Inferring connection proximity in electrically coupled networks (Cali et al. 2007)

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In order to explore electrical coupling in the nervous system and its network-level organization, it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. However, walking from cell to cell over large distances with a glass pipette is challenging, and microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derived analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then proposed an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We provide here some analysis and simulation scripts that used to test our method through computer simulations, in vitro recordings, theoretical and numerical methods. Key words: Gap-Junctions; Electrical Coupling; Networks; ZAP current; Impedance.
1 . Calì C, Berger TK, Pignatelli M, Carleton A, Markram H, Giugliano M (2008) Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis. J Comput Neurosci 24:330-45 [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; Glia;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Na,t; I K; I Potassium;
Gap Junctions: Gap junctions;
Simulation Environment: NEURON; MATLAB; PSpice; Sspice Symbolic SPICE;
Model Concept(s): Methods;
Implementer(s): Giugliano, Michele [mgiugliano at];
Search NeuronDB for information about:  I Na,t; I K; I Potassium;
TITLE SIN current


    Sinusoidal current model for membrane impedance analysis


  This mechanism is implemented as a nonspecific current defined as a
  point process, mimicking a current-clamp stimulation protocol, injecting
  a sinusoidally oscillating waveform I(t).
  I(t) = A * sin (2 pi f ( t - ttstart) )

  Since this is an electrode current, positive values of i depolarize the cell and in the
  presence of the extracellular mechanism there will be a change in vext since i is not a
  transmembrane current but a current injected directly to the inside of the cell.

  This point mechanism has been created by modifying Iclamp..
  Refer to: Cali' et al. (2007)


  This mechanism takes the following parameters:

  off (nA) : initial current offset.
  del (ms) : initial stimulation latency
  dur (ms) : duration of the stimulation
  amp (nA) : amplitude of the stimulation
  freq (Hz) : frequency of the sinusoidal current.

 Written by M. Giugliano and C. Cali', Brain Mind Institute, EPFL, March 2006
 Modified by C. Cali', Brain Mind Institute, EPFL, April 2006

    RANGE del, dur, amp, i, freq, off
    (nA) = (nanoamp)

    off (nA)
    del (ms)
    dur (ms)    <0,1e9>
    amp (nA)
    freq (Hz)
ASSIGNED { i (nA) }

    i = 0


    if (t < del + dur && t >= del) {
        i = off + amp * sin(0.0062831853071795866*freq*t)
        i = off