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1 Center for BioDynamics and Mathematics Department, Boston University, Boston, MA, USA; Department for Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, USA
2 Center for BioDynamics and Mathematics Department, Boston University, Boston, MA, USA
3 Cajal Neuroscience Center and Department of Biology, University of Texas at San Antonio, San Antonio, TX, USA
* To whom correspondence should be addressed. E-mail: alexey{at}math.iupui.edu.
Dopaminergic neurons of the midbrain fire spontaneously at rates less than 10/sec, and ordinarily will not exceed this range even when driven with somatic current injections. When driven at higher rates, these cells undergo spike failure through depolarization block. During spontaneous bursting of dopaminergic neurons in vivo, bursts related to reward expectation in behaving animals, and bursts generated by dendritic application of NMDA agonists, transient firing attains rates well above this range. We suggest a way such high frequency firing may occur in response to dendritic NMDA receptor activation. We have extended the coupled oscillator model of the dopamnergic neuron, which represents the soma and dendrites as electrically coupled compartments with different natural spiking frequencies, by addition of dendritic AMPA (voltage-independent) or NMDA (voltage-dependent) synaptic conductance. Both soma and dendrites contain a simplified version of the calcium-potassium mechanism known to be the mechanism for slow spontaneous oscillation and background firing in dopaminergic cell. The compartments differ only in diameter, and this difference is responsible for the difference in natural frequencies. We show that, because of its voltage dependence, NMDA receptor activation acts to amplify the effect on the soma of the high frequency oscillation of the dendrites, which is normally too weak to exert a large influence on the overall oscillation frequency of the neuron. During the high frequency oscillations that result, sodium inactivation in the soma is removed rapidly after each action potential by the hyperpolarizing influence of the dendritic calcium-dependent potassium current, preventing depolarization block of the spike mechanism, and allowing high frequency spiking.
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