Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This is the simple, minimal model based on the equations in the original published paper. The CellML model runs in both COR and OpenCell and the units are consistent. The model recreates figure 2 from the paper (gc=0 so the soma and the dendritic compartments are uncoupled), however - in order to get the frequency of oscillations correct (with a period of 2s) the variable alpha was set to 0.5 (as opposed to 0.173 which was given in the paper). This change has to be confirmed with the original model authors.
Model Structure
ABSTRACT: Burst firing of dopaminergic neurons of the substantia nigra pars compacta can be induced in vitro by the glutamate agonist N-methyl-D-aspartate. It has been suggested that the interburst hyperpolarization is due to Na+ extrusion by a ouabain-sensitive pump (Johnson et al. (1992) Science 258, 665-667). We formulate and explore a theoretical model, with a minimal number of currents, for this novel mechanism of burst generation. This minimal model is further developed into a more elaborate model based on observations of additional currents and hypotheses about their spatial distribution in dopaminergic neurons (Hounsgaard (1992) Neuroscience 50, 513-518; Llinas et al. (1984) Brain Res. 294, 127-132). Using the minimal model, we confirm that interaction between the regenerative, inward N-methyl-D-aspartate-mediated current and the outward Na(+)-pump current is sufficient to generate the slow oscillation (approximately 0.5 Hz) underlying the burst. The negative-slope region of the N-methyl-D-aspartate channel's current-voltage relation is indispensable for this slow rhythm generation. The time-scale of Na(+)-handling determines the burst's slow frequency. Moreover, we show that, given the constraints of sodium handling, such bursting is best explained mechanistically by using at least two spatial, cable-like compartments: a soma where action potentials are produced and a dendritic compartment where the slow rhythm is generated. Our result is consistent with recent experimental evidence that burst generation originates in distal dendrites (Seutin et al. (1994) Neuroscience 58, 201-206). Responses of the model to a number of electrophysiological and pharmacological stimuli are consistent with known responses observed under similar conditions. These include the persistence of the slow rhythm when the tetrodotoxin-sensitive Na+ channel is blocked and when the soma is voltage-clamped at -60 mV. Using our more elaborate model, we account for details of the observed frequency adaptation in N-methyl-D-aspartate-induced bursting, the origin of multiple spiking and bursting mechanisms, and the interaction between two different bursting mechanisms. Besides reproducing several well established firing patterns, this model also suggests that new firing modes, not yet recorded, might also occur in dopaminergic neurons. This model provides mechanistic insights and explanations into the origin of a variety of experimentally observed membrane potential firing patterns in dopaminergic neurons, including N-methyl-D-aspartate-induced bursting and its dendritic origin. Such a model, capable of reproducing a number of realistic behaviors of dopaminergic neurons, could be useful in further studies of the basal ganglia-thalamocortical motor circuit. It may also shed light on bursting that involves N-methyl-D-aspartate channel activity in other neuron types.
The original paper reference is cited below.
Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons, Y.X. Li, R. Bertram, and J. Rinzel, 1996,
Neuroscience, 71, 397-410. PubMed ID: 9053795
cell schematic for the model
Schematic representation of the minimal model of a DA neuron. It consists of a spike-producing compartment(soma) and a slow rhythm-generating compartment (lumped dendrite). The two compartments are electrotonically coupled with coupling conductance gc. The types of ionic channels considered are just sufficient for a qualitative understanding of the mechanism underlying NMDA-induced bursting in DA neurons. No voltage-dependent channels other than the NMDA channel are considered in the dendrite in this minimal model.
$\mathrm{I\_Na}=\mathrm{g\_Na}h(\mathrm{V\_s}-\mathrm{V\_Na})\mathrm{m\_infinity}^{3}\mathrm{I\_K\_DR}=\mathrm{g\_K\_DR}(\mathrm{V\_s}-\mathrm{V\_K})n^{2}\frac{d \mathrm{V\_s}}{d \mathrm{time}}=\frac{-(1000.0(\mathrm{I\_K\_DR}+\mathrm{I\_Na}+\frac{\mathrm{g\_c}}{p}(\mathrm{V\_s}-\mathrm{V\_D})))}{\mathrm{C\_m}}$
$\mathrm{I\_D}=\mathrm{I\_NMDA}+\mathrm{I\_pump}+\mathrm{I\_L}\mathrm{I\_L}=\mathrm{g\_L}(\mathrm{V\_D}-\mathrm{V\_L})\mathrm{I\_pump}=\mathrm{R\_pump}(\mathrm{phi\_Na}-\mathrm{phi\_Na\_eq})\mathrm{phi\_Na}=\frac{\mathrm{Na}^{3}}{\mathrm{Na}^{3}+\mathrm{K\_p}^{3}}\mathrm{phi\_Na\_eq}=\frac{\mathrm{Na\_eq}^{3}}{\mathrm{Na\_eq}^{3}+\mathrm{K\_p}^{3}}\mathrm{I\_NMDA}=\frac{\mathrm{g\_NMDA}}{1+\frac{\mathrm{Mg\_o}}{\mathrm{K\_Mg}}e^{-\left(\frac{\mathrm{V\_D}}{q}\right)}}(\mathrm{V\_D}-\mathrm{V\_NMDA})\mathrm{I\_Na\_NMDA}=\frac{\mathrm{g\_Na\_NMDA}}{1+\frac{\mathrm{Mg\_o}}{\mathrm{K\_Mg}}e^{-\left(\frac{\mathrm{V\_D}}{q}\right)}}(\mathrm{V\_D}-\mathrm{V\_Na})\frac{d \mathrm{V\_D}}{d \mathrm{time}}=\frac{-(1000.0(\mathrm{I\_NMDA}+\mathrm{I\_pump}+\mathrm{I\_L}+\frac{\mathrm{g\_c}}{1-p}(\mathrm{V\_D}-\mathrm{V\_s})))}{\mathrm{C\_m}}\frac{d \mathrm{Na}}{d \mathrm{time}}=\mathrm{alpha}(-\mathrm{I\_Na\_NMDA}-3\mathrm{I\_pump})$
$\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{-(\mathrm{V\_s}+35)}{6.2}}}\mathrm{n\_infinity}=\frac{1}{1+e^{\frac{-(\mathrm{V\_s}+31)}{5.3}}}\mathrm{h\_infinity}=\frac{1}{1+e^{\frac{\mathrm{V\_s}+30}{8.3}}}\mathrm{tau\_h}=0.4(1+\frac{2}{1+e^{\frac{\mathrm{V\_s}+25}{5}}})\mathrm{tau\_n}=\frac{0.8+\frac{1.6}{1+e^{0.1(\mathrm{V\_s}+25)}}}{1+e^{-0.1(\mathrm{V\_s}+70)}}\frac{d h}{d \mathrm{time}}=\frac{\mathrm{h\_infinity}-h}{\mathrm{tau\_h}}\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}$
Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons (simple model based on the equations in the published paper)
Lloyd
Catherine
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
2010-07-08
neuron
keyword
electrophysiology
neuron
neurobiology
bursting
dopamine
9053795
Li
Y
X
Bertram
R
Rinzel
J
Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons
1996-03
Neuroscience
71
397
410