Active dendritic action potential propagation (Casale & McCormick 2011)

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Accession:143635
This model explores the dendritic sodium and potassium conductances needed to recapitulate voltage-sensitive dye optical recordings of thalamic interneuron dendrites in the dorsal lateral geniculate nucleus. Model ion channels were selected based on pharmacological data.
Reference:
1 . Casale AE, McCormick DA (2011) Active action potential propagation but not initiation in thalamic interneuron dendrites. J Neurosci 31:18289-302 [PubMed]
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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: Thalamus;
Cell Type(s): Thalamus lateral geniculate nucleus interneuron;
Channel(s): I Na,t; I_KHT;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Dendritic Action Potentials; Conductance distributions;
Implementer(s): Casale, Amanda [Amanda.Casale at yale.edu];
Search NeuronDB for information about:  I Na,t; I_KHT;
COMMENT

na.mod

Sodium channel, Hodgkin-Huxley style kinetics.  

Kinetics were fit to data from Huguenard et al. (1988) and Hamill et
al. (1991)

qi is not well constrained by the data, since there are no points
between -80 and -55.  So this was fixed at 5 while the thi1,thi2,Rg,Rd
were optimized using a simplex least square proc

voltage dependencies are shifted approximately from the best
fit to give higher threshold

Author: Zach Mainen, Salk Institute, 1994, zach@salk.edu

ENDCOMMENT

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

NEURON {
	SUFFIX na
	USEION na READ ena WRITE ina
	RANGE m, h, gna, gbar
	GLOBAL tha, thi1, thi2, qa, qi, qinf, thinf
	RANGE minf, hinf, mtau, htau
	GLOBAL Ra, Rb, Rd, Rg
	GLOBAL q10, temp, tadj, vmin, vmax, vshift
}

PARAMETER {
	gbar = 1000   	(pS/um2)	: 0.12 mho/cm2
	vshift = -10	(mV)		: voltage shift (affects all)
								
	tha  = -35	(mV)		: v 1/2 for act		(-42)
	qa   = 9	(mV)		: act slope		
	Ra   = 0.182	(/ms)		: open (v)		
	Rb   = 0.124	(/ms)		: close (v)		

	thi1  = -50	(mV)		: v 1/2 for inact 	
	thi2  = -75	(mV)		: v 1/2 for inact 	
	qi   = 5	(mV)	        : inact tau slope
	thinf  = -65	(mV)		: inact inf slope	
	qinf  = 6.2	(mV)		: inact inf slope
	Rg   = 0.0091	(/ms)		: inact (v)	
	Rd   = 0.024	(/ms)		: inact recov (v) 

	temp = 23	(degC)		: original temp 
	q10  = 2.3			: temperature sensitivity

	v 		(mV)
	dt		(ms)
	celsius		(degC)
	vmin = -120	(mV)
	vmax = 100	(mV)
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)
} 

ASSIGNED {
	ina 		(mA/cm2)
	gna		(pS/um2)
	ena		(mV)
	minf 		hinf
	mtau (ms)	htau (ms)
	tadj
}
 

STATE { m h }

INITIAL { 
	trates(v+vshift)
	m = minf
	h = hinf
}

BREAKPOINT {
        SOLVE states
        gna = tadj*gbar*m*m*m*h
	ina = (1e-4) * gna * (v - ena)
} 

LOCAL mexp, hexp 

PROCEDURE states() {   :Computes state variables m, h, and n 
        trates(v+vshift)      :             at the current v and dt.
        m = m + mexp*(minf-m)
        h = h + hexp*(hinf-h)
        VERBATIM
        return 0;
        ENDVERBATIM
}

PROCEDURE trates(v) {  
                      
        LOCAL tinc
: table commented out to retrieve time constants mtau, htau
:       TABLE minf, mexp, hinf, hexp
:	DEPEND dt, celsius, temp, Ra, Rb, Rd, Rg, tha, thi1, thi2, qa, qi, qinf
	
:	FROM vmin TO vmax WITH 199

	rates(v): not consistently executed from here if usetable == 1

        tadj = q10^((celsius - temp)/10)
        tinc = -dt * tadj

        mexp = 1 - exp(tinc/mtau)
        hexp = 1 - exp(tinc/htau)
}


PROCEDURE rates(vm) {  
        LOCAL  a, b

	a = trap0(vm,tha,Ra,qa)
	b = trap0(-vm,-tha,Rb,qa)
	mtau = 1/(a+b)
	minf = a*mtau

		:"h" inactivation 

	a = trap0(vm,thi1,Rd,qi)
	b = trap0(-vm,-thi2,Rg,qi)
	htau = 1/(a+b)
	hinf = 1/(1+exp((vm-thinf)/qinf))
}


FUNCTION trap0(v,th,a,q) {
	if (fabs(v/th) > 1e-6) {
	        trap0 = a * (v - th) / (1 - exp(-(v - th)/q))
	} else {
	        trap0 = a * q
 	}
}