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 Low threshold calcium current
:
:   Ca++ current responsible for low threshold spikes (LTS)
:   RETICULAR THALAMUS
:   Differential equations
:
:   Model of Huguenard & McCormick, J Neurophysiol 68: 1373-1383, 1992.
:   
:   Written by Alain Destexhe, Salk Institute, Sept 18, 1992
:   
:    - Biophysical properties of the T current were from recordings of
:    - human recombinant Cav3.2 T-channel in HEK-293 cells
:    - see Vitko et al., J. Neurosci 25(19) :4844-4855, 2005
:    - Q10 and shift parameters are fixed 
:   
:
:   Suffix from CaT3_2 to Cav3_2

INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
	SUFFIX Cav3_2
	USEION ca READ cai, cao WRITE ica
	RANGE gcabar, m_inf, tau_m, h_inf, tau_h, shift, i,ica
}

UNITS {
	(molar) = (1/liter)
	(mV) =	(millivolt)
	(mA) =	(milliamp)
	(mM) =	(millimolar)

	FARADAY = (faraday) (coulomb)
	R = (k-mole) (joule/degC)
}

PARAMETER {
	v		(mV)
	celsius	= 36	(degC)
:	eca	= 120	(mV)
	gcabar	= .0008	(mho/cm2)
	shift	= 0 	(mV)
	cai	= 2.4e-4 (mM)		: adjusted for eca=120 mV
	cao	= 2	(mM)
}

STATE {
	m h
}

ASSIGNED {
	ica	(mA/cm2)
	carev	(mV)
	m_inf
	tau_m	(ms)
	h_inf
	tau_h	(ms)
	phi_m
	phi_h
	i	(mA/cm2)
}

BREAKPOINT {
	SOLVE castate METHOD cnexp
	carev = (1e3) * (R*(celsius+273.15))/(2*FARADAY) * log (cao/cai)
	ica = gcabar * m*m*h * (v-carev)
	i = ica		: diagnostic i added to display the current
}

DERIVATIVE castate {
	evaluate_fct(v)

	m' = (m_inf - m) / tau_m
	h' = (h_inf - h) / tau_h
}

UNITSOFF
INITIAL {
:
:   Activation functions and kinetics were obtained from
:   Vitko et al., 2005 at 23-25 deg.
:   Transformation to 36 deg assuming Q10 of 5 and 3 for m and h
:   (as in Coulter et al., J Physiol 414: 587, 1989)
:
	phi_m = 5 ^ (12/10)
	phi_h = 3 ^ (12/10)

	evaluate_fct(v)

	m = m_inf
	h = h_inf
}

PROCEDURE evaluate_fct(v(mV)) { 
:

	m_inf = 1.0 / ( 1 + exp(-(v+shift+54.8)/7.4) )
	h_inf = 1.0 / ( 1 + exp((v+shift+85.5)/7.18) )

	tau_m = ( 1.9 + 1.0 / ( exp((v+shift+37.0)/11.9) + exp(-(v+shift+131.6)/21) ) ) / phi_m
	tau_h = 13.7 + (1942 + exp((v+shift+164)/9.2)) / (1 + exp((v+shift+89.3)/3.7) ) / phi_h
}
UNITSON

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