A detailed Purkinje cell model (Masoli et al 2015)

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Accession:229585
The Purkinje cell is one of the most complex type of neuron in the central nervous system and is well known for its massive dendritic tree. The initiation of the action potential was theorized to be due to the high calcium channels presence in the dendritic tree but, in the last years, this idea was revised. In fact, the Axon Initial Segment, the first section of the axon was seen to be critical for the spontaneous generation of action potentials. The model reproduces the behaviours linked to the presence of this fundamental sections and the interplay with the other parts of the neuron.
Reference:
1 . Masoli S, Solinas S, D'Angelo E (2015) Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization. Front Cell Neurosci 9:47 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Axon;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I Sodium; I Calcium; I Na,t; I K;
Gap Junctions:
Receptor(s):
Gene(s): Cav2.1 CACNA1A; Cav3.1 CACNA1G; Cav3.2 CACNA1H; Cav3.3 CACNA1I; Nav1.6 SCN8A; Kv1.1 KCNA1; Kv1.5 KCNA5; Kv3.3 KCNC3; Kv3.4 KCNC4; Kv4.3 KCND3; KCa1.1 KCNMA1; KCa2.2 KCNN2; KCa3.1 KCNN4; Kir2.1 KCNJ2; HCN1;
Transmitter(s):
Simulation Environment: NEURON; Python;
Model Concept(s): Bursting; Detailed Neuronal Models; Action Potentials; Action Potential Initiation; Axonal Action Potentials;
Implementer(s): Masoli, Stefano [stefano.masoli at unipv.it]; Solinas, Sergio [solinas at unipv.it];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I Na,t; I K; I Sodium; I Calcium;
TITLE Voltage-gated potassium channel from Kv3 subunits

COMMENT
Voltage-gated potassium channel with high threshold and fast activation/deactivation kinetics

KINETIC SCHEME: Hodgkin-Huxley (n^4)
n'= alpha * (1-n) - betha * n
g(v) = gbar * n^4 * ( v-ek )

The rate constants of activation (alpha) and deactivation (beta) were approximated by:

alpha(v) = ca * exp(-(v+cva)/cka)
beta(v) = cb * exp(-(v+cvb)/ckb)

Parameters can, cvan, ckan, cbn, cvbn, ckbn are given in the CONSTANT block.
Values derive from least-square fits to experimental data of G/Gmax(v) and taun(v) in Martina et al. J Neurophys. 97 (563-671, 2007.
Model includes a calculation of Kv gating current

Reference: Akemann et al., Biophys. J. (2009) 96: 3959-3976

Laboratory for Neuronal Circuit Dynamics
RIKEN Brain Science Institute, Wako City, Japan
http://www.neurodynamics.brain.riken.jp

Date of Implementation: April 2007
Contact: akemann@brain.riken.jp

Suffix from Kv3 to Kv3_3

ENDCOMMENT


NEURON {
    THREADSAFE
	SUFFIX Kv3_3
	USEION k READ ek WRITE ik
	NONSPECIFIC_CURRENT i
	RANGE gbar, g, ik, i, igate, nc
	RANGE ninf, taun
	RANGE gateCurrent, gunit
}

UNITS {
	(mV) = (millivolt)
	(mA) = (milliamp)
	(nA) = (nanoamp)
	(pA) = (picoamp)
	(S)  = (siemens)
	(mS) = (millisiemens)
	(nS) = (nanosiemens)
	(pS) = (picosiemens)
	(um) = (micron)
	(molar) = (1/liter)
	(mM) = (millimolar)		
}

CONSTANT {
	e0 = 1.60217646e-19 (coulombs)
	q10 = 2.7

	ca = 0.22 (1/ms)
	cva = 16 (mV)
	cka = -26.5 (mV)
	cb = 0.22 (1/ms)
	cvb = 16 (mV)
	ckb = 26.5 (mV)
	
	zn = 1.9196 (1)		: valence of n-gate
}

PARAMETER {
	gateCurrent = 0 (1)	: gating currents ON = 1 OFF = 0
	
	gbar = 0.005 (S/cm2)   <0,1e9>
	gunit = 16 (pS)		: unitary conductance 
}

ASSIGNED {
	celsius (degC)
	v (mV)
	
	ik (mA/cm2)
	igate (mA/cm2)
	i (mA/cm2)
 
	ek (mV)
	g (S/cm2)
	nc (1/cm2)
	qt (1)

	ninf (1)
	taun (ms)
	alpha (1/ms)
	beta (1/ms)
}

STATE { n }

INITIAL {
	nc = (1e12) * gbar / gunit
	qt = q10^((celsius-22 (degC))/10 (degC))
	rateConst(v)
	n = ninf
}

BREAKPOINT {
	SOLVE state METHOD cnexp
      g = gbar * n^4 
	ik = g * (v - ek)
	igate = nc * (1e6) * e0 * 4 * zn * ngateFlip()

	if (gateCurrent != 0) { 
		i = igate
	}
}

DERIVATIVE state {
	rateConst(v)
	n' = alpha * (1-n) - beta * n
}

PROCEDURE rateConst(v (mV)) {
	alpha = qt * alphaFkt(v)
	beta = qt * betaFkt(v)
	ninf = alpha / (alpha + beta) 
	taun = 1 / (alpha + beta)
}

FUNCTION alphaFkt(v (mV)) (1/ms) {
	alphaFkt = ca * exp(-(v+cva)/cka) 
}

FUNCTION betaFkt(v (mV)) (1/ms) {
	betaFkt = cb * exp(-(v+cvb)/ckb)
}

FUNCTION ngateFlip() (1/ms) {
	ngateFlip = (ninf-n)/taun 
}



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