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

Coupled action potential and calcium dynamics underlie robust spontaneous firing in dopaminergic neurons

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillationsin-vitroandin-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

Does phasic dopamine release cause policy updates?

Phasic dopamine activity is believed to both encode reward-prediction errors (RPEs) and to cause the adaptations that these errors engender. If so, a rat working for optogenetic stimulation of dopamine neurons will repeatedly update its policy and/or action values, thus iteratively increasing its work rate. Here, we challenge this view by demonstrating stable, non-maximal work rates in the face of repeated optogenetic stimulation of midbrain dopamine neurons. Furthermore, we show that rats learn to discriminate between world states distinguished only by their history of dopamine activation. Comparison of these results to reinforcement learning simulations suggests that the induced dopamine transients acted more as rewards than RPEs. However, pursuit of dopaminergic stimulation drifted upwards over a time scale of days and weeks, despite its stability within trials. To reconcile the results with prior findings, we consider multiple roles for dopamine signalling.

Somatodendritic organization of pacemaker activity in midbrain dopamine neurons

The slow and regular pacemaking activity of midbrain dopamine (DA) neurons requires proper spatial organization of the excitable elements between the soma and dendritic compartments, but the somatodendritic organization is not clear. Here, we show that the dynamic interaction between the soma and multiple proximal dendritic compartments (PDCs) generates the slow pacemaking activity in DA neurons. In multipolar DA neurons, spontaneous action potentials (sAPs) consistently originate from the axon-bearing dendrite. However, when the axon initial segment was disabled, sAPs emerge randomly from various primary PDCs, indicating that multiple PDCs drive pacemaking. Ca2+ measurements and local stimulation/perturbation experiments suggest that the soma serves as a stably-oscillating inertial compartment, while multiple PDCs exhibit stochastic fluctuations and high excitability. Despite the stochastic and excitable nature of PDCs, their activities are balanced by the large centrally-connected inertial soma, resulting in the slow synchronized pacemaking rhythm. Furthermore, our electrophysiological experiments indicate that the soma and PDCs, with distinct characteristics, play different roles in glutamate- induced burst-pause firing patterns. Excitable PDCs mediate excitatory burst responses to glutamate, while the large inertial soma determines inhibitory pause responses to glutamate. Therefore, we could conclude that this somatodendritic organization serves as a common foundation for both pacemaker activity and evoked firing patterns in midbrain DA neurons.

Bioelectricity in dental medicine: a narrative review

BACKGROUND

Bioelectric signals, whether exogenous or endogenous, play crucial roles in the life processes of organisms. Recently, the significance of bioelectricity in the field of dentistry is steadily gaining greater attention.

OBJECTIVE

This narrative review aims to comprehensively outline the theory, physiological effects, and practical applications of bioelectricity in dental medicine and to offer insights into its potential future direction. It attempts to provide dental clinicians and researchers with an electrophysiological perspective to enhance their clinical practice or fundamental research endeavors.

METHODS

An online computer search for relevant literature was performed in PubMed, Web of Science and Cochrane Library, with the keywords "bioelectricity, endogenous electric signal, electric stimulation, dental medicine."

RESULTS

Eventually, 288 documents were included for review. The variance in ion concentration between the interior and exterior of the cell membrane, referred to as transmembrane potential, forms the fundamental basis of bioelectricity. Transmembrane potential has been established as an essential regulator of intercellular communication, mechanotransduction, migration, proliferation, and immune responses. Thus, exogenous electric stimulation can significantly alter cellular action by affecting transmembrane potential. In the field of dental medicine, electric stimulation has proven useful for assessing pulp condition, locating root apices, improving the properties of dental biomaterials, expediting orthodontic tooth movement, facilitating implant osteointegration, addressing maxillofacial malignancies, and managing neuromuscular dysfunction. Furthermore, the reprogramming of bioelectric signals holds promise as a means to guide organism development and intervene in disease processes. Besides, the development of high-throughput electrophysiological tools will be imperative for identifying ion channel targets and precisely modulating bioelectricity in the future.

CONCLUSIONS

Bioelectricity has found application in various concepts of dental medicine but large-scale, standardized, randomized controlled clinical trials are still necessary in the future. In addition, the precise, repeatable and predictable measurement and modulation methods of bioelectric signal patterns are essential research direction.

Catatonia Secondary to Depolarization Block

Catatonia is a severe psychomotor disorder that is associated with a 60-fold increased risk of premature death. Its occurrence has been associated with multiple psychiatric diagnoses, the most common being type I bipolar disorder. Catatonia can be understood as a disorder of ion dysregulation with reduced clearance of intracellular sodium ions. As the intraneuronal sodium concentration increases, the transmembrane potential is increased, and the resting potential may ultimately depolarize above the cellular threshold potential creating a condition known as depolarization block. Neurons in depolarization block do not respond to stimulation but are constantly releasing neurotransmitter; they mirror the clinical state of catatonia - active but non-responsive. Hyperpolarizing neurons, e.g., with benzodiazepines, is the most effective treatment.

Multi-timescale analysis of midbrain dopamine neuronal firing activities

Midbrain dopamine (DA) neurons exhibit spiking and bursting patterns under physiological conditions. Based on the data on electrophysiological recordings, Yu et al. developed a 13-dimensional mathematical model to capture the detailed characteristics of the DA neuronal firing activities. We use the fitting method to simplify the original model into a 4-dimensional model. Then, the spiking-to-bursting transition is detected from a simple and robust mathematical condition. Physiologically, this condition is a balance of the restorative and the regenerative ion channels at resting potential. Geometrically, this condition imposes a transcritical bifurcation. Moreover, we combine singularity theory and singular perturbation methods to capture the geometry of three-timescale firing attractors in a universal unfolding of a cusp singularity. In particular, the planar description of the corresponding firing patterns can generate the corresponding firing attractors. This analysis provides a new idea for understanding the firing activities of the DA neuron and the specific mechanisms for the switching and dynamic regulation among different patterns.

