A Model of Action Potentials and Fast Ca Dynamics in Pancreatic β-Cells

We examined the ionic mechanisms mediating depolarization-induced spike activity in pancreatic β-cells. We formulated a Hodgkin-Huxley-type ionic model for the action potential (AP) in these cells based on voltage- and current-clamp results together with measurements of Ca²⁺ dynamics in wild-type and Kv2.1 null mouse islets. The model contains an L-type Ca²⁺ current, a “rapid” delayed-rectifier K⁺ current, a small slowly-activated K⁺ current, a Ca²⁺-activated K⁺ current, an ATP-sensitive K⁺ current, a plasma membrane calcium-pump current and a Na⁺ background current. This model, coupled with an equation describing intracellular Ca²⁺ homeostasis, replicates β-cell AP and Ca²⁺ changes during one glucose-induced spontaneous spike, the effects of blocking K⁺ currents with different inhibitors, and specific complex spike in mouse islets lacking Kv2.1 channels. The currents with voltage-independent gating variables can also be responsible for burst behavior. Original features of this model include new equations for L-type Ca²⁺ current, assessment of the role of rapid delayed-rectifier K⁺ current, and Ca²⁺-activated K⁺ currents, demonstrating the important roles of the Ca²⁺-pump and background currents in the APs and bursts. This model provides acceptable fits to voltage-clamp, AP, and Ca²⁺ concentration data based on in silico analysis.     

Properties of Na+ currents conducted by a skeletal muscle L-type Ca2+ channel pore mutant (SkEIIIK)

Four glutamate residues residing at corresponding positions within the four conserved membrane-spanning repeats of L-type Ca²⁺ channels are important structural determinants for the passage of Ca²⁺ across the selectivity filter. Mutation of the critical glutamate in Repeat III in the a_1S subunit of the skeletal L-type channel (Ca_v1.1) to lysine virtually eliminates passage of Ca²⁺ during step depolarizations. In this study, we examined the ability of this mutant Ca_v1.1 channel (SkEIIIK) to conduct inward Na⁺ current. When 150 mM Na⁺ was present as the sole monovalent cation in the bath solution, dysgenic (Ca_v1.1 null) myotubes expressing SkEIIIK displayed slowly-activating, non-inactivating, nifedipine-sensitive inward currents with a reversal potential (45.6 ± 2.5 mV) near that expected for Na⁺. Ca²⁺ block of SkEIIIK-mediated Na⁺ current was revealed by the substantial enhancement of Na⁺ current amplitude after reduction of Ca²⁺ in the external recording solution from 10 mM to near physiological 1 mM. Inward SkEIIIK-mediated currents were potentiated by either ±Bay K 8644 (10 mM) or 200-ms depolarizing prepulses to +90 mV. In contrast, outward monovalent currents were reduced by ±Bay K 8644 and were unaffected by strong depolarization, indicating a preferential potentiation of inward Na⁺ currents through the mutant Ca_v1.1 channel. Taken together, our results show that SkEIIIK functions as a non-inactivating, junctionally-targeted Na⁺ channel when Na⁺ is the sole monvalent cation present and urge caution when interpreting the impact of mutations designed to ablate Ca²⁺ permeability mediated by Ca_V channels on physiological processes that extend beyond channel gating and permeability.     

Impact of slow K<Superscript>+</Superscript> currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K⁺ currents, such as the M-type K⁺ current (I _M ) or the Ca²⁺-activated K⁺ current (I _AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K⁺ currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K⁺ current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K⁺ currents have a differential effect on the noise tolerance in neural coding.     

Voltage-dependent ionic conductances in the human malignant astrocytoma cell line U87-MG

Although the human malignant astrocytoma cell line U87-MG has been used in numerous studies, few findings are available on the properties of its membrane ion conductances. Characterization of the ion channels expressed in these cells will make it possible to study membrane ion conductance changes when a receptor is activated by its ligand. This will help to elucidate the functional properties of these receptors and their signal-transduction pathways in pathophysiological events. This work studied the voltage-dependent ionic conductances of U87-MG cells using the Whole-Cell Recording patch-clamp technique. Six types of voltage-dependent ionic currents were identified: (i) a TEA-, 4-AP- and CTX-sensitive Ca²⁺-dependent K⁺ current, (ii) a transient K⁺ current inhibited by 4-AP, (iii) an inwardly rectifying K⁺ current blocked by Ba²⁺ and 4-AP, (iv) a DIDS- and SITS-sensitive Cl^? current, (v) a TTX-sensitive Na⁺ conductance and (vi) a L-type Ca²⁺ conductance activated by BayK-8644 and inhibited by Ni and the L-type Ca²⁺ channel inhibitor, nifedipine. In addition, electrical depolarizations elicited inward currents due to voltage-independent, Ca²⁺-dependent K⁺ influx against the electrochemical gradient, probably via an ouabain-sensitive Na⁺-K⁺ pump.     

