Action potential-evoked Na+ influx similar in axon and soma (Fleidervish et al. 2010) (Python)

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Accession:249404
"In cortical pyramidal neurons, the axon initial segment (AIS) is pivotal in synaptic integration. It has been asserted that this is because there is a high density of Na+ channels in the AIS. However, we found that action potential-associated Na+ flux, as measured by high-speed fluorescence Na+ imaging, was about threefold larger in the rat AIS than in the soma. Spike-evoked Na+ flux in the AIS and the first node of Ranvier was similar and was eightfold lower in basal dendrites. ... In computer simulations, these data were consistent with the known features of action potential generation in these neurons."
Reference:
1 . Fleidervish IA, Lasser-Ross N, Gutnick MJ, Ross WN (2010) Na+ imaging reveals little difference in action potential-evoked Na+ influx between axon and soma. Nat Neurosci 13:852-60 [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: Neocortex;
Cell Type(s): Neocortex U1 L5B pyramidal pyramidal tract GLU cell;
Channel(s): I Sodium; I Na,p; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; Python;
Model Concept(s): Action Potentials; Active Dendrites; Reaction-diffusion;
Implementer(s): McDougal, Robert [robert.mcdougal at yale.edu];
Search NeuronDB for information about:  Neocortex U1 L5B pyramidal pyramidal tract GLU cell; I Na,p; I Sodium; I Potassium;
TITLE nacurrent.mod
 
COMMENT
The current implementation here is adapted from modeldb.yale.edu/136715 (the
Fleidervish et al 2010 author's hh_Cs_scaled.mod) which is a modified 
(wrt rate functions and temperature dependence) version of NEURON's hh.mod,
which is an implementation of the original Hodgkin-Huxley equations.

Note: This mechanism is temperature dependent.

Note: Unlike Hodgkin-Huxley (and hh.mod), this file only describes a
      sodium current.
ENDCOMMENT
 
UNITS {
    (mA) = (milliamp)
    (mV) = (millivolt)
    (S) = (siemens)
}
 
NEURON {
    SUFFIX nacurrent
    USEION na READ ena WRITE ina
    RANGE gnabar, gna
    GLOBAL minf, hinf, mtau, htau
    THREADSAFE
}
 
PARAMETER {
    gnabar = .0 (S/cm2)	<0, 1e9>
}
 
STATE {
    m (1)
    h (1)
}
 
ASSIGNED {
    v (mV)
    celsius (degC)
    ena (mV)
    gna (S/cm2)
    ina (mA/cm2)
    minf (1)
    hinf (1)
    mtau (ms)
    htau (ms)
}
 
BREAKPOINT {
    SOLVE states METHOD cnexp
    gna = gnabar * m * m * m * h
    ina = gna * (v - ena)
}
 
INITIAL {
    rates(v)
    m = minf
    h = hinf
}

DERIVATIVE states {  
    rates(v)
    m' = (minf - m) / mtau
    h' = (hinf - h) / htau
}
 
PROCEDURE rates(v(mV)) {
    : Computes rate and other constants at specified v.
    LOCAL  alpha, beta, sum, q10
    TABLE minf, mtau, hinf, htau DEPEND celsius FROM -100 TO 100 WITH 200

UNITSOFF
    q10 = 3 ^ ((celsius - 23) / 10)
    : "m" sodium activation 
    alpha = -.182 * vtrap(-(v + 40), 6)
    beta =  -.124 * vtrap((v + 40), 6)
    sum = alpha + beta
    mtau = 0.25 / (q10 * sum)
    minf = alpha / sum
    : "h" sodium inactivation
    alpha = -0.015 * vtrap((v + 66), 6)
    beta = -0.015 * vtrap(-(v + 66), 6)
    sum = alpha + beta
    htau = 1 / (q10 * sum)
    hinf = alpha / sum
}
 
FUNCTION vtrap(x, y) {
    : Avoids divide by zero errors in rate functions by replacing with limit
    if (fabs(x / y) < 1e-6) {
        vtrap = -y * (1 - x / y / 2)
    } else {
        vtrap = x / (1 - exp(x / y))
    }
}
 
UNITSON

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