Rat subthalamic projection neuron (Gillies and Willshaw 2006)

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A computational model of the rat subthalamic nucleus projection neuron is constructed using electrophysiological and morphological data and a restricted set of channel specifications. The model cell exhibits a wide range of electrophysiological behaviors characteristic of rat subthalamic neurons. It reveals that a key set of three channels play a primary role in distinguishing behaviors: a high-voltage-activated calcium channel (Cav 1.2.-1.3), a low-voltage-activated calcium channel (Cav 3.-), and a small current calcium-activated potassium channel (KCa 2.1-2.3). See paper for more and details.
1 . Gillies A, Willshaw D (2006) Membrane channel interactions underlying rat subthalamic projection neuron rhythmic and bursting activity. J Neurophysiol 95:2352-65 [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:
Cell Type(s): Subthalamus nucleus projection neuron;
Channel(s): I Na,p; I Na,t; I L high threshold; I N; I T low threshold; I K; I h; I K,Ca; I Calcium; I Mixed;
Gap Junctions:
Gene(s): Cav1.3 CACNA1D; Cav1.2 CACNA1C; KCa2.1 KCNN1; Kv2.1 KCNB1; Kv3.1 KCNC1; HCN Cnga1; Cav2.2 CACNA1B; KCa2.2 KCNN2;
Simulation Environment: NEURON;
Model Concept(s): Bursting;
Implementer(s): Gillies, Andrew [andrew at anc.ed.ac.uk];
Search NeuronDB for information about:  I Na,p; I Na,t; I L high threshold; I N; I T low threshold; I K; I h; I K,Ca; I Calcium; I Mixed;

FUNCTION ghkg(v(mV), ci(mM), co(mM), z) (mV) {
        LOCAL nu,f,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
        f   = (1.0e3/z)*R*(celsius+273.15)/FARADAY
        nu  = v/f
	enu = exp(nu)
	if (fabs(nu) < 1e-4) {
                fnu = 1 - nu/2
                fnu = nu/(enu - 1) 
        ghkg= -f*(1 - (ci/co)*enu)*fnu

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