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NJIT Mathematical Biology Seminar

Tuesday, January 22, 2008, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Phase response curves of square wave bursting oscillator

Ikemebuna Agbanusi & Alborz Yarahmadi

Undergraduate Biology and Math Training Program, NJIT

ABSTRACT: We study the phase response properties of the PD neuron in the Stomato-gastric Ganglion (STG). We use model equations describing a square wave bursting oscillation to define and analyze the phase response dynamics for weak and strong perturbations and we construct phase response curves (PRCs). In the real and model neurons, we observe that the PRC saturates with amplitude. We also see that for strong perturbations, much of the phase response is due either to the addition of spikes in the active phase, the deletion of spikes or the termination of the active phase of the oscillation. We break apart the phase response over the active and silent phases of the oscillation and describe algorithms to predict the full phase response from both pieces to a first approximation. We also discuss here two possible methods to understand the phase response in the active phase.We also use ideas from geometric singular perturbation theory and dynamical systems theory to describe burst truncation and in particular it is shown that the saturation of the PRC can be explained using the calcium dynamics for strong inhibition in the active phase and strong excitation in the silent. Furthermore, the discontinuity in the PRC for strong excitation is shown to be a topological property in the sense that it cannot be removed.