Christoph Kirst (Max Planck Institute for Dynamics and Self-Organization, Network Dynamics Group, Göttingen, Germany)

Abstract:

Here we show that a transition from type I to type II can be dynamically induced in a large number of conductance-based neuron models (including Wang-Buszaki, Morris-Lecar, Connor- Stevens, Erisir et al.), e.g. by an increase in leak conductance. We mathematically prove that the bifurcation structure of this transition is organized by a degenerate Bogdanov-Takens-cusp bifurcation point of co-dimension 3 [3] which implies a switch from type I to type II for the spiking dynamics, a transition from integration to resonance near spike threshold, as well as a region of bistability of resting and regular spiking dynamics.

We confirm these predictions experimentally for different neurons using dynamic patch clamp recordings. We further find that activation of synaptic shunting inhibition is sufficient to induce the excitability switch and discuss consequences for the collective neuronal network dynamics.

[1] A. L. Hodgkin, J. Physiol. 107, 165 (1948).
[2] E. M. Izhikevic, Dynamical Systems in Neuroscience, MIT Press (2007).
[3] F. Dumortier, R. Roussarie, J. Sotomayor, and H. Zoladek.
Bifurcations of Planar Vector Fields, Springer (1991).