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GRASP Seminar Series: Spring 2006
March 23, 12:00 p.m., Berger Auditorium, Skirkanich Hall (210 S. 33rd Street)
Mustafa Khammash
University of California at Santa Barbara
"Noise in Gene Regulatory Networks: Biological Role and Mathematical Analysis"
Abstract: The
cellular environment is abuzz with noise. Generated by random molecular
events, cellular noise not only results in random fluctuations within
individual cells but it is also a source of phenotypic variability
among
clonal cellular populations. In some instances fluctuations
are suppressed
downstream through an intricate dynamical network that acts to filter
the
noise. Yet in other instances, noise induced fluctuations are exploited
to
the cell's advantage. Intriguing mechanisms that rely on noise include
stochastic switches, coherence resonance in oscillators, and stochastic
focusing. While mathematical models of genetic networks often
represents
gene expression and regulation as deterministic processes with
continuous
variables, the stochastic nature of cellular noise necessitates an
approach
that models these variables as discrete and stochastic. In
this framework,
probability densities of the system states evolve according to a
(usually
infinite dimensional) Chemical Master Equation (CME). Until recently,
sample
trajectories have been computed almost exclusively with Kinetic Monte
Carlo
methods, such as Gillespie's Stochastic Simulation Algorithm. In this
talk
we present a new direct approach for computing the relevant statistics,
which involves the projection of the solution of the CME onto finite
subsets. We illustrate the algorithm underlying our Finite State
Projection
approach and introduce a variety of systems theory based modifications
and
enhancements that enable large reductions and increased efficiency with
little to no loss in accuracy. Model reduction techniques based on
linear
perturbation theory allow for the systematic projection of multiple
time
scale dynamics onto a slowly varying manifold of much smaller
dimension. The
proposed projection approach is illustrated on few important models of
genetic regulatory networks.
Biography: Mustafa
Khammash is the Director of the Center for Control, Dynamical
systems, and Computations (CCDC) at the University of California at
Santa
Barbara (UCSB). He also holds a Professor appointment in the Mechanical
Engineering at UCSB. He received his B.S. degree from Texas A&M
University
in 1986 and his Ph.D. from Rice University in 1990, both in electrical
engineering. In 1990, he joined the Electrical Engineering Department
at
Iowa State University where he created the dynamics and control program
and
led that control group until 2002, when he joined the dynamics and
control
group in the department of Mechanical and Environmental Engineering at
UCSB.
Khammash¹s research interests are in the area of control
theory and its
applications to engineering and to biological systems. His theoretical
work
lies in the area of robustness analysis and synthesis of interconnected
dynamic systems, where he has developed methodology for the analysis
and
design of robust control systems under persistent disturbances and
model
uncertainty. His work also focuses on using control theory for the
quantitative analysis of networks of dynamically interacting biological
components, with the goal of reverse engineering these networks to
understand how they robustly achieve biological function.
Khammash is a
Fellow of the IEEE. He is the recipient of the National Science
Foundation
Young Investigator Award, the Japan Society for the Promotion of
Science
(JSPS) Fellowship, the Iowa State University Foundation Early
Achievement in
Research and Scholarship Award, the ISU College of Engineering Young
Faculty
Research Award, and the Ralph Budd Best Engineering PhD Thesis Award.
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