My research activities have focused on understanding
intra-cellular and inter-cellular processes.
Most of the work has been performed
in the amoebae organism Dictyostelium discoideum which
is an ideal organism to study both single cell events as
well as multi-cellular processes.
On the single cell level, the movement of
Dictyostelium cells are dictated via
chemotactic signals.
Understanding how the cells receive and incorporate these
signals
and how they establish their internal compass is a
fascinating scientific question. In addition,
since chemotaxis plays an important
role in a variety of biological processes including wound
healing,
embryogenesis and cancer, this research has potentially
far reaching applications.
In collaboration with Dr. Loomis, Dr. Levine
and Dr. Thomas of the Salk Institute, I have investigated
the initial stages of chemotaxis in eukaryotic cells.
Several recent studies have demonstrated that these cells,
including Dictyostelium cells
and neutrophils, respond to
chemoattractants by translocation of PH-domain proteins
to the cell membrane where these proteins participate in the
modulation of
the cytoskeleton and relay of the signal.
When the chemoattractant is released from a
pipette, the localization is found predominantly on the
proximal
side of the cell.
The recruitment of PH-domain proteins,
particularly for Dictyostelium
cells,
occurs very rapidly (<2 seconds).
Thus, the mechanism responsible for the
first step in the directional
sensing process of a cell must be able to establish
an asymmetry on the same time scale.
We have proposed a simple mechanism in which a second
messenger, generated by local activation of the membrane,
diffuses
through the interior of the cell, suppresses the activation
of the
back of the cell and converts the temporal gradient into an
initial cellular asymmetry.
A mpeg movie of a numerical simulation of a
two-dimensional cell can be seen
here.
The chemoattractant (cAMP) is released from the left
at the beginning of the movie.
It diffuses to and around the cell, leading to production
of cGMP in the interior of the cell.
There is strong experimental evidence that cGMP is the
leading candidate for our inhibitor.
Thus, the cGMP produced at the membrane at the leading edge
of the cell can suppress
activity at the back of the cell.
Consequently, a PH-domain protein which is attracted to the
active membrane will be primarily localized at the leading
edge of the cell.
The concentration level of the membrane-bound PH-domain protein
is represented in the movie by a greyscale, with white being a high
concentration.
On the multi-cellular level,
Dictyostelium
displays a remarkable self-organization when deprived of
food:
upon starvation, single amoebae aggregate into
to a multicellular slug.
The various stages in its development are
nicely captured in these composite pictures:
Recent experiments, performed by Dr. A. Nicol, show a
fascinating new multi-cellular state when amoebae are
confined to two dimensions.
After aggregation,
the amoebae collect into round ''pancake" structures in which
the cells rotate
around the center of the pancake. This vortex state persists
for many hours and is not, as previously believed,
due to rotating waves of cAMP.
To provide an alternative mechanism for the self-organization
of
the Dictyostelium cells, we have developed a new model
of the
dynamics of self-propelled deformable objects.
In this model, we show that cohesive energy between the
cells,
together with a coupling between the self-generated
propulsive force and
the cell's configuration produces a self-organized
vortex state.
The angular velocity profiles of the experiment and of the
model
are qualitatively similar.
This work was highlighted in the
The American Institute of Physics Bulletin of Physics News
(August 16, 1999)
and featured in a New York Times article (August 31, 1999).
Several mpeg movies which illustrate the research can be downloaded or viewed
by clicking on the thumbnails below:
Experimental movies
Cell sorting in a two-dimensional mound in Dictyostelium; cells are
labeled with cotb::gfp.
Cell sorting in a two-dimensional toroidal mound in Dictyostelium; cells
are
labeled with cotb::gfp.
Cells marked with tagb:gfp in a two-dimensional mound in Dictyostelium.
Cells in a two-dimensional mound in Dictyostelium.
Transient phase of rotational organization in a two-dimensional mound in
Dictyostelium.
Cells marked with car1:gfp in a two-dimensional mound in Dictyostelium.
Movies of simulations
A model of the self-organized rotational state.
A model for cell sorting via differential adhesion.
A sorting model including both persistent motion and differential adhesion
A model of the self-organized rotational state.
Self-organization and pattern formation through the
motion of self-propelled entities are not limited
to Dictyostelium.
Examples can be found in a variety of fields and include
animal aggregation (fish schools and bird flocks) and
traffic patterns (traffic jams).
Particularly fascinating is
the problem of flocking, in which a large number of
moving particles (e.g. fish or birds) remain coherent over
long times and distances.
The challenge for modelers is to construct a model that
is simple enough to analyze numerically or analytically yet
captures the essential ingredients in a realistic way.