A Multi-Scale Computational Model of Levodopa-Induced Toxicity in Parkinson's Disease

Parkinson's disease (PD) is caused by the progressive loss of dopaminergic cells in substantia nigra pars compacta (SNc). The root cause of this cell loss in PD is still not decisively elucidated. A recent line of thinking has traced the cause of PD neurodegeneration to metabolic deficiency. Levodopa (L-DOPA), a precursor of dopamine, used as a symptom-relieving treatment for PD, leads to positive and negative outcomes. Several researchers inferred that L-DOPA might be harmful to SNc cells due to oxidative stress. The role of L-DOPA in the course of the PD pathogenesis is still debatable. We hypothesize that energy deficiency can lead to L-DOPA-induced toxicity in two ways: by promoting dopamine-induced oxidative stress and by exacerbating excitotoxicity in SNc. We present a systems-level computational model of SNc-striatum, which will help us understand the mechanism behind neurodegeneration postulated above and provide insights into developing disease-modifying therapeutics. It was observed that SNc terminals are more vulnerable to energy deficiency than SNc somas. During L-DOPA therapy, it was observed that higher L-DOPA dosage results in increased loss of terminals in SNc. It was also observed that co-administration of L-DOPA and glutathione (antioxidant) evades L-DOPA-induced toxicity in SNc neurons. Our proposed model of the SNc-striatum system is the first of its kind, where SNc neurons were modeled at a biophysical level, and striatal neurons were modeled at a spiking level. We show that our proposed model was able to capture L-DOPA-induced toxicity in SNc, caused by energy deficiency.

NeuroGPU: Accelerating multi-compartment, biophysically detailed neuron simulations on GPUs

BACKGROUND

The membrane potential of individual neurons depends on a large number of interacting biophysical processes operating on spatial-temporal scales spanning several orders of magnitude. The multi-scale nature of these processes dictates that accurate prediction of membrane potentials in specific neurons requires the utilization of detailed simulations. Unfortunately, constraining parameters within biologically detailed neuron models can be difficult, leading to poor model fits. This obstacle can be overcome partially by numerical optimization or detailed exploration of parameter space. However, these processes, which currently rely on central processing unit (CPU) computation, often incur orders of magnitude increases in computing time for marginal improvements in model behavior. As a result, model quality is often compromised to accommodate compute resources.

NEW METHOD

Here, we present a simulation environment, NeuroGPU, that takes advantage of the inherent parallelized structure of the graphics processing unit (GPU) to accelerate neuronal simulation.

RESULTS & COMPARISON WITH EXISTING METHODS

NeuroGPU can simulate most biologically detailed models 10-200 times faster than NEURON simulation running on a single core and 5 times faster than GPU simulators (CoreNEURON). NeuroGPU is designed for model parameter tuning and best performs when the GPU is fully utilized by running multiple (> 100) instances of the same model with different parameters. When using multiple GPUs, NeuroGPU can reach to a speed-up of 800 fold compared to single core simulations, especially when simulating the same model morphology with different parameters. We demonstrate the power of NeuoGPU through large-scale parameter exploration to reveal the response landscape of a neuron. Finally, we accelerate numerical optimization of biophysically detailed neuron models to achieve highly accurate fitting of models to simulation and experimental data.

CONCLUSIONS

Thus, NeuroGPU is the fastest available platform that enables rapid simulation of multi-compartment, biophysically detailed neuron models on commonly used computing systems accessible by many scientists.

Inactivation mode of sodium channels defines the different maximal firing rates of conventional versus atypical midbrain dopamine neurons

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.

We developed a theoretical and mathematical framework that could explain the major electrophysiological differences between the conventional midbrain dopamine (DA) neurons with a low maximum firing rate, and the more recently identified atypical DA neurons. Testable predictions from this framework were then verified with in vitro patch-clamp recordings from DA neurons with identified phenotypes and projection targets. Since different subpopulations of DA neurons participate in different circuits, and these circuits are likely differentially dysregulated in diseases such as addiction, Parkinson disease, and schizophrenia, it is important to identify the differences of their intrinsic electrophysiological properties as a prelude to developing more precisely targeted therapies.

TRPC3 and NALCN channels drive pacemaking in substantia nigra dopaminergic neurons

Midbrain dopamine (DA) neurons are slow pacemakers that maintain extracellular DA levels. During the interspike intervals, subthreshold slow depolarization underlies autonomous pacemaking and determines its rate. However, the ion channels that determine slow depolarization are unknown. Here we show that TRPC3 and NALCN channels together form sustained inward currents responsible for the slow depolarization of nigral DA neurons. Specific TRPC3 channel blockade completely blocked DA neuron pacemaking, but the pacemaking activity in TRPC3 knock-out (KO) mice was perfectly normal, suggesting the presence of compensating ion channels. Blocking NALCN channels abolished pacemaking in both TRPC3 KO and wild-type mice. The NALCN current and mRNA and protein expression are increased in TRPC3 KO mice, indicating that NALCN compensates for TRPC3 currents. In normal conditions, TRPC3 and NALCN contribute equally to slow depolarization. Therefore, we conclude that TRPC3 and NALCN are two major leak channels that drive robust pacemaking in nigral DA neurons.

Intrinsic Morphologic and Physiologic Development of Human Derived Retinal Ganglion Cells In Vitro

Purpose

Human retinal ganglion cells (hRGC) derived from human pluripotent stem cells are promising candidates to model, protect, and replace degenerating RGCs. Here, we examined intrinsic morphologic and physiologic development of hRGCs.

