Sodium Channels in Human Pain Disorders: Genetics and Pharmacogenomics.

Acute pain is adaptive, but chronic pain is a global challenge. Many chronic pain syndromes are peripheral in origin and reflect hyperactivity of peripheral pain-signaling neurons. Current treatments are ineffective or only partially effective and in some cases can be addictive, underscoring the need for better therapies. Molecular genetic studies have now linked multiple human pain disorders to voltage-gated sodium channels, including disorders characterized by insensitivity or reduced sensitivity to pain and others characterized by exaggerated pain in response to normally innocuous stimuli. Here, we review recent developments that have enhanced our understanding of pathophysiological mechanisms in human pain and advances in targeting sodium channels in peripheral neurons for the treatment of pain using novel and existing sodium channel blockers.

A Reinterpretation of the Relationship between Persistent and Resurgent Sodium Currents.

The resurgent sodium current (INaR) activates on membrane repolarization, such as during the downstroke of neuronal action potentials. Due to its unique activation properties, INaR is thought to drive high rates of repetitive neuronal firing. However, INaR is often studied in combination with the persistent or noninactivating portion of sodium currents (INaP). We used dynamic clamp to test how INaR and INaP individually affect repetitive firing in adult cerebellar Purkinje neurons from male and female mice. We learned INaR does not scale repetitive firing rates due to its rapid decay at subthreshold voltages and that subthreshold INaP is critical in regulating neuronal firing rate. Adjustments to the voltage-gated sodium conductance model used in these studies revealed INaP and INaR can be inversely scaled by adjusting occupancy in the slow-inactivated kinetic state. Together with additional dynamic clamp experiments, these data suggest the regulation of sodium channel slow inactivation can fine-tune INaP and Purkinje neuron repetitive firing rates.

Contributions of the Sodium Leak Channel NALCN to Pacemaking of Medial Ventral Tegmental Area and Substantia Nigra Dopaminergic Neurons.

We tested the role of the sodium leak channel, NALCN, in pacemaking of dopaminergic neuron (DAN) subpopulations from adult male and female mice. In situ hybridization revealed NALCN RNA in all DANs, with lower abundance in medial ventral tegmental area (VTA) relative to substantia nigra pars compacta (SNc). Despite lower relative abundance of NALCN, we found that acute pharmacological blockade of NALCN in medial VTA DANs slowed pacemaking by 49.08%. We also examined the electrophysiological properties of projection-defined VTA DAN subpopulations identified by retrograde labeling. Inhibition of NALCN reduced pacemaking in DANs projecting to medial nucleus accumbens (NAc) and others projecting to lateral NAc by 70.74% and 31.98%, respectively, suggesting that NALCN is a primary driver of pacemaking in VTA DANs. In SNc DANs, potentiating NALCN by lowering extracellular calcium concentration speeded pacemaking in wildtype but not NALCN conditional knockout mice, demonstrating functional presence of NALCN. In contrast to VTA DANs, however, pacemaking in SNc DANs was unaffected by inhibition of NALCN. Instead, we found that inhibition of NALCN increased the gain of frequency-current plots at firing frequencies slower than spontaneous firing. Similarly, inhibition of the hyperpolarization-activated cyclic nucleotide-gated (HCN) conductance increased gain but had little effect on pacemaking. Interestingly, simultaneous inhibition of NALCN and HCN resulted in significant reduction in pacemaker rate. Thus, we found NALCN makes substantial contributions to driving pacemaking in VTA DAN subpopulations. In SNc DANs, NALCN is not critical for pacemaking but inhibition of NALCN makes cells more sensitive to hyperpolarizing stimuli.SIGNIFICANCE STATEMENT Pacemaking in midbrain dopaminergic neurons (DAN) relies on multiple subthreshold conductances, including a sodium leak. Whether the sodium leak channel, NALCN, contributes to pacemaking in DANs located in the VTA and the SNc has not yet been determined. Using electrophysiology and pharmacology, we show that NALCN plays a prominent role in driving pacemaking in projection-defined VTA DAN subpopulations. By contrast, pacemaking in SNc neurons does not rely on NALCN. Instead, the presence of NALCN regulates the excitability of SNc DANs by reducing the gain of the neuron's response to inhibitory stimuli. Together, these findings will inform future efforts to obtain DAN subpopulation-specific treatments for use in neuropsychiatric disorders.

