Biomedical Engineering Reference
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Fig. 9
The spectrum of spherical harmonics describing the equilibrium thermal fluctuations of the
capsid surface for the T
D
1 mutant of the
Sesbania mosaic virus
,shownin
bottom left
. A nearly
identical spectrum is produced for an all-atom MD simulation of an entire capsid, as that from and
elastic network model (ENM), that is scaled via an MD simulation of only the asymmetric unit.
In both cases the fluctuation spectrum is well described by the theoretical model in (
4
) (Figure 1
of May and Brooks, Phys. Rev. Lett. 106:18801-18804, 2011, copyright, 2011 American Physical
Society.)
parameters (, , )
˝
j
a
l
j
2
˛
D
k
B
T
8b
C
l.l
1/.l
C
1/.l
C
2/
R
2
:
(4)
Our formulation of the ENM is a nondimensional model, and therefore we use
MD to scale the trajectory to make it quantitatively accurate. The MD simulations
are performed on the asymmetric unit of the capsid under icosahedral rotational
boundary conditions [
95
]. From the MD simulations a scaling factor is calculated,
which is passed to the ENM model to connect the cruder ENM model to the more
accurate MD force field. We were able to show that this multiscale approach,
combining an ENM with MD on the asymmetric unit, was a good approximation
to the fluctuations generated by simulating the entire capsid explicitly with MD.
The agreement between the theoretical model and the observed fluctuations, as
well as the agreement between the multiscale (ENM) and the brute force MD
approach are shown in Fig.
9
. From the fits to the data, we are able to determine
Y , ,and for the T
D
1 mutant of
Sesbania mosaic virus
(SeMV). We have
applied this multiscale approach to HK97 [
85
,
86
] in the mature and immature
forms and predicted a significant change in (
800 mature)
between the states. These values are in agreement with the LMN theory, which
predicts structures with < 250 should be spherical and those with higher values
200 immature,
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