Cortical Layer 5b pyr. cell with [Na+]i mechanisms, from Hay et al 2011 (Zylbertal et al 2017)

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Accession:230326
" ... Based on a large body of experimental recordings from both the soma and dendrites of L5b pyramidal cells in adult rats, we characterized key features of the somatic and dendritic firing and quantified their statistics. We used these features to constrain the density of a set of ion channels over the soma and dendritic surface via multi-objective optimization with an evolutionary algorithm, thus generating a set of detailed conductance-based models that faithfully replicate the back-propagating action potential activated Ca(2+) spike firing and the perisomatic firing response to current steps, as well as the experimental variability of the properties. Furthermore, we show a useful way to analyze model parameters with our sets of models, which enabled us to identify some of the mechanisms responsible for the dynamic properties of L5b pyramidal cells as well as mechanisms that are sensitive to morphological changes. ..."
References:
1 . Hay E, Hill S, Schürmann F, Markram H, Segev I (2011) Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active properties. PLoS Comput Biol 7:e1002107 [PubMed]
2 . Zylbertal A, Yarom Y, Wagner S (2017) The Slow Dynamics of Intracellular Sodium Concentration Increase the Time Window of Neuronal Integration: A Simulation Study Front. Comput. Neurosci. 11(85):1-16 [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: Neocortex;
Cell Type(s): Neocortex L5/6 pyramidal GLU cell;
Channel(s): Na/Ca exchanger; Na/K pump; I Sodium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Dendritic Action Potentials; Detailed Neuronal Models; Action Potentials; Reaction-diffusion; Synaptic Plasticity; Active Dendrites; Olfaction;
Implementer(s): Zylbertal, Asaph [asaph.zylbertal at mail.huji.ac.il];
Search NeuronDB for information about:  Neocortex L5/6 pyramidal GLU cell; I Sodium; Na/Ca exchanger; Na/K pump;
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: Calcium ion accumulation with radial diffusion, buffering and pumping

NEURON {
	THREADSAFE
    SUFFIX cadp
    USEION ca READ cao, cai, ica WRITE cai, ica
    RANGE ica_pmp, diam_factor, TotalPump, ca, CaEndBuffer, EndBuffer, pump, pumpca
    GLOBAL vrat, TotalEndBuffer, k1, k2, k3, k4, k1bufend, k2bufend
:    USEION dep READ depi VALENCE 1

    NONSPECIFIC_CURRENT icont                                                       
}

:DEFINE Nannuli 4

UNITS {
    (molar) = (1/liter)
    (mM) = (millimolar)
    (um) = (micron)
    (mA) = (milliamp)
    FARADAY = (faraday) (10000 coulomb)
    PI = (pi) (1)
    (mol) = (1)

}

PARAMETER {

    DCa = 0.6 (um2/ms)
    k1bufend = 100 (/mM-ms) : Yamada et al. 1989
    k2bufend = 0.1 (/ms)
    TotalEndBuffer = 0.003 (mM)

    k1bufex = 100 (/mM-ms) 
    k2bufex = 0.017 (/ms)       :   Based on OGB-1 kd
    TotalExBuffer = 0.04 (mM)   : 

    k1 = 1 (/mM-ms)
    
    k3 = 1 (/ms)
                            : to eliminate pump, set TotalPump to 0 in hoc
    TotalPump = 1e-14 (mol/cm2)

    fl_ratio=14 (1)

    diam_factor=1 (1)
:    dep_factor=1 (1)


}

ASSIGNED {
    diam (um)
    L (um)
    ica (mA/cm2)
    cai (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
    
:    depi
    k2          (/ms)
    k4          (/mM-ms)

    ka_end (/mM)
:    ka_ex (/mM)

    B0end (mM)
:    B0ex (mM)

    cao (mM)
    ica_pmp (mA/cm2)
    icont (mA/cm2)
    parea (um)
:    AvgCaExBuffer (mM)  : [CaExBuffer] averaged over all shells.

