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 SK2 multi-state model Cerebellum Golgi Cell Model

COMMENT

Author:Sergio Solinas, Lia Forti, Egidio DAngelo
Based on data from: Hirschberg, Maylie, Adelman, Marrion J Gen Physiol 1998
Last revised: May 2007

Published in:
             Sergio M. Solinas, Lia Forti, Elisabetta Cesana, 
             Jonathan Mapelli, Erik De Schutter and Egidio D`Angelo (2008)
             Computational reconstruction of pacemaking and intrinsic 
             electroresponsiveness in cerebellar golgi cells
             Frontiers in Cellular Neuroscience 2:2
ENDCOMMENT

NEURON{
	SUFFIX SK2
	USEION ca READ cai
	USEION k READ ek WRITE ik 
	RANGE gkbar, g, ik, tcorr
}

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

PARAMETER {
	celsius  (degC)
	cai (mM)
	gkbar = 0.038 (mho/cm2)
	Q10 = 3 (1)
	diff = 3 (1) : diffusion factor

: rates ca-indipendent
	invc1 = 80e-3  ( /ms)
	invc2 = 80e-3  ( /ms)
	invc3 = 200e-3 ( /ms)

	invo1 = 1      ( /ms)
	invo2 = 100e-3 ( /ms)
	diro1 = 160e-3 ( /ms)
	diro2 = 1.2    ( /ms)

: rates ca-dipendent
	dirc2 = 200 ( /ms-mM )
	dirc3 = 160 ( /ms-mM )
	dirc4 = 80  ( /ms-mM )

}

ASSIGNED{ 
	v	(mV) 
	ek	(mV) 
	g	(mho/cm2) 
	ik	(mA/cm2) 
	invc1_t  ( /ms)
	invc2_t  ( /ms)
	invc3_t  ( /ms)
	invo1_t  ( /ms)
	invo2_t  ( /ms)
	diro1_t  ( /ms)
	diro2_t  ( /ms)
	dirc2_t  ( /ms-mM)
	dirc3_t  ( /ms-mM)
	dirc4_t  ( /ms-mM)
	tcorr	 (1)

	dirc2_t_ca  ( /ms)
	dirc3_t_ca  ( /ms)
	dirc4_t_ca  ( /ms)
} 

STATE {
	c1
	c2
	c3
	c4
	o1
	o2
}

BREAKPOINT{ 
	SOLVE kin METHOD sparse 
	g = gkbar*(o1+o2)	:(mho/cm2)
	ik = g*(v-ek)		:(mA/cm2)
} 

INITIAL{
	rate(celsius)
	SOLVE kin STEADYSTATE sparse
} 

KINETIC kin{ 
	rates(cai/diff) 
	~c1<->c2 (dirc2_t_ca, invc1_t) 
	~c2<->c3 (dirc3_t_ca, invc2_t) 
	~c3<->c4 (dirc4_t_ca, invc3_t) 
	~c3<->o1 (diro1_t, invo1_t) 
	~c4<->o2 (diro2_t, invo2_t) 
	CONSERVE c1+c2+c3+c4+o2+o1=1 
} 

FUNCTION temper (Q10, celsius (degC)) {
	temper = Q10^((celsius -23(degC)) / 10(degC)) 
}

PROCEDURE rates(cai(mM)){
	dirc2_t_ca = dirc2_t*cai
	dirc3_t_ca = dirc3_t*cai
	dirc4_t_ca = dirc4_t*cai 
} 

PROCEDURE rate (celsius(degC)) {
	tcorr = temper (Q10,celsius)
	invc1_t = invc1*tcorr  
	invc2_t = invc2*tcorr
	invc3_t = invc3*tcorr 
	invo1_t = invo1*tcorr 
	invo2_t = invo2*tcorr 
	diro1_t = diro1*tcorr 
	diro2_t = diro2*tcorr 
	dirc2_t = dirc2*tcorr
	dirc3_t = dirc3*tcorr
	dirc4_t = dirc4*tcorr
}

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