Abstract
Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca2+ current and the small conductance K+ (SK) current that is unmasked by fast Na+ current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca2+ and the A-type K+ currents. The model identifies the channel densities for the fast Na+ and the delayed rectifier K+ currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca2+ accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.
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Acknowledgments
This work was supported by National Institutes of Health grants NS 37963 and 61097 to CCC, National Science Foundation grant DMS-0817717 to ASK, and National Institutes of Health grant MH 079276 to CAP. AYK thanks M. Hines and N. Carnevale for advice on NEURON, support from the IUPUI Center for Mathematical Biosciences, Department of Mathematical Sciences at IUPUI, and B. Boukai, C. Wilson for consultation on fitting calcium concentration, and C. Paladini’s and C. Wilson’s labs for help with literature.
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Appendix
Appendix
In the following equations the subscript “i” indicates a nonspecific compartment, whereas the subscripts “d”, “p”, and “s” indicate distal dendritic compartment, proximal dendritic compartment and somatic compartment respectively. All compartments are considered cylindrical in shape with diameter and length given by di and Li, respectively.
Equations governing membrane potential in each compartment:
Here Istim is the stimulus current applied to the soma.
Linear leakage current:
where
Sodium pump current:
Sodium balance:
Calcium pump current:
Calcium Balance:
Fast sodium current:
Calcium current:
Delayed rectifier current:
Transient outward potassium current:
SK potassium current:
Intercompartmental coupling currents:
Parameters
The same parameters were used for the models with schematic morphology and reconstructed morphology. The only difference was in the morphology.
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Kuznetsova, A.Y., Huertas, M.A., Kuznetsov, A.S. et al. Regulation of firing frequency in a computational model of a midbrain dopaminergic neuron. J Comput Neurosci 28, 389–403 (2010). https://doi.org/10.1007/s10827-010-0222-y
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DOI: https://doi.org/10.1007/s10827-010-0222-y