Dopaminergic subtantia nigra neuron (Moubarak et al 2019)

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Axon initial segment (AIS) geometry critically influences neuronal excitability. Interestingly, the axon of substantia nigra pars compacta (SNc) dopaminergic (DA) neurons displays a highly variable location and most often arises from an axon-bearing dendrite (ABD). We combined current-clamp somatic and dendritic recordings, outside-out recordings of dendritic sodium and potassium currents, morphological reconstructions and multi-compartment modelling to determine cell-to-cell variations in AIS and ABD geometry and their influence on neuronal output (spontaneous pacemaking frequency, AP shape). Both AIS and ABD geometries are highly variable between SNc DA neurons. Surprisingly, we found that AP shape and pacemaking frequency were independent of AIS geometry. Modelling realistic morphological and biophysical variations clarify this result: in SNc DA neurons, the complexity of the ABD combined with its excitability predominantly define pacemaking frequency and AP shape, such that large variations in AIS geometry negligibly affect neuronal output, and are tolerated.
1 . Moubarak E, Engel D, Dufour MA, Tapia M, Tell F, Goaillard JM (2019) Robustness to Axon Initial Segment Variation Is Explained by Somatodendritic Excitability in Rat Substantia Nigra Dopaminergic Neurons. J Neurosci 39:5044-5063 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type:
Brain Region(s)/Organism: Basal ganglia;
Cell Type(s): Substantia nigra pars compacta DA cell;
Channel(s): Ca pump; I A; I Calcium; I h; I Na,t; I K;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Pacemaking mechanism;
Implementer(s): Tell, Fabien [fabien.tell at]; Moubarak, Estelle ;
Search NeuronDB for information about:  Substantia nigra pars compacta DA cell; I Na,t; I A; I K; I h; I Calcium; Ca pump;
Decay of internal calcium concentration

Internal calcium concentration due to calcium currents and pump.

Differential equations.

Simple model of ATPase pump with 3 kinetic constants (Destexhe 92)
     Cai + P <-> CaP -> Cao + P  (k1,k2,k3)
A Michaelis-Menten approximation is assumed, which reduces the complexity
of the system to 2 parameters: 
    kt = <tot enzyme concentration> * k3  -> TIME CONSTANT OF THE PUMP
	kd = k2/k1 (dissociation constant)    -> EQUILIBRIUM CALCIUM VALUE
The values of these parameters are chosen assuming a high affinity of 
the pump to calcium and a low transport capacity (cfr. Blaustein, 
TINS, 11: 438, 1988, and references therein).  

Units checked using "modlunit" -> factor 10000 needed in ca entry

VERSION OF PUMP + DECAY (decay can be viewed as simplified buffering)

All variables are range variables

This mechanism was published in:  Destexhe, A. Babloyantz, A. and 
Sejnowski, TJ.  Ionic mechanisms for intrinsic slow oscillations in
thalamic relay neurons. Biophys. J. 65: 1538-1552, 1993)

Written by Alain Destexhe, Salk Institute, Nov 12, 1992

26 Ago 2002 Modification of original channel to allow 
variable time step and to correct an initialization error.
Done by Michael Hines(michael.hines@yale.e) and 
Ruggero Scorcioni( at EU Advance Course 
in Computational Neuroscience. Obidos, Portugal

20110202 replaced METHOD euler with METHOD cnexp
and made threadsafe by Ted Carnevale's suggestions
20120105 replaced cnexp with derivimplicit - TMM


	USEION ca READ ica, cai WRITE cai
	GLOBAL depth,cainf,taur

	(molar) = (1/liter)			: moles do not appear in units
	(mM)	= (millimolar)
	(um)	= (micron)
	(mA)	= (milliamp)
	(msM)	= (ms mM)
	FARADAY = (faraday) (coulomb)

	depth	= .1	(um)		: depth of shell
	taur	= 200	(ms)		: rate of calcium removal
	cainf	= 100e-6(mM)
	cai		(mM)

	ca		(mM) <1e-5>

	ca = cainf
	cai = ca

	ica		(mA/cm2)
	drive_channel	(mM/ms)
:	SOLVE state METHOD euler
	SOLVE state METHOD derivimplicit


	drive_channel =  - (10000) * ica / (2 * FARADAY * depth)
	if (drive_channel <= 0.) { drive_channel = 0. }	: cannot pump inward

	ca' = drive_channel + (cainf-ca)/taur
	cai = ca

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