    :f    (1)
    diamf   (um)


}

CONSTANT { volo = 1e10 (um2) }

STATE {
    : ca[0] is equivalent to cai
    : ca[] are very small, so specify absolute tolerance
    :ca[Nannuli] (mM) <1e-10>
    ca (mM) <1e-10>
    CaEndBuffer (mM)
    EndBuffer (mM)
    :CaExBuffer[Nannuli] (mM)
    :ExBuffer[Nannuli] (mM)

    pump (mol/cm2)
    pumpca (mol/cm2)

}


BREAKPOINT {


    SOLVE state METHOD sparse

    ica = ica_pmp
    icont = -ica_pmp
    :AvgCaExBuffer = 0.0
    
    :FROM i=0 TO Nannuli-1 {
    :    AvgCaExBuffer = AvgCaExBuffer + (CaExBuffer[i] * vrat[i])
    :}

    :AvgCaExBuffer = AvgCaExBuffer * (4/PI)
    :f = TotalExBuffer + (fl_ratio - 1) * AvgCaExBuffer
    
}

LOCAL factors_done

INITIAL {
    k2=sqrt(cai/cao)    :Set the equilibrium at cai0_ca_ion
    k4=sqrt(cai/cao)
    diamf=diam*diam_factor

    parea = PI*diamf
    vrat = PI*0.25
    pump = TotalPump/(1 + (cai*k1/k2))
    pumpca = 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
:    }

    ka_end = k1bufend/k2bufend
    :ka_ex = k1bufex/k2bufex

    B0end = TotalEndBuffer/(1 + ka_end*cai)
    :B0ex = TotalExBuffer/(1 + ka_ex*cai)

:    ex_buffer_ratio = 0.0
    EndBuffer = B0end
    CaEndBuffer = TotalEndBuffer - B0end
    ca=cai
:    FROM i=0 TO Nannuli-1 {
:        ca[i] = cai
:        EndBuffer[i] = B0end
:        CaEndBuffer[i] = TotalEndBuffer - B0end
:        ExBuffer[i] = B0ex
:        CaExBuffer[i] = TotalExBuffer - B0ex
:        :ex_buffer_ratio = ex_buffer_ratio + (CaExBuffer[i] * vrat[i])

:    }
    :ex_buffer_ratio=(ex_buffer_ratio/(PI/4))/(TotalExBuffer - (ex_buffer_ratio/(PI/4)))

}

: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
:    }
:}

LOCAL dsq, dsqvol   : can't define local variable in KINETIC block
                    : or use in COMPARTMENT statement

KINETIC state {
    COMPARTMENT diamf*diamf*vrat {ca CaIndBuffer IndBuffer}
    COMPARTMENT (1e10)*parea {pump pumpca}
    COMPARTMENT volo {cao}

    :LONGITUDINAL_DIFFUSION DCa*diamf*diamf*vrat {ca}

    :pump
    ~ ca + pump <-> pumpca (k1*parea*(1e10), k2*parea*(1e10))
    ~ pumpca <-> pump + cao (k3*parea*(1e10), k4*parea*(1e10))

    CONSERVE pump + pumpca = TotalPump * parea * (1e10)
    ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea

    : all currents except pump
    ~ ca << (-(ica-ica_pmp)*PI*diamf/(2*FARADAY)) : ica is Ca efflux

    :FROM i=0 TO Nannuli-2 {
    :    ~ ca[i] <-> ca[i+1] (DCa*frat[i+1], DCa*frat[i+1])
    :}
    dsqvol = diamf*diamf*vrat
    ~ ca + EndBuffer <-> CaEndBuffer (k1bufend*dsqvol, k2bufend*dsqvol)
    cai=ca
:    FROM i=0 TO Nannuli-1 {
:        dsqvol = dsq*vrat[i]
:        ~ ca[i] + EndBuffer[i] <-> CaEndBuffer[i] (k1bufend*dsqvol, k2bufend*dsqvol)
:        ~ ca[i] + ExBuffer[i] <-> CaExBuffer[i] (k1bufex*dsqvol, k2bufex*dsqvol):
:
:    }
:    cai = ca[0]
}


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