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]];
TITLE Sodium ion accumulation
: Sodium ion accumulation inside and outside
: modified by Jay Coggan

NEURON {
	SUFFIX naaccum2
	:USEION na READ ina, nai, nao WRITE nai, nao
	USEION na READ ina, nao WRITE  nao
	RANGE fhspace, k
}

UNITS {
	(molar) = (1/liter)
	(mV) = (millivolt)
	(um) = (micron)
	(mM) = (millimolar)
	(mA) = (milliamp)
	FARADAY = 96520 (coul)
	R = 8.3134	(joule/degC)
}

PARAMETER {
	nabath = 143	(mM)		
	diam		(um)
	ina		(mA/cm2)
	fhspace	= 20000	(angstrom)	: 20000 orig width of frankenhaeuser-hodgkin space
					: transfer rate from bath to
	:k = .145	(ms)		: FH space
	k = .05				
	:nai0 = 12 	(mM)
	nao0 = 143	(mM)		
}

STATE {
	:nai 	(mM)
	nao 	(mM)
}


INITIAL {
	
	:nai = nai0
	nao = nao0
	
}

BREAKPOINT {
	SOLVE state METHOD euler
}

DERIVATIVE state {
	:nai' = -ina * 4/(diam*FARADAY) * (1e4)
	:nai' = 0

	:nao' = ina/fhspace/FARADAY*(1e8) + k*(nabath - nao)*(1e-3)
	nao' = ina/fhspace/FARADAY*(1e8) + (nabath - nao)/k
	:nao' = 0 + k*(nabath - nao)*(1e-3)
}
	
COMMENT
This model uses ina but does not WRITE it; thus this model does
not add anything to the total ionic current.

The initial block works around a difficulty that arises from a STATE in
this model having the same name as an ion.  (Note: in the cabpump model
there is no name conflict between the ca[] states and the cai ion
concentration.) The sequence of events when finitialize is called is
that the na_ion's nai,nao are initialized to the global variables
nai0_na_ion and nao0_na_ion respectively. Then this model's INITIAL block
is called. By default, nai/nao would be set to the initial state values
nai0/nao0 implicitly declared in this model and on exit from the intitial
block, the na_ion values would be assigned these local values. We therefore
directly set the local state values to the na_ion values. See the
"nocmodl nacum" generated nacum.c file to see the precise sequence on
the nrn_init() call.

diam is a special range variable in NEURON and refers to the diameter in
microns.  Under scop and hocmodl its default value is specified in the
PARAMETER block. In NEURON, however, its value is taken from the
"morphology" mechanism.
ENDCOMMENT

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