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DG adult-born granule cell: nonlinear a5-GABAARs control AP firing (Lodge et al, 2021)

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GABA can depolarize immature neurons close to the action potential (AP) threshold in development and adult neurogenesis. Nevertheless, GABAergic synapses effectively inhibit AP firing in newborn granule cells of the adult hippocampus as early as 2 weeks post mitosis. Parvalbumin and dendrite-targeting somatostatin interneurons activate a5-subunit containing GABAA receptors (a5-GABAARs) in young neurons, which show a voltage dependent conductance profile with increasing conductance around the AP threshold. The present computational models show that the depolarized GABA reversal potential promotes NMDA receptor activation. However, the voltage-dependent conductance of a5-GABAARs in young neurons is crucial for inhibition of AP firing to generate balanced and sparse firing activity.
1 . Lodge M, Hernandez MC, Schulz JM, Bischofberger J (2021) Sparsification of AP firing in adult-born hippocampal granule cells via voltage-dependent a5-GABAA receptors Cell Reports [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Dentate gyrus;
Cell Type(s): Dentate gyrus granule GLU cell;
Channel(s): I K; I Krp; I Na,t;
Gap Junctions:
Receptor(s): AMPA; GabaA; NMDA;
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Action Potentials; Detailed Neuronal Models; Development; Neurogenesis; Pattern Separation; Synaptic Integration;
Implementer(s): Schulz, Jan M [j.schulz at]; Bischofberger, Josef;
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; GabaA; AMPA; NMDA; I Na,t; I K; I Krp; Gaba; Glutamate;
: Eight state kinetic sodium channel gating scheme
: Based on Schmidt-Hieber C, Bischofberger J. (2010) J Neurosci 30:10233-42
: Rates reflect fit of somatic recordings Schmidt-Hieber, 2010
: additional kinetic factor allows for slowing of gating kinetics in young GCs
: by JM Schulz, 2020

    SUFFIX na8st
    USEION na READ ena WRITE ina
    GLOBAL vShift, vShift_inact, maxrate
    RANGE vShift_inact_local
    RANGE g, gbar, kinfact
    RANGE a1_0, a1_1, b1_0, b1_1, a2_0, a2_1
    RANGE b2_0, b2_1, a3_0, a3_1, b3_0, b3_1
    RANGE bh_0, bh_1, bh_2, ah_0, ah_1, ah_2

UNITS { (mV) = (millivolt) }

: initialize parameters

    gbar = 33     (millimho/cm2)

    a1_0 = 4.584982656184167e+01 (/ms)
    a1_1 = 2.393541665657613e-02 (/mV) 
    b1_0 = 1.440952344322651e-02 (/ms)
    b1_1 = 8.847609128769419e-02 (/mV)

    a2_0 = 1.980838207143563e+01 (/ms)
    a2_1 = 2.217709530008501e-02 (/mV) 
    b2_0 = 5.650174488683913e-01 (/ms)
    b2_1 = 6.108403283302217e-02 (/mV)

    a3_0 = 7.181189201089192e+01 (/ms)
    a3_1 = 6.593790601261940e-02 (/mV) 
    b3_0 = 7.531178253431512e-01 (/ms)
    b3_1 = 3.647978133116471e-02 (/mV)

    bh_0 = 2.830146966213825e+00 (/ms) : bh_0 = 1.687524670388565e-02 (/ms) : 
    bh_1 = 2.890045633775495e-01 
    bh_2 = 6.960300544163878e-02 (/mV)

    ah_0 = 5.757824421450554e-01 (/ms)
    ah_1 = 1.628407420157048e+02  
    ah_2 = 2.680107016756367e-02 (/mV)

    vShift = 12            (mV)  : shift to the right to account for Donnan potentials
                                 : 12 mV for cclamp, 0 for oo-patch vclamp simulations
    vShift_inact = 10      (mV)  : global additional shift to the right for inactivation
                                 : 10 mV for cclamp, 0 for oo-patch vclamp simulations
    vShift_inact_local = 0 (mV)  : additional shift to the right for inactivation, used as local range variable
    maxrate = 8.00e+03     (/ms) : limiting value for reaction rates
                                 : See Patlak, 1991
    kinfact = 1               : scales transition rates limiting value for reaction rates

    v    (mV)
    ena  (mV)
    g    (millimho/cm2)
    ina  (milliamp/cm2)
    a1   (/ms)
    b1   (/ms)
    a2   (/ms)
    b2   (/ms)
    a3   (/ms)
    b3   (/ms)
    ah   (/ms)
    bh   (/ms)

STATE { c1 c2 c3 i1 i2 i3 i4 o }

    SOLVE kin METHOD sparse
    g = gbar*o
    ina = g*(v - ena)*(1e-3)


    ~ c1 <-> c2 (a1, b1)
    ~ c2 <-> c3 (a2, b2)
    ~ c3 <-> o (a3, b3)
    ~ i1 <-> i2 (a1, b1)
    ~ i2 <-> i3 (a2, b2)
    ~ i3 <-> i4 (a3, b3)
    ~ i1 <-> c1 (ah, bh)
    ~ i2 <-> c2 (ah, bh)
    ~ i3 <-> c3 (ah, bh)
    ~ i4 <-> o  (ah, bh)
    CONSERVE c1 + c2 + c3 + i1 + i2 + i3 + i4 + o = 1

: FUNCTION_TABLE tau1(v(mV)) (ms)
: FUNCTION_TABLE tau2(v(mV)) (ms)

PROCEDURE rates(v(millivolt)) {
    LOCAL vS
    vS = v-vShift

    a1 = kinfact*a1_0*exp( a1_1*vS)
    a1 = a1*maxrate / (a1+maxrate)
    b1 = kinfact*b1_0*exp(-b1_1*vS)
    b1 = b1*maxrate / (b1+maxrate)
    a2 = kinfact*a2_0*exp( a2_1*vS)
    a2 = a2*maxrate / (a2+maxrate)
    b2 = kinfact*b2_0*exp(-b2_1*vS)
    b2 = b2*maxrate / (b2+maxrate)
    a3 = kinfact*a3_0*exp( a3_1*vS)
    a3 = a3*maxrate / (a3+maxrate)
    b3 = kinfact*b3_0*exp(-b3_1*vS)
    b3 = b3*maxrate / (b3+maxrate)
    bh = kinfact*bh_0/(1+bh_1*exp(-bh_2*(vS-vShift_inact-vShift_inact_local)))
    bh = bh*maxrate / (bh+maxrate)
    ah = kinfact*ah_0/(1+ah_1*exp( ah_2*(vS-vShift_inact-vShift_inact_local)))
    ah = ah*maxrate / (ah+maxrate)

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