Methods

We used CRISPR-Cas9 to selectively express tdTomato under the RGC-specific promoter, BRN3B. Human pluripotent stem cells were chemically differentiated into hRGCs and cultured up to 7 weeks. We measured soma area, neurite complexity, synaptic protein, axon-related messenger RNA and protein, and voltage-dependent responses.

Results

Soma area, neurite complexity, and postsynaptic density protein 95 increased over time. Soma area and neurite complexity increased proportionally week to week, and this relationship was dynamic, strengthening between 2 and 3 weeks and diminishing by 4 weeks. Postsynaptic density 95 localization was dependent on culture duration. After 1 to 2 weeks, postsynaptic density 95 localized within somas but redistributed along neurites after 3 to 4 weeks. Axon initial segment scaffolding protein, Ankyrin G, expression also increased over time, and by 7 weeks, Ankyrin G often localized within putative axons. Voltage-gated inward currents progressively developed, but outward currents matured by 4 weeks. Current-induced spike generation increased over time but limited by depolarization block.

Conclusions

Human RGCs develop up to 7 weeks after culture. Thus, the state of hRGC maturation should be accounted for in designing models and treatments for optic neuropathies.

Translational Relevance

We characterized hRGC morphologic and physiologic development towards identifying key time points when hRGCs express mechanisms that may be harnessed to enhance the efficacy of neuroprotective and cell replacement therapies.

Computational and theoretical insights into the homeostatic response to the decreased cell size of midbrain dopamine neurons

Midbrain dopamine neurons communicate signals of reward anticipation and attribution of salience. This capacity is distorted in heroin or cocaine abuse or in conditions such as human mania. A shared characteristic among rodent models of these behavioral disorders is that dopamine neurons in these animals acquired a small size and manifest an augmented spontaneous and burst activity. The biophysical mechanism underlying this increased excitation is currently unknown, but is believed to primarily follow from a substantial drop in K+ conductance secondary to morphology reduction. This work uses a dopamine neuron mathematical model to show, surprisingly, that under size diminution a reduction in K+ conductance is an adaptation that attempts to decrease cell excitability. The homeostatic response that preserves the intrinsic activity is the conservation of the ion channel density for each conductance; a result that is analytically demonstrated and challenges the experimentalist tendency to reduce intrinsic excitation to K+ conductance expression level. Another unexpected mechanism that buffers the raise in intrinsic activity is the presence of the ether-a-go-go-related gen K+ channel since its activation is illustrated to increase with size reduction. Computational experiments finally demonstrate that size attenuation results in the paradoxical enhancement of afferent-driven bursting as a reduced temporal summation indexed correlates with improved depolarization. This work illustrates, on the whole, that experimentation in the absence of mathematical models may lead to the erroneous interpretation of the counterintuitive aspects of empirical data.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

Robustness to Axon Initial Segment Variation Is Explained by Somatodendritic Excitability in Rat Substantia Nigra Dopaminergic Neurons

In many neuronal types, axon initial segment (AIS) geometry critically influences neuronal excitability. Interestingly, the axon of rat SNc dopaminergic (DA) neurons displays a highly variable location and most often arises from an axon-bearing dendrite (ABD). We combined current-clamp somatic and dendritic recordings, outside-out recordings of dendritic sodium and potassium currents, morphological reconstructions and multicompartment modeling on male and female rat SNc DA neurons to determine cell-to-cell variations in AIS and ABD geometry, and their influence on neuronal output (spontaneous pacemaking frequency, action potential [AP] shape). Both AIS and ABD geometries were found to be highly variable from neuron to neuron. Surprisingly, we found that AP shape and pacemaking frequency were independent of AIS geometry. Modeling realistic morphological and biophysical variations helped us clarify this result: in SNc DA neurons, the complexity of the ABD combined with its excitability predominantly define pacemaking frequency and AP shape, such that large variations in AIS geometry negligibly affect neuronal output and are tolerated.SIGNIFICANCE STATEMENT In many neuronal types, axon initial segment (AIS) geometry critically influences neuronal excitability. In the current study, we describe large cell-to-cell variations in AIS length or distance from the soma in rat substantia nigra pars compacta dopaminergic neurons. Using neuronal reconstruction and electrophysiological recordings, we show that this morphological variability does not seem to affect their electrophysiological output, as neither action potential properties nor pacemaking frequency is correlated with AIS morphology. Realistic multicompartment modeling suggests that this robustness to AIS variation is mainly explained by the complexity and excitability of the somatodendritic compartment.

Morphological and Biophysical Determinants of the Intracellular and Extracellular Waveforms in Nigral Dopaminergic Neurons: A Computational Study

Action potentials (APs) in nigral dopaminergic neurons often exhibit two separate components: the first reflecting spike initiation in the dendritically located axon initial segment (AIS) and the second the subsequent dendro-somatic spike. These components are separated by a notch in the ascending phase of the somatic extracellular waveform and in the temporal derivative of the somatic intracellular waveform. Still, considerable variability exists in the presence and magnitude of the notch across neurons. To systematically address the contribution of AIS, dendritic and somatic compartments to shaping the two-component APs, we modeled APs of previously in vivo electrophysiologically characterized and 3D-reconstructed male mouse and rat dopaminergic neurons. A parsimonious two-domain model, with high (AIS) and lower (dendro-somatic) Na⁺ conductance, reproduced the notch in the temporal derivatives, but not in the extracellular APs, regardless of morphology. The notch was only revealed when somatic active currents were reduced, constraining the model to three domains. Thus, an initial AIS spike is followed by an actively generated spike by the axon-bearing dendrite (ABD), in turn followed mostly passively by the soma. The transition from being a source compartment for the AIS spike to a source compartment for the ABD spike satisfactorily explains the extracellular somatic notch. Larger AISs and thinner ABD (but not soma-to-AIS distance) accentuate the AIS component. We conclude that variability in AIS size and ABD caliber explains variability in AP extracellular waveform and separation of AIS and dendro-somatic components, given the presence of at least three functional domains with distinct excitability characteristics.SIGNIFICANCE STATEMENT Midbrain dopamine neurons make an important contribution to circuits mediating motivation and movement. Understanding the basic rules that govern the electrical activity of single dopaminergic neurons is therefore essential to reveal how they ultimately contribute to movement and motivation as well as what goes wrong in associated disorders. Our computational study focuses on the generation and propagation of action potentials and shows that different morphologies and excitability characteristics of the cell body, dendrites and proximal axon can explain the diversity of action potentials shapes in this population. These compartments likely make differential contributions both to normal dopaminergic signaling and could potentially underlie pathological dopaminergic signaling implicated in addiction, schizophrenia, Parkinson's disease, and other disorders.

