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internal pressure, such as that exerted by the genome encapsulation, or external
pressure, such as osmotic pressure. It is notable that the eigenvalue of this mode
is higher than other low frequency modes (Fig. 7.8), implying that the capsid
exhibits a relatively stronger resistance against deformations of this type.
Figure 7.9b shows the slowest mode with five-fold degeneracy (
l
= 2), i.e.,
modes 1-5 in Fig. 7.8. The motion induced in these modes can be visualized
physically as the result of
squeezing
a sphere radially inwards at the poles,
allowing it to bulge outwards at the equator, and vice versa. Such a deformation
occurs when a molecule is probed with an atomic force microscope. Our recent
calculations (Yang
et al.
, 2008) showed that hollow spheres are quite soft in
response to this mechanism of deformation (Michel
et al.
, 2006; Kol
et al
.,
2006). This is the top ranking (lowest frequency) mode in both STMV and
STMV+RNA, which indicates that this kind of deformation is highly favorable
from an energetic point of view.
The
l
= 3 mode (Fig. 7.9c) is similar to the
l
= 2 mode above, but the
deformation direction is split into three. This mode involves two groups of
degenerate modes, 6-8 and 9-12
.
The torsional mode illustrated in Fig. 7.9d is
a fivefold degenerate mode with
l
= 2. This mode can be visualized as the result
of twisting the upper and lower hemispheres in opposite directions.
Effect of RNA.
There is no difference between the first 21 modes of the STMV
capsid (alone) and those of the capsid with RNA in so far as the mechanism of
motion is concerned, but their orders (or relative frequencies) exhibit slight
changes. The eigenvalues of the capsid with RNA are slightly higher than their
counterparts for the protein coat only (Fig. 7.8), but this is essentially due to the
larger number of nodes and higher mass of the capsid with RNA. The eigenvalue
of the
l
= 2 spheroidal squeezing modes (modes 1-5) increases by 8% in the
presence of the genome, whereas that of the
l
= 2 torsional twisting modes
(modes 13-17) increases by only 0.4%. Differences appear after the 21
st
mode;
for example, the breathing mode appears earlier in the case of the capsid with
RNA.
7.4. Conclusion
Elastic network models lead to a unique analytical solution and provide a
thorough sampling of the energy landscape near the energy minimum. Advances
in accurate representation of systems and in validation procedures have
highlighted coarse-grained approaches as valuable tools for analysis, allowing a
direct comparison with experimental results on macromolecular dynamics.
