Biophysical properties and slow voltage-dependent inactivation of a sustained sodium current in entorhinal cortex layer-II principal neurons: a whole-cell and single-channel study

On the role of subthreshold currents in the Huber-Braun cold receptor model

We study the role of the strength of subthreshold currents in a four-dimensional Hodgkin-Huxley-type model of mammalian cold receptors. Since a total diminution of subthreshold activity corresponds to a decomposition of the model into a slow, subthreshold, and a fast, spiking subsystem, we first elucidate their respective dynamics separately and draw conclusions about their role for the generation of different spiking patterns. These results motivate a numerical bifurcation analysis of the effect of varying the strength of subthreshold currents, which is done by varying a suitable control parameter. We work out the key mechanisms which can be attributed to subthreshold activity and furthermore elucidate the dynamical backbone of different activity patterns generated by this model.

Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells

Significant inroads have been made to understand cerebellar cortical processing but neural coding at the output stage of the cerebellum in the deep cerebellar nuclei (DCN) remains poorly understood. The DCN are unlikely to just present a relay nucleus because Purkinje cell inhibition has to be turned into an excitatory output signal, and DCN neurons exhibit complex intrinsic properties. In particular, DCN neurons exhibit a range of rebound spiking properties following hyperpolarizing current injection, raising the question how this could contribute to signal processing in behaving animals. Computer modeling presents an ideal tool to investigate how intrinsic voltage-gated conductances in DCN neurons could generate the heterogeneous firing behavior observed, and what input conditions could result in rebound responses. To enable such an investigation we built a compartmental DCN neuron model with a full dendritic morphology and appropriate active conductances. We generated a good match of our simulations with DCN current clamp data we recorded in acute slices, including the heterogeneity in the rebound responses. We then examined how inhibitory and excitatory synaptic input interacted with these intrinsic conductances to control DCN firing. We found that the output spiking of the model reflected the ongoing balance of excitatory and inhibitory input rates and that changing the level of inhibition performed an additive operation. Rebound firing following strong Purkinje cell input bursts was also possible, but only if the chloride reversal potential was more negative than −70 mV to allow de-inactivation of rebound currents. Fast rebound bursts due to T-type calcium current and slow rebounds due to persistent sodium current could be differentially regulated by synaptic input, and the pattern of these rebounds was further influenced by HCN current. Our findings suggest that active properties of DCN neurons could play a crucial role for signal processing in the cerebellum.

Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing

One of the two primary classes of models of grid cell spatial firing uses interference between oscillators at dynamically modulated frequencies. Generally, these models are presented in terms of idealized oscillators (modeled as sinusoids), which differ from biological oscillators in multiple important ways. Here we show that two more realistic, noisy neural models (Izhikevich's simple model and a biophysical model of an entorhinal cortex stellate cell) can be successfully used as oscillators in a model of this type. When additive noise is included in the models such that uncoupled or sparsely coupled cells show realistic interspike interval variance, both synaptic and gap-junction coupling can synchronize networks of cells to produce comparatively less variable network-level oscillations. We show that the frequency of these oscillatory networks can be controlled sufficiently well to produce stable grid cell spatial firing on the order of at least 2-5 min, despite the high noise level. Our results suggest that the basic principles of oscillatory interference models work with more realistic models of noisy neurons. Nevertheless, a number of simplifications were still made and future work should examine increasingly realistic models.

Voltage and Spike Timing Interact in STDP - A Unified Model

A phenomenological model of synaptic plasticity is able to account for a large body of experimental data on spike-timing-dependent plasticity (STDP). The basic ingredient of the model is the correlation of presynaptic spike arrival with postsynaptic voltage. The local membrane voltage is used twice: a first term accounts for the instantaneous voltage and the second one for a low-pass filtered voltage trace. Spike-timing effects emerge as a special case. We hypothesize that the voltage dependence can explain differential effects of STDP in dendrites, since the amplitude and time course of backpropagating action potentials or dendritic spikes influences the plasticity results in the model. The dendritic effects are simulated by variable choices of voltage time course at the site of the synapse, i.e., without an explicit model of the spatial structure of the neuron.