Dynamic excitation states and firing patterns are controlled by sodium channel kinetics in myenteric neurons: a simulation study

Enteric neurons located in the gastro-intestinal tract are of particular importance to control digestive functions such as motility and secretion. In our recent publication, we showed that mouse myenteric neurons exhibit 2 types of tetrodotoxin-resistant Na⁺ currents: a fast inactivating Na⁺ current produced by Nav1.5 channels, present in nearly all myenteric neurons, and a persistent Na⁺ current attributed to Nav1.9 channels, restricted to the intrinsic primary afferent neurons (IPANs). By combination of experimental recording and computer simulation we found that Nav1.5 contributed to the upstroke velocity of action potentials (APs), whereas Nav1.9 opposed AP repolarization. Here, we detailed the Na⁺, Ca²⁺ and K⁺ currents used in our computational model of IPAN. We refined the prototype cell to reproduce the sustained firing pattern recorded in situ. As shown in experimental conditions we demonstrated that Nav1.9 channels critically determine the up-state life-time and thus, are essential to sustain tonic firing.     

Dynamic excitation states and firing patterns are controlled by sodium channel kinetics in myenteric neurons: a simulation study

Enteric neurons located in the gastro-intestinal tract are of particular importance to control digestive functions such as motility and secretion. In our recent publication, we showed that mouse myenteric neurons exhibit 2 types of tetrodotoxin-resistant Na⁺ currents: a fast inactivating Na⁺ current produced by Nav1.5 channels, present in nearly all myenteric neurons, and a persistent Na⁺ current attributed to Nav1.9 channels, restricted to the intrinsic primary afferent neurons (IPANs). By combination of experimental recording and computer simulation we found that Nav1.5 contributed to the upstroke velocity of action potentials (APs), whereas Nav1.9 opposed AP repolarization. Here, we detailed the Na⁺, Ca²⁺ and K⁺ currents used in our computational model of IPAN. We refined the prototype cell to reproduce the sustained firing pattern recorded in situ. As shown in experimental conditions we demonstrated that Nav1.9 channels critically determine the up-state life-time and thus, are essential to sustain tonic firing.     

Modeling the Cellular Mechanisms and Olfactory Input Underlying the Triphasic Response of Moth Pheromone-Sensitive Projection Neurons

In the antennal lobe of the noctuid moth Agrotis ipsilon, most pheromone-sensitive projection neurons (PNs) exhibit a triphasic firing pattern of excitation (E₁)-inhibition (I)-excitation (E₂) in response to a pulse of the sex pheromone. To understand the mechanisms underlying this stereotypical discharge, we developed a biophysical model of a PN receiving inputs from olfactory receptor neurons (ORNs) via nicotinic cholinergic synapses. The ORN is modeled as an inhomogeneous Poisson process whose firing rate is a function of time and is fitted to extracellular data recorded in response to pheromone stimulations at various concentrations and durations. The PN model is based on the Hodgkin-Huxley formalism with realistic ionic currents whose parameters were derived from previous studies. Simulations revealed that the inhibitory phase I can be produced by a SK current (Ca²⁺-gated small conductance K⁺ current) and that the excitatory phase E₂ can result from the long-lasting response of the ORNs. Parameter analysis further revealed that the ending time of E₁ depends on some parameters of SK, Ca²⁺, nACh and Na⁺ currents; I duration mainly depends on the time constant of intracellular Ca²⁺ dynamics, conductance of Ca²⁺ currents and some parameters of nACh currents; The mean firing frequency of E₁ and E₂ depends differentially on the interaction of various currents. Thus it is likely that the interplay between PN intrinsic currents and feedforward synaptic currents are sufficient to generate the triphasic firing patterns observed in the noctuid moth A. ipsilon.     

