Dr. Eugene Izhikevich
The Neurosciences Institute
San Diego, CA

Title

"Minimal Electrophysiological Models for Spiking and Bursting"

Abstract

There are more than 20 known voltage- and second-messenger-gated membrane currents in neurons having diverse activation and inactivation dynamics. Almost any combination of the currents would result in interesting non-linear behavior, such as neural excitability or bursting. Therefore, there are more than 2²⁰ (millions) different electrophysiological Hodgkin-Huxley-type models. We are interested in classifying all such models.

Let us do the following thought experiment: Consider any such model having a limit cycle attractor. Let us remove completely a current or one of its gating variables, and ask the question ``Does the reduced model have a limit cycle attractor, at least for some values of parameters?'' If it does, we remove one more gating variable or current, and proceed until we arrive at the model that satisfies the following two properties:
1. It has a limit cycle attractor, at least for some values of parameters.
2. If one removes any current or gating variable, the model has only equilibrium attractors for any values of parameters.

We refer to such a model as being *minimal*. We show that there are only a few such minimal models, and any other electrophysiological model is a combination of the minimal ones.