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A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block.

Yu N, Canavier CC - J Math Neurosci (2015)

Bottom Line: The two slow variables contribute as follows.A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking.The slow activation of the ether-a-go-go-related (ERG) K(+) current is largely responsible for termination of the depolarized plateau.

View Article: PubMed Central - PubMed

Affiliation: Department of Cell Biology and Anatomy, Louisiana State University School of Medicine, New Orleans, LA 70112 USA ; Department of Mathematics and Computer Science, Lawrence Technological University, 21000 West 10 Mile Road, Southfield, MI 48075 USA.

ABSTRACT
Midbrain dopamine neurons exhibit a novel type of bursting that we call "inverted square wave bursting" when exposed to Ca(2+)-activated small conductance (SK) K(+) channel blockers in vitro. This type of bursting has three phases: hyperpolarized silence, spiking, and depolarization block. We find that two slow variables are required for this type of bursting, and we show that the three-dimensional bifurcation diagram for inverted square wave bursting is a folded surface with upper (depolarized) and lower (hyperpolarized) branches. The activation of the L-type Ca(2+) channel largely supports the separation between these branches. Spiking is initiated at a saddle node on an invariant circle bifurcation at the folded edge of the lower branch and the trajectory spirals around the unstable fixed points on the upper branch. Spiking is terminated at a supercritical Hopf bifurcation, but the trajectory remains on the upper branch until it hits a saddle node on the upper folded edge and drops to the lower branch. The two slow variables contribute as follows. A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking. The slow activation of the ether-a-go-go-related (ERG) K(+) current is largely responsible for termination of the depolarized plateau. The mechanisms and slow processes identified herein may contribute to bursting as well as entry into and recovery from the depolarization block to different degrees in different subpopulations of dopamine neurons in vivo.

No MeSH data available.


Related in: MedlinePlus

Simulation results of the NEURON model with a realistic morphology. aLeft: digital reconstruction of neural morphology [33]. Right: Morphology rendered by the NEURON simulation package. b With the default parameter set except , the model paces regularly at 3.5 Hz. Membrane potential from a somatic compartment is illustrated. c Setting  to zero produces inverted square wave bursting. d Setting  produces oscillatory plateau potentials
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Fig6: Simulation results of the NEURON model with a realistic morphology. aLeft: digital reconstruction of neural morphology [33]. Right: Morphology rendered by the NEURON simulation package. b With the default parameter set except , the model paces regularly at 3.5 Hz. Membrane potential from a somatic compartment is illustrated. c Setting to zero produces inverted square wave bursting. d Setting produces oscillatory plateau potentials

Mentions: We ported the same parameter set used in the previous sections to a realistic morphology (Fig. 6a, left) implemented using the NEURON simulation package (Fig. 6a, right) as described in the Methods. For simulations with no SK channel current, and therefore no dependence on the rate of calcium ion accumulation set by the diameter of each compartment, the exact same results were obtained for the single-compartment and the full morphology. Setting to zero in the multi-compartmental model resulted in bursting activity (Fig. 6c). In addition, the ability to generate oscillatory plateau potentials with , , and all set to zero was preserved (Fig. 6d). Therefore, in these cases, the bifurcation structure of this very complex multi-compartmental model, which is not always possible to determine directly, is qualitatively identical to the reduced, one-compartment model examined in the previous sections. However, for simulations with nonzero SK conductance (Fig. 6b), the parameter set from the single-compartment model resulted in quiescence rather than spiking. The dendrites have a higher surface to volume ratio than the single-compartment somatic model. This allows for faster accumulation and removal of free Ca2+, and faster activation of the SK channel current, which abolished pacemaking. In order to match the frequency and waveform of pacemaking in the single-compartment model, the free Ca2+ fraction was reduced by a factor of 10, from 0.018 to 0.0018. Fig. 6


A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block.

Yu N, Canavier CC - J Math Neurosci (2015)

Simulation results of the NEURON model with a realistic morphology. aLeft: digital reconstruction of neural morphology [33]. Right: Morphology rendered by the NEURON simulation package. b With the default parameter set except , the model paces regularly at 3.5 Hz. Membrane potential from a somatic compartment is illustrated. c Setting  to zero produces inverted square wave bursting. d Setting  produces oscillatory plateau potentials
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4385104&req=5

Fig6: Simulation results of the NEURON model with a realistic morphology. aLeft: digital reconstruction of neural morphology [33]. Right: Morphology rendered by the NEURON simulation package. b With the default parameter set except , the model paces regularly at 3.5 Hz. Membrane potential from a somatic compartment is illustrated. c Setting to zero produces inverted square wave bursting. d Setting produces oscillatory plateau potentials
Mentions: We ported the same parameter set used in the previous sections to a realistic morphology (Fig. 6a, left) implemented using the NEURON simulation package (Fig. 6a, right) as described in the Methods. For simulations with no SK channel current, and therefore no dependence on the rate of calcium ion accumulation set by the diameter of each compartment, the exact same results were obtained for the single-compartment and the full morphology. Setting to zero in the multi-compartmental model resulted in bursting activity (Fig. 6c). In addition, the ability to generate oscillatory plateau potentials with , , and all set to zero was preserved (Fig. 6d). Therefore, in these cases, the bifurcation structure of this very complex multi-compartmental model, which is not always possible to determine directly, is qualitatively identical to the reduced, one-compartment model examined in the previous sections. However, for simulations with nonzero SK conductance (Fig. 6b), the parameter set from the single-compartment model resulted in quiescence rather than spiking. The dendrites have a higher surface to volume ratio than the single-compartment somatic model. This allows for faster accumulation and removal of free Ca2+, and faster activation of the SK channel current, which abolished pacemaking. In order to match the frequency and waveform of pacemaking in the single-compartment model, the free Ca2+ fraction was reduced by a factor of 10, from 0.018 to 0.0018. Fig. 6

Bottom Line: The two slow variables contribute as follows.A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking.The slow activation of the ether-a-go-go-related (ERG) K(+) current is largely responsible for termination of the depolarized plateau.

View Article: PubMed Central - PubMed

Affiliation: Department of Cell Biology and Anatomy, Louisiana State University School of Medicine, New Orleans, LA 70112 USA ; Department of Mathematics and Computer Science, Lawrence Technological University, 21000 West 10 Mile Road, Southfield, MI 48075 USA.

ABSTRACT
Midbrain dopamine neurons exhibit a novel type of bursting that we call "inverted square wave bursting" when exposed to Ca(2+)-activated small conductance (SK) K(+) channel blockers in vitro. This type of bursting has three phases: hyperpolarized silence, spiking, and depolarization block. We find that two slow variables are required for this type of bursting, and we show that the three-dimensional bifurcation diagram for inverted square wave bursting is a folded surface with upper (depolarized) and lower (hyperpolarized) branches. The activation of the L-type Ca(2+) channel largely supports the separation between these branches. Spiking is initiated at a saddle node on an invariant circle bifurcation at the folded edge of the lower branch and the trajectory spirals around the unstable fixed points on the upper branch. Spiking is terminated at a supercritical Hopf bifurcation, but the trajectory remains on the upper branch until it hits a saddle node on the upper folded edge and drops to the lower branch. The two slow variables contribute as follows. A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking. The slow activation of the ether-a-go-go-related (ERG) K(+) current is largely responsible for termination of the depolarized plateau. The mechanisms and slow processes identified herein may contribute to bursting as well as entry into and recovery from the depolarization block to different degrees in different subpopulations of dopamine neurons in vivo.

No MeSH data available.


Related in: MedlinePlus