Burst firing in medial substantia nigra (mSN) dopamine (DA) neurons has been selectively linked to novelty-induced exploration behavior in mice. Burst firing in mSN DA neurons, in contrast to lateral SN DA neurons, requires functional ATP-sensitive potassium (K-ATP) channels both in vitro and in vivo. However, the precise role of K-ATP channels in promoting burst firing is unknown. We show experimentally that L-type calcium channel activity in mSN DA neurons enhances open probability of K-ATP channels. We then generate a mathematical model to study the role of Ca dynamics driving K-ATP channel function in mSN DA neurons during bursting. In our model, Ca influx leads to local accumulation of ADP due to Ca-ATPase activity, which in turn activates K-ATP channels. If K-ATP channel activation reaches levels sufficient to terminate spiking, rhythmic bursting occurs. The model explains the experimental observation that, in vitro, coapplication of NMDA and a selective K-ATP channel opener, NN414, is required to elicit bursting as follows. Simulated NMDA receptor activation increases the firing rate and the rate of Ca influx, which increases the activation of K-ATP. The model suggests that additional sources of hyperpolarization, such as GABAergic synaptic input, are recruited in vivo for burst termination or rebound burst discharge. The model predicts that NN414 increases the sensitivity of the K-ATP channel to ADP, promoting burst firing in vitro, and that that high levels of Ca buffering, as might be expected in the calbindin-positive SN DA neuron subpopulation, promote rhythmic bursting pattern, consistent with experimental observations in vivo. NEW & NOTEWORTHY Recently identified distinct subpopulations of midbrain dopamine neurons exhibit differences in their two primary activity patterns in vivo: tonic (single spike) firing and phasic bursting. This study elucidates the biophysical basis of bursts specific to dopamine neurons in the medial substantia nigra, enabled by ATP-sensitive K channels and necessary for novelty-induced exploration. A better understanding of how dopaminergic signaling differs between subpopulations may lead to therapeutic strategies selectively targeted to specific subpopulations.

The low-threshold L-type calcium channel Ca v 1.3 accelerates the pacemaker rate in the heart, but its functional role for the extended dynamic range of neuronal firing is still unresolved. Here, we show that Ca v 1.3 calcium channels act as unexpectedly simple, full-range linear amplifiers of firing rates for lateral dopamine substantia nigra (DA SN) neurons in mice. This means that they boost in vitro or in vivo firing frequencies between 2 and 50 hertz by about 30%. Furthermore, we demonstrate that clinically relevant, low nanomolar concentrations of the L-type channel inhibitor isradipine selectively reduce the in vivo firing activity of these nigrostriatal DA SN neurons at therapeutic plasma concentrations. Thus, our study identifies the pacemaker function of neuronal Ca v 1.3 channels and provides direct evidence that repurposing dihydropyridines such as isradipine is feasible to selectively modulate the in vivo activity of highly vulnerable DA SN subpopulations in Parkinson’s disease.

Many hippocampal CA1 pyramidal cells function as place cells, increasing their firing rate when a specific place field is traversed. The dependence of CA1 place cell firing on position within the place field is asymmetric. We investigated the source of this asymmetry by injecting triangular depolarizing current ramps to approximate the spatially-tuned, temporally-diffuse depolarizing synaptic input received by these neurons while traversing a place field. Ramps were applied to CA1 pyramidal neurons from male rats in vitro (slice electrophysiology) and in silico (multicompartmental NEURON model). Under control conditions, CA1 neurons fired more action potentials at higher frequencies on the up-ramp versus the down-ramp. This effect was more pronounced for dendritic compared to somatic ramps. We incorporated a four-state Markov scheme for Na V 1.6 channels into our model and calibrated the spatial dependence of long-term inactivation according to the literature; this spatial dependence was sufficient to explain the difference in dendritic versus somatic ramps. Long-term inactivation reduced the firing frequency by decreasing open-state occupancy, and reduced spike amplitude during trains by decreasing occupancy in closed states, which comprise the available pool. PKC activator phorbol-dibutyrate, known to reduce Na V long-term inactivation, removed spike amplitude attenuation in vitro more visibly in dendrites and greatly reduced adaptation, consistent with our hypothesized mechanism. Intracellular application of a peptide inducing long-term Na V inactivation elicited spike amplitude attenuation during spike trains in the soma and greatly enhanced adaptation. Our synergistic experimental/computational approach shows that longterm inactivation of Na V 1.6 is a key mechanism of adaptation in CA1 pyramidal cells.

Two subpopulations of midbrain dopamine (DA) neurons are known to have different dynamic firing ranges in vitro that correspond to distinct projection targets: the originally identified conventional DA neurons project to the dorsal striatum and the lateral shell of the nucleus accumbens, whereas an atypical DA population with higher maximum firing frequencies projects to prefrontal regions and other limbic regions including the medial shell of nucleus accumbens. Using a computational model, we show that previously identified differences in biophysical properties do not fully account for the larger dynamic range of the atypical population and predict that the major difference is that originally identified conventional cells have larger occupancy of voltage-gated sodium channels in a long-term inactivated state that recovers slowly; stronger sodium and potassium conductances during action potential firing are also predicted for the conventional compared to the atypical DA population. These differences in sodium channel gating imply that longer intervals between spikes are required in the conventional population for full recovery from long-term inactivation induced by the preceding spike, hence the lower maximum frequency. These same differences can also change the bifurcation structure to account for distinct modes of entry into depolarization block: abrupt versus gradual. The model predicted that in cells that have entered depolarization block, it is much more likely that an additional depolarization can evoke an action potential in conventional DA population. New experiments comparing lateral to medial shell projecting neurons confirmed this model prediction, with implications for differential synaptic integration in the two populations.