Role of the Axon Initial Segment in the Control of Spontaneous Frequency of Nigral Dopaminergic Neurons In Vivo

The spontaneous tonic discharge activity of nigral dopamine neurons plays a fundamental role in dopaminergic signaling. To investigate the role of neuronal morphology and architecture with respect to spontaneous activity in this population, we visualized the 3D structure of the axon initial segment (AIS) along with the entire somatodendritic domain of adult male mouse dopaminergic neurons, previously recorded in vivo We observed a positive correlation of the firing rate with both proximity and size of the AIS. Computational modeling showed that the size of the AIS, but not its position within the somatodendritic domain, is the major causal determinant of the tonic firing rate in the intact model, by virtue of the higher intrinsic frequency of the isolated AIS. Further mechanistic analysis of the relationship between neuronal morphology and firing rate showed that dopaminergic neurons function as a coupled oscillator whose frequency of discharge results from a compromise between AIS and somatodendritic oscillators. Thus, morphology plays a critical role in setting the basal tonic firing rate, which in turn could control striatal dopaminergic signaling that mediates motivation and movement.SIGNIFICANCE STATEMENT The frequency at which nigral dopamine neurons discharge action potentials sets baseline dopamine levels in the brain, which enables activity in motor, cognitive, and motivational systems. Here, we demonstrate that the size of the axon initial segment, a subcellular compartment responsible for initiating action potentials, is a key determinant of the firing rate in these neurons. The axon initial segment and all the molecular components that underlie its critical function may provide a novel target for the regulation of dopamine levels in the brain.

Pedunculopontine glutamatergic neurons control spike patterning in substantia nigra dopaminergic neurons

Burst spiking in substantia nigra pars compacta (SNc) dopaminergic neurons is a key signaling event in the circuitry controlling goal-directed behavior. It is widely believed that this spiking mode depends upon an interaction between synaptic activation of N-methyl-D-aspartate receptors (NMDARs) and intrinsic oscillatory mechanisms. However, the role of specific neural networks in burst generation has not been defined. To begin filling this gap, SNc glutamatergic synapses arising from pedunculopotine nucleus (PPN) neurons were characterized using optical and electrophysiological approaches. These synapses were localized exclusively on the soma and proximal dendrites, placing them in a good location to influence spike generation. Indeed, optogenetic stimulation of PPN axons reliably evoked spiking in SNc dopaminergic neurons. Moreover, burst stimulation of PPN axons was faithfully followed, even in the presence of NMDAR antagonists. Thus, PPN-evoked burst spiking of SNc dopaminergic neurons in vivo may not only be extrinsically triggered, but extrinsically patterned as well.

Calcium-activated SK channels control firing regularity by modulating sodium channel availability in midbrain dopamine neurons

Dopamine neurons in the substantia nigra pars compacta and ventral tegmental area regulate behaviours such as reward-related learning, and motor control. Dysfunction of these neurons is implicated in Schizophrenia, addiction to drugs, and Parkinson’s disease. While some dopamine neurons fire single spikes at regular intervals, others fire irregular single spikes interspersed with bursts. Pharmacological inhibition of calcium-activated potassium (SK) channels increases the variability in their firing pattern, sometimes also increasing the number of spikes fired in bursts, indicating that SK channels play an important role in maintaining dopamine neuron firing regularity and burst firing. However, the exact mechanisms underlying these effects are still unclear. Here, we develop a biophysical model of a dopamine neuron incorporating ion channel stochasticity that enabled the analysis of availability of ion channels in multiple states during spiking. We find that decreased firing regularity is primarily due to a significant decrease in the AHP that in turn resulted in a reduction in the fraction of available voltage-gated sodium channels due to insufficient recovery from inactivation. Our model further predicts that inhibition of SK channels results in a depolarisation of action potential threshold along with an increase in its variability.

Cell-Autonomous Excitation of Midbrain Dopamine Neurons by Endocannabinoid-Dependent Lipid Signaling

The major endocannabinoid in the mammalian brain is the bioactive lipid 2-arachidonoylglycerol (2-AG). The best-known effects of 2-AG are mediated by G-protein-coupled cannabinoid receptors. In principle, 2-AG could modify neuronal excitability by acting directly on ion channels, but such mechanisms are poorly understood. Using a preparation of dissociated mouse midbrain dopamine neurons to isolate effects on intrinsic excitability, we found that 100 nM 2-AG accelerated pacemaking and steepened the frequency-current relationship for burst-like firing. In voltage-clamp experiments, 2-AG reduced A-type potassium current (I_A) through a cannabinoid receptor-independent mechanism mimicked by arachidonic acid, which has no activity on cannabinoid receptors. Activation of orexin, neurotensin, and metabotropic glutamate G_q/11-linked receptors mimicked the effects of exogenous 2-AG and their actions were prevented by inhibiting the 2-AG-synthesizing enzyme diacylglycerol lipase α. The results show that 2-AG and related lipid signaling molecules can directly tune neuronal excitability in a cell-autonomous manner by modulating I_A.

