A detailed Purkinje cell model (Masoli et al 2015)

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The Purkinje cell is one of the most complex type of neuron in the central nervous system and is well known for its massive dendritic tree. The initiation of the action potential was theorized to be due to the high calcium channels presence in the dendritic tree but, in the last years, this idea was revised. In fact, the Axon Initial Segment, the first section of the axon was seen to be critical for the spontaneous generation of action potentials. The model reproduces the behaviours linked to the presence of this fundamental sections and the interplay with the other parts of the neuron.
1 . Masoli S, Solinas S, D'Angelo E (2015) Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization. Front Cell Neurosci 9:47 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Axon;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I Sodium; I Calcium; I Na,t; I K;
Gap Junctions:
Gene(s): Cav2.1 CACNA1A; Cav3.1 CACNA1G; Cav3.2 CACNA1H; Cav3.3 CACNA1I; Nav1.6 SCN8A; Kv1.1 KCNA1; Kv1.5 KCNA5; Kv3.3 KCNC3; Kv3.4 KCNC4; Kv4.3 KCND3; KCa1.1 KCNMA1; KCa2.2 KCNN2; KCa3.1 KCNN4; Kir2.1 KCNJ2; HCN1;
Simulation Environment: NEURON; Python;
Model Concept(s): Bursting; Detailed Neuronal Models; Action Potentials; Action Potential Initiation; Axonal Action Potentials;
Implementer(s): Masoli, Stefano [stefano.masoli at unipv.it]; Solinas, Sergio [solinas at unipv.it];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I Na,t; I K; I Sodium; I Calcium;
TITLE Large conductance Ca2+ activated K+ channel mslo


Parameters from Cox et al. (1987) J Gen Physiol 110:257-81 (patch 1).

Current Model Reference: Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cell. Cerebellum*

*Article available as Open Access

PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/20981513

Written by Sungho Hong, Okinawa Institute of Science and Technology, March 2009.
Contact: Sungho Hong (shhong@oist.jp)

Suffix from mslo to Kca1_1


  SUFFIX Kca1_1
  USEION ca READ cai
  RANGE g, gbar, ik


    (mV) = (millivolt)
    (S) = (siemens)
    (molar) = (1/liter)
    (mM) = (millimolar)
    FARADAY = (faraday) (kilocoulombs)
    R = (k-mole) (joule/degC)

    q10 = 3

    gbar = 0.01 (S/cm2)
    Qo = 0.73
    Qc = -0.67
    k1 = 1.0e3 (/mM)
    onoffrate = 1 (/ms)
    L0 = 1806
    Kc = 11.0e-3 (mM)
    Ko = 1.1e-3 (mM)
    pf0 = 2.39e-3  (/ms)
    pf1 = 7.0e-3  (/ms)
    pf2 = 40e-3   (/ms)
    pf3 = 295e-3  (/ms)
    pf4 = 557e-3  (/ms)
    pb0 = 3936e-3 (/ms)
    pb1 = 1152e-3 (/ms)
    pb2 = 659e-3  (/ms)
    pb3 = 486e-3  (/ms)
    pb4 = 92e-3  (/ms)

    : rates
    c01    (/ms)
    c12    (/ms)
    c23    (/ms)
    c34    (/ms)
    o01    (/ms)
    o12    (/ms)
    o23    (/ms)
    o34    (/ms)
    f0     (/ms)
    f1     (/ms)
    f2     (/ms)
    f3     (/ms)
    f4     (/ms)

    c10    (/ms)
    c21    (/ms)
    c32    (/ms)
    c43    (/ms)
    o10    (/ms)
    o21    (/ms)
    o32    (/ms)
    o43    (/ms)
    b0     (/ms)
    b1     (/ms)
    b2     (/ms)
    b3     (/ms)
    b4     (/ms)
    v            (mV)
    cai          (mM)
    ek           (mV)
    ik           (milliamp/cm2)
    g            (S/cm2)
    celsius      (degC)

    C0 FROM 0 TO 1
    C1 FROM 0 TO 1
    C2 FROM 0 TO 1
    C3 FROM 0 TO 1
    C4 FROM 0 TO 1
    O0 FROM 0 TO 1
    O1 FROM 0 TO 1
    O2 FROM 0 TO 1
    O3 FROM 0 TO 1
    O4 FROM 0 TO 1

    SOLVE activation METHOD sparse
    g = gbar * (O0 + O1 + O2 + O3 + O4)
    ik = g * (v - ek)

:    rates(v, cai)
:    SOLVE seqinitial
    SOLVE activation STEADYSTATE sparse

KINETIC activation {
    rates(v, cai)
    ~ C0 <-> C1      (c01,c10)
    ~ C1 <-> C2      (c12,c21)
    ~ C2 <-> C3      (c23,c32)
    ~ C3 <-> C4      (c34,c43)
    ~ O0 <-> O1      (o01,o10)
    ~ O1 <-> O2      (o12,o21)
    ~ O2 <-> O3      (o23,o32)
    ~ O3 <-> O4      (o34,o43)
    ~ C0 <-> O0      (f0 , b0)
    ~ C1 <-> O1      (f1 , b1)
    ~ C2 <-> O2      (f2 , b2)
    ~ C3 <-> O3      (f3 , b3)
    ~ C4 <-> O4      (f4 , b4)

CONSERVE C0 + C1 + C2 + C3 + C4 + O0 + O1 + O2 + O3 + O4 = 1

PROCEDURE rates(v(mV), ca (mM)) { 
    LOCAL qt, alpha, beta
    qt = q10^((celsius-23 (degC))/10 (degC))
    c01 = 4*ca*k1*onoffrate*qt
    c12 = 3*ca*k1*onoffrate*qt
    c23 = 2*ca*k1*onoffrate*qt
    c34 = 1*ca*k1*onoffrate*qt
    o01 = 4*ca*k1*onoffrate*qt
    o12 = 3*ca*k1*onoffrate*qt
    o23 = 2*ca*k1*onoffrate*qt
    o34 = 1*ca*k1*onoffrate*qt
    c10 = 1*Kc*k1*onoffrate*qt
    c21 = 2*Kc*k1*onoffrate*qt
    c32 = 3*Kc*k1*onoffrate*qt
    c43 = 4*Kc*k1*onoffrate*qt
    o10 = 1*Ko*k1*onoffrate*qt
    o21 = 2*Ko*k1*onoffrate*qt
    o32 = 3*Ko*k1*onoffrate*qt
    o43 = 4*Ko*k1*onoffrate*qt
    alpha = exp(Qo*FARADAY*v/R/(273.15 + celsius))
    beta  = exp(Qc*FARADAY*v/R/(273.15 + celsius))
    f0  = pf0*alpha*qt
    f1  = pf1*alpha*qt
    f2  = pf2*alpha*qt
    f3  = pf3*alpha*qt
    f4  = pf4*alpha*qt
    b0  = pb0*beta*qt
    b1  = pb1*beta*qt
    b2  = pb2*beta*qt
    b3  = pb3*beta*qt
    b4  = pb4*beta*qt

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