### Monday, August 3, 2015 (10:00 a.m. in Yost 306)

**Title: **Channel Noise And Firing Irregularity In Hybrid Markov Models Of The Morris-Lecar Neuron

**Speaker:** Casey Bennett (Case Western Reserve University)

**Advisor:** Peter Thomas (Associate Professor, Case Western Reserve University)

**Abstract: **Using a stochastic version of the Morris-Lecar model neuron, a scaling method is introduced in which the ODE that propagates voltage is invariant, but the underlying Markov chain which controls the discrete channel states converges to progressively simpler stochastic descriptions. The relationship between the underlying stochastic description of channel states can then be directly related to the induced interspike interval (ISI) variability as the system is scaled. Specifically, an exact Markov chain model, a piecewise constant propensity approximation to the exact model, and a Langevin approximation are derived. For large systems the ISI variance is found in terms of channel specific phase response curves. Through the development of powerful numerical implementations on a high performance computing cluster and ecient error estimation techniques, convergence of each model to the others is systematically evaluated, so that given any channel configuration and error tolerance, the fastest method can be easily identified.

The full thesis can be found here: http://wikisend.com/download/752814/CaseyBennett_Thesis_Committee_July10.pdf