Activity of the Sodium Leak Channel Maintains the Excitability of Paraventricular Thalamus Glutamatergic Neurons to Resist Anesthetic Effects of Sevoflurane in Mice.

BACKGROUND: Stimulation of the paraventricular thalamus has been found to enhance anesthesia recovery; however, the underlying molecular mechanism by which general anesthetics modulate paraventricular thalamus is unclear. This study aimed to test the hypothesis that the sodium leak channel (NALCN) maintains neuronal activity in the paraventricular thalamus to resist anesthetic effects of sevoflurane in mice. METHODS: Chemogenetic and optogenetic manipulations, in vivo multiple-channel recordings, and electroencephalogram recordings were used to investigate the role of paraventricular thalamus neuronal activity in sevoflurane anesthesia. Virus-mediated knockdown and/or overexpression was applied to determine how NALCN influenced excitability of paraventricular thalamus glutamatergic neurons under sevoflurane. Viral tracers and local field potentials were used to explore the downstream pathway. RESULTS: Single neuronal spikes in the paraventricular thalamus were suppressed by sevoflurane anesthesia and recovered during emergence. Optogenetic activation of paraventricular thalamus glutamatergic neurons shortened the emergence period from sevoflurane anesthesia, while chemogenetic inhibition had the opposite effect. Knockdown of the NALCN in the paraventricular thalamus delayed the emergence from sevoflurane anesthesia (recovery time: from 24 ± 14 to 64 ± 19 s, P < 0.001; concentration for recovery of the righting reflex: from 1.13% ± 0.10% to 0.97% ± 0.13%, P < 0.01). As expected, the overexpression of the NALCN in the paraventricular thalamus produced the opposite effects. At the circuit level, knockdown of the NALCN in the paraventricular thalamus decreased the neuronal activity of the nucleus accumbens, as indicated by the local field potential and decreased single neuronal spikes in the nucleus accumbens. Additionally, the effects of NALCN knockdown in the paraventricular thalamus on sevoflurane actions were reversed by optical stimulation of the nucleus accumbens. CONCLUSIONS: Activity of the NALCN maintains the excitability of paraventricular thalamus glutamatergic neurons to resist the anesthetic effects of sevoflurane in mice.

Long-Term Inactivation of Sodium Channels as a Mechanism of Adaptation in CA1 Pyramidal Neurons.

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

The M-current works in tandem with the persistent sodium current to set the speed of locomotion.

The central pattern generator (CPG) for locomotion is a set of pacemaker neurons endowed with inherent bursting driven by the persistent sodium current (INaP). How they proceed to regulate the locomotor rhythm remained unknown. Here, in neonatal rodents, we identified a persistent potassium current critical in regulating pacemakers and locomotion speed. This current recapitulates features of the M-current (IM): a subthreshold noninactivating outward current blocked by 10,10-bis(4-pyridinylmethyl)-9(10H)-anthracenone dihydrochloride (XE991) and enhanced by N-(2-chloro-5-pyrimidinyl)-3,4-difluorobenzamide (ICA73). Immunostaining and mutant mice highlight an important role of Kv7.2-containing channels in mediating IM. Pharmacological modulation of IM regulates the emergence and the frequency regime of both pacemaker and CPG activities and controls the speed of locomotion. Computational models captured these results and showed how an interplay between IM and INaP endows the locomotor CPG with rhythmogenic properties. Overall, this study provides fundamental insights into how IM and INaP work in tandem to set the speed of locomotion.

Chronic exercise increases excitability of lamina X neurons through enhancement of persistent inward currents and dendritic development in mice.

