GPi/GPe neuron models (Johnson and McIntyre 2008)

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Accession:114685
Model files for two types of non-human primate neurons used in the paper: simplified versions of 1) a GPi neuron and 2) a GPe axon collateralizing in GPi en route to STN.
Reference:
1 . Johnson MD, McIntyre CC (2008) Quantifying the neural elements activated and inhibited by globus pallidus deep brain stimulation. J Neurophysiol 100:2549-63 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Axon;
Brain Region(s)/Organism:
Cell Type(s): Globus pallidus neuron;
Channel(s): I Sodium; I Calcium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Simplified Models; Axonal Action Potentials; Parkinson's; Extracellular Fields;
Implementer(s): Johnson, Matthew D [johnsom11 at ccf.org];
Search NeuronDB for information about:  I Sodium; I Calcium; I Potassium;
FUNCTION ghkg(v(mV), ci(mM), co(mM), z) (mV) {
    
    : Called by Ih.mod

    LOCAL nu,ff,enu,fnu
    : Here we calculate an effective drive from the GHK equation
    : define
    :    f   = 10^3 RT/(zF)
    :    nu  = v/f  
    :        = z v10^-3 F / (RT) 
    : note the 10e-3 converts [mV] to [V]
    :    nu  = z V F / (RT)
    :
    :    enu = exp(nu)
    :        = exp(z V F / (RT))
    :
    :    fnu = nu/(enu-1) 
    :        = (z V F / (RT)) / (exp(z V F / (RT))-1)
    :        = (z V F / (RT))   (exp(-zV F / (RT))/(1-exp(-zV F / (RT))))
    :
    : now the effective drive is calculated as
    :
    :   ghkg = -f (1 - (ci/co)  enu) fnu
    :        = -10^3 RT/(zF)  (1 - (ci/co) exp(z V F / (RT))) *
    :         (z V F / (RT)) (exp(-zV F / (RT))/(1-exp(-zV F / (RT))))
    :        = -10^3 V (1/co) (co - ci exp(z V F / (RT))) (exp(-zV F / (RT))/(1-exp(-zV F / (RT))))
    :        = 10^3 V/co (ci - co exp(-zV F / (RT)))/(1-exp(-zV F / (RT)))
    :
    : [note, the 10^3 converts back to mV]
    : and you can see this is the ghk equation if the relationship
    : between conductance and permeability is
    :
    :      g = rho z^2 co F^2/RT
    :
    : Then g*ghkg reduces to the GHK current equation
    :
    
    ff   = (1.0e3/z)*R*(celsius+273.15)/FARADAY
    nu  = v/ff
	enu = exp(nu)
	if (fabs(nu) < 1e-4) {
        fnu = 1 - nu/2
    }else{
        fnu = nu/(enu-1) 
    }
    ghkg= -ff*(1-(ci/co)*enu)*fnu
}

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