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QUICK
CONTACT
purohit(at)seas(dot)
upenn(dot)edu
Tel no.: (215) 898 3870
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Mechanics
of DNA packaging and ejection in viruses:
Ingenious experiments have led to the quantitative
characterization of the force exerted by
the portal motor of a virus as it packages
DNA into the viral head. In this project
we present an analytical model for the process
based on a rod like model for DNA coupled
with its electrostatic interactions in solution.
The structural strength of the viral capsid
is estimated using a cohesive model for
protein interactions based on data obtained
from molecular simulations. We also use
the model to predict the length of DNA ejected
from a virus as a function of applied osmotic
pressure. We show that the extremely tight
packaging of the viral genome is crucial
in determining its infectiousness.
Mechanics
of protein mediated DNA loop formation:
Protein mediated DNA loops are highly recurrent
structural motifs in biology. They are used
for gene regulation and mechanical manipulation
of DNA (for example, cutting by restriction
enzymes) in many prokaryotes and eukaryotes.
The free energy of forming the loop determines
the probability that a gene
will be switched on or off, or in the case
of restriction enzymes, the probability
of obtaining a piece of DNA of a certain
length after the cut. We calculate these
free energies starting from the Kirchhoff
theory of rods and accounting for thermal
fluctuations using a path integral technique.
Mechanics
of mitochondrial membranes:
Traditional wisdom about the structure of
the interior of mitochondria (the energy
producing oranelles in our cells) has been
questioned by recent cryo-electron microscopy
experiments. In order to better understand
the results of these experiments we use
the spontaneous curvature model of lipid
membranes coupled with the effect of protein
interactions to determine energetically
favorable configurations of biological membranes
in confined spaces. We are using these models
to understand the process of crista formation
in mitochondria since this could have implications
in the study of mitochodrial diseases.
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Mechanics
of shape memory beams and rods:
Shape memory alloys, such as Nitinol,
are used in a variety of medical instruments
such as stents, guide-wires, dental wires,
etc. These devices employ them in slender
configurations like rods or ribbons where
bending and shearing are the principal modes
of deformation. But, most quantitative theories
for these materials treat only extensional
deformations. We develop a simple and practical
engineering theory for shape memory beams
starting from the Cosserat theory of rods
complemented with a constitutive law motivated
by crystallography. We then propose simple
experiments that enable easy tracking of
the moving phase boundaries that are principally
responsible for the superelastic properties
of these materials.
Biologically
inspired shape memory based device for propulsion
at small scales:
The goal of this work was to test the feasibility
of using shape-memory materials for the
fabrication of a small scale device capable
of propelling itself through a fluid. We
wanted to mimic the string like flagella
of certain microorganisms. The idea was
to generate movement by e ecting shape changes
by nucleating and propagating a new material
phase using energy supplied by an outside
source such as a laser. We showed that it
is possible to generate motion by moving
a phase boundary from one end of a shape-memory
beam to the other.
Discrete
model for phase boundaries in solids:
Continuum theories for phase boundary motion
in solids argue that the temporal evolutiuon
of the phase boundary depends critically
on a kinetic law. Our discrete simulations
are motivated by the view that this kinetic
law is a manifestation of the physics of
rearrangement of atoms at the phase boundary
that is neglected in a continuum theory.
We explore this possiblity through simulations
on a chain of masses with bi-stable springs
much like the models used for studying the
propagation of electrical impulses in axons.
We reproduce much of the continuum results
and find that the discrete model is actually
much richer.
Dynamics
of phase boundary motion in strings:
Phase boundary motion had hitherto been
formally treated in 3D continua with specific
problems solved in the one-dimensional context
of bars. We studied the problem in strings
and observed a rich class of phenomena arising
as a result of the interplay of geometric
nonlinearity of the string and material
nonlinearity associated with change of phase.
We also developed a computational method
to solve initial boundary value problems
for strings made of phase transforming materials.
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