Gamma-beta alternation in the olfactory bulb (David, Fourcaud-Trocmé et al., 2015)

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This model, a simplified olfactory bulb network with mitral and granule cells, proposes a framework for two regimes of oscillation in the olfactory bulb: 1 - a weak inhibition regime (with no granule spike) where the network oscillates in the gamma (40-90Hz) band 2 - a strong inhibition regime (with granule spikes) where the network oscillates in the beta (15-30Hz) band. Slow modulations of sensory and centrifugal inputs, phase shifted by a quarter of cycle, possibly combined with short term depression of the mitral to granule AMPA synapse, allows the network to alternate between the two regimes as observed in anesthetized animals.
1 . David F, Courtiol E, Buonviso N, Fourcaud-Trocmé N (2015) Competing Mechanisms of Gamma and Beta Oscillations in the Olfactory Bulb Based on Multimodal Inhibition of Mitral Cells Over a Respiratory Cycle. eNeuro [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Olfactory bulb;
Cell Type(s): Olfactory bulb main mitral GLU cell; Olfactory bulb main interneuron granule MC GABA cell;
Channel(s): I_Ks;
Gap Junctions:
Receptor(s): GabaA; AMPA;
Simulation Environment: Brian; Python;
Model Concept(s): Short-term Synaptic Plasticity; Gamma oscillations; Beta oscillations; Olfaction;
Search NeuronDB for information about:  Olfactory bulb main mitral GLU cell; Olfactory bulb main interneuron granule MC GABA cell; GabaA; AMPA; I_Ks;
# -*- coding: utf-8 -*-
Simple quadratic integrate-and-fire (QIF) model for the granule cells.
Parameters were fitted to match model f-I curve with granule f-I curve of Davison (2001, PhD Thesis)

from brian import *

print "Granule equation initialization"

# Granule membrane parameters
I_T=0.02*nA # threshold of the Davison f-I curve

# All next 3 variables are linked to reproduce the Davison f-I curve (# example with a multiplicative factor)
Delta_T=0.1*mV # Delta_T*factor
tau_m=60*ms # tau_m/factor
gL_G=16.666*nS # gL_G*factor => not a real leak constant (because such a constant has no meaning in a QIF model)

# Synaptic current parameters
Ee = 0.*mV
gE_max=4.*nS # gE_max*factor <-- if excitation must remain the same when a factor is applied above
dV/dt =  ((1/(2*Delta_T))*(V-V_T)**2 - I_T/gL_G + Iinj/gL_G - (sE*gE_max + gEinj)/gL_G*(V-Ee))/tau_m  : volt
Iinj : amp
gEinj : siemens
dsE/dt = -sE/tauE : 1

def QIF_reset(P, spikes):
    P.V[spikes]=-70.*mV # -70*mV in UB4.c