Dendritic signals command firing dynamics in a Cerebellar Purkinje Cell model (Genet et al. 2010)

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This model endows the dendrites of a reconstructed Purkinje cells (PC) with the mechanism of Ca-dependent plateau potentials and spikes described in Genet, S., and B. Delord. 2002. A biophysical model of nonlinear dynamics underlying plateau potentials and calcium spikes in Purkinje cell dendrites. J. Neurophysiol. 88:2430–2444). It is a part of a comprehensive mathematical study suggesting that active electric signals in the dendrites of PC command epochs of firing and silencing of the PC soma.
1 . Genet S, Sabarly L, Guigon E, Berry H, Delord B (2010) Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells. Biophys J 99:427-36 [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;
Brain Region(s)/Organism:
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I K; I Ca,p; Ca pump;
Gap Junctions:
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Dendritic Action Potentials; Simplified Models; Active Dendrites; Detailed Neuronal Models; Action Potentials; Calcium dynamics; Conductance distributions;
Implementer(s): Genet, Stéphane [];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I K; I Ca,p; Ca pump; Gaba; Glutamate;
: Inner Ca calculation with longitudinal diffusion

     SUFFIX calcium
     USEION ca READ ica WRITE cai
     GLOBAL BT, Kd, k, cab, delt

     (molar)  = (1/liter)
     (mM)     = (millimolar)
     (um)     = (micron)
     (mA)     = (milliamp)
     FARADAY  = (faraday)    (10000 coulomb)
     PI       = (pi)         (1)

     Kd    = 0.001    (mM)      : buffer dissociation constant
     BT    = 0.15     (mM)      : total buffer concentration
     k     = 0.00001  (cm/ms)   : constant of pumping in the ER
     cab   = 0.00005  (mM)      : calcium concentration in inner dendritic core
     delt  = 0.3      (um)      : thickness of cytoplasmic compartment

     diam     (um)
     ica      (mA/cm2)

STATE { cai (mM) }


LOCAL x, y

    cai = 96e-6

KINETIC state {   
     COMPARTMENT PI*delt*(diam-delt)  {cai}
     ~ cai << ( (-(1/(1+(BT/Kd)/(1+cai/Kd)^2))*((ica*(diam/2))/(FARADAY*delt*(diam/2-delt))
         +(1e4)* ((2*k*(cai-cab)*(diam/2-delt))/(delt*(diam/2-delt))))*PI*delt*(diam/2-delt)) )