Chronic exercise has been shown to enhance excitability of spinal interneurons in rodents. However, the mechanisms underlying this enhancement remain unclear. In this study we investigated adaptability of lamina X neurons with 3-week treadmill exercise in mice of P21-P24. Whole-cell patch-clamp recording was performed on the interneurons from slices of T12-L4. The experimental results included the following. (1) Treadmill exercise reduced rheobase by 7.4 ± 2.2 pA (control: 11.3 ± 6.1 pA, n = 12; exercise: 3.8 ± 4.6 pA, n = 13; P = 0.002) and hyperpolarized voltage threshold by 7.1 ± 1.5 mV (control: -36.6 ± 4.6 mV, exercise: -43.7 ± 2.7 mV; P = 0.001). (2) Exercise enhanced persistent inward currents (PICs) with increase of amplitude (control: 140.6 ± 56.3 pA, n = 25; exercise: 225.9 ± 62.5 pA, n = 17; P = 0.001) and hyperpolarization of onset voltage (control: -50.3 ± 3.6 mV, exercise: -56.5 ± 5.5 mV; P = 0.001). (3) PICs consisted of dihydropyridine-sensitive calcium (Ca-PIC) and tetrodotoxin-sensitive sodium (Na-PIC) components. Exercise increased amplitude of both components but hyperpolarized onset voltage of Na-PIC only. (4) Exercise reduced derecruitment current of repetitive firing evoked by a current bi-ramp and prolonged firing in the falling phase of the bi-ramp. The derecruitment reduction was eliminated by bath application of 3 µM riluzole or 25 µM nimodipine, suggesting that both Na-PIC and Ca-PIC contributed to the exercise-prolonged hysteresis of firing. (5) Exercise facilitated dendritic development with significant increase in dendritic length by 285.1 ± 113 µm (control: 457.8 ± 171.8 µm, n = 12; exercise: 742.9 ± 357 µm, n = 14; P = 0.019). We concluded that 3-week treadmill exercise increased excitability of lamina X interneurons through enhancement of PICs and increase of dendritic length. This study provided insight into cellular and channel mechanisms underlying adaptation of the spinal motor system in exercise. KEY POINTS: Chronic exercise alters adaptability of the spinal motor system in rodents; multiple mechanisms are responsible for the adaptation, including regulation of neuronal excitability and change in dendritic morphology. Spinal interneurons in lamina X are a cluster of heterogeneous neurons playing multifunctional roles in the spinal cord; chronic exercise in juvenile mice increased excitability of these interneurons and facilitated dendritic development. Lamina X neurons expressed persistent inward currents (PICs) with calcium (Ca-PIC) and sodium (Na-PIC) components; the exercise-increased excitability of lamina X neurons was mediated by enhancing the Ca-PIC and Na-PIC components and increasing dendritic length. This study unveiled novel morphological and ionic mechanisms underlying adaptation of lamina X neurons in rodents during chronic exercise.

Changes of the biophysical properties of voltage-gated Na+ currents during maturation of the sodium-taste cells in rat fungiform papillae.

Taste cells are a heterogeneous population of sensory receptors that undergo continuous turnover. Different chemo-sensitive cell lines rely on action potentials to release the neurotransmitter onto nerve endings. The electrical excitability is due to the presence of a tetrodotoxin-sensitive, voltage-gated sodium current (INa ) similar to that found in neurons. Since the biophysical properties of neuronal INa change during development, we wondered whether the same also occurred in taste cells. Here, we used the patch-clamp recording technique to study INa in salt-sensing cells (sodium cells) of rat fungiform papillae. We identified these cells by exploiting the known blocking effect of amiloride on ENaC, the sodium (salt) receptor. Based on the amplitude of INa , which is known to increase during development, we subdivided sodium cells into two groups: cells with small sodium current (SSC cells; INa  < 1 nA) and cells with large sodium current (LSC cells; INa  > 1 nA). We found that: the voltage dependence of activation and inactivation significantly differed between these subsets; a slowly inactivating sodium current was more prominent in LSC cells; membrane capacitance in SSC cells was larger than in LSC cells. mRNA expression analysis of the α-subunits of voltage-gated sodium channels in fungiform taste buds supported the functional data. Lucifer Yellow labelling of recorded cells revealed that our electrophysiological criterion for distinguishing two broad groups of taste cells was in good agreement with morphological observations for cell maturity. Thus, all these findings are consistent with developmental changes in the voltage-dependent properties of sodium-taste cells. KEY POINTS: Taste cells are sensory receptors that undergo continuous turnover while they detect food chemicals and communicate with afferent nerve fibres. The voltage-gated sodium current (INa ) is a key ion current for generating action potentials in fully differentiated and chemo-sensitive taste cells, which use electrical signalling to release neurotransmitters. Here we show that, during the maturation of rat taste cells involved in salt detection (sodium cells), the biophysical properties of INa , such as voltage dependence of activation and inactivation, change significantly. Our results help reveal how taste cells gain electrical excitability during turnover, a property critical to their operation as chemical detectors that relay sensory information to nerve fibres.