Implications of cellular models of dopamine neurons for disease

This review addresses the present state of single-cell models of the firing pattern of midbrain dopamine neurons and the insights that can be gained from these models into the underlying mechanisms for diseases such as Parkinson's, addiction, and schizophrenia. We will explain the analytical technique of separation of time scales and show how it can produce insights into mechanisms using simplified single-compartment models. We also use morphologically realistic multicompartmental models to address spatially heterogeneous aspects of neural signaling and neural metabolism. Separation of time scale analyses are applied to pacemaking, bursting, and depolarization block in dopamine neurons. Differences in subpopulations with respect to metabolic load are addressed using multicompartmental models.

Synergy of AMPA and NMDA Receptor Currents in Dopaminergic Neurons: A Modeling Study

Dopaminergic (DA) neurons display two modes of firing: low-frequency tonic and high-frequency bursts. The high frequency firing within the bursts is attributed to NMDA, but not AMPA receptor activation. In our models of the DA neuron, both biophysical and abstract, the NMDA receptor current can significantly increase their firing frequency, whereas the AMPA receptor current is not able to evoke high-frequency activity and usually suppresses firing. However, both currents are produced by glutamate receptors and, consequently, are often co-activated. Here we consider combined influence of AMPA and NMDA synaptic input in the models of the DA neuron. Different types of neuronal activity (resting state, low frequency, or high frequency firing) are observed depending on the conductance of the AMPAR and NMDAR currents. In two models, biophysical and reduced, we show that the firing frequency increases more effectively if both receptors are co-activated for certain parameter values. In particular, in the more quantitative biophysical model, the maximal frequency is 40% greater than that with NMDAR alone. The dynamical mechanism of such frequency growth is explained in the framework of phase space evolution using the reduced model. In short, both the AMPAR and NMDAR currents flatten the voltage nullcline, providing the frequency increase, whereas only NMDA prevents complete unfolding of the nullcline, providing robust firing. Thus, we confirm a major role of the NMDAR in generating high-frequency firing and conclude that AMPAR activation further significantly increases the frequency.

Differential Regulation of Action Potential Shape and Burst-Frequency Firing by BK and Kv2 Channels in Substantia Nigra Dopaminergic Neurons

Little is known about the voltage-dependent potassium currents underlying spike repolarization in midbrain dopaminergic neurons. Studying mouse substantia nigra pars compacta dopaminergic neurons both in brain slice and after acute dissociation, we found that BK calcium-activated potassium channels and Kv2 channels both make major contributions to the depolarization-activated potassium current. Inhibiting Kv2 or BK channels had very different effects on spike shape and evoked firing. Inhibiting Kv2 channels increased spike width and decreased the afterhyperpolarization, as expected for loss of an action potential-activated potassium conductance. BK inhibition also increased spike width but paradoxically increased the afterhyperpolarization. Kv2 channel inhibition steeply increased the slope of the frequency-current (f-I) relationship, whereas BK channel inhibition had little effect on the f-I slope or decreased it, sometimes resulting in slowed firing. Action potential clamp experiments showed that both BK and Kv2 current flow during spike repolarization but with very different kinetics, with Kv2 current activating later and deactivating more slowly. Further experiments revealed that inhibiting either BK or Kv2 alone leads to recruitment of additional current through the other channel type during the action potential as a consequence of changes in spike shape. Enhancement of slowly deactivating Kv2 current can account for the increased afterhyperpolarization produced by BK inhibition and likely underlies the very different effects on the f-I relationship. The cross-regulation of BK and Kv2 activation illustrates that the functional role of a channel cannot be defined in isolation but depends critically on the context of the other conductances in the cell.

SIGNIFICANCE STATEMENT

This work shows that BK calcium-activated potassium channels and Kv2 voltage-activated potassium channels both regulate action potentials in dopamine neurons of the substantia nigra pars compacta. Although both channel types participate in action potential repolarization about equally, they have contrasting and partially opposite effects in regulating neuronal firing at frequencies typical of bursting. Our analysis shows that this results from their different kinetic properties, with fast-activating BK channels serving to short-circuit activation of Kv2 channels, which tend to slow firing by producing a deep afterhyperpolarization. The cross-regulation of BK and Kv2 activation illustrates that the functional role of a channel cannot be defined in isolation but depends critically on the context of the other conductances in the cell.

Ion channel degeneracy enables robust and tunable neuronal firing rates

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.

A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block

Midbrain dopamine neurons exhibit a novel type of bursting that we call "inverted square wave bursting" when exposed to Ca(2+)-activated small conductance (SK) K(+) channel blockers in vitro. This type of bursting has three phases: hyperpolarized silence, spiking, and depolarization block. We find that two slow variables are required for this type of bursting, and we show that the three-dimensional bifurcation diagram for inverted square wave bursting is a folded surface with upper (depolarized) and lower (hyperpolarized) branches. The activation of the L-type Ca(2+) channel largely supports the separation between these branches. Spiking is initiated at a saddle node on an invariant circle bifurcation at the folded edge of the lower branch and the trajectory spirals around the unstable fixed points on the upper branch. Spiking is terminated at a supercritical Hopf bifurcation, but the trajectory remains on the upper branch until it hits a saddle node on the upper folded edge and drops to the lower branch. The two slow variables contribute as follows. A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking. The slow activation of the ether-a-go-go-related (ERG) K(+) current is largely responsible for termination of the depolarized plateau. The mechanisms and slow processes identified herein may contribute to bursting as well as entry into and recovery from the depolarization block to different degrees in different subpopulations of dopamine neurons in vivo.

