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NJIT Mathematical Biology Seminar

Tuesday, April 1, 2008, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Phase Response in Bursting Neurons

Erik Sherwood

Department of Mathematics, Boston University

Central pattern generators (CPGs) are localized, autonomous neuronal networks that coordinate the neuromuscular activity underlying essential behaviors such as respiration, digestion, circulation, and locomotion. A key step in deciphering CPGs' production and modulation of broad repertoires of patterned rhythmic output is understanding how phase relationships are established and maintained in networks of rhythmically active, or `bursting,' neurons. This, in turn, requires investigation of the phase response properties of individual bursting neurons.

I will talk about some discoveries about the phase response characteristics of endogenously bursting neurons made in the course modeling the locomotor locomotor CPG responsible for coordinating hindlimb movement in the rodent. I will briefly introduce the CPG model and report some of its surprising phasing behaviors, then discuss in more detail an empirical study of phase response in biophysically realistic bursting neuronal models. The results of this study challenge the validity of several assumptions commonly made by modelers and experimentalists regarding phase resetting behavior; the phase response curves of endogenous bursters differ significantly from those of non-bursting neural oscillators in characteristic ways. Analysis using fast-slow dissection, phase plane analysis, and isochron portraits explains the distinctive shape of burst phase response curves and the dynamics of burst phase response in regimes of both weak and strong coupling, highlighting the role of fast subsystem structures and bifurcations in determining phase response. Time permitting, I will also describe a set of algorithmically coupled discrete maps, derived from the burst phase response curves of single bursters, with which we can represent burst activity in arbitrary network architectures, reducing the interaction of bursting neurons to the properly sequenced iteration of low-dimensional maps.