Activation of reverse Na+-Ca2+ exchange by the Na+ current augments the cardiac Ca2+ transient: evidence from NCX knockout mice

The hypothesis that Na(+) influx during the action potential (AP) activates reverse Na(+)-Ca(2+) exchange (NCX) and subsequent entry of trigger Ca(2+) is controversial. We tested this hypothesis by monitoring intracellular Ca(2+) before and after selective inactivation of I(Na) prior to a simulated action potential in patch-clamped ventricular myocytes isolated from adult wild-type (WT) and NCX knockout (KO) mice. First, we inactivated I(Na) using a ramp prepulse to 45 mV. In WT cells, inactivation of I(Na) decreased the Ca(2+) transient amplitude by 51.1 +/- 4.6% (P < 0.001, n = 14) and reduced its maximum release flux by 53.0 +/- 4.6% (P < 0.001, n = 14). There was no effect on diastolic Ca(2+). In striking contrast, Ca(2+) transients in NCX KO cardiomyocytes were unaffected by the presence or absence of I(Na) (n = 8). We obtained similar results when measuring trigger Ca(2+) influx in myocytes with depleted sarcoplasmic reticulum. In WT cells, inactivation of I(Na) decreased trigger Ca(2+) influx by 37.8 +/- 6% and maximum rate of flux by 30.6 +/- 7.7% at 2.5 mm external Ca(2+) (P < 0.001 and P < 0.05, n = 9). This effect was again absent in the KO cells (n = 8). Second, exposure to 10 mum tetrodotoxin to block I(Na) also reduced the Ca(2+) transients in WT myocytes but not in NCX KO myocytes. We conclude that I(Na) and reverse NCX modulate Ca(2+) release in murine WT cardiomyocytes by augmenting the pool of Ca(2+) that triggers ryanodine receptors. This is an important mechanism for regulation of Ca(2+) release and contractility in murine heart.

Synaptic integration of rhythmogenic neurons in the locomotor circuitry: the case of Hb9 interneurons

Innovative molecular and genetic techniques have recently led to the identification of genetically defined populations of ipsilaterally projecting excitatory interneurons with probable functions in the rhythm-generating kernel of the central pattern generators (CPGs). The role of interneuronal populations in specific motor function is determined by their synaptic inputs, intrinsic properties, and target neurons. In this review we examine whether Hb9-expressing interneurons (Hb9 INs) fulfill a set of criteria that are the hallmarks of rhythm generators in the locomotor circuitry. Induced locomotor-like activity in this distinct population of ventral interneurons is in phase with bursts of motor activity, raising the possibility that they are part of the locomotor generator. To increase our understanding of the integrative function of Hb9 INs in the locomotor CPG, we investigated the cellular mechanisms underlying their rhythmic activity and examined the properties of synaptic inputs from low-threshold afferents and possible synaptic contacts with segmental motoneurons. Our findings suggest that the rhythmogenic Hb9 INs are integral components of the sensorimotor circuitry that regulate locomotor-like activity in the spinal cord.

Cholinergic modulation of the resonance properties of stellate cells in layer II of medial entorhinal cortex

In vitro whole cell patch-clamp recordings of stellate cells in layer II of medial entorhinal cortex show a subthreshold membrane potential resonance in response to a sinusoidal current injection of varying frequency. Physiological recordings from awake behaving animals show that neurons in layer II medial entorhinal cortex, termed "grid cells," fire in a spatially selective manner such that each cell's multiple firing fields form a hexagonal grid. Both the spatial periodicity of the grid fields and the resonance frequency change systematically in neurons along the dorsal to ventral axis of medial entorhinal cortex. Previous work has also shown that grid field spacing and acetylcholine levels change as a function of the novelty to a particular environment. Using in vitro whole cell patch-clamp recordings, our study shows that both resonance frequency and resonance strength vary as a function of cholinergic modulation. Furthermore, our data suggest that these changes in resonance properties are mediated through modulation of h-current and m-current.