In recent work,
we have developed a discrete model consisting
of self-propelled particles that obey simple
interaction rules.
An example of the dynamics displayed by this model can be seen in the
mpeg movie to the right.
Here, the particles' velocity depends on the average velocity within
a certain neighborhood. When started from random initial conditions, as
in the movie, a set of interacting particles can form a rotating vortex,
often seen in fish schools but also
observed in bacteria and amoebae (see above),
in which the particles rotate around a common center.
In a first step towards an analytical treatment of the
problem, we developed a continuum version of our
discrete model. The agreement
between the discrete and the continuum model is excellent.
Our future work will focus on
understanding the pathways involved in
the signaling stage of Dicty's development and how this,
ultimately, leads to multicellular organization.
An attractive network has been proposed by Bill Loomis
and Mike Laub.
To better understand the dynamics of the Laub-Loomis model
I have created a Java applet. This applet allows the user
to simulate the network for arbitrary rate constants.
To run this applet, simply click on the picture of the
network below.
In healthy people,
an electric wave passes over the heart's surface about once a
second
causing the tissue to contract in a regular fashion.
Some people however, suffer from
cardiac arrhythmias which cause irregular activity of the
heart.
Certain arrhythmias are relatively benign, but others have
dire consequences.
Ventricular fibrillation (VF) is a fatal cardiac
arrhythmia during which the heart looses its ability to
contract and pump in a coherent manner.
Unless prompt medical attention is available, VF will lead to
death within minutes.
It is the main cause of sudden cardiac death among 300,000
Americans annually.
My research focuses on the understanding and prevention of
VF.
In collaboration with Prof. A. Karma of
Northeastern University and Dr. F. Fenton of the Long Island
Jewish
Medical Center and Hofstra University, I have developed a control scheme which
prevents the occurrence of alternans, a precursor of VF.
The control scheme
is based on applying a feedback current at
a discrete set of control points during the
repolarizing phase of the action potential.
We have shown the feasibility of the scheme in both one
and two dimensions and have suggested experimental
implementations.
Tissue heterogeneities are believed to play a crucial role in
the onset of VF and other cardiac arrhythmias.
In a first step towards understanding the role of tissue
heterogeneities,
I have studied the effect of cardiac tissue anisotropy
in the breakup of vortex
filaments using two detailed cardiac models:
the Luo-Rudy model and the Beeler-Reuter model.
These vortex
filaments can arise in cardiac tissue when an electric wave
is partially blocked and reenters previously excited tissue.
A consequent break-up can results in incoherent behavior
similar to ventricular fibrillation.
I found that break-up only occurs in one of the two
cardiac models (the BR model) and
this model dependent behavior
might be based on spiral tip trajectories.
Thus, these results strongly suggest that the spiral tip
trajectory
plays a crucial role in anisotropy induced filament break-up.
To investigate the role
of tissue heterogeneities and to
faithfully model the electrical wave propagation in actual
hearts
requires a rigorous implementation of the geometry and the
tissue fiber orientation of the heart.
To date, most numerical simulations of cardiac dynamics have
sidestepped this issue by using
simplified geometries including sheets of tissue and tissue
wedges.
I have recently developed a novel algorithm for modeling
electric wave propagation in anatomical models of the heart.
The algorithm is demonstrated via the simulation of a
detailed electrophysiological model on a spatially
resolved anatomical model of the rabbit
heart.
Particular care was paid to the implementation of
no-flux boundary conditions at the heart surface.
The algorithm, with its extensive use of look-up tables and
memory saving techniques, can be used on single processor
machines.
This algorithm will allow me, and other investigators,
to address a multitude of exciting problems including the
effect of the heart geometry on the initiation of
arrhythmias,
the consequence of spatial heterogeneity in the ventricular
walls
and the efficacy of cardiac drugs.
Several AVI movies which show the propagation of electrical waves
in the rabbit heart are demonstrated below.
The anatomical data pertaining to the rabbit heart, i.e. actual geometry
and the fiber architecture, were kindly provided by the
McCulloch lab in the Biomedical Engineering department of UCSD.
The propagation of an electrical wave in a rabbit
heart with (left) and without (right) the inclusion of the
fiber architecture.
The membrane potential is color-coded according to the
bar in the figure, with red representing depolarized tissue and blue
hyperpolarized tissue.
The isosurfaces of membrane potential for the above
propagation in the anisotropic heart.
The creation of a spiral wave in the isotropic heart.
Note that after several rotations, the spirals disappear.
The creation of a spiral wave in the anisotropic heart.