A Minimal Biophysical Model of Neocortical Pyramidal Cells: Implications for Frontal Cortex Microcircuitry and Field Potential Generation.

Ca2+ spikes initiated in the distal trunk of layer 5 pyramidal cells (PCs) underlie nonlinear dynamic changes in the gain of cellular response, critical for top-down control of cortical processing. Detailed models with many compartments and dozens of ionic channels can account for this Ca2+ spike-dependent gain and associated critical frequency. However, current models do not account for all known Ca2+-dependent features. Previous attempts to include more features have required increasing complexity, limiting their interpretability and utility for studying large population dynamics. We overcome these limitations in a minimal two-compartment biophysical model. In our model, a basal-dendrites/somatic compartment included fast-inactivating Na+ and delayed-rectifier K+ conductances, while an apical-dendrites/trunk compartment included persistent Na+, hyperpolarization-activated cation (I h ), slow-inactivating K+, muscarinic K+, and Ca2+ L-type. The model replicated the Ca2+ spike morphology and its critical frequency plus three other defining features of layer 5 PC synaptic integration: linear frequency-current relationships, back-propagation-activated Ca2+ spike firing, and a shift in the critical frequency by blocking I h Simulating 1000 synchronized layer 5 PCs, we reproduced the current source density patterns evoked by Ca2+ spikes and describe resulting medial-frontal EEG on a male macaque monkey. We reproduced changes in the current source density when I h was blocked. Thus, a two-compartment model with five crucial ionic currents in the apical dendrites reproduces all features of these neurons. We discuss the utility of this minimal model to study the microcircuitry of agranular areas of the frontal lobe involved in cognitive control and responsible for event-related potentials, such as the error-related negativity.SIGNIFICANCE STATEMENT A minimal model of layer 5 pyramidal cells replicates all known features crucial for distal synaptic integration in these neurons. By redistributing voltage-gated and returning transmembrane currents in the model, we establish a theoretical framework for the investigation of cortical microcircuit contribution to intracranial local field potentials and EEG. This tractable model will enable biophysical evaluation of multiscale electrophysiological signatures and computational investigation of cortical processing.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells.

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na+ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na+ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Temperature-robust activity patterns arise from coordinated axonal Sodium channel properties.

Action potentials are a key component of neuronal communication and their precise timing is critical for processes like learning, memory, and complex behaviors. Action potentials propagate through long axons to their postsynaptic partners, which requires axons not only to faithfully transfer action potentials to distant synaptic regions but also to maintain their timing. This is particularly challenging when axons differ in their morphological and physiological properties, as timing is predicted to diverge between these axons when extrinsic conditions change. It is unknown if and how diverse axons maintain timing during temperature changes that animals and humans encounter. We studied whether ambient temperature changes cause different timing in the periphery of neurons that centrally produce temperature-robust activity. In an approach combining modeling, imaging, and electrophysiology, we explored mechanisms that support timing by exposing the axons of three different neuron types from the same crustacean (Cancer borealis) motor circuit and involved in the same functional task to a range of physiological temperatures. We show that despite substantial differences between axons, the effects of temperature on action potential propagation were moderate and supported temperature-robust timing over long-distances. Our modeling demonstrates that to maintain timing, the underlying channel properties of these axons do not need to be temperature-insensitive or highly restricted, but coordinating the temperature sensitivities of the Sodium activation gate time constant and the maximum Sodium conductance is required. Thus, even highly temperature-sensitive ion channel properties can support temperature-robust timing between distinct neuronal types and across long distances.

Magnolol attenuates inflammatory pain by inhibiting sodium currents in mouse dorsal root ganglion neurons.