Persistent Nav1.6 current at axon initial segments tunes spike timing of cerebellar granule cells

Cerebellar granule (CG) cells generate high-frequency action potentials that have been proposed to depend on the unique properties of their voltage-gated ion channels. To address the in vivo function of Nav1.6 channels in developing and mature CG cells, we combined the study of the developmental expression of Nav subunits with recording of acute cerebellar slices from young and adult granule-specific Scn8a KO mice. Nav1.2 accumulated rapidly at early-formed axon initial segments (AISs). In contrast, Nav1.6 was absent at early postnatal stages but accumulated at AISs of CG cells from P21 to P40. By P40-P65, both Nav1.6 and Nav1.2 co-localized at CG cell AISs. By comparing Na(+) currents in mature CG cells (P66-P74) from wild-type and CG-specific Scn8a KO mice, we found that transient and resurgent Na(+) currents were not modified in the absence of Nav1.6 whereas persistent Na(+) current was strongly reduced. Action potentials in conditional Scn8a KO CG cells showed no alteration in threshold and overshoot, but had a faster repolarization phase and larger post-spike hyperpolarization. In addition, although Scn8a KO CG cells kept their ability to fire action potentials at very high frequency, they displayed increased interspike-interval variability and firing irregularity in response to sustained depolarization. We conclude that Nav1.6 channels at axon initial segments contribute to persistent Na(+) current and ensure a high degree of temporal precision in repetitive firing of CG cells.

Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration

Synchronization of globus pallidus (GP) neurons and cortically entrained oscillations between GP and other basal ganglia nuclei are key features of the pathophysiology of Parkinson's disease. Phase response curves (PRCs), which tabulate the effects of phasic inputs within a neuron's spike cycle on output spike timing, are efficient tools for predicting the emergence of synchronization in neuronal networks and entrainment to periodic input. In this study we apply physiologically realistic synaptic conductance inputs to a full morphological GP neuron model to determine the phase response properties of the soma and different regions of the dendritic tree. We find that perisomatic excitatory inputs delivered throughout the interspike interval advance the phase of the spontaneous spike cycle yielding a type I PRC. In contrast, we demonstrate that distal dendritic excitatory inputs can either delay or advance the next spike depending on whether they occur early or late in the spike cycle. We find this latter pattern of responses, summarized by a biphasic (type II) PRC, was a consequence of dendritic activation of the small conductance calcium-activated potassium current, SK. We also evaluate the spike-frequency dependence of somatic and dendritic PRC shapes, and we demonstrate the robustness of our results to variations of conductance densities, distributions, and kinetic parameters. We conclude that the distal dendrite of GP neurons embodies a distinct dynamical subsystem that could promote synchronization of pallidal networks to excitatory inputs. These results highlight the need to consider different effects of perisomatic and dendritic inputs in the control of network behavior.

Dynamics of populations and networks of neurons with voltage-activated and calcium-activated currents

The profile of transmembrane-channel expression in neurons is class dependent and a crucial determinant of neuronal dynamics. Here, a generalization of the experimentally verified exponential integrate-and-fire model is introduced that includes biophysical, nonlinear gated conductance-based currents, and a spike shape. A Fokker-Planck-based method is developed that allows for the rapid numerical calculation of steady-state and linear-response properties for recurrent networks of neurons with gating-variable dynamics slower than that of the voltage. This limit includes many cases of biological interest, particularly under in vivo conditions of high synaptic conductance. The utility of the method is illustrated by applying it to two biophysically detailed models adapted from the literature: an entorhinal layer-II cortical neuron and a neuron featuring both calcium-activated and voltage-activated spike-frequency-adaptation currents. The framework generalizes to networks comprised of different neuronal classes and so will allow for the modeling of emergent states in neural tissue at significantly increased levels of biological detail.

Analytical studies of rapidly inactivating and noninactivating sodium currents in differentiated NG108-15 neuronal cells

