TY - JOUR

T1 - M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains

AU - Zhou, Yujia

AU - Vo, Theodore

AU - Rotstein, Horacio G.

AU - McCarthy, Michelle M.

AU - Kopell, Nancy

N1 - Funding Information:
Funding This work is supported by National Science Foundation (NSF) grants DMS-1225647 and DMS-DMS-1514796.
Publisher Copyright:
© 2018, The Author(s).

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Averaging

KW - Biophysical modeling

KW - Bistability

KW - Geometric singular perturbation theory

KW - Multiple timescales

KW - Phase-amplitude coupling

KW - Theta rhythm

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U2 - 10.1186/s13408-018-0068-6

DO - 10.1186/s13408-018-0068-6

M3 - Article

AN - SCOPUS:85058865153

SN - 2190-8567

VL - 8

JO - Journal of Mathematical Neuroscience

JF - Journal of Mathematical Neuroscience

IS - 1

M1 - 13

ER -