Authors: Muhammad Abdulla, Jonathan Rubin, Ryan Phillips
Faculty Mentor: Dr. Jonathan Rubin
College: College of Liberal Arts and Sciences
This research investigates the mechanisms underlying neuronal bursting. Neurons have been modeled as relatively simple dynamical systems for decades. However, neuronal “bursting,” periodic behavior characterized by periods of high frequency spiking alternating with periods of quiescence, is quite complex, and can’t be modeled as simply as other behaviors. Multiple parameters, operating on different time scales, i.e. one parameter having significantly faster dynamics than the other, are necessary to model this behavior. (Ermentrout, 2010) In the past, different biological factors, including positive feedback currents (Butera, 1999), dynamic ion concentrations (Barreto, 2010), and different experimental conditions (Bacak, 2016), have been incorporated into mathematical models to capture various aspects of neuronal bursting. This paper proposes a mathematical model that includes both dynamic ion concentrations and positive feedback via persistent sodium currents, to model neuronal bursting under physiological conditions. Bifurcation analysis of this autonomous dynamical system offers insights into the mathematical mechanisms underlying biologically observed solutions, in which neuronal activity gradually evolves from sparse tonic spiking to full bursting, as well as other activity patterns emerging as neurons transition into the bursting state.