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

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 (US)
Article number13
JournalJournal of Mathematical Neuroscience
Issue number1
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Neuroscience (miscellaneous)


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


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