The biophysical basis of repetitive action potential firing can be understood in terms of the opposing positive and negative feedback processes that generate the repetitive activity. The relative timescales of these processes, which can include ion channel activation and inactivation as well as ion accumulation within a cell, are key factors in the generation of repetitive single‐spike firing, intrinsic burst firing and repetitive activity resulting from network interactions. Bifurcation theory, in concert with the steady state current–voltage relationship, explains why the onset of repetitive firing can be gradual or abrupt and accounts for different excitability types and distinct types of bistability. Moreover, bifurcation theory allows for the classification of different mechanisms underlying rhythmic bursting. Key Concepts A branch of mathematics called bifurcation theory can explain initiation of repetitive firing without reference to the specific ionic currents involved. Two major bifurcations can underlie the initiation of repetitive firing. Initiation of repetitive firing is gradual if the underlying bifurcation is a saddle‐node on an invariant circle (SNIC). A SNIC requires that the steady state IV curve intersect the zero current axis in three places. Initiation of repetitive firing is abrupt at a threshold frequency if due to a Hopf bifurcation. Most rhythmic bursting can be classified as square wave, parabolic, or elliptical, depending upon the bifurcations that initiate and terminate spiking. Rhythmic bursting requires at least one slow process, and parabolic bursting requires two. Repetitive firing can also arise via network mechanisms, in addition to the intrinsic ones described above.

Inhibition of midbrain dopamine neurons is thought to underlie the signaling of events that are less rewarding than expected and drive learning based on these negative prediction errors. It has recently been shown that Kv4.3 channels influence the integration of inhibitory inputs in specific subpopulations of dopamine neurons. The functional properties of Kv4.3 channels are themselves strongly determined by the binding of auxiliary β -subunits; among them KChIP4a stands-out for its unique combination of modulatory effects. These include decreasing surface membrane trafficking and slowing inactivation kinetics. Therefore, we hypothesized that KChIP4a expression in dopamine neurons could play a crucial role in behavior, in particular by affecting the computation of negative prediction errors. We developed a mouse line where the alternative exon that codes for the KChIP4a splice variant was selectively deleted in midbrain dopamine neurons. In a reward-based reinforcement learning task, we observed that dopamine neuron-specific KChIP4a deletion selectively accelerated the rate of extinction learning, without impacting the acquisition of conditioned responses. We further found that this effect was due to a faster decrease in the initiation rate of goal-directed behaviors, and not faster increases in action disengagement. Furthermore, computational fitting of the behavioral data with a Rescorla-Wagner model confirmed that the observed phenotype was attributable to a selective increase in the learning rate from negative prediction errors. Finally, KChIP4a deletion did not affect performance in other dopamine-sensitive behavioral tasks that did not involve learning from disappointing events, including an absence of effects on working memory, locomotion and novelty preference. Taken together, our results demonstrate that an exon-and midbrain dopamine neuron-specific deletion of an A-type K + channel β -subunit leads to a selective gain of function in extinction learning. One Sentence Summary:Exon-and midbrain dopamine neuron-specific deletion of the Kv4 channel β -subunit KChIP4a selectively accelerates extinction learning

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The hippocampus is involved in memory and spatial navigation. Many CA1 pyramidal cells function as place cells, increasing their firing rate when a specific place field is traversed. The dependence of CA1 place cell firing on position within the place field is asymmetric. We investigated the source of this asymmetry by injecting triangular depolarizing current ramps to approximate the spatially-tuned, temporally-diffuse depolarizing synaptic input received by these neurons while traversing a place field. Ramps were applied to rat CA1 pyramidal neurons in vitro (slice electrophysiology) and in silico (multi-compartmental NEURON model). Under control conditions, CA1 neurons fired more action potentials at higher frequencies on the up-ramp versus the down-ramp. This effect was more pronounced for dendritic compared to somatic ramps. We incorporated a five-state Markov scheme for NaV1.6 channels into our model and calibrated the spatial dependence of long-term inactivation according to the literature; this spatial dependence was sufficient to explain the difference in dendritic versus somatic ramps. Long-term inactivation reduced the firing frequency by decreasing open-state occupancy, and reduced spike amplitude during trains by decreasing occupancy in closed states, which comprise the available pool. PKC activators like phorbol ester phorbol-dibutyrate (PDBu) are known to reduce NaV long-term inactivation. PDBu application removed spike amplitude attenuation during spike trains in vitro, more visibly in dendrites, consistent with decreased NaV long-term inactivation. Moreover, PDBu greatly reduced adaptation, consistent with our hypothesized mechanism. Our synergistic experimental/computational approach shows that long-term inactivation of NaV1.6 is the primary mechanism of adaptation in CA1 pyramidal cells.Significance statementThe hippocampus plays an important role in certain types of memory, in part through context-specific firing of “place cells” that were first identified in rodents as cells that are particularly active when an animal is in a specific location in an environment, called the place field of that neuron. In this in vitro/in silico study, we found that long-term inactivation of sodium channels causes adaptation in the firing rate that could potentially skew the firing of CA1 hippocampal pyramidal neurons earlier within a place field. A computational model of the sodium channel revealed differential regulation of spike frequency and amplitude by long-term inactivation, which may be a general mechanism for spike frequency adaptation in the central nervous system.