School of Mathematical Sciences, Nottingham University, UK
Wednesday 27 May 2009
Seminar Room B10 (Basement)
Alexandra House, 17 Queen Square, London, WC1N 3AR
Dynamics of Morris-Lecar networks
The Morris-Lecar (ML) neuron model is a two dimensional conductance based model that is often used as an idealised fast-spiking pyramidal neuron. Its planar nature has encouraged much analysis of the single neuron model using tools from phase-plane 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 weakly-coupled 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 piece-wise 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 ultra-low frequency synchronised oscillations.