A detailed Purkinje cell model (Masoli et al 2015)

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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.
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:
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;
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 Cardiac IKur  current & nonspec cation current with identical kinetics
: Hodgkin - Huxley type channels, modified to fit IKur data from Feng et al Am J Physiol 1998 275:H1717 - H 1725
: Suffix from Kv15 to Kv1_5

	USEION k READ ek,ki,ko WRITE ik
	USEION na READ nai,nao
	USEION no WRITE ino VALENCE 1: nonspecific cation current
	RANGE gKur, ik, ino, Tauact, Tauinactf,Tauinacts, gnonspec, nao, nai, ko,ki
	RANGE minf, ninf, uinf, mtau , ntau, utau

	(mA) = (milliamp)
	(mV) = (millivolt)
        (mM) = (milli/liter)
	F = (faraday) (coulombs)
	R 	= (k-mole)	(joule/degC)

	 gKur=0.13195e-3 (S/cm2) <0,1e9>
	Tauact=1 (ms)
	Tauinactf=1 (ms)
	Tauinacts=1 (ms)
	gnonspec=0   (S/cm2) <0,1e9>
	 m n u

	v (mV)
	celsius (degC) : 37
       	ik (mA/cm2)
	minf ninf uinf
	mtau (ms)
        ntau (ms)
	utau (ms)
	ek (mV)
	ino (mA/cm2)
	ki (mM)
	ko (mM)
	nai (mM)
	nao (mM)

	m = minf
        n = ninf
	u = uinf

	z = (R*(celsius+273.15))/F
	SOLVE states METHOD derivimplicit
		ik = gKur*(0.1 + 1/(1 + exp(-(v - 15)/13)))*m*m*m*n*u*(v - ek)
	ino=gnonspec*(0.1 + 1/(1 + exp(-(v - 15)/13)))*m*m*m*n*u*(v - z*log((nao+ko)/(nai+ki)))

DERIVATIVE states {	: exact when v held constant
	m' = (minf - m)/mtau
        n' = (ninf - n)/ntau
	u' = (uinf - u)/utau

FUNCTION alp(v(mV),i) { LOCAL q10 : order m n
	v = v
	q10 = 2.2^((celsius - 37)/10)
       if (i==0) {
	          alp = q10*0.65/(exp(-(v + 10)/8.5) + exp(-(v - 30)/59))
          } else if (i==1) {
                   alp = 0.001*q10/(2.4 +10.9* exp(-(v + 90)/78))

FUNCTION bet(v(mV),i) (/ms) { LOCAL q10 : order m n u
	v = v 
	q10 = 2.2^((celsius - 37)/10)
        if (i==0){
	         bet = q10*0.65/(2.5 + exp((v + 82)/17))
        }else if (i==1){
                  bet = q10*0.001*exp((v - 168)/16)
FUNCTION ce(v(mV),i)(/ms) {   :  order m n u 
        v = v
        if (i==0) {
                ce = 1/(1 + exp(-(v + 30.3)/9.6))
        }else if (i==1){
                ce = 1*(0.25+1/(1.35 + exp((v + 7)/14)))
	}else if (i==2){
                ce = 1*(0.1+1/(1.1 + exp((v + 7)/14)))

PROCEDURE rates(v) {LOCAL a,b,c :
		a = alp(v,0)  b=bet(v,0) c = ce(v,0)
		mtau = 1/(a + b)/3*Tauact
		minf = c
               a = alp(v,1)  b=bet(v,1) c = ce(v,1)
		ntau = 1/(a + b)/3*Tauinactf
		ninf = c
		c = ce(v,2)
		uinf = c
		utau = 6800*Tauinacts

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