EECS500 Fall 2014 Department Colloquium

Peter Thomas
Control of Rhythmic Motions in Biological Systems
Case Western Reserve University
White Building, Room 411
11:30 AM - 12:30 PM
November 18, 2014

We explore the role of metastable dynamical equilibria in two biological motor control systems.  In a closed-loop model for a respiratory control circuit we demonstrate the possibility of multistable dynamics supporting both eupnea (normal breathing) and tachypnea (pathologically rapid, shallow breathing), and show that the ion channel proteins normally expressed in the brainstem breathing control center (the pre-Bötzinger complex) have intrinsic dynamical properties that protect against brief bouts of imposed hypoxia.  In a model for how sensory feedback regulates biting and swallowing motions in the marine mollusk Aplysia californica, we show that feedback can regulate the passage of a limit cycle trajectory near a sequence of saddle fixed points, thereby controlling the timing and intensity of a sequence of motor activations.  Moreover we demonstrate a transition between a "high sensitivity" and a "low sensitivity" regime coinciding with a sliding bifurcation, and we provide evidence that our model is consistent with experimental data.

This is joint work with Chris Wilson and Casey
Diekman (respiratory model) and Hillel Chiel, Kendrick Shaw, David Lyttle, Jeff Gill, and Youngmin Park (biting/swallowing model).


Peter J. Thomas joined CWRU in 2006.  He is currently Associate Professor of Mathematics, Applied Mathematics, and Statistics, with secondary appointments in Biology and in Cognitive Science.  Prof. Thomas' research interests include the application of control theory, information theory, dynamical systems, and stochastic processes to understanding the function of signal transduction and neural networks.  Prior to CWRU, Prof. Thomas taught at Oberlin College, did postdoctoral work in computational neurobiology at the Salk Institute for Biological Studies with Terrence Sejnowski, and developed a mathematical theory for the organization of the mammalian visual cortex as a doctoral student of Jack Cowan at the University of Chicago.  In his spare time he enjoys music, hiking, and aikido.