Regulation of firing frequency in a computational model of a midbrain dopaminergic neuron

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.

Ion channel degeneracy enables robust and tunable neuronal firing rates

“…The sensitivity of Type I behavior is observed experimentally and numerically. g s and its associated membrane current must be small throughout the AHP region, and this is, in fact, seen in precise and difficult biophysical experiments (31) as well as detailed modeling studies (32). Furthermore, increasing I A in the Type II* regime of the ConnorStevens model will only serve to exacerbate the jump to high minimum firing frequency and can never linearize the FI curve.…”

“…Nonetheless, Type I behavior is essential in neural circuits that encode information in firing rate (14), or in situations where slow pacemaking is important physiologically (32,50). The fact that Type I is a bounded and sometimes small region in parameter space presents a potential regulation problem for a neuron that has only a few different membrane currents.…”

Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

“…Depolarizing current steps elicit steady firing rates up to 10 Hz, and additional depolarization causes a cessation of spiking, although transients as fast as 30 Hz have been evoked by current steps (Blythe et al 2009). Our previous modeling work (Kuznetsova et al 2010) and experimental studies (Deister et al 2009) suggested that the failure to recover from sodium channel inactivation between spikes was responsible for entry into depolarization block and predicted that increasing the availability of sodium channels would delay entry into depolarization block. Subsequently, we showed that decreasing the sodium conductance pharmacologically causes dopamine neurons to go into depolarization block with lower maximal frequencies at lower values of applied current, whereas augmenting this conductance with the dynamic clamp has the opposite effect .…”

“…Also, various manipulations in vitro (Deister et al 2009;Ji et al 2012;Ping and Shepard 1996;Yu et al 2014) can evoke a train of action potentials of variable frequency prior to entering depolarization block. Previous models (Drion et al 2011;Kuznetsova et al 2010;Oster and Gutkin 2011) do not capture critical aspects of the firing rate limitation and how it is circumvented. Therefore we examined depolarization block in a simple model that faithfully reproduces the sodium current measured in these neurons (Seutin and Engel 2010) and also in a model with an additional slow component of sodium channel inactivation, recently observed in these neurons (Ding et al 2011).…”

Effects of SKF83959 on the excitability of hippocampal CA1 pyramidal neurons: a modeling study

“…Depolarization block is regarded to have pathological relevance for some brain disorders, including epilepsy and schizophrenia [32][33][34] . Among all the mechanisms known to cause depolarization block, the inactivation of voltage-dependent Na + channels is believed to play a key role [31,35,36] . SKF83959 can decrease the amplitude of Na + currents [17] ; however, whether the drug has an effect on the depolarization block of pyramidal neurons in the hippocampus remains to be determined.…”