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

Dopamine neurons in freely moving rats often fire behaviorally relevant high-frequency bursts, but depolarization block limits the maximum steady firing rate of dopamine neurons in vitro to ∼10 Hz. Using a reduced model that faithfully reproduces the sodium current measured in these neurons, we show that adding an additional slow component of sodium channel inactivation, recently observed in these neurons, qualitatively changes in two different ways how the model enters into depolarization block. First, the slow time course of inactivation allows multiple spikes to be elicited during a strong depolarization prior to entry into depolarization block. Second, depolarization block occurs near or below the spike threshold, which ranges from -45 to -30 mV in vitro, because the additional slow component of inactivation negates the sodium window current. In the absence of the additional slow component of inactivation, this window current produces an N-shaped steady-state current-voltage (I-V) curve that prevents depolarization block in the experimentally observed voltage range near -40 mV. The time constant of recovery from slow inactivation during the interspike interval limits the maximum steady firing rate observed prior to entry into depolarization block. These qualitative features of the entry into depolarization block can be reversed experimentally by replacing the native sodium conductance with a virtual conductance lacking the slow component of inactivation. We show that the activation of NMDA and AMPA receptors can affect bursting and depolarization block in different ways, depending upon their relative contributions to depolarization versus to the total linear/nonlinear conductance.

Role of nicotinic acetylcholine receptors in regulating dopamine neuron activity

Midbrain dopamine (DA) neurons play a central role in a wide range of behaviors, from attention and motivation to motor control and reinforcement. The release of DA is modulated by a number of factors, and its deregulation has been implicated in multiple psychiatric disorders, such as addiction. In particular, nicotinic acetylcholine receptors (nAChRs) are key modulators of DA cells. Nicotine, the main addictive component in tobacco, strongly interacts with these receptors in the midbrain DA systems, resulting in reinforcing effects that are at the core of tobacco addiction. nAChRs are virtually expressed on every cell of the DA system, both at pre-, post- and extra-synaptic locations. The complex issue of interpreting the role of the large portfolio of different nAChR subtypes expressed on ventral tegmental area (VTA) and substantia nigra pars compacta (SNc) neurons, and especially their role in defining functional DAergic subpopulations, is far from being solved. In this review we will try to provide the reader with an integrative view of the nicotinic modulation of DA neurons and its influence at the cellular, systemic and behavioral levels (exploratory behavior), as well as its implication in the reinforcing effects of nicotine.

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

AIM

3-Methyl-6-chloro-7,8-hydroxy-1-(3-methylphenyl)-2,3,4,5-tetrahydro-1H-3-benzazepine (SKF83959) have been shown to affect several types of voltage-dependent channels in hippocampal pyramidal neurons. The aim of this study was to determine how modulation of a individual type of the channels by SKF83959 contributes to the overall excitability of CA1 pyramidal neurons during either direct current injections or synaptic activation.

METHODS

Rat hippocampal slices were prepared. The kinetics of voltage-dependent Na(+) channels and neuronal excitability and depolarization block in CA1 pyramidal neurons were examined using whole-cell recording. A realistic mathematical model of hippocampal CA1 pyramidal neuron was used to simulate the effects of SKF83959 on neuronal excitability.

RESULTS

SKF83959 (50 μmol/L) shifted the inactivation curve of Na(+) current by 10.3 mV but had no effect on the activation curve in CA1 pyramidal neurons. The effects of SKF83959 on passive membrane properties, including a decreased input resistance and depolarized resting potential, predicted by our simulations were in agreement with the experimental data. The simulations showed that decreased excitability of the soma by SKF83959 (examined with current injection at the soma) was only observed when the membrane potential was compensated to the control levels, whereas the decreased dendritic excitability (examined with current injection at the dendrite) was found even without membrane potential compensation, which led to a decreased number of action potentials initiated at the soma. Moreover, SKF83959 significantly facilitated depolarization block in CA1 pyramidal neurons. SKF83959 decreased EPSP temporal summation and, of physiologically greater relevance, the synaptic-driven firing frequency.

CONCLUSION

SKF83959 decreased the excitability of CA1 pyramidal neurons even though the drug caused the membrane potential depolarization. The results may reveal a partial mechanism for the drug's anti-Parkinsonian effects and may also suggest that SKF83959 has a potential antiepileptic effect.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

Balance between the proximal dendritic compartment and the soma determines spontaneous firing rate in midbrain dopamine neurons

Midbrain dopamine (DA) neurons are slow intrinsic pacemakers that require the elaborate composition of many ion channels in the somatodendritic compartments. Understanding the major determinants of the spontaneous firing rate (SFR) of midbrain DA neurons is important because they determine the basal DA levels in target areas, including the striatum. As spontaneous firing occurs synchronously at the soma and dendrites, the electrical coupling between the soma and dendritic compartments has been regarded as a key determinant for the SFR. However, it is not known whether this somatodendritic coupling is served by the whole dendritic compartments or only parts of them. In the rat substantia nigra pars compacta (SNc) DA neurons, we demonstrate that the balance between the proximal dendritic compartment and the soma determines the SFR. Isolated SNc DA neurons showed a wide range of soma size and a variable number of primary dendrites but preserved a quite consistent SFR. The SFR was not correlated with soma size or with the number of primary dendrites, but it was strongly correlated with the area ratios of the proximal dendritic compartments to the somatic compartment. Tetrodotoxin puff and local Ca(2+) perturbation experiments, computer simulation, and local glutamate uncaging experiments suggest the importance of the proximal dendritic compartments in pacemaker activity. These data indicate that the proximal dendritic compartments, not the whole dendritic compartments, play a key role in the somatodendritic balance that determines the SFR in DA neurons.

