Competition for AP initiation sites in a circuit controlling simple learning (Cruz et al. 2007)

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"The spatial and temporal patterns of action potential initiations were studied in a behaving leech preparation to determine the basis of increased firing that accompanies sensitization, a form of non-associative learning requiring the S-interneurons. ... The S-interneurons, one in each ganglion and linked by electrical synapses with both neighbors to form a chain, are interposed between sensory and motor neurons. ... the single site with the largest initiation rate, the S-cell in the stimulated segment, suppressed initiations in adjacent ganglia. Experiments showed this was both because (1) it received the earliest, greatest input and (2) the delayed synaptic input to the adjacent S-cells coincided with the action potential refractory period. A compartmental model of the S-cell and its inputs showed that a simple, intrinsic mechanism of inexcitability after each action potential may account for suppression of impulse initiations. Thus, a non-synaptic competition between neurons alters synaptic integration in the chain. In one mode, inputs to different sites sum independently, whereas in another, synaptic input to a single site precisely specifies the overall pattern of activity."
1 . Cruz GE, Sahley CL, Muller KJ (2007) Neuronal competition for action potential initiation sites in a circuit controlling simple learning. Neuroscience 148:65-81 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Leech;
Cell Type(s): Leech S cell;
Channel(s): I Na,t; I K,leak;
Gap Junctions:
Transmitter(s): Serotonin;
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Activity Patterns; Spatio-temporal Activity Patterns;
Implementer(s): Cruz, Ginny [gcruz at];
Search NeuronDB for information about:  I Na,t; I K,leak; Serotonin;
TITLE  hh2.mod

	(mA) = (milliamp)
	(mV) = (millivolt)
	(S)  = (siemens)

? interface

	SUFFIX  hh2
	USEION  na	READ ena	WRITE ina
	RANGE  gnabar, gkbar, gl, el, gna, gk
	RANGE  mvhalfa, mvhalfb, hvhalfa, hvhalfb, nvhalfa, nvhalfb
	GLOBAL minf, hinf, ninf, mtau, htau, ntau

	gnabar = .12 (S/cm2)	<0, 1e9>
	gkbar = .036 (S/cm2)	<0, 1e9>
	gl = .0003 (S/cm2)	<0, 1e9>
	el = -54.3 (mV)
	mvhalfa = -45 (mV)
	mvhalfb = -55 (mV)
	hvhalfa = -62 (mV)
	hvhalfb = -31 (mV)
	nvhalfa = -53 (mV)
	nvhalfb = -63 (mV)

	m  h  n

	v (mV)
	celsius (degC)
	ena (mV)
	ek (mV)

	gna (S/cm2)
	gk (S/cm2)
	ina (mA/cm2)
	ik (mA/cm2)
	il (mA/cm2)
	minf  hinf  ninf
	mtau (ms)   htau (ms)   ntau (ms)

LOCAL		mexp, hexp, nexp


	SOLVE	states METHOD cnexp
	gna = gnabar*m*m*m*h
	ina = gna*(v-ena)
	gk = gkbar*n*n*n*n
	ik = gk*(v-ek)
	il = gl*(v-el)

	rates (v)
	m = minf
	h = hinf
	n = ninf

	m' = (minf-m)/mtau
	h' = (hinf-h)/htau
	n' = (ninf-n)/ntau

LOCAL  q10

PROCEDURE  rates (v(mV))	{  :Computes rate and other constants at current v.
					:Call once from HOC to initialize inf at resting v.
LOCAL	alpha, beta, sum
:TABLE minf, mtau, hinf, htau, ninf, ntau  DEPEND celsius  FROM -100 TO 100 WITH 200

	q10 = 3^((celsius - 6.3)/10)
		:"m" sodium activation system
	alpha = .1 * vtrap(-(v-mvhalfa), 10)
	beta = 4 * exp(-(v-mvhalfb)/18)
	sum = alpha + beta

    mtau = 1/(q10*sum)
	minf = alpha/sum
		:"h" sodium inactivation system
	alpha = .07 * exp(-(v-hvhalfa)/39)
	beta = 1/(exp(-(v-hvhalfb)/10) + 1)
	sum = alpha + beta
    htau = 1/(q10*sum)
	hinf = alpha/sum
		:"n" potassium activation system
	alpha = .01*vtrap(-(v-nvhalfa), 12)
	beta = .125*exp(-(v-nvhalfb)/79)
	sum = alpha + beta
    ntau = 1/(q10*sum)
	ninf = alpha/sum

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


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