A simplified model of dopaminergic neuron
BMC Neuroscience volume 9, Article number: P140 (2008)
A minimal model of a dopamine cell in vitro in the presence of tetrodoxin (TTX) and tetraethyl ammonium (TEA) was developed to simulate two types of subthreshold oscillations: the slow oscillatory potential (SOP – see Figure 1A) and the square wave (Figure 1B) that can be produced by the abolition of the SOP by apamin. The L-type calcium current drives both types of oscillation. The small conductance potassium channel repolarizes the SOP, and we propose that the ether-a-go-go related potassium channel repolarizes the square wave. We further suggest that the role of this current in vivo is to relieve depolarization block. The model predicts that blocking the ether-a-go-go current will elongate the plateau of the square wave and blocking the hyperpolarization-activated potassium current shortens the period of oscillations. In addition, the model predicts that blocking the ether-a-go-go current will speed up the SOP. The model also predicts that calcium chelation converts SOPs into square waves by blocking the increase in the small conductance (SK) current. Multiple-parameter bifurcation diagrams were used to investigate the properties of the firing patterns generated by our model (Figure 2).
The minimal model of a single-compartment Hodgkin-Huxley (HH)-type parallel conductance membrane contains the following currents: an L-type calcium current, a small conductance potassium current, a slowly-activating and fast-inactivating potassium current (tentatively identified as a ether-a-go-go current), an after-hyperpolarization current, and a linear background current (see [1, 2] for detailed equations). The fast sodium current blocked by TTX and the delayed rectifier blocked by TEA are not modeled. Calcium extrusion was modeled by a nonelectrogenic pump, and buffering was modeled by assuming a fixed fraction of free calcium in the cytosol. We assumed that exogenous buffers such as BAPTA reduced this fraction . We found that regardless of the values of other synaptic conductances, the model undergoes Hopf bifurcations leading to a transition from a stable steady state to a stable limit cycle. The SOP period at supercritical Hopf bifurcation points is in the range of 500 to 700 ms and gradually increases to about 1500 ms.
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Canavier CC, Oprisan SA, Callaway JC, Ji H, Shepard PD: Computational model predicts a role for ERG current in repolarizing plateau potentials in dopamine neurons: Implications for modulation of neuronal activity. J Neurophysiol. 2007, 98: 3006-3022. 10.1152/jn.00422.2007.
Supported by NASA-SCSGC NNX07AL01A grant to Rui (Jim) Qiao and Sorinel A. Oprisan and R & D grant from the College of Charleston to Sorinel A. Oprisan.
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Oprisan, S.A. A simplified model of dopaminergic neuron. BMC Neurosci 9 (Suppl 1), P140 (2008). https://doi.org/10.1186/1471-2202-9-S1-P140