Voltage-gated sodium channels are currently recognized as one of the targets of analgesics. Magnolol (Mag), an active component isolated from Magnolia officinalis, has been reported to exhibit analgesic effects. The objective of this study was to investigate whether the analgesic effect of Mag was associated with blocking Na+ channels. Inflammatory pain was induced by the injection of carrageenan into the hind paw of mice. Mag was administered orally. Mechanical hyperanalgesia was evaluated by using von Frey filaments. Na+ currents and neuronal excitability in acutely isolated mouse dorsal root ganglion (DRG) neurons were recorded with the whole-cell patch clamp technique. Results showed that Mag (10 ~ 40 mg/kg) dose-dependently inhibited the paw edema and reduced mechanical pain in the inflammatory animal model. Injection of carrageenan significantly increased the amplitudes of TTX-sensitive and TTX-resistant Na+ currents. Compared with the carrageenan group, Mag inhibited the upregulation of two types of Na+ currents induced by carrageenan in a dose-dependent manner. Mag 40 mg/kg shifted the inactivation curves of two types of Na+ currents to hyperpolarization and returned to normal animal level without changing their activation curves. Mag 40 mg/kg significantly reduced the percentage of cells firing multiple spikes and inhibited the neuronal hyperexcitability induced by carrageenan. Our data suggest that the analgesic effect of Mag may be associated with a decreased neuronal excitability by blocking Na+ current.

Coincidence Detection within the Excitable Rat Olfactory Bulb Granule Cell Spines.

In the mammalian olfactory bulb, the inhibitory axonless granule cells (GCs) feature reciprocal synapses that interconnect them with the principal neurons of the bulb, mitral, and tufted cells. These synapses are located within large excitable spines that can generate local action potentials (APs) upon synaptic input ("spine spike"). Moreover, GCs can fire global APs that propagate throughout the dendrite. Strikingly, local postsynaptic Ca2+ entry summates mostly linearly with Ca2+ entry due to coincident global APs generated by glomerular stimulation, although some underlying conductances should be inactivated. We investigated this phenomenon by constructing a compartmental GC model to simulate the pairing of local and global signals as a function of their temporal separation Δt. These simulations yield strongly sublinear summation of spine Ca2+ entry for the case of perfect coincidence Δt = 0 ms. Summation efficiency (SE) sharply rises for both positive and negative Δt. The SE reduction for coincident signals depends on the presence of voltage-gated Na+ channels in the spine head, while NMDARs are not essential. We experimentally validated the simulated SE in slices of juvenile rat brain (both sexes) by pairing two-photon uncaging of glutamate at spines and APs evoked by somatic current injection at various intervals Δt while imaging spine Ca2+ signals. Finally, the latencies of synaptically evoked global APs and EPSPs were found to correspond to Δt ≈ 10 ms, explaining the observed approximately linear summation of synaptic local and global signals. Our results provide additional evidence for the existence of the GC spine spike.SIGNIFICANCE STATEMENT Here we investigate the interaction of local synaptic inputs and global activation of a neuron by a backpropagating action potential within a dendritic spine with respect to local Ca2+ signaling. Our system of interest, the reciprocal spine of the olfactory bulb granule cell, is known to feature a special processing mode, namely, a synaptically triggered action potential that is restricted to the spine head. Therefore, coincidence detection of local and global signals follows different rules than in more conventional synapses. We unravel these rules using both simulations and experiments and find that signals coincident within ≈±7 ms around 0 ms result in sublinear summation of Ca2+ entry because of synaptic activation of voltage-gated Na+ channels within the spine.

Modeling of lamprey reticulospinal neurons: multiple distinct parameter sets yield realistic simulations.

