Controlling KCa channels with different Ca2+ buffering models in Purkinje cell (Anwar et al. 2012)

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Accession:138382
In this work, we compare the dynamics of different buffering models during generation of a dendritic Ca2+ spike in a single compartment model of a Purkinje cell dendrite. The Ca2+ buffering models used are 1) a single Ca2+ pool, 2) two Ca2+ pools respectively for the fast and slow transients, 3) a detailed calcium model with buffers, pump (Schmidt et al., 2003), and diffusion and 4) a calcium model with buffers, pump and diffusion compensation. The parameters of single pool and double pool are tuned, using Neurofitter (Van Geit et al., 2007), to approximate the behavior of detailed calcium dynamics over range of 0.5 µM to 8 µM of intracellular calcium. The diffusion compensation is modeled using a buffer-like mechanism called DCM. To use DCM robustly for different diameter compartments, its parameters are estimated, using Neurofitter (Van Geit et al., 2007), as a function of compartment diameter (0.8 µm-20 µm).
Reference:
1 . Anwar H, Hong S, De Schutter E (2012) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells. Cerebellum 11:681-93 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Dendrite;
Brain Region(s)/Organism:
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I K,Ca; I Calcium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Calcium dynamics;
Implementer(s):
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I K,Ca; I Calcium;
TITLE Large conductance Ca2+ activated K+ channel mslo

COMMENT

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)

Adapted by: Haroon Anwar (anwar@oist.jp)

ENDCOMMENT

NEURON {
  SUFFIX mslo_DP
  USEION k READ ek WRITE ik
  USEION ca READ cai
  USEION ca2 READ ca2i VALENCE 2
  RANGE g, gbar, ik
  GLOBAL frac1, frac2

}

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

CONSTANT {
    q10 = 3
}

PARAMETER {
    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)
}

ASSIGNED {
    : 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)
    ca2i         (mM)
    ek           (mV)
    ik           (milliamp/cm2)
    g            (S/cm2)
    celsius      (degC)

    frac1
    frac2	
}

STATE {
    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
}

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

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

KINETIC activation {
    rates(v, cai*frac1 + ca2i*frac2)
    ~ 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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