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 resurgent sodium channel

COMMENT
Neuron implementation of a resurgent sodium channel (with blocking particle)
Based om updated kinetic parameters from Raman and Bean, Biophys.J. 80 (2001) 729  

Modified from Khaliq et al., J.Neurosci. 23(2003)4899
by qt-correction of all rate constants 

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

Reference: Akemann and Knoepfel, J.Neurosci. 26 (2006) 4602
Date of Implementation: May 2005
Contact: akemann@brain.riken.jp

Suffix from Narsg to Nav1_6

ENDCOMMENT

NEURON {
  SUFFIX Nav1_6
  USEION na READ ena WRITE ina
  RANGE g, gbar, ina, f0O, fin, fip

}

UNITS { 
	(mV) = (millivolt)
	(S) = (siemens)
}

CONSTANT {
	q10 = 3
}

PARAMETER {
	gbar = 0.016 (S/cm2)
	celsius (degC)

	: kinetic parameters
	Con = 0.005			(/ms)					: closed -> inactivated transitions
	Coff = 0.5			(/ms)					: inactivated -> closed transitions
	Oon = 0.75			(/ms)					: open -> Ineg transition
	Ooff = 0.005		(/ms)					: Ineg -> open transition
	alpha = 150			(/ms)					: activation
	beta = 3			(/ms)					: deactivation
	gamma = 150			(/ms)					: opening
	delta = 40			(/ms)					: closing, greater than BEAN/KUO = 0.2
	epsilon = 1.75		(/ms)					: open -> Iplus for tau = 0.3 ms at +30 with x5
	zeta = 0.03			(/ms)					: Iplus -> open for tau = 25 ms at -30 with x6

	: Vdep
	x1 = 20				(mV)								: Vdep of activation (alpha)
	x2 = -20			(mV)								: Vdep of deactivation (beta)
	x3 = 1e12			(mV)								: Vdep of opening (gamma)
	x4 = -1e12			(mV)								: Vdep of closing (delta)
	x5 = 1e12			(mV)								: Vdep into Ipos (epsilon)
	x6 = -25			(mV)								: Vdep out of Ipos (zeta)
}

ASSIGNED {
	alfac   				: microscopic reversibility factors
	btfac				

	: rates
	f01  		(/ms)
	f02  		(/ms)
	f03 		(/ms)
	f04			(/ms)
	f0O 		(/ms)
	fip 		(/ms)
	f11 		(/ms)
	f12 		(/ms)
	f13 		(/ms)
	f14 		(/ms)
	f1n 		(/ms)
	fi1 		(/ms)
	fi2 		(/ms)
	fi3 		(/ms)
	fi4 		(/ms)
	fi5 		(/ms)
	fin 		(/ms)

	b01 		(/ms)
	b02 		(/ms)
	b03 		(/ms)
	b04		(/ms)
	b0O 		(/ms)
	bip 		(/ms)
	b11  		(/ms)
	b12 		(/ms)
	b13 		(/ms)
	b14 		(/ms)
	b1n 		(/ms)
	bi1 		(/ms)
	bi2 		(/ms)
	bi3 		(/ms)
	bi4 		(/ms)
	bi5 		(/ms)
	bin 		(/ms)
	
	v					(mV)
 	ena					(mV)
	ina 					(milliamp/cm2)
	g					(S/cm2)
	qt
}

STATE {
	C1 FROM 0 TO 1
	C2 FROM 0 TO 1
	C3 FROM 0 TO 1
	C4 FROM 0 TO 1
	C5 FROM 0 TO 1
	I1 FROM 0 TO 1
	I2 FROM 0 TO 1
	I3 FROM 0 TO 1
	I4 FROM 0 TO 1
	I5 FROM 0 TO 1
	O FROM 0 TO 1
	B FROM 0 TO 1
	I6 FROM 0 TO 1
}

BREAKPOINT {
	SOLVE activation METHOD sparse
 	g = gbar * O
 	ina = g * (v - ena)
}

INITIAL {
	qt = q10^((celsius-22 (degC))/10 (degC))
	rates(v)
}

KINETIC activation
{
	rates(v)
	~ C1 <-> C2					(f01,b01)
	~ C2 <-> C3					(f02,b02)
	~ C3 <-> C4					(f03,b03)
	~ C4 <-> C5					(f04,b04)
	~ C5 <-> O					(f0O,b0O)
	~ O <-> B					(fip,bip)
	~ O <-> I6					(fin,bin)
	~ I1 <-> I2					(f11,b11)
	~ I2 <-> I3					(f12,b12)
	~ I3 <-> I4					(f13,b13)
	~ I4 <-> I5					(f14,b14)
	~ I5 <-> I6					(f1n,b1n)
	~ C1 <-> I1					(fi1,bi1)
	~ C2 <-> I2					(fi2,bi2)
	~ C3 <-> I3					(fi3,bi3)
 	~ C4 <-> I4					(fi4,bi4)
 	~ C5 <-> I5					(fi5,bi5)

CONSERVE C1 + C2 + C3 + C4 + C5 + O + B + I1 + I2 + I3 + I4 + I5 + I6 = 1
}


PROCEDURE rates(v(mV) )
{
 alfac = (Oon/Con)^(1/4)
 btfac = (Ooff/Coff)^(1/4) 
 f01 = 4 * alpha * exp(v/x1) * qt
 f02 = 3 * alpha * exp(v/x1) * qt
 f03 = 2 * alpha * exp(v/x1) * qt
 f04 = 1 * alpha * exp(v/x1) * qt
 f0O = gamma * exp(v/x3) * qt
 fip = epsilon * exp(v/x5) * qt
 f11 = 4 * alpha * alfac * exp(v/x1) * qt
 f12 = 3 * alpha * alfac * exp(v/x1) * qt
 f13 = 2 * alpha * alfac * exp(v/x1) * qt
 f14 = 1 * alpha * alfac * exp(v/x1) * qt
 f1n = gamma * exp(v/x3) * qt
 fi1 = Con * qt
 fi2 = Con * alfac * qt
 fi3 = Con * alfac^2 * qt
 fi4 = Con * alfac^3 * qt
 fi5 = Con * alfac^4 * qt
 fin = Oon * qt

 b01 = 1 * beta * exp(v/x2) * qt
 b02 = 2 * beta * exp(v/x2) * qt
 b03 = 3 * beta * exp(v/x2) * qt
 b04 = 4 * beta * exp(v/x2) * qt
 b0O = delta * exp(v/x4) * qt
 bip = zeta * exp(v/x6) * qt
 b11 = 1 * beta * btfac * exp(v/x2) * qt
 b12 = 2 * beta * btfac * exp(v/x2) * qt
 b13 = 3 * beta * btfac * exp(v/x2) * qt
 b14 = 4 * beta * btfac * exp(v/x2) * qt
 b1n = delta * exp(v/x4) * qt
 bi1 = Coff * qt
 bi2 = Coff * btfac * qt
 bi3 = Coff * btfac^2 * qt
 bi4 = Coff * btfac^3 * qt
 bi5 = Coff * btfac^4 * qt
 bin = Ooff * qt
}


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