The response of a population of classical Hodgkin-Huxley neurons to an inhibitory pulse

C. Börgers (1) , Martin Krupa (2, 3) , S. Gielen (3)

1 Tufts University [Medford]
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
3 Donders Institute for Brain, Cognition and Behaviour

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.

Domaines: Systèmes dynamiques [math.DS]

C. Börgers, Martin Krupa, S. Gielen. The response of a population of classical Hodgkin-Huxley neurons to an inhibitory pulse. Journal of Computational Neuroscience, 2010, 28 (3), pp.509-526. ⟨10.1007/s10827-010-0233-8⟩. ⟨hal-00845990⟩