A network of AOB mitral cells that produces infra-slow bursting (Zylbertal et al. 2017)

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Infra-slow rhythmic neuronal activity with very long (> 10 s) period duration was described in many brain areas but little is known about the role of this activity and the mechanisms that produce it. Here we combine experimental and computational methods to show that synchronous infra-slow bursting activity in mitral cells of the mouse accessory olfactory bulb (AOB) emerges from interplay between intracellular dynamics and network connectivity. In this novel mechanism, slow intracellular Na+ dynamics endow AOB mitral cells with a weak tendency to burst, which is further enhanced and stabilized by chemical and electrical synapses between them. Combined with the unique topology of the AOB network, infra-slow bursting enables integration and binding of multiple chemosensory stimuli over prolonged time scale. The example protocol simulates a two-glomeruli network with a single shared cell. Although each glomerulus is stimulated at a different time point, the activity of the entire population becomes synchronous (see paper Fig. 8)
1 . Zylbertal A, Yarom Y, Wagner S (2017) Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity. J Neurosci 37:2656-2672 [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 (accessory) mitral cell;
Channel(s): I CAN; Na/Ca exchanger; Na/K pump; I Calcium; I Na,t;
Gap Junctions: Gap junctions;
Simulation Environment: NEURON; Python;
Model Concept(s): Bursting; Synchronization; Activity Patterns; Oscillations; Persistent activity; Olfaction;
Implementer(s): Zylbertal, Asaph [asaph.zylbertal at mail.huji.ac.il];
Search NeuronDB for information about:  I Na,t; I CAN; I Calcium; Na/Ca exchanger; Na/K pump;
: Sodium ion accumulation with radial and longitudinal diffusion, buffering and pumping

    SUFFIX nadp
    USEION na READ nao, nai, ina WRITE nai, ina, ena
    RANGE ina_pmp, TotalPump, ik_ratio, na, pump, pumpna
    GLOBAL vrat, DNa, k1, k2, k3, k4

DEFINE Nannuli 4

    (molar) = (1/liter)
    (mM) = (millimolar)
    (um) = (micron)
    (mA) = (milliamp)
    (mV) = (millivolt)
    FARADAY = (faraday) (10000 coulomb)
    R = (k-mole) (joule/degC)    
    PI = (pi) (1)
    (mol) = (1)



    DNa = 0.6 (um2/ms)

    k1 = 1.0 (/mM3-ms)

    k2 = 0.001 (/ms)
    k3 = 0.3 (/ms)
                            : to eliminate pump, set TotalPump to 0 in hoc
    TotalPump = 1e-14 (mol/cm2)
    ik_ratio = -0.66666666 (1)


    diam (um)
    L (um)
    ina (mA/cm2)
    nai (mM)
    vrat[Nannuli] : numeric value of vrat[i] equals the volume
                 : of annulus i of a 1um diameter cylinder
                 : multiply by diam^2 to get volume per um length
    k4          (/mM3-ms)

    nao (mM)
    ena (mV)

    ina_pmp (mA/cm2)
    parea (um)

    ik_pump (mA/cm2)


CONSTANT { volo = 1e10 (um2) }

    : na[0] is equivalent to nai
    na[Nannuli] (mM) <1e-3>

    pump (mol/cm2)
    pumpna (mol/cm2)



    SOLVE state METHOD sparse

    ina = ina_pmp
    ik_pump = ik_ratio*ina_pmp


LOCAL factors_done

    k4=(((nai/nao)^3)*k1*k3)/k2    :Set the equilibrium at nai0_na_ion
    parea = PI*diam
    pump = TotalPump/(1 + (nai*k1/k2))
    pumpna = TotalPump - pump
    if (factors_done == 0) {    : flag becomes 1 in the first segment
        factors_done = 1        : all subsequent segments will have
        factors()               : vrat = 0 unless vrat is GLOBAL

    FROM i=0 TO Nannuli-1 {
        na[i] = nai


LOCAL frat[Nannuli]     : scales the rate constants for model geometry

PROCEDURE factors() {
    LOCAL r, dr2
    r = 1/2                 : starts at edge (half diam)
    dr2 = r/(Nannuli-1)/2   : full thickness of outermost annulus,
                            : half thickness of all other annuli
    vrat[0] = 0
    frat[0] = 2*r
    FROM i=0 TO Nannuli-2 {
        vrat[i] = vrat[i] + PI*(r-dr2/2)*2*dr2  : interior half
        r = r - dr2
        frat[i+1] = 2*PI*r/(2*dr2)              : outer radius of annulus
                                                : div by distance between centers
        r = r - dr2
        vrat[i+1] = PI*(r+dr2/2)*2*dr2 : outer half of annulus

KINETIC state {
    COMPARTMENT i, diam*diam*vrat[i] {na}
    COMPARTMENT (1e10)*parea {pump pumpna}
    COMPARTMENT volo {nao}

    LONGITUDINAL_DIFFUSION i, DNa*diam*diam*vrat[i] {na}

    ~ 3 na[0] + pump <-> pumpna (k1*parea*(1e10), k2*parea*(1e10))
    ~ pumpna <-> pump + 3 nao (k3*parea*(1e10), k4*parea*(1e10))

    CONSERVE pump + pumpna = TotalPump * parea * (1e10)
    ina_pmp = FARADAY*(f_flux - b_flux)/parea

    : all currents except pump
    ~ na[0] << (-(ina-ina_pmp)*PI*diam/(FARADAY)) : ina is Na efflux

    FROM i=0 TO Nannuli-2 {
        ~ na[i] <-> na[i+1] (DNa*frat[i+1], DNa*frat[i+1])
    nai = na[0]
    ena = ((R*(273.15+celsius))/(FARADAY*10))*log(nao/nai)