Explaining pathological changes in axonal excitability by dynamical analysis (Coggan et al. 2011)

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Accession:143072
"... To help decipher the biophysical basis for ‘paroxysmal’ spiking, we replicated afterdischarge (i.e. continued spiking after a brief stimulus) in a minimal conductance-based axon model. ... A perturbation could abruptly switch the system between two (quasi-)stable attractor states: rest and repetitive spiking. ... Initiation of afterdischarge was explained by activation of the persistent inward current forcing the system to cross a saddle point that separates the basins of attraction associated with each attractor. Termination of afterdischarge was explained by the attractor associated with repetitive spiking being destroyed. ... The model also explains other features of paroxysmal symptoms, including temporal summation and refractoriness."
Reference:
1 . Coggan JS, Ocker GK, Sejnowski TJ, Prescott SA (2011) Explaining pathological changes in axonal excitability through dynamical analysis of conductance-based models. J Neural Eng 8:065002 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Axon;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Nociception;
Implementer(s): Prescott, Steven [steve.prescott at sickkids.ca]];
: modified by Jay Coggan

: 	High threshold potassium chanel from 
:	Contribution of the Kv3.1 potassium channel to high-frequency firing in mouse auditory neurones
:	Lu-Yang Wang, Li Gan, Ian D. Forsythe and Leonard K. Kaczmarek
:	J. Physiol (1998), 501.9, pp. 183-194

NEURON {
	SUFFIX HT
	USEION k READ ek WRITE ik
 	RANGE gbar, g, ik
	GLOBAL ninf, ntau, pinf, ptau, an, bn, ap, bp
}

: area in paper is 1000 (um2) so divide our density parameters by 10

UNITS {
	(mV) = (millivolt)
	(S) = (mho)
	(mA) = (milliamp)
}

PARAMETER {
	gbar = .15 (S/cm2) 
	gamma = .1
	kan = .2120 (/ms) 
	ean = .04 (/mV)		
	kbn = .1974 (/ms) 
	ebn = 0 (/mV)
	ek = -90 (mV)
	:e_k = -90 (mV)
	kap = .00713 (/ms)	
	eap = -.1942 (/mV)	
	kbp = .0935 (/ms)	
	ebp = .0058 (/mV)	
}

ASSIGNED {
	v (mV)
	:ek (mV)
	ik (mA/cm2)

	ninf
	ntau (ms)
	pinf
	ptau (ms)

	an (/ms)
	bn (/ms)
	ap (/ms)
	bp (/ms)
}

STATE {
	n p
}

INITIAL {
	rates(v)
	n = ninf
	p = pinf
}

BREAKPOINT {
	SOLVE state METHOD cnexp
	:ik = gbar*n^3*(1 - gamma + gamma*p)*(v - e_k)
	ik = gbar*n^3*(1 - gamma + gamma*p)*(v - ek)

:	ik = gbar*n^3*(1 - gamma + gamma*p)*(v - (-90))
}

DERIVATIVE state {
	rates(v)
	n' = (ninf - n)/ntau
	p' = (pinf - p)/ptau
}

PROCEDURE rates(v(mV)) {

	an = kan*exp(ean*v)
	bn = kbn*exp(ebn*v)

	ap = kap*exp(eap*v)
	bp = kbp*exp(ebp*v)

	ninf = an/(an + bn)
	ntau = 1/(an + bn)
	pinf = ap/(ap + bp)
	ptau = 1/(ap + bp)
}


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