- Poster presentation
- Open Access
A simplified model of dopaminergic neuron
© Oprisan; licensee BioMed Central Ltd. 2008
- Published: 11 July 2008
- Hopf Bifurcation
- Minimal Model
- Potassium Current
- Stable Limit Cycle
- Synaptic Conductance
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.
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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