The rapidly inactivating (I(Naf)) and noninactivating Na(+) currents (I(Na)(()(NI)())) were characterized in NG108-15 neuronal cells differentiated with dibutyryl cyclic AMP in this study. Standard activation and inactivation protocols were used to evaluate the steady-state and kinetic properties of the I(Naf) present in these cells. The voltage protocols with a slowly depolarizing ramp were implemented to examine the properties of I(Na)(()(NI)()). Based on experimental data and computer simulations, a window component of the rapidly inactivating sodium current (I(Naf)(()(W)())) was also generated in response to the slowly depolarizing ramp. The I(Naf)(()(W)()) was subtracted from I(Na)(()(NI)()) to yield the persistent Na(+) current (I(Na)(()(P)())). Our results demonstrate the presence of I(Na)(()(P)()) in these cells. In addition to modifying the steady-state inactivation of I(Naf), ranolazine or riluzloe could be effective in blocking I(Naf)(()(W)()) and I(Na)(()(P)()). The ability of ranolazine and riluzole to suppress I(Na)(()(P)()) was greater than their ability to inhibit I(Naf)(()(W)()). In current-clamp recordings, current-induced voltage oscillations were applied to elicit action potentials (APs) through a gradual transition between spontaneous depolarization and upstroke. Ranolazine or riluzole at a concentration of 3 microM then effectively suppressed the AP firing generated by oscillatory changes in membrane current. The data suggest that a small rise in I(Na)(()(NI)()) facilitates neuronal hyper-excitability due the decreased threshold of AP initiation. The underlying mechanism of the inhibitory actions of ranolazine or riluzole on membrane potential in neurons or neuroendocrine cells in vivo may thus be associated with their blocking of I(Na)(()(NI)()).

Control of presynaptic function by a persistent Na(+) current

Little is known about ion channels that regulate the graded, subthreshold properties of nerve terminals. Using the calyx of Held, we demonstrate here a large presynaptic persistent Na(+) current with unusually hyperpolarized activation voltage. This feature allowed the current to determine both the resting potential and resting conductance of the nerve terminal. Calyces express presynaptic glycine receptors whose activation depolarizes the synapse. We found that activation of the persistent Na(+) current was an essential component in the response to glycine. This Na(+) current originated at or very close to the terminal and was sustained even after trains of large spike-like depolarizations. Because Na(+) channels also underlie the presynaptic action potential, we conclude that their action both triggers and modulates exocytosis through control of presynaptic membrane voltage.

The cost of linearization

Linear additivity of synaptic input is a pervasive assumption in computational neuroscience, and previously Bernander et al. (Journal of Neurophysiology 72:2743-2753, 1994) point out that the sublinear additivity of a passive neuronal model can be linearized with voltage-dependent currents. Here we re-examine this perspective in light of more recent findings and issues. Based on in vivo intracellular recordings, three voltage-dependent conductances seem to be of interest for pyramidal cells of the forebrain: two of them are amplifying, I ( NaP ) and I ( h ); and one of them is attenuating, I ( A ). Based on particular I-V characteristics reported in the literature, each of these three voltage-dependent currents linearizes a particular range of synaptic excitation. Computational simulations use a steady-state, one-compartment model. They establish maximal linear ranges, where supralinear effects-due to adding too much of any one conductance-limit these ranges. Specific, carefully selected pairwise combinations of these currents can linearize larger ranges than either current alone. In terms of parameters, the steady-state I-V characteristics of each current are critical. On the other hand, the relationships between the results here and resting conductance to ground, synaptic conductance, and number of active synapses are simple and easily scaled; thus in regard to these three latter dependences, the results here are easily generalized. Finally, to improve our understanding of evolved function, the relative metabolic costs of linearization are quantified. In one case, there is a clear preference arising from this cost consideration (a particular I ( h ), I ( NaP ) pairing is less costly compared to a particular I ( A ), I ( NaP ) pairing that produces an equivalent, linearized range). However in other cases, a preference will depend on the required range; but in any event, the largest linearized range observed here (28 mV), from a combination of I ( h ) and I ( A ), is significantly more costly than the 20 mV range that the I ( h ), I ( NaP ) pair produces.

A riluzole- and valproate-sensitive persistent sodium current contributes to the resting membrane potential and increases the excitability of sympathetic neurones

Non-adapting superior cervical ganglion (SCG) neurones with a clustering activity and sub-threshold membrane potential oscillations were occasionally recorded, suggesting the presence of a persistent sodium current (I(NaP)). The perforated-patch technique was used to establish its properties and physiological role. Voltage-clamp experiments demonstrated that all SCG cells have a TTX-sensitive I(NaP) activating at about -60 mV and with half-maximal activation at about -40 mV. The mean maximum I(NaP) amplitude was around -40 pA at -20 mV. Similar results were achieved when voltage steps or voltage ramps were used to construct the current-voltage relationships, and the general I(NaP) properties were comparable in mouse and rat SCG neurons. I(NaP) was inhibited by riluzole and valproate with an IC(50) of 2.7 and 3.8 microM, respectively, while both drugs inhibited the transient sodium current (I (NaT)) with a corresponding IC(50) of 34 and 150 microM. It is worth noting that 30 microM valproate inhibited the I(NaP) by 70% without affecting the I(NaT). In current clamp, valproate (30 microM) hyperpolarised resting SCG membranes by about 2 mV and increased the injected current necessary to evoke an action potential by about 20 pA. Together, these results demonstrate for the first time that a persistent sodium current exists in the membrane of SCG sympathetic neurones which could allow them to oscillate in the sub-threshold range. This current also contributes to the resting membrane potential and increases cellular excitability, so that it is likely to play an important role in neuronal behaviour.