Implications of cellular models of dopamine neurons for schizophrenia

Midbrain dopamine neurons are pacemakers in vitro, but in vivo they fire less regularly and occasionally in bursts that can lead to a temporary cessation in firing produced by depolarization block. The therapeutic efficacy of antipsychotic drugs used to treat the positive symptoms of schizophrenia has been attributed to their ability to induce depolarization block within a subpopulation of dopamine neurons. We summarize the results of experiments characterizing the physiological mechanisms underlying the ability of these neurons to enter depolarization block in vitro, and our computational simulations of those experiments. We suggest that the inactivation of voltage-dependent Na(+) channels, and, in particular, the slower component of this inactivation, is critical in controlling entry into depolarization block. In addition, an ether-a-go-related gene (ERG) K(+) current also appears to be involved by delaying entry into and speeding recovery from depolarization block. Since many antipsychotic drugs share the ability to block this current, ERG channels may contribute to the therapeutic effects of these drugs.

Diversity of layer 5 projection neurons in the mouse motor cortex

In the primary motor cortex (M1), layer 5 projection neurons signal directly to distant motor structures to drive movement. Despite their pivotal position and acknowledged diversity these neurons are traditionally separated into broad commissural and corticofugal types, and until now no attempt has been made at resolving the basis for their diversity. We therefore probed the electrophysiological and morphological properties of retrogradely labeled M1 corticospinal (CSp), corticothalamic (CTh), and commissural projecting corticostriatal (CStr) and corticocortical (CC) neurons. An unsupervised cluster analysis established at least four phenotypes with additional differences between lumbar and cervical projecting CSp neurons. Distinguishing parameters included the action potential (AP) waveform, firing behavior, the hyperpolarisation-activated sag potential, sublayer position, and soma and dendrite size. CTh neurons differed from CSp neurons in showing spike frequency acceleration and a greater sag potential. CStr neurons had the lowest AP amplitude and maximum rise rate of all neurons. Temperature influenced spike train behavior in corticofugal neurons. At 26°C CTh neurons fired bursts of APs more often than CSp neurons, but at 36°C both groups fired regular APs. Our findings provide reliable phenotypic fingerprints to identify distinct M1 projection neuron classes as a tool to understand their unique contributions to motor function.

Interaction of NMDA receptor and pacemaking mechanisms in the midbrain dopaminergic neuron

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (α-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether-a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.

A single compartment model of pacemaking in dissasociated substantia nigra neurons: stability and energy analysis

Spontaneous oscillations in the mid-brain dopaminergic neurons are an important feature of motor control. The degeneration of these neurons is involved in movement disorders, particularly Parkinson's Disease. Modelling of this activity is an important part of developing an understanding of the pathogenic process. We develop a mathematical paradigm to describe this activity with a single compartment approach and a CellML version is made publicly available. The model explicitly describes the dynamics of the transmembrane potential with changes in the levels of important cations and is consistent with two major observations in the literature regarding its behaviour in the presence of channel blockers. Stability of the model behaviour is determined from the properties of its Monodromy matrix. We also discuss from the perspective of energy, a pharmacological intervention suggested in the treatment of Parkinson's Disease.

Pacemaker rate and depolarization block in nigral dopamine neurons: a somatic sodium channel balancing act

Midbrain dopamine (DA) neurons are slow intrinsic pacemakers that undergo depolarization (DP) block upon moderate stimulation. Understanding DP block is important because it has been correlated with the clinical efficacy of chronic antipsychotic drug treatment. Here we describe how voltage-gated sodium (Na(V)) channels regulate DP block and pacemaker activity in DA neurons of the substantia nigra using rat brain slices. The distribution, density, and gating of Na(V) currents were manipulated by blocking native channels with tetrodotoxin and by creating virtual channels and anti-channels with dynamic clamp. Although action potentials initiate in the axon initial segment and Na(V) channels are distributed in multiple dendrites, selective reduction of Na(V) channel activity in the soma was sufficient to decrease pacemaker frequency and increase susceptibility to DP block. Conversely, increasing somatic Na(V) current density raised pacemaker frequency and lowered susceptibility to DP block. Finally, when Na(V) currents were restricted to the soma, pacemaker activity occurred at abnormally high rates due to excessive local subthreshold Na(V) current. Together with computational simulations, these data show that both the slow pacemaker rate and the sensitivity to DP block that characterizes DA neurons result from the low density of somatic Na(V) channels. More generally, we conclude that the somatodendritic distribution of Na(V) channels is a major determinant of repetitive spiking frequency.

Functional characterization of ether-à-go-go-related gene potassium channels in midbrain dopamine neurons - implications for a role in depolarization block

Bursting activity by midbrain dopamine neurons reflects the complex interplay between their intrinsic pacemaker activity and synaptic inputs. Although the precise mechanism responsible for the generation and modulation of bursting in vivo has yet to be established, several ion channels have been implicated in the process. Previous studies with nonselective blockers suggested that ether-à-go-go-related gene (ERG) K(+) channels are functionally significant. Here, electrophysiology with selective chemical and peptide ERG channel blockers (E-4031 and rBeKm-1) and computational methods were used to define the contribution made by ERG channels to the firing properties of midbrain dopamine neurons in vivo and in vitro. Selective ERG channel blockade increased the frequency of spontaneous activity as well as the response to depolarizing current pulses without altering spike frequency adaptation. ERG channel block also accelerated entry into depolarization inactivation during bursts elicited by virtual NMDA receptors generated with the dynamic clamp, and significantly prolonged the duration of the sustained depolarization inactivation that followed pharmacologically evoked bursts. In vivo, somatic ERG blockade was associated with an increase in bursting activity attributed to a reduction in doublet firing. Taken together, these results show that dopamine neuron ERG K(+) channels play a prominent role in limiting excitability and in minimizing depolarization inactivation. As the therapeutic actions of antipsychotic drugs are associated with depolarization inactivation of dopamine neurons and blockade of cardiac ERG channels is a prominent side effect of these drugs, ERG channels in the central nervous system may represent a novel target for antipsychotic drug development.

