Applied Maths Seminar: Linda Petzold -- Computational Methods for Phase Response Analysis of Circadian Clocks

Abstract: Circadian clocks govern daily behaviors of organisms in all kingdoms
of life. In mammals, the master clock resides in the suprachiasmatic
nucleus (SCN) of the hypothalamus. It is composed of thousands of
neurons, each of which contains a sloppy oscillator - a molecular
clock governed by a transcriptional feedback network. Via
intercellular signaling, the cell population synchronizes
spontaneously, forming a coherent oscillation. This multi-oscillator
is then entrained to its environment by the daily light/dark cycle.

Both at the cellular and tissular levels, the most important feature
of the clock is its ability not simply to keep time, but to adjust its
time, or phase, to signals. We present the parametric impulse phase
response curve (pIPRC), an analytical analog to the phase response
curve (PRC) used experimentally. We use the pIPRC to understand both
the consequences of intercellular signaling and the light entrainment
process. Further, we determine which model components determine the
phase response behavior of a single oscillator by using a novel model
reduction technique. We reduce the number of model components while
preserving the pIPRC and then incorporate the resultant model into a
couple SCN tissue model. Emergent properties, including the ability of
the population to synchronize spontaneously are preserved in the
reduction.  Finally, we present some mathematical tools for the study
of synchronization in a network of coupled, noisy oscillators.

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Professor Linda Petzold, Australian Mathematical Sciences 
Institute Lecturer 2007-2008: see http://www.amsi.org.au/

Dr. Linda Petzold is currently Professor in the Department of Computer
Science (Chair 2003-2007) and the Department of Mechanical
Engineering, and Director of the Computational Science and Engineering
Program at the University of California Santa Barbara.

She received her Ph.D. in Computer Science in 1978 from the University
of Illinois. From 1978-1985 she was a member of the Applied
Mathematics Group at Sandia National Laboratories in Livermore,
California, from 1985-1991 she was Group Leader of the Numerical
Mathematics Group at Lawrence Livermore National Laboratory, and from
1991-1997 she was Professor in the Department of Computer Science at
the University of Minnesota.

Dr. Petzold is a member of the US National Academy of Engineering. She
is a Fellow of the ASME and of the AAAS. She was awarded the Wilkinson
Prize for Numerical Software in 1991, the Dahlquist Prize in 1999, and
the AWM/SIAM Sonia Kovalevski Prize in 2003.  She served as SIAM
(Society for Industrial and Applied Mathematics) Vice President at
Large from 2000-2001, as SIAM Vice President for Publications from
1993-1998, and as Editor in Chief of the SIAM Journal on Scientific
Computing from 1989-1993.