Effects of Chloride accumulation and diffusion on GABAergic transmission (Jedlicka et al 2011)

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"In the CNS, prolonged activation of GABA(A) receptors (GABA(A)Rs) has been shown to evoke biphasic postsynaptic responses, consisting of an initial hyperpolarization followed by a depolarization. A potential mechanism underlying the depolarization is an acute chloride (Cl(-)) accumulation resulting in a shift of the GABA(A) reversal potential (E(GABA)). The amount of GABA-evoked Cl(-) accumulation and accompanying depolarization depends on presynaptic and postsynaptic properties of GABAergic transmission, as well as on cellular morphology and regulation of Cl(-) intracellular concentration ([Cl(-)](i)). To analyze the influence of these factors on the Cl(-) and voltage behavior, we studied spatiotemporal dynamics of activity-dependent [Cl(-)](i) changes in multicompartmental models of hippocampal cells based on realistic morphological data. ..."
1 . Jedlicka P, Deller T, Gutkin BS, Backus KH (2011) Activity-dependent intracellular chloride accumulation and diffusion controls GABA(A) receptor-mediated synaptic transmission. Hippocampus 21:885-98 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Extracellular;
Brain Region(s)/Organism:
Cell Type(s): Dentate gyrus granule GLU cell;
Channel(s): I Chloride; I_HCO3;
Gap Junctions:
Receptor(s): GabaA;
Transmitter(s): Gaba;
Simulation Environment: NEURON;
Model Concept(s): Influence of Dendritic Geometry; Short-term Synaptic Plasticity; Chloride regulation;
Implementer(s): Jedlicka, Peter [jedlicka at em.uni-frankfurt.de]; Mohapatra, Namrata [mohapatra at em.uni-frankfurt.de];
Search NeuronDB for information about:  Dentate gyrus granule GLU cell; GabaA; I Chloride; I_HCO3; Gaba;

Chloride accumulation and diffusion with decay (time constant tau) to resting level cli0.
The decay approximates a reversible chloride pump with first order kinetics.
To eliminate the chloride pump, just use this hoc statement
To make the time constant effectively "infinite".
tau and the resting level are both RANGE variables

Diffusion model is modified from Ca diffusion model in Hines & Carnevale: 
Expanding NEURON with NMODL, Neural Computation 12: 839-851, 2000 (Example 8)


	SUFFIX cldifus
	USEION hco3 READ hco3i, hco3o VALENCE -1
	GLOBAL vrat		:vrat must be GLOBAL
	RANGE tau, cli0, clo0, egaba, delta_egaba, init_egaba, ehco3_help, ecl_help

DEFINE Nannuli 4

	(molar) = (1/liter)
	(mM) = (millimolar)
	(um) = (micron)
	(mA) = (milliamp)
	(mV)    = (millivolt)
	FARADAY = (faraday) (10000 coulomb)
	PI = (pi) (1)
	F = (faraday) (coulombs)
	R = (k-mole)  (joule/degC)

	DCl = 2 (um2/ms) : Kuner & Augustine, Neuron 27: 447
	tau = 3000 (ms)
	cli0 = 8 (mM)
	clo0 = 133.5 (mM)
	hco3i0 = 16	(mM)
	hco3o0 = 26	(mM)
	P_help = 0.18
	celsius = 37    (degC)


	diam 	(um)
	icl 	(mA/cm2)
	cli 	(mM)
	hco3i	(mM)
	hco3o	(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
	egaba 	(mV)
	ehco3_help 	(mV)
	ecl_help	(mV)
	init_egaba  (mV)
	delta_egaba (mV)

	: cl[0] is equivalent to cli
	: cl[] are very small, so specify absolute tolerance
	cl[Nannuli]	(mM) <1e-10>

		SOLVE state METHOD sparse
		ecl_help = log(cli/clo0)*(1000)*(celsius + 273.15)*R/F
		egaba = P_help*ehco3_help + (1-P_help)*ecl_help
		delta_egaba = egaba - init_egaba

LOCAL factors_done

	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
	cli = cli0
	hco3i = hco3i0
	hco3o = hco3o0
	FROM i=0 TO Nannuli-1 {
		cl[i] = cli
	ehco3_help = log(hco3i/hco3o)*(1000)*(celsius + 273.15)*R/F
	ecl_help = log(cli/clo0)*(1000)*(celsius + 273.15)*R/F
	egaba = P_help*ehco3_help + (1-P_help)*ecl_help
	init_egaba = egaba
	delta_egaba = egaba - init_egaba 

LOCAL frat[Nannuli]	: scales the rate constants for model geometry

PROCEDURE factors() {
	LOCAL r, dr2
	r = 1/2			: starts at edge (half diam), diam = 1, length = 1
	dr2 = r/(Nannuli-1)/2	: full thickness of outermost annulus,
				: half thickness of all other annuli
	vrat[0] = 0
	frat[0] = 2*r		: = diam
	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 Ai+1/delta_r=2PI*r*1/delta_r
						: div by distance between centers 
		r = r - dr2
		vrat[i+1] = PI*(r+dr2/2)*2*dr2	: outer half of annulus

KINETIC state {
	COMPARTMENT i, diam*diam*vrat[i] {cl}
	LONGITUDINAL_DIFFUSION i, DCl*diam*diam*vrat[i] {cl}
	~ cl[0] << ((icl*PI*diam/FARADAY) + (diam*diam*vrat[0]*(cli0 - cl[0])/tau)) : icl is Cl- influx 
	FROM i=0 TO Nannuli-2 {
		~ cl[i] <-> cl[i+1]	(DCl*frat[i+1], DCl*frat[i+1])
	cli = cl[0]