Zhou, YujiaVo, TheodoreRotstein, Horacio G.McCarthy, Michelle M.Kopell, Nancy2020-04-092020-04-092018-12-05Yujia Zhou, Theodore Vo, Horacio G Rotstein, Michelle M McCarthy, Nancy Kopell. 2018. "M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains." JOURNAL OF MATHEMATICAL NEUROSCIENCE, Volume 8, 32 pp. https://doi.org/10.1186/s13408-018-0068-62190-8567https://hdl.handle.net/2144/40066Theta (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.32 pagesen-USThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)http://creativecommons.org/licenses/by/4.0/Science & technologyLife sciences & biomedicinePhysical sciencesMathematical & computational biologyMathematics, interdisciplinary applicationsMathematicsNeurosciences & neurologyPhase-amplitude couplingTheta rhythmGeometric singular perturbation theoryAveragingBistabilityMultiple timescalesBiophysical modelingFast inhibitionH-currentOscillationsSynchronizationInterneuronsResonanceHippocampusMechanismsApplied mathematicsArticle10.1186/s13408-018-0068-60000-0002-8568-8750 (Kopell, Nancy)407785