N. Gov,
A. Gopinathan, "Dynamics of Membranes Driven by Actin Polymerization",
Biophys .J, 90(2), 454(2006)
Actin based propulsion : A key process
in motility is the production of a protrusive force that drives
the cell’s leading edge forward. It has been well established that
the cytoskeletal protein actin forms a dense, branched and crosslinked
network of filaments at the leading edge and it is the polymerization
of these filaments that gives rise to the force. The discovery that
intracellular pathogens like listeria use the cell’s actin machinery
to propel themselves played a vital role in establishing the biochemical
basis of motility. However, there still remains a hotly debated
question: How does the polymerization activity at the molecular
scale translate into a macroscopic force? This led to the
development of both the microscopic view that considers the protrusive
force as arising from the monomer-by-monomer growth of a population
of these filaments and macroscopic models that treat the filaments
as a continuum gel. Both of these describe the phenomenon albeit
at very different length and time scales and are unable to satisfactorily
account for all aspects of the motility (see for example the work
by Kuo Lab. To get a
correct and unified picture, we introduced a “dynamic gel” picture
where we treated the actin network as an elastic gel modeled by a finite
element mesh while allowing for spatial variations in polymerization
activity .We treat the actin comet tail
as an elastic continuum tethered to the rear of the bacterium. The
interplay of polymerization and tethering gives rise to inhomogeneous
stresses calculated with a finite element analysis. We quantitatively
reproduce many distinctive features of actin propulsion that have been
observed experimentally, including stepped motion, hopping, tail shape
and the propulsion of flat surfaces.
Ajay Gopinathan and Andrea Liu, "Elastic Actin Tails: Shape,
Stresses and Propulsion" in preparation
Biopolymer bundles:
Bundles of stiff biopolymer bundles such as actin and microtubules
among others form important structural elements in the cell
including filopodia, microvili, cilia and contractile rings.
These structures have specific functions to perform that rely crucially
on their mechanical properties which in turn depend on the internal
organization of the bundles. Recent investigations of microtubule
bundles that were assembled in vitro in the presence of different
linker molecules were carried out here at the Safinya Lab.
The resultant bundles were significantly curved at wavelengths
several orders of magnitude less than their persistence length. We
show that these severe distortions of the bundles can be explained
by the presence of edge dislocation and twist defects indicating that
these defects could play a significant role in vivo.
Ajay Gopinathan, M. Henle, U. Raviv and D. Needleman, "Defect
Induced Morphologies of Biopolymer Bundles" in preparation
Polymer Translocation in Crowded Environments
: Polymer translocation is an extensively studied topic and
is biologically an important process that occurs in a variety
of circumstances where biopolymers (like DNA say from a virus) are
transported across a membrane into a different environment (say
the cell interior). An important question that arises is : How does
the crowded nature of the cellular cytoplasm affect this process?
While this has been addressed in the context of protein folding
and biochemical rates in vivo, one would expect this to have a dramatic
effect on translocation. We systematically treat the entropic penalty
due to the crowded environment and find new power law scalings of
the translocation time with polymer length. We also find that the
crowding inflicts a significant barrier and that adding a chemical
potential gradient in order to overcome this results in very interesting
translocation regimes as a function of crowding, chemical potential
and polymer length.
work in progress (with Yong-Woon KIm)
Cytoskeletal Kinetics : Controlling the polymerization
activity of cytoskeletal actin network plays an important
role in cell motility. Even in the absence of motility, the
actin network is not static but evolves via kinetic processes
such as actin polymerization, depolymerization, capping, branching
and severing which are regulated by various proteins in the
cell .
Abnormal levels of expression of these regulatory
proteins lead to diseased states characterized by drastic morphological
changes in the cytoskeleton and loss of function. It is therefore
imperative to understand how the regulatory protein concentrations
act in concert to maintain a normal cytoskeletal morphology. Previous
work treated one or more but not all of the above mentioned processes.
We recently studied the steady-state morphology of such networks
and derived simple expressions for characteristics such as the length
distribution of filaments and branches, branch spacing, and monomer
to filamentous actin ratio as functions of regulatory protein concentrations.
We found that these characteristics exhibit several scaling regimes
with respect to the different protein concentrations and that the
severing and branching activities are optimally coupled in the cell.
A. Gopinathan, A.J. Liu, "Severing, Branching and their
Optimal Coupling in Dynamic Actin Structures", to be submitted
to Phys. Rev. Lett
Statistically locked-in transport : Measurements
of colloidal transport through arrays of micrometer-scale potential wells
created with holographic optical tweezers were performed at the Grier Lab . Varying the orientation
of the trap array relative to the external driving force resulted in a hierarchy
of lock-in transitions analogous to symmetry-selecting processes in a wide
variety of systems with implications for immediate applications for continuously
fractionating particles, biological cells, and macromolecules. Classical
particles driven through periodically modulated potential energy
landscapes are predicted to follow a Devil's staircase hierarchy
of commensurate trajectories depending on the orientation of
the driving force.The experiments did indeed reveal such a hierarchy,
but not with the predicted structure. The microscopic trajectories,
moreover, appeared to be random, with commensurability emerging
only in a statistical sense. We introduced an idealized model for
periodically modulated transport in the
presence of randomness that captures both the structure
and statistics of such statistically locked-in trajectories.