For the lamprey and other vertebrates, reticulospinal (RS) neurons project descending axons to the spinal cord and activate motor networks to initiate locomotion and other behaviors. In the present study, a biophysically detailed computer model of lamprey RS neurons was constructed consisting of three compartments: dendritic, somatic, and axon initial segment (AIS). All compartments included passive channels. In addition, the soma and AIS had fast potassium and sodium channels. The soma included three additional voltage-gated ion channels (slow sodium and high- and low-voltage-activated calcium) and calcium-activated potassium channels. An initial manually adjusted default parameter set, which was based, in part, on modified parameters from models of lamprey spinal neurons, generated simulations of single action potentials and repetitive firing that scored favorably (0.658; maximum = 0.964) compared with experimentally derived properties of lamprey RS neurons. Subsequently, a dual-annealing search paradigm identified 4,302 viable parameter sets at local maxima within parameter space that yielded higher scores than the default parameter set, including many with much higher scores of approximately 0.85-0.87 (i.e., ~30% improvement). In addition, 5- and 2-conductance grid searches identified a relatively large number of viable parameters sets for which significant correlations were present between maximum conductances for pairs of ion channels. The present results indicated that multiple model parameter sets ("solutions") generated action potentials and repetitive firing that mimicked many of the properties of lamprey RS neurons. To our knowledge, this is the first study to systematically explore parameter space for a biophysically detailed model of lamprey RS neurons.NEW & NOTEWORTHY A computer model of lamprey reticulospinal neurons with a default parameter set produced simulations of action potentials and repetitive firing that scored favorably compared with the properties of these neurons. A dual-annealing search algorithm explored ~50 million parameter sets and identified 4,302 distinct viable parameter sets within parameter space that yielded higher/much higher scores than the default parameter set. In addition, 5- and 2-conductance grid searches identified significant correlations between maximum conductances for pairs of ion channels.

Computational analysis of a 9D model for a small DRG neuron.

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Nav1.7 and a Nav1.8 sodium channel, a leak channel, a delayed rectifier potassium, and an A-type transient potassium channel. The dynamics of this model strongly depend on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Nav1.8 channel maximal conductance ([Formula: see text]). Numerical bifurcation analysis shows that depending on [Formula: see text] and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. As the external current is decreased, we find that MMOs appear after a cyclic limit point. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. For decreasing external current, the number of small amplitude peaks is increasing and the distance between the large amplitude action potentials is growing, finally tending to infinity and thereby leading to a stable steady state. A closer inspection reveals more complex concatenated MMOs in between these periodic MMO branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations which seem to be chaotic. The dynamical patterns found here-as consequences of bifurcation points regulated by different parameters-have potential translational significance as repetitive firing of action potentials imply pain of some form and intensity; manipulating these patterns by regulating the different parameters could aid in investigating pain dynamics.

Volatile Anesthetics Activate a Leak Sodium Conductance in Retrotrapezoid Nucleus Neurons to Maintain Breathing during Anesthesia in Mice.

BACKGROUND: Volatile anesthetics moderately depress respiratory function at clinically relevant concentrations. Phox2b-expressing chemosensitive neurons in the retrotrapezoid nucleus, a respiratory control center, are activated by isoflurane, but the underlying mechanisms remain unclear. The hypothesis of this study was that the sodium leak channel contributes to the volatile anesthetics-induced modulation of retrotrapezoid nucleus neurons and to respiratory output. METHODS: The contribution of sodium leak channels to isoflurane-, sevoflurane-, and propofol-evoked activity of Phox2b-expressing retrotrapezoid nucleus neurons and respiratory output were evaluated in wild-type and genetically modified mice lacking sodium leak channels (both sexes). Patch-clamp recordings were performed in acute brain slices. Whole-body plethysmography was used to measure the respiratory activity. RESULTS: Isoflurane at 0.42 to 0.50 mM (~1.5 minimum alveolar concentration) increased the sodium leak channel-mediated holding currents and conductance from -75.0 ± 12.9 to -130.1 ± 34.9 pA (mean ± SD, P = 0.002, n = 6) and 1.8 ± 0.5 to 3.6 ± 1.0 nS (P = 0.001, n = 6), respectively. At these concentrations, isoflurane increased activity of Phox2b-expressing retrotrapezoid nucleus neurons from 1.1 ± 0.2 to 2.8 ± 0.2 Hz (P < 0.001, n = 5), which was eliminated by bath application of gadolinium or genetic silencing of sodium leak channel. Genetic silencing of sodium leak channel in the retrotrapezoid nucleus resulted in a diminished ventilatory response to carbon dioxide in mice under control conditions and during isoflurane anesthesia. Sevoflurane produced an effect comparable to that of isoflurane, whereas propofol did not activate sodium leak channel-mediated holding conductance. CONCLUSIONS: Isoflurane and sevoflurane increase neuronal excitability of chemosensitive retrotrapezoid nucleus neurons partly by enhancing sodium leak channel conductance. Sodium leak channel expression in the retrotrapezoid nucleus is required for the ventilatory response to carbon dioxide during anesthesia by isoflurane and sevoflurane, thus identifying sodium leak channel as a requisite determinant of respiratory output during anesthesia of volatile anesthetics.