Bursting as a source of non-linear determinism in the firing patterns of nigral dopamine neurons

Nigral dopamine (DA) neurons in vivo exhibit complex firing patterns consisting of tonic single-spikes and phasic bursts that encode information for certain types of reward-related learning and behavior. Non-linear dynamical analysis has previously demonstrated the presence of a non-linear deterministic structure in complex firing patterns of DA neurons, yet the origin of this non-linear determinism remains unknown. In this study, we hypothesized that bursting activity is the primary source of non-linear determinism in the firing patterns of DA neurons. To test this hypothesis, we investigated the dimension complexity of inter-spike interval data recorded in vivo from bursting and non-bursting DA neurons in the chloral hydrate-anesthetized rat substantia nigra. We found that bursting DA neurons exhibited non-linear determinism in their firing patterns, whereas non-bursting DA neurons showed truly stochastic firing patterns. Determinism was also detected in the isolated burst and inter-burst interval data extracted from firing patterns of bursting neurons. Moreover, less bursting DA neurons in halothane-anesthetized rats exhibited higher dimensional spiking dynamics than do more bursting DA neurons in chloral hydrate-anesthetized rats. These results strongly indicate that bursting activity is the main source of low-dimensional, non-linear determinism in the firing patterns of DA neurons. This finding furthermore suggests that bursts are the likely carriers of meaningful information in the firing activities of DA neurons.

SK2 and SK3 expression differentially affect firing frequency and precision in dopamine neurons

The firing properties of dopamine (DA) neurons in the substantia nigra (SN) pars compacta are strongly influenced by the activity of apamin-sensitive small conductance Ca(2+)-activated K(+) (SK) channels. Of the three SK channel genes expressed in central neurons, only SK3 expression has been identified in DA neurons. The present findings show that SK2 was also expressed in DA neurons. Immuno-electron microscopy (iEM) showed that SK2 was primarily expressed in the distal dendrites, while SK3 was heavily expressed in the soma and, to a lesser extent, throughout the dendritic arbor. Electrophysiological recordings of the effects of the SK channel blocker apamin on DA neurons from wild type and SK(-/-) mice show that SK2-containing channels contributed to the precision of action potential (AP) timing, while SK3-containing channels influenced AP frequency. The expression of SK2 in DA neurons may endow distinct signaling and subcellular localization to SK2-containing channels.

Properties of I(A) in a neuron of the dorsal raphe nucleus

Voltage clamp data were analyzed in order to characterize the properties of the fast potassium transient current I(A) for a presumed serotonergic neuron of the rat dorsal raphe nucleus (DRN). We obtain maximal conductance, time constants of activation and inactivation, and the steady state activation and inactivation functions m(∞) and h(∞), as Boltzmann curves, defined by half-activation potentials and slope factors. I(A) is estimated as g¯(V-V(rev))m(4)h, with g¯=20.5nS. For activation, the half-activation potential is V(a)=-52.5mV with slope factor k(a)=16.5mV, whereas for inactivation the corresponding quantities are -91.5mV and -9.3mV. We discuss the results in terms of the corresponding properties of I(A) in other cell types and their possible relevance to pacemaking activity in cells of the DRN. Methods of identification of serotonergic DRN neurons and the nature of the K(v) channels underlying the A-type current are also discussed.

Cocaine sensitization inhibits the hyperpolarization-activated cation current Ih and reduces cell size in dopamine neurons of the ventral tegmental area

The progressive augmentation of motor activity that results from repeated cocaine administration is termed behavioral sensitization. This phenomenon is thought to be a critical component in compulsive drug taking and relapse. Still, the cellular mechanisms that underlie sensitization remain elusive. Cocaine abuse, nonetheless, is known to evoke neuroplastic adaptations in dopamine (DA) neurotransmission originating from the midbrain's ventral tegmental area (VTA). Here, we report that concomitant with the development of locomotor sensitization to cocaine the hyperpolarization-activated cation current (I(h)) amplitude is depressed by ∼40% in VTA DA cells. Such effect did not result from a negative shift in I(h) voltage dependence. Nonstationary fluctuation analysis indicates that this inhibition was caused by an ∼45% reduction in the number of h-channels with no change in their unitary properties. The cocaine-induced I(h) depression was accompanied by a reduction in cell capacitance of similar magnitude (∼33%), leaving h-current density unaltered. Two implications follow from these data. First, I(h) inhibition may contribute to cocaine addiction by increasing bursting probability in DA cells and this effect could be intensified by the decrease in cell capacitance. Second, the cocaine-induced diminution of DA cell capacitance may also lead to reward tolerance promoting drug-seeking behaviors.

Stochastic amplification of calcium-activated potassium currents in Ca2+ microdomains

Small conductance (SK) calcium-activated potassium channels are found in many tissues throughout the body and open in response to elevations in intracellular calcium. In hippocampal neurons, SK channels are spatially co-localized with L-Type calcium channels. Due to the restriction of calcium transients into microdomains, only a limited number of L-Type Ca(2+) channels can activate SK and, thus, stochastic gating becomes relevant. Using a stochastic model with calcium microdomains, we predict that intracellular Ca(2+) fluctuations resulting from Ca(2+) channel gating can increase SK2 subthreshold activity by 1-2 orders of magnitude. This effectively reduces the value of the Hill coefficient. To explain the underlying mechanism, we show how short, high-amplitude calcium pulses associated with stochastic gating of calcium channels are much more effective at activating SK2 channels than the steady calcium signal produced by a deterministic simulation. This stochastic amplification results from two factors: first, a supralinear rise in the SK2 channel's steady-state activation curve at low calcium levels and, second, a momentary reduction in the channel's time constant during the calcium pulse, causing the channel to approach its steady-state activation value much faster than it decays. Stochastic amplification can potentially explain subthreshold SK2 activation in unified models of both sub- and suprathreshold regimes. Furthermore, we expect it to be a general phenomenon relevant to many proteins that are activated nonlinearly by stochastic ligand release.