Seizure-like afterdischarges simulated in a model neuron

To explore non-synaptic mechanisms in paroxysmal discharges, we used a computer model of a simplified hippocampal pyramidal cell, surrounded by interstitial space and a “glial-endothelial” buffer system. Ion channels for Na⁺, K⁺, Ca²⁺ and Cl⁻ _, ion antiport 3Na/Ca, and “active” ion pumps were represented in the neuron membrane. The glia had “leak” conductances and an ion pump. Fluxes, concentration changes and cell swelling were computed. The neuron was stimulated by injecting current. Afterdischarge (AD) followed stimulation if depolarization due to rising interstitial K⁺ concentration ([K⁺]_o) activated persistent Na⁺ current (I _Na,P). AD was either simple or self-regenerating; either regular (tonic) or burst-type (clonic); and always self-limiting. Self-regenerating AD required sufficient I _Na,P to ensure re-excitation. Burst firing depended on activation of dendritic Ca²⁺ currents and Ca-dependent K⁺ current. Varying glial buffer function influenced [K⁺]_o accumulation and afterdischarge duration. Variations in Na⁺ and K⁺ currents influenced the threshold and the duration of AD. The data show that high [K⁺]_o and intrinsic membrane currents can produce the feedback of self-regenerating afterdischarges without synaptic input. The simulated discharge resembles neuron behavior during paroxysmal firing in living brain tissue. Action Editor: David Terman     

Effects of carbamazepine on nerve activity and transmitter release in neuroblastoma-glioma hybrid cells and the frog neuromuscular junction

Effects of the antiepileptic drug carbamazepine on nerve action potential and transmitter release in mouse neuroblastoma-glioma hybrid cells (NG108-15) and the frog neuromuscular junction were studied. Carbamazepine within a concentration range of 0.1–0.5 mmol/L reduced the peak height of the action potential of the NG108-15 cells, whereas the membrane potential and membrane resistance were unaffected. Voltage clamp revealed that the decrease in the action potential was due to the blockage of the Na⁺, delayed K⁺ and transient Ca²⁺ currents. Carbamazepine did not affect Ca²⁺-activated and A type K⁺ currents and long-lasting Ca²⁺ current. In the frog neuromuscular junction, carbamazepine decreased the mean quantal content by a parallel shift in the frequency augmentation–potentiation (FAP) relation. It is concluded that carbamazepine blocks the voltage-dependent Na⁺, delayed K⁺, and transient Ca²⁺ currents and quantal transmitter release through a decrease of nerve excitation.     

Fast Na+ channels and slow Ca2+ current in smooth muscle from pregnant rat uterus

Summary Smooth muscle cells normally do not possess fast Na²⁺ channels, but inward current is carried through two types of Ca²⁺ channels: slow (L-type) Ca²⁺ channels and fast (T-type) Ca²⁺ channels. Using whole-cell voltage clamp of single smooth muscle cells isolated from the longitudinal layer of 18-day pregnant rat uterus, depolarizing pusles, applied from a holding potential of –90 mV, evoked two types of inward current, fast and slow [8]. The fast inward current decayed within 30 ms, depended on [Na]₀, and was inhibited by TTX (K_0.5 = 27 nM). The slow inward current decayed slowly, was dependent on [Ca]₀, and was inhibited by nifedipine. These results suggest that the fast inward current is a fast Na²⁺ channel current, and that the slow inward current is a Ca²⁺ channel current was not evident. Thus, the ion channels which generate inward currents in pregnant rat uterine cells are TTX-sensitive fast Na⁺ channels and dihudropuridine-sensitive slow Ca²⁺ channels. The number of fast Na⁺ channels increased during gestation [9]. The averaged current density increased from 0 on day 5, to 0.19 on day 9, to 0.56 on day 14, to 0.90 on day 18, and to 0.86 pA/pF on day 21. This almost linear increase occurs because of an increase in the fraction of cells which possess fast Na²⁺ channels, and it suggested that the fast Na⁺ current may be involved in spread of excitation. The Ca²⁺ channel current density also was higher during the latter half of gestation. These results indicate that the fast Na⁺ channels and Ca²⁺ slow channels in myometrium become more numerous as term approaches, and may facilitate parturition. Isoproterenol (beta-agonist) did not affect either I_Ca(s) or I_Na(f), whereas Mg²⁺ (K_0.5 of 12 mM) and nifedipine (K_0.5 of 3.3 nM) depressed I_Ca(s). Oxytocin had no effect on I_Na(f) and actually depressed I_Ca(s) to a small extect. Therefore, the tocolytic action of beta-agonists cannot be explained by an inhibition of I_Ca(s), whereas that of Mg²⁺ can be so explained. The stimulating action of oxytocin on uterine contractions is not due to stimulation of I_Ca(s).     

