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 Low threshold calcium current Cerebellum Purkinje Cell Model

COMMENT

Kinetics adapted to fit the Cav3.1 Iftinca et al 2006, Temperature dependence of T-type Calcium channel gating, NEUROSCIENCE

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 Haroon Anwar, Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 2010.
Contact: Haroon Anwar (anwar@oist.jp)

ENDCOMMENT


INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
        SUFFIX CaT3_1
        USEION ca READ cai, cao WRITE ica VALENCE 2
        RANGE g, pcabar, minf, taum, hinf, tauh
	RANGE ica, m ,h

    }

UNITS {
        (molar) = (1/liter)
        (mV) =  (millivolt)
        (mA) =  (milliamp)
        (mM) =  (millimolar)

}

CONSTANT {
	F = 9.6485e4 (coulombs)
	R = 8.3145 (joule/kelvin)
}

PARAMETER {
        v               (mV)
        celsius (degC)
        eca (mV)
	pcabar  = 2.5e-4 (cm/s)
        cai  (mM)           : adjusted for eca=120 mV
	cao  (mM)
	
	v0_m_inf = -52 (mV)
	v0_h_inf = -72 (mV)
	k_m_inf = -5 (mV)
	k_h_inf = 7  (mV)
	
	C_tau_m = 1
	A_tau_m = 1.0
	v0_tau_m1 = -40 (mV)
	v0_tau_m2 = -102 (mV)
	k_tau_m1 = 9 (mV)
	k_tau_m2 = -18 (mV)
	
	C_tau_h = 15
	A_tau_h = 1.0
	v0_tau_h1 = -32 (mV)
	k_tau_h1 = 7 (mV)
	
    }
    

STATE {
        m h
}

ASSIGNED {
        ica     (mA/cm2)
	g        (coulombs/cm3) 
        minf
        taum   (ms)
        hinf
        tauh   (ms)
	T (kelvin)
	E (volt)
	zeta
}

BREAKPOINT {
	SOLVE castate METHOD cnexp 

        ica = (1e3) *pcabar*m*m *h * g
}

DERIVATIVE castate {
        evaluate_fct(v)

        m' = (minf - m) / taum
        h' = (hinf - h) / tauh
}

FUNCTION ghk( v (mV), ci (mM), co (mM), z )  (coulombs/cm3) {
    E = (1e-3) * v
      zeta = (z*F*E)/(R*T)


    if ( fabs(1-exp(-zeta)) < 1e-6 ) {
        ghk = (1e-6) * (z*F) * (ci - co*exp(-zeta)) * (1 + zeta/2)
    } else {
        ghk = (1e-6) * (z*zeta*F) * (ci - co*exp(-zeta)) / (1-exp(-zeta))
    }
}


UNITSOFF
INITIAL {
	
	T = kelvinfkt (celsius)

        evaluate_fct(v)
        m = minf
        h = hinf
}

PROCEDURE evaluate_fct(v(mV)) { 

        minf = 1.0 / ( 1 + exp((v  - v0_m_inf)/k_m_inf) )
        hinf = 1.0 / ( 1 + exp((v - v0_h_inf)/k_h_inf) )
        if (v<=-90) {
	taum = 1
	} else {
	taum = ( C_tau_m + A_tau_m / (exp((v - v0_tau_m1)/ k_tau_m1) + exp((v - v0_tau_m2)/k_tau_m2)))
	}
	tauh = ( C_tau_h + A_tau_h / exp((v - v0_tau_h1)/k_tau_h1) ) 
	g = ghk(v, cai, cao, 2)
}

FUNCTION kelvinfkt( t (degC) )  (kelvin) {
    kelvinfkt = 273.19 + t
}

UNITSON

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