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

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Accession:94321
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.
Reference:
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]
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;
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; MATLAB; PSpice; Sspice Symbolic SPICE;
Model Concept(s): Methods;
Implementer(s): Giugliano, Michele [mgiugliano at gmail.com];
Search NeuronDB for information about:  I Na,t; I K; I Potassium; 
//
// "Inferring connection proximity in networks of electrically coupled cells 
//  by subthreshold frequency response analysis "
//
//  by C. Cali', ...., & M. Giugliano (2007)
//
// C. Cali' & M. Giugliano, Brain Mind Institute, EPFL, Apr 2006
//
//
//
// THIS SIMULATIONS CREATES A LINEAR CHAIN OF nsoma (single/multi)COMPARTMENTAL NEURONS,
// EACH CONNECTED ONLY TO ITS 2 NEAREST NEIGHBORS..
//
//

nsoma    = 5                // How many neurons do we want to simulate ?
stim     = 0
// Out of nsoma cells, which one does need to be stimulated (just one at the time) ?
// Careful: stim can goes from 0, 1, 2..., nsoma-1 !!
sc       = 0                // Set it to 1 for single-compartmental models, 0, otherwise..
ggap     = 40               // [nS] Strength of individual gap junctions between cells.


ChirpDuration = 2000        // [ms] duration of the chirp stimulation
Vrest         = -65         // 
celsius       = 35          // temperature in degrees celsius

//cvode_active(0)     // fixed integration time step
dt            = 0.00250    // integration time step to 2.5 ns

print "Dec 2006 - Michele Giugliano and Corrado Cali'"
print "Brain Mind Institute, EPFL of Lausanne"
print "Initializing and starting a simulation with ", nsoma, " neurons"
print "coupled by gap junction of conductance ", ggap, " nS"

load_file("nrngui.hoc")                    // Loading of the standard GUI controls...
load_file("mylibs/graphs.hoc")             // Loading some ad-hoc proc for displaying live traces...
load_file("mylibs/nsinglecompneuron.hoc")  // Loading the model cell template..
load_file("mylibs/gap.hoc")                // Loading the model template for gap junctions by Migliore et al., 2005
load_file("mylibs/ncellsgj.hoc")           // Loading model neuron (morphology, biophysics, etc)...
load_file("mylibs/Izap_proc.hoc")          // Loading che procedure for a zap current injection...
load_file("mylibs/filemanagement.hoc")     // Loading che procedure for file management...

//-----------------------------------------------------------------------------------
//
// Let's now (randomly) define the passive properties of cellular membranes
//
// e.g. cm = 1 uF/cm^2, g_pas = 0.04 mS/cm^2  --> tau = 25 ms
// e.g. cm = 1 uF/cm^2, g_pas = 0.1  mS/cm^2  --> tau = 10 ms
objref r
r = new Random()
r.uniform(0.04e-3, 0.1e-3)
for i = 0,nsoma-1{              // For each neuron, defined and created..
 // SOMA
 soma[i].cm    = 1              // [uF]
 soma[i].g_pas = r.repick       // [S] avoids constructor/destructor overhead..
 Rin           = 1e-6 / (surf2 * soma[i].g_pas)         // MOhm
 tau           = 1e-3 * soma[i].cm / soma[i].g_pas      // ms
 print "Cell #", i, "Input resistance:", Rin, "MOhm"
 print "Cell #", i, "Time constant:", tau, "ms"

 if (sc == 0) {                 // In case it is a multicompartmental model..
 // PRIDEN                      // let's take care of dendrite parameters..
 priden[i].cm    = 1            // [uF]
 priden[0].g_pas = r.repick()   // [S] avoids constructor/destructor overhead..
 } // end  if (sc == 0)
} //-----------------------------------------------------------------------------------

//
// ACCESSING THE CELL THAT IS GOING TO RECEIVE THE STIMULATION
//
access soma[stim]
timeref.record(&t)
InjectChirp(10, 400, .75, .75, -0.3, ChirpDuration, .5)     // Chirp current injection (Point process)
i_inputref = new Vector()                       // Input (injected) current is assigned to a vector
i_inputref.record(&fl.i)                        // and written, to be later recovered from file..
//
//f1            = 10  Hz      initial frequency of the chirp
//f2            = 200 Hz      final frequency of the chirp
//Astart        = 500 pA      initial amplitude of the chirp
//Astop         = 500 pA      final amplitude of the chirp
//Offset        = -0.1 nA     offset level [CHECK THIS]
//ChirpDuration = 1000 ms     duration of the chirp stimulation
//Location      = 0.5         location within the neuronal morphology
//

//
// SIMULATION CONTROL
//

tstart = 0         // [ms]
tstop  = 200. + ChirpDuration + 100.
addgraph("soma[0].v(0.5)",-68.2, -63.7)
addgraph("soma[1].v(0.5)",-65.43, -64.86)

t      = 0.
tstart = 0.        // [ms]
tstop  = 200       // [ms]
finitialize(Vrest) //
run()

tstop  = t + ChirpDuration + 100    // [ms]
continuerun(tstop)

load_file("mylibs/write_on_disk.hoc")     // Loading che procedure for file management...

print "Simulation done! Find the raw data in the <output> directory!"

quit()

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