Specialization for rapid excitation in fast squid tentacle muscle involves action potentials absent in slow arm muscle.

An important aspect of the performance of many fast muscle fiber types is rapid excitation. Previous research on the cross-striated muscle fibers responsible for the rapid tentacle strike in squid has revealed the specializations responsible for high shortening velocity, but little is known about excitation of these fibers. Conventional whole-cell patch recordings were made from tentacle fibers and the slower obliquely striated muscle fibers of the arms. The fast-contracting tentacle fibers show an approximately 10-fold greater sodium conductance than that of the arm fibers and, unlike the arm fibers, the tentacle muscle fibers produce action potentials. In situ hybridization using an antisense probe to the voltage-dependent sodium channel present in this squid genus shows prominent expression of sodium channel mRNA in tentacle fibers but undetectable expression in arm fibers. Production of action potentials by tentacle muscle fibers and their absence in arm fibers is likely responsible for the previously reported greater twitch-tetanus ratio in the tentacle versus the arm fibers. During the rapid tentacle strike, a few closely spaced action potentials would result in maximal activation of transverse tentacle muscle. Activation of the slower transverse muscle fibers in the arms would require summation of excitatory postsynaptic potentials over a longer time, allowing the precise modulation of force required for supporting slower movements of the arms.

Soma-axon coupling configurations that enhance neuronal coincidence detection.

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, IKLT in the axon enhances coincidence detection more effectively than IKLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons.

Resurgent Na+ Current Offers Noise Modulation in Bursting Neurons.

Neurons utilize bursts of action potentials as an efficient and reliable way to encode information. It is likely that the intrinsic membrane properties of neurons involved in burst generation may also participate in preserving its temporal features. Here we examined the contribution of the persistent and resurgent components of voltage-gated Na+ currents in modulating the burst discharge in sensory neurons. Using mathematical modeling, theory and dynamic-clamp electrophysiology, we show that, distinct from the persistent Na+ component which is important for membrane resonance and burst generation, the resurgent Na+ can help stabilize burst timing features including the duration and intervals. Moreover, such a physiological role for the resurgent Na+ offered noise tolerance and preserved the regularity of burst patterns. Model analysis further predicted a negative feedback loop between the persistent and resurgent gating variables which mediate such gain in burst stability. These results highlight a novel role for the voltage-gated resurgent Na+ component in moderating the entropy of burst-encoded neural information.

Properties of cardiac conduction in a cell-based computational model.

The conduction of electrical signals through cardiac tissue is essential for maintaining the function of the heart, and conduction abnormalities are known to potentially lead to life-threatening arrhythmias. The properties of cardiac conduction have therefore been the topic of intense study for decades, but a number of questions related to the mechanisms of conduction still remain unresolved. In this paper, we demonstrate how the so-called EMI model may be used to study some of these open questions. In the EMI model, the extracellular space, the cell membrane, the intracellular space and the cell connections are all represented as separate parts of the computational domain, and the model therefore allows for study of local properties that are hard to represent in the classical homogenized bidomain or monodomain models commonly used to study cardiac conduction. We conclude that a non-uniform sodium channel distribution increases the conduction velocity and decreases the time delays over gap junctions of reduced coupling in the EMI model simulations. We also present a theoretical optimal cell length with respect to conduction velocity and consider the possibility of ephaptic coupling (i.e. cell-to-cell coupling through the extracellular potential) acting as an alternative or supporting mechanism to gap junction coupling. We conclude that for a non-uniform distribution of sodium channels and a sufficiently small intercellular distance, ephaptic coupling can influence the dynamics of the sodium channels and potentially provide cell-to-cell coupling when the gap junction connection is absent.