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

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Accession:185014
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.
Reference:
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;
Gene(s):
Transmitter(s):
Simulation Environment: Brian; Python;
Model Concept(s): Short-term Synaptic Plasticity; Gamma oscillations; Beta oscillations; Olfaction;
Implementer(s):
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 -*-
"""
This script provides equations for the mitral model initially
published in David et al. (2009, PLOS Comp Biology)
"""

from brian import *

print "Mitral equation initialization"

# Mitral membrane and ionic current params
Cm     = 0.01*farad*meter**-2 
gL     = 0.1*siemens*meter**-2 
EL     = -66.5*mV 
gNa    = 500*siemens*meter**-2
gNap   = 1.1*siemens*meter**-2
gKA    = 100.*siemens*meter**-2
gKS    = 310.*siemens*meter**-2
gKF    = 100.*siemens*meter**-2
mhKA   = 0.004
ENa    = 45.*mV
EK     = -75.*mV
taumKF = 2.6*ms

# Synaptic current params
Ee = 0.*mV
Ei = -70.*mV
tauIr = 2.*ms # Weak inhibition synapse rise time
gI_max=0.18*siemens*meter**-2 # Weak inhibition max conductance (conductance time integral depends on rise time)
gI_G=3.0*siemens*meter**-2 # Strong inhibition max conductance 

Mitral_eqs=Equations('''
dV/dt=(-gL*(V-EL)-gNa*mNa*mNa*mNa*(V-ENa)-gKA*mhKA*(V-EK)-gKS*W*X*(V-EK)-gNap/(1.+exp(-(V+51.*mV)/(5.*mV)))*(V-ENa)-gKF*Y*(V-EK) + Iinj - gEinj * (V-Ee) - (gI_cst + sI * gI_max + sI_G * gI_G)  * (V-Ei) )/Cm : volt
dW/dt = ( 1./( exp( -(V+34.*mV)/(6.5*mV) ) + 1.) - W ) / taumKS : 1
dX/dt = 2.*( 1./( exp(  (V+65.*mV)/(6.6*mV) ) + 1.) - X ) / ((200. + 220./( exp(-(V+71.6*mV)/(6.85*mV)) + 1.))*ms) : 1
dY/dt = -Y/taumKF : 1
aNa=0.32 * (-(V+50.*mV))/( exp(-(V+50.*mV)/(4.*mV)) - 1. ) : mV
bNa=0.28 * (V+23.*mV) / (exp((V+23.*mV)/(5.*mV)) - 1. )  : mV
mNa=aNa/(aNa+bNa) : 1
dsI/dt = (rI -sI) /tauI: 1
drI/dt= -rI/tauIr : 1
dsI_G/dt = -sI_G /tauI_G : 1
Iinj : amp*meter**-2
gEinj : siemens*meter**-2
taumKS : ms
tauI : ms
tauI_G : ms
gI_cst : siemens*meter**-2

dsI2/dt = (rI2 -sI2) /tauI: 1
drI2/dt= -rI2/tauIr : 1
LFP=sI2 * gI_max :siemens*meter**-2

Isyn=- (sI * gI_max + sI_G * gI_G)  * (V-Ei) :amp*meter**-2
Isyn_all=(- gEinj * (V-Ee) - (gI_cst + sI * gI_max + sI_G * gI_G)  * (V-Ei)) :amp*meter**-2
Gsyn=(sI * gI_max + sI_G * gI_G):siemens*meter**-2
''')

def Mitral_reset(P, spikes):
    P.V[spikes]=-65.*mV # -70*mV in UB4.c
    P.W[spikes]+=0.03 # mKs, 0.03 in UB4.c
    P.X[spikes]+=0.002 # hKs
    P.Y[spikes]+=0.4 # mKf