CIMMS Meeting

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CIMMS Meeting

• Rob Phillips and Prashant K. Purohit

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Viral packing problem
Viruses are protein shells filled with some
genetic material
The shells are a few tens of nm in size and
contain DNA or RNA a few microns long. In some
viruses the shell forms first and the DNA is
packed in by a mol- -ecular motor at the mouth of
the shell.
The force exerted by the motor during the process
of packaging have been measured experimentally
using single molecule probes like optical
tweezers. Maximum force is about 60 pN.
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How to model it?
Experiments reveal that DNA is arranged as a
series of hoops inside the viral shell starting
from the outside.
We model the DNA as a charged rod with a
temperature dependent bending modulus. The
energetics of packing therefore involves bending
energy and electrostatic energy that depends on
distance between adjacent hoops.
Hoop spacing determined by mini- -mising the
energy and we get the force by taking derivative
of energy w.r.t length of DNA packed.
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Structural mechanics of viruses
Pressures inside a fully packed shell may be in
the range of 60 atm. Max sustainable pressure
determined using solid mechanics.
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Finite temperature QC
The quasi-continuum method was devised to study
defects like fracture and dislocations that are
microscopic but their effect is felt at the
macrosc- -opic level.
Problem Defect mechanics changes with
temperature. But, QC did not acknowledge this
since it was meant for solving static problems.
Thermal fluctuations are also impor- -tant in the
study of biological macro- molecules.
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Simple models
The springs could be non-linear.
Recipe Interpolate the motion of the second mass
like in finite elements but add random forces to
the other two masses as done in Langevin dynamics.
What should be the statistical nature of the
random force to recover thermal properties of
the full system in a coarse-grained setting.