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GRASP Seminar Series: Spring 2006
April 20, 12:00 p.m., Berger Auditorium, Skirkanich Hall (210 S. 33rd Street)
Joao Hespanha
University of California at Santa Barbara
"Modeling Chemical Reactions Inside Cells Using Stochastic Hybrid Systems"
Abstract: The time evolution of chemically reacting molecules is sometimes modeled using a stochastic formulation, which takes into account the inherent randomness of molecular motion. This formulation is especially useful for complex reactions inside living cells, where small populations of key reactants can set the stage for significant stochastic effects. In this talk, we show how Stochastic Hybrid Systems can be used to construct stochastic models for chemical reactions.
Hybrid systems combine continuous-time dynamics with
discrete modes of operation. The states of such system usually have
two distinct components: one that evolves continuously, typically according
to a differential equation; and another one that only changes through
instantaneous jumps. To model chemical reactions, we actually need Stochastic
Hybrid Systems (SHSs) where transitions between discrete modes are triggered
by stochastic events, much like transitions between states of a continuous-time
Markov chains. However, the rate at which transitions occur is allowed
to depend on both the continuous and the discrete states of the SHS.
Several tools are available to analyze SHSs. Among these, we discuss
the use of the extended generator, infinite-dimensional moment dynamics,
and finite-dimensional truncations by moment closure. The application
of these tools is illustrated in the context of modeling the evolution
of populations of molecules undergoing a system of chemical reactions.
Biography: João P. Hespanha
received the Licenciatura in electrical and computer engineering from
the Instituto Superior Técnico, Lisbon, Portugal in 1991 and
the Ph.D. degree in electrical engineering and applied science from
Yale University in 1998. He currently holds a Professor position with
the Department of Electrical and Computer Engineering at the University
of California, Santa Barbara. His research interests include hybrid
and switched systems; the modeling and control of communication networks;
distributed control over communication networks (also known as networked
control systems); the use of vision in feedback control; stochastic
modeling in biology; and the control of haptic devices.
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