Abstracts of Posters 8-th European Conference on Mathematical ...

<strong>European</strong> <strong>Conference</strong> on Ma<strong>th</strong>ematical and Theoretical Biology 2011
Poster Session; Friday, July 1, 20:00
Peter Rowat
Institute for Neural Computation, University <strong>of</strong> California San Diego,
USA
e-mail: prowat@ucsd.edu
Priscilla Greenwood
Department <strong>of</strong> Ma<strong>th</strong>ematics, University <strong>of</strong> British Columbia, Vancouver,
BC, Canada
Identification and continuity <strong>of</strong> <strong>th</strong>e distributions <strong>of</strong>
burst-leng<strong>th</strong> and inter-spike-intervals in <strong>th</strong>e stochastic
Morris-Lecar neuron
Using <strong>th</strong>e Morris-Lecar model neuron wi<strong>th</strong> a type II parameter set and K+ channel
noise, we investigate <strong>th</strong>e inter-spike interval distribution as increasing levels <strong>of</strong> applied
current drive <strong>th</strong>e model <strong>th</strong>rough a sub-critical Hopf bifurcation. Our goal was
to provide a quantitative description <strong>of</strong> <strong>th</strong>e distributions associated wi<strong>th</strong> spiking as
a function <strong>of</strong> applied current. The model generates bursty spiking behavior wi<strong>th</strong>
sequences <strong>of</strong> random numbers <strong>of</strong> spikes (bursts) separated by inter-burst intervals
<strong>of</strong> random leng<strong>th</strong>. This kind <strong>of</strong> spiking behavior is found in many places in <strong>th</strong>e nervous
system, most notably, perhaps, in stuttering inhibitory interneurons in cortex.
Here we show several practical and inviting aspects <strong>of</strong> <strong>th</strong>is model, combining analysis
<strong>of</strong> <strong>th</strong>e stochastic dynamics <strong>of</strong> <strong>th</strong>e model wi<strong>th</strong> estimation based on simulations.
We show <strong>th</strong>at <strong>th</strong>e parameter <strong>of</strong> <strong>th</strong>e exponential tail <strong>of</strong> <strong>th</strong>e ISI distribution is in
fact continuous over <strong>th</strong>e entire range <strong>of</strong> plausible applied current, regardless <strong>of</strong> <strong>th</strong>e
bifurcations in <strong>th</strong>e phase-portrait <strong>of</strong> <strong>th</strong>e model. Fur<strong>th</strong>er, we show <strong>th</strong>at <strong>th</strong>e spike
sequence leng<strong>th</strong>, apparently studied for <strong>th</strong>e first time here, has a geometric distribution
whose associated parameter is continuous as a function <strong>of</strong> applied current
over <strong>th</strong>e entire input range. Hence <strong>th</strong>is model is applicable over a much wider range
<strong>of</strong> applied current <strong>th</strong>an has been <strong>th</strong>ought.
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