LMN theory, a single parameter, the Foppl-von K
an number ( ),
predicts whether a capsid will adopt a rounded or faceted form, and as can be seen
in Fig.
1
, both states are known to exist in nature. The shape dependence on is
predicted to have a relatively sharp transition between rounded and faceted states,
is given by
K
arm
K
YR
2
D
;
(2)
where Y is the two-dimensional Young's modulus, R is the shell radius, and
is the bending modulus. Determining Y and for capsid structures will allow
to be determined, but it is inherently important to calculate these moduli to
better understand the mechanical properties of these systems. Furthermore, the
material characterization of capsids should accelerate the development of virus-
based nanotechnologies.
It is difficult to measure the elastic properties of nano-sized objects such as virus
capsids experimentally because most experimental techniques involve averaging
over a large number of particles. However, the single-molecule technique of atomic
force microscopy (AFM) is well suited for probing the mechanical strength of
capsids through nanoindentation studies. These studies typically are conducted in
conjunction with finite-element (FE) simulations in which the three-dimensional
Search WWH ::
Custom Search