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CA1 pyramidal neuron: dendritic Ca2+ inhibition (Muellner et al. 2015)

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In our experimental study, we combined paired patch-clamp recordings and two-photon Ca2+ imaging to quantify inhibition exerted by individual GABAergic contacts on hippocampal pyramidal cell dendrites. We observed that Ca2+ transients from back-propagating action potentials were significantly reduced during simultaneous activation of individual nearby GABAergic synapses. To simulate dendritic Ca2+ inhibition by individual GABAergic synapses, we employed a multi-compartmental CA1 pyramidal cell model with detailed morphology, voltage-gated channel distributions, and calcium dynamics, based with modifications on the model of Poirazi et al., 2003, modelDB accession # 20212.
1 . Müllner FE, Wierenga CJ, Bonhoeffer T (2015) Precision of Inhibition: Dendritic Inhibition by Individual GABAergic Synapses on Hippocampal Pyramidal Cells Is Confined in Space and Time. Neuron 87:576-89 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Hippocampus CA1 pyramidal GLU cell;
Channel(s): I Calcium; I Sodium; I Potassium; I h;
Gap Junctions:
Transmitter(s): Gaba;
Simulation Environment: NEURON;
Model Concept(s): Action Potentials; Dendritic Action Potentials; Active Dendrites; Calcium dynamics;
Implementer(s): Muellner, Fiona E [fiona.muellner at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; I h; I Sodium; I Calcium; I Potassium; Gaba;
previously used
ampa.mod *
cagk.mod *
cal.mod *
calH.mod *
d3.mod *
h.mod *
hha_old.mod *
hha2.mod *
kadist.mod *
kaprox.mod *
kca.mod *
km.mod *
nap.mod *
nmda.mod *

Taken from Jedlicka et al. 2011, "Activity-Dependent Intracellular Chloride Accumulation and Diffusion Controls GABAA Receptor-Mediated Synaptic Transmission".

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 cl READ icl WRITE cli, ecl VALENCE -1
	USEION hco3 READ hco3i, hco3o VALENCE -1
	GLOBAL vrat		:vrat must be GLOBAL
	RANGE tau, cli0, clo0, egaba, delta_egaba, init_egaba, ehco3, ecl

DEFINE Nannuli 11
	(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 = 7.5 (mM)
	clo0 = 136.1 (mM)
	hco3i0 = 16	(mM)
	hco3o0 = 26	(mM)
	P = 0.18
	celsius = 34    (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 	(mV)
	ecl	(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 = log(cli/clo0)*(1000)*(celsius + 273.15)*R/F
		egaba = P*ehco3 + (1-P)*ecl
		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 = log(hco3i/hco3o)*(1000)*(celsius + 273.15)*R/F
	ecl = log(cli/clo0)*(1000)*(celsius + 273.15)*R/F
	egaba = P*ehco3 + (1-P)*ecl
	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]

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