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 high threshold calcium current (L-current)

COMMENT
        *********************************************
        reference:      McCormick & Huguenard (1992) 
			J.Neurophysiology 68(4), 1384-1400
        found in:       hippocampal pyramidal cells
        *********************************************
	Assembled for MyFirstNEURON by Arthur Houweling
	
ENDCOMMENT




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


NEURON {
	SUFFIX iCaL
	USEION ca READ cai,cao WRITE ica
        RANGE pcabar, m_inf, tau_m, ica
}

UNITS {
	(mA)	= (milliamp)
	(mV)	= (millivolt)
	(mM)	= (milli/liter)
        FARADAY = 96480 (coul)
        R       = 8.314 (volt-coul/degC)
}

PARAMETER {
	v			(mV)
	celsius			(degC)
        dt              	(ms)
	cai			(mM)
	cao			(mM)
	pcabar= 0.000276	(cm/s)		
}

STATE {
	m
}

ASSIGNED {
	ica		(mA/cm2)
	tau_m		(ms)
	m_inf 
	tadj
}

BREAKPOINT { 
	SOLVE states :METHOD euler
	ica = pcabar * m*m * ghk(v,cai,cao,2)
}

:DERIVATIVE states {
:       rates(v)
:
:       m'= (m_inf-m) / tau_m 
:}
  
PROCEDURE states() {
        rates(v)
	
        m= m + (1-exp(-dt/tau_m))*(m_inf-m)
	:printf("\n iCaL tau_m=%g", tau_m)
}

UNITSOFF

INITIAL {
	tadj = 3.0 ^ ((celsius-23.5)/10)
	rates(v)
	m = m_inf
}

FUNCTION ghk( v(mV), ci(mM), co(mM), z)  (millicoul/cm3) {
        LOCAL e, w
        w = v * (.001) * z*FARADAY / (R*(celsius+273.16))
        
	if (fabs(w)>1e-4) 
          { e = w / (exp(w)-1) }
        else
	: denominator is small -> Taylor series
        { e = 1-w/2 }
	
        ghk = - (.001) * z*FARADAY * (co-ci*exp(w)) * e
}
UNITSOFF

PROCEDURE rates(v(mV)) { LOCAL a,b
	a = 1.6 / (1+ exp(-0.072*(v-5)))
	b = 0.02 * vtrap( -(v-1.31), 5.36)

	tau_m = 1/(a+b) / tadj
	m_inf = 1/(1+exp((v+10)/-10))
}

FUNCTION vtrap(x,c) { 
	: Traps for 0 in denominator of rate equations
        if (fabs(x/c) < 1e-6) {
          vtrap = c + x/2 }
        else {
          vtrap = x / (1-exp(-x/c)) }
}
UNITSON

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