Cerebellar purkinje cell: interacting Kv3 and Na currents influence firing (Akemann, Knopfel 2006)

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Accession:80769
Purkinje neurons spontaneously generate action potentials in the absence of synaptic drive and thereby exert a tonic, yet plastic, input to their target cells in the deep cerebellar nuclei. Purkinje neurons express two ionic currents with biophysical properties that are specialized for high-frequency firing: resurgent sodium currents and potassium currents mediated by Kv3.3. Numerical simulations indicated that Kv3.3 increases the spontaneous firing rate via cooperation with resurgent sodium currents. We conclude that the rate of spontaneous action potential firing of Purkinje neurons is controlled by the interaction of Kv3.3 potassium currents and resurgent sodium currents. See paper for more and details.
Reference:
1 . Akemann W, Knöpfel T (2006) Interaction of Kv3 potassium channels and resurgent sodium current influences the rate of spontaneous firing of Purkinje neurons. J Neurosci 26:4602-12 [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:
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I Na,t; I A; I K; I h; I K,Ca; I Calcium;
Gap Junctions:
Receptor(s):
Gene(s): Kv1.1 KCNA1; Kv4.3 KCND3; Kv3.3 KCNC3; HCN1;
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Ion Channel Kinetics; Oscillations; Action Potentials; Calcium dynamics;
Implementer(s): Akemann, Walther [akemann at brain.riken.jp];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I Na,t; I A; I K; I h; I K,Ca; 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

ENDCOMMENT

NEURON {
  SUFFIX Narsg
  USEION na READ ena WRITE ina
  RANGE g, gbar, ina

}

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)
	SOLVE seqinitial
}

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
}

LINEAR seqinitial { : sets initial equilibrium
 ~          I1*bi1 + C2*b01 - C1*(    fi1+f01) = 0
 ~ C1*f01 + I2*bi2 + C3*b02 - C2*(b01+fi2+f02) = 0
 ~ C2*f02 + I3*bi3 + C4*b03 - C3*(b02+fi3+f03) = 0
 ~ C3*f03 + I4*bi4 + C5*b04 - C4*(b03+fi4+f04) = 0
 ~ C4*f04 + I5*bi5 + O*b0O - C5*(b04+fi5+f0O) = 0
 ~ C5*f0O + B*bip + I6*bin - O*(b0O+fip+fin) = 0
 ~ O*fip + B*bip = 0

 ~          C1*fi1 + I2*b11 - I1*(    bi1+f11) = 0
 ~ I1*f11 + C2*fi2 + I3*b12 - I2*(b11+bi2+f12) = 0
 ~ I2*f12 + C3*fi3 + I4*bi3 - I3*(b12+bi3+f13) = 0
 ~ I3*f13 + C4*fi4 + I5*b14 - I4*(b13+bi4+f14) = 0
 ~ I4*f14 + C5*fi5 + I6*b1n - I5*(b14+bi5+f1n) = 0
 
 ~ 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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