Nullcline Analysis Provides Dynamic Mechanisms for the Differences in Electrical Activity of Distinct Subpopulations of Midbrain Dopamine Neurons

Previously, electrophysiological differences between subpopulations of midbrain dopamine (DA) neurons were identified based on projection targets, including distinct responses to hyperpolarization and in the regularity of pacemaking. Here we explored single-compartment models of three subpopulations of DA neurons, projecting to medial shell of the nucleus accumbens (VTA-mNAcc), dorsomedial striatum (SNc-DMS) or dorsolateral striatum (SNc-DLS). We reduced the dimensionality to a phase plane consisting of membrane potential and one slow variable, either total slow potassium conductance or Kv4 channel inactivation. Nullclines are curves on which the rate of change of each variable is zero, given the value of the other variable. The voltage nullclines had three branches: upper spiking, unstable middle, and lower quiescent branch. Recruitment of Kv4 channels by the more prominent after-hyperpolarizing potential (AHP) in the DA-DMS and DA-DLS models channels stabilized pacemaking by creating a restorative moving fixed point along the quiescent branch. The slow inactivation of KV4 channels dominated and regularized the dynamics during the interspike interval; a dominant slow process may be a general mechanisn for stable regular pacemaking in a frequency range between 1-10 Hz. In contrast, the smaller AHP in VTA-mNAcc models prevented recruitment of this Kv4-mediated moving fixed point, which increased the sensitivity to synaptic inputs. On rebound from hyperpolarization the ability to produce robust ramps reverses between the DA neurons: now VTA-mNAcc projecting DA models fully recruited Kv4 channels and produced stable ramp-like pauses, whereas SNc-DLS projecting cells recruited significant regenerative inward CaV3 channels that overwhelmed Kv4 channels and produced rebound bursts. Author SummaryMidbraim dopamine (DA) neurons in the mammalian midbrain are linked to motivation, control of voluntary movement initiation, and reward-based learning. Their dysfunction is implicated in major disorders like Parkinsons disease, schizophrenia or substance use disorders. Firing patters like bursts or pauses in most DA subpopulations are thought to signal better or worse than expected outcomes. Here we use dynamic systems analysis to capture how functional diversity of DA neurons of their intrinsic properties results in differences of synaptic input integration leading to the generation of burst and pause patterns of electrical activity.