Block of N-type Calcium Channels in Chick Sensory Neurons by External Sodium

L-type Ca²⁺ channels select for Ca²⁺ over sodium Na⁺ by an affinity-based mechanism. The prevailing model of Ca²⁺ channel permeation describes a multi-ion pore that requires pore occupancy by at least two Ca²⁺ ions to generate a Ca²⁺ current. At [Ca²⁺] < 1 μM, Ca²⁺ channels conduct Na⁺. Due to the high affinity of the intrapore binding sites for Ca²⁺ relative to Na⁺, addition of μM concentrations of Ca²⁺ block Na⁺ conductance through the channel. There is little information, however, about the potential for interaction between Na⁺ and Ca²⁺ for the second binding site in a Ca²⁺ channel already occupied by one Ca²⁺. The two simplest possibilities, (a) that Na⁺ and Ca²⁺ compete for the second binding site or (b) that full time occupancy by one Ca²⁺ excludes Na⁺ from the pore altogether, would imply considerably different mechanisms of channel permeation. We are studying permeation mechanisms in N-type Ca²⁺ channels. Similar to L-type Ca²⁺ channels, N-type channels conduct Na⁺ well in the absence of external Ca²⁺. Addition of 10 μM Ca²⁺ inhibited Na⁺ conductance by 95%, and addition of 1 mM Mg²⁺ inhibited Na⁺ conductance by 80%. At divalent ion concentrations of 2 mM, 120 mM Na⁺ blocked both Ca²⁺ and Ba²⁺ currents. With 2 mM Ba²⁺, the IC₅₀ for block of Ba²⁺ currents by Na⁺ was 119 mM. External Li⁺ also blocked Ba²⁺ currents in a concentration-dependent manner, with an IC₅₀ of 97 mM. Na⁺ block of Ba²⁺ currents was dependent on [Ba²⁺]; increasing [Ba²⁺] progressively reduced block with an IC₅₀ of 2 mM. External Na⁺ had no effect on voltage-dependent activation or inactivation of the channel. These data suggest that at physiological concentrations, Na⁺ and Ca²⁺ compete for occupancy in a pore already occupied by a single Ca²⁺. Occupancy of the pore by Na⁺ reduced Ca²⁺ channel conductance, such that in physiological solutions, Ca²⁺ channel currents are between 50 and 70% of maximal.     

Ca2+-activated K+ currents inNecturus choroid plexus

Summary The tight-seal whole-cell recording method has been used to studyNecturus choroid plexus epithelium. A cell potential of –59±2 mV and a whole cell resistance of 56±6 M were measured using this technique. Application of depolarizing step potentials activated voltage-dependent outward currents that developed with time. For example, when the cell was bathed in 110mm NaCl Ringer solution and the interior of the cell contained a solution of 110mm KCl and 5nm Ca²⁺, stepping the membrane potential from a holding value of –50 to –10 mV evoked outward currents which, after a delay of greater than 50 msec, increased to a steady state in 500 msec. The voltage dependence of the delayed currents suggests that they may be currents through Ca²⁺-activated K^_ channels. Based on the voltage dependence of the activation of Ca²⁺-activated K⁺ channels, we have devised a general method to isolate the delayed currents. The delayed currents were highly selective for K⁺ as their reversal potential at different K⁺ concentration gradients followed the Nernst potential for K⁺. These currents were reduced by the addition of TEA⁺ to the bath solution and were eliminated when Cs⁺ or Na⁺ replaced intracellular K⁺. Increasing the membrane potential to more positive values decreased both the delay and the half-times (t _1/2) to the steady value. Increasing the pipette Ca²⁺ also decreased the delay and decreasedt _1/2. For instance, when pipette Ca²⁺ was increased from 5 to 500nm, the delay andt _1/2 decreased from values greater than 50 and 150 msec to values less than 10 and 50 msec. We conclude that the delayed currents are K⁺ currents through Ca²⁺-activated K⁺ channels.At the resting membrane potential of –60 mV, Ca²⁺-activated K⁺ channels contribute between 13 to 25% of the total conductance of the cell. The contribution of these channels to cell conductance nearly doubles with membrane depolarization of 20–30 mV. Such depolarizations have been observed when cerebrospinal fluid (CSF) secretion is stimulated by cAMP and with intracellular Ca²⁺. Thus the Ca²⁺-activated K⁺ channels may play a specific role in maintaining intracellular K⁺ concentrations during CSF secretion.     

