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The Four Program Areas
The Nonlinear Systems Program highlights the
following four areas in which groups of faculty have
organized interdisciplinary research training groups
(IRTG).
Complex Networks
Gene Regulation
Machines and Organisms-Locomotion
and Manipulation
Pattern Formation
Complex Networks
The study of complex networks is one of the
most fascinating and important challenges in science
today. IGERT faculty and students at Cornell are exploring
such questions as: What's the most efficient way to
search a large, decentralized network like the World
Wide Web, and what's the best way spread information
across it? For populations with hidden structure, such
as the network of injection drug users in a major city,
how can sociologists obtain statistically reliable information
about the population at a reasonable cost? Why does
the same mathematical pattern show up in the statistics
of forest fires, earthquakes, and blackouts? What accounts
for the remarkable resilience of ecosystems composed
of hundreds of interacting species? How can one make
sense of the cascade of interlocking biochemical reactions
in a single cell? Though these questions are scientifically
diverse, their study is unified by certain mathematical
ideas and techniques borrowed from graph theory, dynamical
systems, statistical physics, and computer science.
Gene Regulation
This group is modeling cellular gene regulation
and signal transduction. Exciting new approaches and
results are just now emerging, and opportunities for
new research projects -- combining modeling, large-scale
computation, and immediate contact with the biotechnology
revolution. Our activities are designed to address three
crucial questions in the post-genomics era. In increasing
order of complexity and specificity, these are:
- How are Genes Regulated?
We are extracting from the genome the regulatory structures
and the large-scale grouping of genes and proteins
into functional units. The goal here is to go from
the genome to the control structures.
- How are RNA and Proteins Manufactured?
We are quantitatively describing transcription (DNA$\to$RNA)
and translation (RNA$\to$protein) by developing dynamical
models of the internal and coupled behavior of the
relevant molecular motors (RNA polymerase and the
ribosome). The goal is to use computational models
to go from RNA to DNA and proteins: to extrapolate
from the massively parallel RNA concentration measurements
from microarray chips backwards to investigate DNA
regulation and forward to predict protein creation
rates.
- How are signals from outside transmitted to the
genome? The goal is to go from the topology} of the
protein interaction network and time series data to
dynamical predictions of environmental changes, dose-response,
and mutations. We use methods from statistical mechanics
and probabalistic Bayesian networks, and model data
drawn directly from protein networks regulating the
cell cycle and cancer.
Through the use of theoretical models and large-scale
computation, and leveraging the enormous experimental
investment by the biology community, we plan to leap
over the next few barriers to develop biologically useful
theories of large subsystems of cellular function.
Machines and Organisms-Locomotion
and Manipulation
Arthropods and vertebrates are complex and nonlinear
biological systems whose versatility and robustness
are the inspiration, if not the envy, of engineers developing
machine locomotion, flight and manipulation. How and
why can a fly with a handful of neurons outperform autonomous
aircraft? Why did four legged animals evolve to transition
from trot to gallop? How can the human hand be the epitome
of dexterous manipulation when it has nonlinear viscoelastic
actuators and sensory delays? This group views machines
and organisms as part of the continuum of solutions
to the mechanical challenges of locomotion, flight and
manipulation. Comparing and contrasting moving machines
and organisms enables us to understand both better.
The group studies the materials, mechanics and structural
topology that give rise to complex mechanical function.
The mechanical capabilities of muscles and tendons are
remarkable and still poorly understood compared to engineering
materials and actuators. Conversely, the best use of
engineering materials and actuators in machine design
is a challenging problem. The group also studies the
stability and control of mechanical function. Arthropods
and vertebrates have evolved to move quickly, efficiently,
and stably. We seek to understand organism function
and optimize machine design by identifying the mechanical
characteristics that make animals fast, efficient, stable
and dexterous. Lastly, the group considers the evolution
of machine design and the design consequences of biological
evolution. That is, how step-by-step changes in a design
subject to multidimensional constraints can add functionality
and improve performance. We open and pursue research
avenues and educational opportunities in these areas
via a synergistic combination of mathematics, neuroscience,
robotics, mechanics, anatomy, physiology,and engineering.
Further information can be found at http://www.mae.cornell.edu/igert/.
Pattern Formation
The past two decades have witnessed major progress
in the theory of pattern formation and in the development
of experimental techniques to analyze the nonequilibrium
dynamics of extended systems. In particular, new imaging
technologies (e.g., fluorescent resonant electron transfer
(FRET), expression and translocation of GFP-fused proteins)
have provided fundamental information regarding complexity
and pattern formation from the molecular and intracellular
scale to the multicellular scale of whole organs and
organisms. Other emerging technologies (e.g., micro-fluidics
and nano patterning and sensors) also are allowing experimentalists
to test specific theoretical predictions. Such tests
currently are being conducted by several teams of investigators,
in conjunction with the IGERT program. The systems being
investigated include the intracellular dynamics of chemotaxis
and cell migration and the dynamics of cardiac cellular
electrical activity.
Signaling molecules and pathways that
regulate cell migration are being studied using micro-machined
single cell incubator and chemo-attractant systems that
allow cells to develop under tailored spatio-temporal
chemical signals. These systems also permit optical
investigations of the spatio-temporal responses of individual
intracellular signaling molecules (via fusion with GFP),
as well as their interactions (via FRET) to temporally
varying chemo-attractant gradients. The gradients are
produced by microfluidic networks, which are being built
with the help of Cornell Nanofabrication Facility and
and Eximer Laser system. These novel approaches based
on nanotechnology will significantly enhance our understanding
of signaling mechanisms of cell migration.
Studies of cardiac cellular electrical
activity are being conducted during catastrophic rhythm
disturbances of the heart, such as ventricular fibrillation
(VF). High resolution 2D and 3D activation and repolarization
maps are constructed using recordings obtained from
nanofabricated multielectrode recording arrays. The
mapping data subsequently are analyzed using a fast
Fourier transform (FFT) technique developed previously
to analyze other dynamical systems (Figure). The resulting
phase maps are used to identify phase singularities
and associated scroll wave filaments, as well as wave
vectors. Identification of the underlying dynamical
features of VF is expected to lead to more effective
therapeutic approaches for prevention of this lethal
arrhythmia.
Contact IGERT for more info
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