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Role of the AIS in the control of spontaneous frequency of dopaminergic neurons (Meza et al 2017)

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Computational modeling showed that the size of the Axon Initial Segment (AIS), but not its position within the somatodendritic domain, is the major causal determinant of the tonic firing rate in the intact model, by virtue of the higher intrinsic frequency of the isolated AIS. Further mechanistic analysis of the relationship between neuronal morphology and firing rate showed that dopaminergic neurons function as a coupled oscillator whose frequency of discharge results from a compromise between AIS and somatodendritic oscillators.
1 . Meza RC, López-Jury L, Canavier CC, Henny P (2018) Role of the Axon Initial Segment in the Control of Spontaneous Frequency of Nigral Dopaminergic Neurons In Vivo. J Neurosci 38:733-744 [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: Basal ganglia; Mouse;
Cell Type(s): Substantia nigra pars compacta DA cell;
Channel(s): Na/K pump; I K,Ca; I K; I L high threshold; I T low threshold; I A; I N; I Na,t;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Activity Patterns; Temporal Pattern Generation; Oscillations; Pacemaking mechanism;
Implementer(s): Lopez-Jury, Luciana [lucianalopezjury at]; Canavier, CC;
Search NeuronDB for information about:  Substantia nigra pars compacta DA cell; I Na,t; I L high threshold; I N; I T low threshold; I A; I K; I K,Ca; Na/K pump;
/* Sets nseg in each section to an odd value
   so that its segments are no longer than 
     d_lambda x the AC length constant
   at frequency freq in that section.

   Be sure to specify your own Ra and cm before calling geom_nseg()

   To understand why this works, 
   and the advantages of using an odd value for nseg,
   see  Hines, M.L. and Carnevale, N.T.
        NEURON: a tool for neuroscientists.
        The Neuroscientist 7:123-135, 2001.

// these are reasonable values for most models
freq = 100      // Hz, frequency at which AC length constant will be computed
d_lambda = 0.1

func lambda_f() { local i, x1, x2, d1, d2, lam
        if (n3d() < 2) {
                return 1e5*sqrt(diam/(4*PI*$1*Ra*cm))
// above was too inaccurate with large variation in 3d diameter
// so now we use all 3-d points to get a better approximate lambda
        x1 = arc3d(0)
        d1 = diam3d(0)
        lam = 0
        for i=1, n3d()-1 {
                x2 = arc3d(i)
                d2 = diam3d(i)
                lam += (x2 - x1)/sqrt(d1 + d2)
                x1 = x2   d1 = d2
        //  length of the section in units of lambda
        lam *= sqrt(2) * 1e-5*sqrt(4*PI*$1*Ra*cm)

        return L/lam

proc geom_nseg() {
  soma area(0.5) // make sure diam reflects 3d points
forall { nseg = int((L/(d_lambda*lambda_f(freq))+0.9)/2)*2 + 1  }


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