Effects of transition metal ions on spontaneous electrical activity and chemical synaptic transmission of neurons in the medicinal leech

Leech neurons exposed to salines containing inorganic Ca²⁺-channel blockers generate rhythmic bursts of impulses. According to an earlier model, these blockers unmask persistent Na⁺ currents that generate plateau-like depolarizations, each triggering a burst of impulses. The resulting increase in intracellular Na⁺ activates an outward Na⁺/K⁺ pump current that contributes to burst termination. We tested this model by examining systematically the effects of six transition metal ions (Co²⁺, Ni²⁺, Mn²⁺, Cd²⁺, La³⁺, and Zn²⁺) on the electrical activity of neurons in isolated leech ganglia. Each ion induced bursting activity, but the amplitude, form, and persistence of bursting differed with the ion used and its concentration relative to Ca²⁺. All ions tested suppressed chemical synaptic transmission between identified motor neurons, consistent with block of voltage-dependent Ca²⁺ currents in these cells. In addition, a strong correlation between suppression of synaptic transmission and burst amplitudes was obtained. Finally, burst duration was increased and the rate of repolarization decreased in reduced K⁺ saline, as expected for pump-dependent repolarization. These results provide further support for the hypothesis that a novel form of oscillatory electrical activity driven by persistent Na⁺ currents and the Na⁺/K⁺ pump occurs in leech ganglia exposed to Ca²⁺-channel blockers. Accepted: 15 May 1997     

Electrophysiological evidence suggests a defective Ca2+ control mechanism in a newParamecium mutant

Summary A new mutant ofParamecium tetraurelia, k-shyA, was characterized behaviorally and electrophysiologically. The mutant cell exhibited prolonged backward swimming episodes in response to depolarizing conditions. Electrophysiological comparison of k-shyA with wild type cells under voltage clamp revealed that the properties of three Ca²⁺-regulated currents were altered in the mutant. (i) The voltage-dependent Ca²⁺ current recovered from Ca²⁺-dependent inactivation two- to 10-fold more slowly than wild type. Ca²⁺ current amplitudes were also reduced in the mutant, but could be restored by EGTA injection. (ii) The decay of the Ca²⁺-dependent K⁺ tail current was slower in the mutant. (iii) The decay of the Ca²⁺-dependent Na⁺ tail current was also slower in the mutant. All other membrane properties studied, including the resting membrane potential and resistance and the voltage-sensitive K⁺ currents, were normal in k-shyA. Considered together, these observations are consistent with a defect in the ability of k-shyA to reduce the free intracellular Ca²⁺ concentration following stimulation. The possible targets of the genetic lesion and alternative explanations are discussed. The k-shy mutants may provide a useful tool for molecular and physiological analyses of the regulation of Ca²⁺ metabolism inParamecium.     

Sodium inward currents through calcium channels in mealworm muscle fibers

The contribution of Na⁺ ions to the nonsynaptic electrogenesis was studied in the larval muscle fibers of mealworm, Tenebrio molitor, using currentclamp and voltage-clamp techniques. Na-dependent graded responses were generated by depolarizing current stimuli in Ca²⁺-free solutions. These responses were insensitive to tetrodotoxin and were blocked by Co²⁺. Large inward-going currents were elicited by step depolarizations in Ca²⁺-free solutions under voltage-clamp conditions. The inward currents were totally eliminated by removal of Na⁺ from the bathing solution. These results indicate that the calcium channel of mealworm muscle is permeable to Na⁺.     

K+-Dependent Selectivity and External Ca2+ Block of Shab K+ Channels

Potassium channels allow the selective flux of K⁺ excluding the smaller, and more abundant in the extracellular solution, Na⁺ ions. Here we show that Shab is a typical K⁺ channel that excludes Na⁺ under bi-ionic, Na_o/K_i or Na_o/Rb_i, conditions. However, when internal K⁺ is replaced by Cs⁺ (Na_o/Cs_i), stable inward Na⁺ and outward Cs⁺ currents are observed. These currents show that Shab selectivity is not accounted for by protein structural elements alone, as implicit in the snug-fit model of selectivity. Additionally, here we report the block of Shab channels by external Ca²⁺ ions, and compare the effect that internal K⁺ replacement exerts on both Ca²⁺ and TEA block. Our observations indicate that Ca²⁺ blocks the channels at a site located near the external TEA binding site, and that this pore region changes conformation under conditions that allow Na⁺ permeation. In contrast, the latter ion conditions do not significantly affect the binding of quinidine to the pore central cavity. Based on our observations and the structural information derived from the NaK bacterial channel, we hypothesize that Ca²⁺ is probably coordinated by main chain carbonyls of the pore´s first K⁺-binding site.     

Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents

Dopamine (DA) released from the hypothalamus tonically inhibits pituitary lactotrophs. DA (at micromolar concentration) opens potassium channels, hyperpolarizing the lactotrophs and thus preventing the calcium influx that triggers prolactin hormone release. Surprisingly, at concentrations ∼1000 lower, DA can stimulate prolactin secretion. Here, we investigated whether an increase in a K⁺ current could mediate this stimulatory effect. We considered the fast K⁺ currents flowing through large-conductance BK channels and through A-type channels. We developed a minimal lactotroph model to investigate the effects of these two currents. Both I _BK and I _A could transform the electrical pattern of activity from spiking to bursting, but through distinct mechanisms. I _BK always increased the intracellular Ca²⁺ concentration, while I _A could either increase or decrease it. Thus, the stimulatory effects of DA could be mediated by a fast K⁺ conductance which converts tonically spiking cells to bursters. In addition, the study illustrates that a heterogeneous distribution of fast K⁺ conductances could cause heterogeneous lactotroph firing patterns. Action Editor: Christiane Linster     

Pacemaking mechanism of the afterdischarge of the ovulation hormone-producing caudo-dorsal cells in the gastropod mollusc Lymnaea stagnalis

The ovulation hormone-producing caudo-dorsal cells (CDC) of Lymnaea stagnalis have three states of excitability (active, inhibited, and resting), which are related to the egg-laying cycle. Active state CDC produce a firing pattern of prolonged spiking activity (1 spike/2 s), which in the animal occurs shortly before egg laying. In preparations it is evoked as an afterdischarge upon repetitive stimulation of CDC. The afterdischarge is not synaptically driven, but rests on a pacemaking mechanism. CDC are silent in the inhibited and resting states, which follow egg laying. In these states the membrane potential is mainly dependent on [K⁺]₀. In the active state the ratio of the K⁺, Na⁺, and Ca²⁺ permeabilities has changed considerably, probably resulting from an increased permeability to Na⁺ and Ca²⁺. The firing rate in the afterdischarge is dependent on the membrane potential, which is confirmed experimentally by varying [K⁺]₀.[Na⁺]₀ and [Ca²⁺]₀ directly influence the firing rate. Firing stops in Na⁺-free saline, but is enhanced by Ca²⁺-free or high-Mg²⁺ saline. TTX does not affect firing. Relatively high concentrations of Co²⁺ and La³⁺ (2 × 10^?3M) strongly inhibit CDC. Regular firing can be changed into bursting by various means, such as high K⁺ or addition of 1 mM Ba²⁺. Bursting normally occurs at the beginning of the afterdischarge. Postburst hyperpolarizations are reduced in Ca²⁺-free saline and by low Co²⁺ (10^?4-5 10^?4M). Active CDC are driven by a pacemaking mechanism constituted by a voltage-dependent Na⁺/Ca²⁺ channel and a Ca²⁺-dependent K⁺ channel, thus resembling that of bursting pacemakers. The pacemaking mechanism is inactive in the resting and inhibited state.     

Frequency switching in a two-compartmental model of the dopaminergic neuron

Mid-brain dopaminergic (DA) neurons display two functionally distinct modes of electrical activity: low- and high-frequency firing. The high-frequency firing is linked to important behavioral events in vivo. However, it cannot be elicited by standard manipulations in vitro. We had suggested a two-compartmental model of the DA cell that united data on firing frequencies under different experimental conditions. We now analyze dynamics of this model. The analysis was possible due to introduction of timescale separation among variables. We formulate the requirements for low and high frequencies. We found that the modulation of the SK current gating controls the frequency rise under applied depolarization. This provides a new mechanism that limits the frequency in the control conditions and allows high-frequency responses to depolarization if the SK current gating is downregulated. The mechanism is based on changing Ca^2 + balance and can also be achieved by direct modulation of the balance. Interestingly, such changes do not affect the high-frequency oscillations under NMDA. Therefore, altering Ca^2 + balance allows combining the high-frequency response to NMDA activation with the inability of other treatments to effectively elevate the frequency. We conclude that manipulations affecting Ca^2 + balance are most effective in controlling the frequency range. This modeling prediction gives a clue to the mechanism of the high-frequency firing in the DA neuron in vivo and in vitro.