M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains

Yujia Zhou, Theodore Vo, Horacio G. Rotstein, Michelle McCarthy, Nancy Kopell

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Theta (4–8 Hz) and gamma (30–80 Hz) rhythms in the brain are commonly associated with memory and learning (Kahana in J Neurosci 26:1669–1672, 2006; Quilichini et al. in J Neurosci 30:11128–11142, 2010). The precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. We consider an inhibitory neuron model with M-current under forcing from gamma pulses and a sinusoidal current of theta frequency. The M-current has a long time constant (∼90 ms) and it has been shown to generate resonance at theta frequencies (Hutcheon and Yarom in Trends Neurosci 23:216–222, 2000; Hu et al. in J Physiol 545:783–805, 2002). We have found that this slow M-current contributes to the precise co-firing between the network and fast gamma pulses in the presence of a slow sinusoidal forcing. The M-current expands the phase-locking frequency range of the network, counteracts the slow theta forcing, and admits bistability in some parameter range. The effects of the M-current balancing the theta forcing are reduced if the sinusoidal current is faster than the theta frequency band. We characterize the dynamical mechanisms underlying the role of the M-current in enabling a network to be entrained to gamma frequency inputs using averaging methods, geometric singular perturbation theory, and bifurcation analysis.

Original languageEnglish
Article number13
Number of pages32
JournalThe Journal of Mathematical Neuroscience
Issue number1
Publication statusPublished - 1 Dec 2018
Externally publishedYes


  • Averaging
  • Biophysical modeling
  • Bistability
  • Geometric singular perturbation theory
  • Multiple timescales
  • Phase-amplitude coupling
  • Theta rhythm

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