Ajay Gopinathan,
D.G. Grier, "Statistically Locked-in Transport through Periodic
Potential Arrays", Phys. Rev. Lett., 92, 130602 (2004)
Self Assembly of Nanowires
: Experiments at the Jaeger lab
have shown that when metals are evaporated and deposited
on a templated substrate, like a phase separated diblock
copolymer surface, certain metals show a marked preference
for one phase over the other and in certain cases form continuous
wires of nanometer scale. What surprised us was the stability
of these wires which by surface energy considerations should exhibit
the pearling instability (a liquid cylinder breaking up into
drops ). We proposed an explanation based on the rate limiting
step of nanocluster coalescence being nucleation of new terraces.
We show that the different morphologies obtained can be understood
in terms of the relative importance of the energetics and kinetics. We
also show the existence of ``non-trivial'' correlations between
adjacent wires that can be understood based on a purely kinetic mechanism.
We also compare these correlations quantitatively to those obtained from
simulations done with the relevant experimental parameters and find them
in good agreement.
Ajay Gopinathan,
"Kinetic Self-Assembly of Metals on Co-Polymer Templates",
Phys. Rev. E, 71(4) 041601
(2005)
Non-equilibrium kinetics
: Deliberately miscutting a crystal surface
can produce a regular array of monoatomic steps. Under
suitable conditions (temperature, oxygen dosage) these
steps can be made to merge to form double height double width
steps. Experiments performed at the Sibener lab have been
instrumental in elucidating the mechanism of this process.
It is found that step doubling proceeds via a nucleation
step where two adjacent step edges come together at a "point"
and then the two steps "zipper" together irreversibly. Theoretical
effort has gone into describing the mechanism for a pair
of steps. However when there is a large array of steps, as
in reality, the dynamical process of nucleation and zippering
gives rise to a non-equilibrium evolution of the surface morphology.
One also expects defect structures of various types. We
study the time evolution of the surface morphology by making an approximate
mapping to the parking lot problem. This allows us to predict
the number and nature of the defects as well as the time evolution.
We also suggest protocols that can help generate surfaces with fewer
defects in less time.
Defect Formation
and Kinetics of Atomic Terrace Merging, Ajay
Gopinathan and T.A. Witten, Phys. Rev. E 70, 041603
(2004)
Crumpling - Dynamics
: A crumpled sheet has certain characteristic features
that we are all familiar with. There are the sharply curved
places - ridges and the almost flat places- the facets.
Extensive work characterizing the static properties of the
ridges and facets has been done by Witten and coworkers.
But we knew of no characterization of the dynamics. We were interested
in the question : what happens if we tap a certain point on a crumpled
sheet and listen at another? What changes in elastic wave propagation
arise due to the unique structures in a crumpled sheet ? To answer
this we first derived the wave equation governing transverse elastic
waves on an arbitratily curved and strained surface using a
Lagrangian formalism. Our analysis led us to the conclusion that the
ridges act as barriers leading to the trapping of certain modes
within the facets!!
Trapping of Vibrational
Energy in Crumpled Sheets : Ajay Gopinathan,
T.A. Witten and S.C. Venkataramani. Phys. Rev. E.,
65, 036613 (2002)
Charged Colloidal Systems
: There is now a growing body of evidence that like
charge colloidal spheres dispersed in water need not simply
repel each other. Under certain conditions they actually attract.
Experiments like those performed at the Grier Lab are helping us
gain insights into this phenomenon.In this work we investigated the influence
of geometric confinement on the free energy of an idealized model for charge-stabilized
colloidal suspensions. The mean-field Poisson-Boltzmann formulation for
this system predicts pure repulsion among macroionic colloidal spheres.
However fluctuations in the simple ions distribution provide a mechanism
for the macroions to attract each other at large separations.Although
this Casimir interaction long-ranged,we found it was too weak to influence
colloidal crystals dynamics.
Weak Long-Ranged Casimir
Attraction in Colloidal Crystals : Ajay Gopinathan,
Tong Zhou, S.N. Coppersmith, L.P. Kadanoff and
D.G. Grier. Europhys. Lett., 57 (3), 451 (2002)
Phase Ordering Kinetics
: Consider a collection of spins at a high temperature
that is suddenly quenched to zero temperature. What follows
is domain coarsening where domains of up and down spins grow
and grow. An interesting question is : given a spin what is the
probability that after time t it still retains its original state
without ever having flipped? An exponent characterizing how this
probability scales with the typical length scale in the system
is called the persistence exponent beta. We found an exact
expression for this quantity for 1D q-state Potts' system (spin
with q states) with a suitably chosen model of coarsening.
Scaling Exponent Beta
for Coarsening in a 1D q-state Potts' System : Ajay
Gopinathan. J.Phys. A, 31 (1998) 5499