Unlike the isotropic case, spiral activity is sustained.
A snapshot in time during the spiral wave propagation in the anisotropic
heart.
Coupled nonlinear oscillators
are present in a wide variety
of systems in nearly every field of science, including
biology, physics, chemistry and medicine.
Furthermore, they play an important role in many
technological applications.
Not surprisingly, they have been studied intensively
in the past and a great deal of progress has been made
in understanding the dynamics of coupled nonlinear
oscillators.
My research has paid particular attention to the response
of coupled nonlinear oscillator systems to noise.
This interest is partially driven by the realization that
noise is not necessarily "bad" and can sometimes be
used to increase the system's sensitivity to input signals.
I have investigated,
in collaboration with Dr. Adi Bulsara and Dr. J. Acebrón,
noise-related phenomena
in
dc Superconducting Quantum Interference Devices (SQUIDs).
SQUIDs are the most sensitive magnetic field detectors in
existence
and are widely used in a variety of fields including
biomagnetics, geophysics and explosive detection.
Unfortunately, SQUIDs are very sensitive to noise which
often limits their applicability.
Past research activities have focused primarily on
designing and developing sophisticated shielding devices.
Instead, our efforts have concentrated
on ways to use the noise
to increase the sensitivity of the device and
searches for the area in parameter space where the
SQUID is optimally sensitive.
To investigate the dynamics of noisy SQUIDs we first
derived Fokker-Planck equations (FPE) for both
the single SQUID and for arrays of globally coupled SQUIDs.
To solve the FPE numerically, we have developed
an efficient spectral method
which exploits the periodicity of the
probability density.
The numerical method, combined with the exact solutions,
has allowed us to rapidly
explore the noise-mediated dynamics as
a function of the control parameters.
In addition, we have studied the single and globally coupled
arrays
of SQUIDs in the presence of
a weak external time-sinusoidal probe signal.
When the frequency of this ``probe'' signal is close to the
frequency of
the unprobed system we observed a resonance behavior,
enabling us to determine the underlying frequency of the
SQUID system.
Furthermore, we found that the frequency of the
underlying solution decreases with increasing coupling
strength.
Combining this finding with the resonance phenomenon
we were able to suggest ways
to dramatically enhance the sensitive of SQUIDs to weak low
frequency signals.
We have verified that the resonance behavior
is not limited to SQUIDs and
can thus be used to find underlying frequency of noisy
systems.
We are currently investigating
this resonance in arrays of coupled FitzHugh-Nagumo elements,
a commonly used simplified model of nerve cells, as
a first step in determining if neurons use this resonance to
detect signals.
In earlier work,
a mean field model of the complex Ginzburg-Landau
equation was investigated and
its dynamical states were determined.
In collaboration with Dr. Hakim of the
Ecole Normale Supérieure, I found that the inclusion of
noise
can enhance the periodicity
of the signal and can induce periodic behavior.
A model of globally coupled lasers,
offering similarities with the complex Ginzburg-Landau
equation
mentioned above, was also studied.
Finally,
the dynamics of
large networks of globally pulse-coupled
integrate and fire neurons was investigated in collaboration
with
Dr. Karma and a noise-induced synchronized state
was discovered.
As the resulting gain in coherence and synchronization
is achieved nearly instantaneously, it suggests the
interesting possibility that neurons use noise to produce
coherent signals.
My research focuses on the study
of pattern forming systems in general and
complex solidification problems in particular.
Through the use of efficient modeling techniques,
questions concerning
the selection of solidification micro structures are
addressed.
This is of paramount importance in materials processing since
the selected micro structures directly determine
the strength of the material.
A recent new asymptotic
analysis of the phase field method has lead
to a very fast and accurate modeling technique.
An example of this work, the temperature field around
a two-dimensional dendrite, is shown here:
With the new phase field we have been able to simulate, for the
first time ever, the dynamical growth of three dimensional
dendrites. In this case, the surface energy anisotropy plays a crucial role:
without anisotropy there does not exist a stable operating state
and the crystal undergoes a series of tip splitting
instabilities. For an example of a zero anisotropy shape obtained by
our simulations click on the thumbnail.
With anisotropy on the other hand, steady state dendrites will
be selected. Our simulations were performed for a six-fold
anisotropy, corresponding to a large class of materials.
Here is an example of our numerical result for 5% anisotropy.
Recently, we have extended our phase-field method to include
thermal noise which is believed to responsible for the formation
of sidebranches. A comparison between a linear analytical theory
and our numerical results revealed that the theory is only valid
near the tip but fails to describe sidebranches accurately
further away from the tip.
