Mode-locking of periodically stimulated neurons

IFB responseThe minimal integrate-and-fire-or-burst (IFB) neuron model reproduces the salient features of experimentally observed thalamocortical relay neuron response properties, including the temporal tuning of both tonic spiking (i.e, conventional action potentials) and post-inhibitory rebound bursting mediated by the low-threshold Ca2+ current, IT. In collaboration with Greg Smith and Markus Owen I am developing an exact theory of mode-locking under the influence of arbitrary periodic forcing. In this analysis, the instabilities of mode-locked states are identified as both smooth bifurcations of an associated firing time map and non-smooth bifurcations of the underlying discontinuous flow.

Relevant publications:

S Coombes 1999 Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems, Physics Letters A, Vol 255, 49-57
S Coombes and P C Bressloff 1999 Mode-locking and Arnold tongues in integrate-and-fire neural oscillators, Physical Review E, Vol 60, 2086-2096
S Coombes, M R Owen and G D Smith 2001 Mode-locking in a periodically forced integrate-and-fire-or-burst neuron model, Physical Review E, 64, 041914
C R Laing and S Coombes 2005 Mode-locking in a periodically forced "ghostbursting" neuron model, International Journal of Bifurcation and Chaos, Vol 15, 1433-1444
C-M Svensson and S Coombes 2009 Mode locking in a spatially extended neuron model: active soma and compartmental tree, International Journal of Bifurcation and Chaos, Vol 19, 2597-2607
J Laudanski, S Coombes, A R Palmer and C J Sumner 2010 Mode-locked spike trains in responses of ventral cochlear nucleus chopper and onset neurons to periodic stimuli, Journal of Neurophysiology, Vol 103, 1226-1237
S Coombes, R Thul, J Laudanski, A R Palmer and C J Sumner 2011 Neuronal spike-train responses in the presence of threshold noise, Frontiers in Life Science, Vol 5, 91-105