
School of Mathematical Sciences, Nottingham University, UK
Wednesday 27 May 2009
16.00
Seminar Room B10 (Basement)
Alexandra House, 17 Queen Square, London, WC1N 3AR
Dynamics of MorrisLecar networks
The MorrisLecar (ML) neuron model is a two dimensional conductance based model that is often used as an idealised fastspiking pyramidal neuron. Its planar nature has encouraged much analysis of the single neuron model using tools from phaseplane analysis and the "geometry of excitability". When treating synaptic or gap junction coupled networks of oscillating ML neurons these techniques are the natural basis for developing a weaklycoupled oscillator theory. However, to probe network dynamics in the strong coupling regime requires an alternative approach. I will show how results in this area can be obtained by using a piecewise linear caricature of the ML model. In illustration of the usefulness of such an approach I will first consider gap junction coupling and show how to analyse emergent fluctuations in the mean membrane potential (as instabilities of an asynchronous network state). Next I will treat synaptically coupled networks with a phenomenological form of retrograde second messenger signalling that can support depolarisation induced suppression of excitation. In this case I will describe a mechanism for the emergence of ultralow frequency synchronised oscillations.