Mathematical model for windup (Aguiar et al. 2010)

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Accession:128559
"Windup is characterized as a frequency-dependent increase in the number of evoked action potentials in dorsal horn neurons in response to electrical stimulation of afferent C-fibers. ... The approach presented here relies on mathematical and computational analysis to study the mechanism(s) underlying windup. From experimentally obtained windup profiles, we extract the time scale of the facilitation mechanisms that may support the characteristics of windup. Guided by these values and using simulations of a biologically realistic compartmental model of a wide dynamic range (WDR) neuron, we are able to assess the contribution of each mechanism for the generation of action potentials windup. ..."
Reference:
1 . Aguiar P, Sousa M, Lima D (2010) NMDA channels together with L-type calcium currents and calcium-activated nonspecific cationic currents are sufficient to generate windup in WDR neurons. J Neurophysiol 104:1155-66 [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): Wide dynamic range neuron;
Channel(s): I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Activity Patterns; Action Potentials;
Implementer(s):
Search NeuronDB for information about:  GabaA; AMPA; NMDA; I Na,p; I Na,t; I L high threshold; I N; I K; I K,Ca;
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WDR-Model
readme.html
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TITLE Persistent Sodium

COMMENT
12/1/2005 NTC Made compatible with adaptive integration
Unused stuff removed
ENDCOMMENT

: modified by Steven Prescott based on current described below
: Prescott and De Koninck. 2005. J Neurosci 25: 4743-4754
: sodium current active a subthreshold potentials, works synergistically
: with persistent calcium current to prolong subthreshold depolarization
:
: original current described below...
: Fast Na+ and K+ currents responsible for action potentials
: Iterative equations
:
: Equations modified by Traub, for Hippocampal Pyramidal cells, in:
: Traub & Miles, Neuronal Networks of the Hippocampus, Cambridge, 1991
:
: range variable vtraub adjust threshold
:
: Written by Alain Destexhe, Salk Institute, Aug 1992
:
: Modifications by Arthur Houweling for use in MyFirstNEURON

NEURON {
	SUFFIX iNaP
	USEION na READ ena WRITE ina
	RANGE gnabar, vtraub, vsm, vsh, gamma
	RANGE m_inf, h_inf
	RANGE tau_m, tau_h
	RANGE ina 
}


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

PARAMETER {
	gnabar	= .00029 	(mho/cm2)
	ena			(mV)
	celsius			(degC)
	v               	(mV)
	vtraub	= -55		(mV)	: adjusts threshold
	vsm	= -2            (mV)	: collapses activation curve as increasingly -ve
	vsh	= -5            (mV)	: shifts inactivation curve left as increasingly -ve
	gamma	= 0.5		        : collapses inactivation curve when <1
}

STATE {
	m h
}

ASSIGNED {
	ina	(mA/cm2)
	m_inf
	h_inf
	tau_m (ms)
	tau_h (ms)
	tadj
}


BREAKPOINT {
	SOLVE states METHOD cnexp
	ina = gnabar * m*h * (v - ena)
}

DERIVATIVE states {
	evaluate_fct(v)
	m' = (m_inf-m)/tau_m
	h' = (h_inf-h)/tau_h
}

UNITSOFF
INITIAL {
:
:  Q10 was assumed to be 3 for both currents
:
	tadj = 3.0 ^ ((celsius-36)/ 10 )
	evaluate_fct(v)
	m= m_inf
	h= h_inf
}

PROCEDURE evaluate_fct(v(mV)) { LOCAL a,b,v2

	v2 = v - vtraub : convert to traub convention

	a = 0.32 * (vsm+13-v2) / ( exp((vsm+13-v2)/4) - 1)
	b = 0.28 * (vsm+v2-40) / ( exp((vsm+v2-40)/5) - 1)
	tau_m = 1 / (a + b) / tadj
	m_inf = a / (a + b)

	a = 0.128 * exp((vsh+17-v2)/18)
	b = 4 / ( 1 + exp((vsh+40-v2)/5*gamma))
	tau_h = 1 / (a + b) / tadj
	h_inf = a / (a + b)
}

UNITSON

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