Regulation of persistent Na current by interactions between beta subunits of voltage-gated Na channels

The beta subunits of voltage-gated Na channels (Scnxb) regulate the gating of pore-forming alpha subunits, as well as their trafficking and localization. In heterologous expression systems, beta1, beta2, and beta3 subunits influence inactivation and persistent current in different ways. To test how the beta4 protein regulates Na channel gating, we transfected beta4 into HEK (human embryonic kidney) cells stably expressing Na(V)1.1. Unlike a free peptide with a sequence from the beta4 cytoplasmic domain, the full-length beta4 protein did not block open channels. Instead, beta4 expression favored open states by shifting activation curves negative, decreasing the slope of the inactivation curve, and increasing the percentage of noninactivating current. Consequently, persistent current tripled in amplitude. Expression of beta1 or chimeric subunits including the beta1 extracellular domain, however, favored inactivation. Coexpressing Na(V)1.1 and beta4 with beta1 produced tiny persistent currents, indicating that beta1 overcomes the effects of beta4 in heterotrimeric channels. In contrast, beta1(C121W), which contains an extracellular epilepsy-associated mutation, did not counteract the destabilization of inactivation by beta4 and also required unusually large depolarizations for channel opening. In cultured hippocampal neurons transfected with beta4, persistent current was slightly but significantly increased. Moreover, in beta4-expressing neurons from Scn1b and Scn1b/Scn2b null mice, entry into inactivated states was slowed. These data suggest that beta1 and beta4 have antagonistic roles, the former favoring inactivation, and the latter favoring activation. Because increased Na channel availability may facilitate action potential firing, these results suggest a mechanism for seizure susceptibility of both mice and humans with disrupted beta1 subunits.

Role of Axonal NaV1.6 Sodium Channels in Action Potential Initiation of CA1 Pyramidal Neurons

In many neuron types, the axon initial segment (AIS) has the lowest threshold for action potential generation. Its active properties are determined by the targeted expression of specific voltage-gated channel subunits. We show that the Na+ channel NaV1.6 displays a striking aggregation at the AIS of cortical neurons. To assess the functional role of this subunit, we used Scn8a med mice that are deficient for NaV1.6 subunits but still display prominent Na+ channel aggregation at the AIS. In CA1 pyramidal cells from Scn8a med mice, we found a depolarizing shift in the voltage dependence of activation of the transient Na+ current ( INaT), indicating that NaV1.6 subunits activate at more negative voltages than other NaV subunits. Additionally, persistent and resurgent Na+ currents were significantly reduced. Current-clamp recordings revealed a significant elevation of spike threshold in Scn8a med mice as well as a shortening of the estimated delay between spike initiation at the AIS and its arrival at the soma. In combination with simulations using a realistic computer model of a CA1 pyramidal cell, our results imply that a hyperpolarized voltage dependence of activation of AIS NaV1.6 channels is important both in determining spike threshold and localizing spike initiation to the AIS. In addition to altered spike initiation, Scn8a med mice also showed a strongly reduced spike gain as expected with combined changes in persistent and resurgent currents and spike threshold. These results suggest that NaV1.6 subunits at the AIS contribute significantly to its role as spike trigger zone and shape repetitive discharge properties of CA1 neurons.

Development of theta rhythmicity in entorhinal stellate cells of the juvenile rat

Mature stellate cells of the rat medial entorhinal cortex (EC), layer II, exhibit subthreshold membrane potential oscillations (MPOs) at theta frequencies (4-12 Hz) in vitro. We find that MPOs appear between postnatal days 14 (P14) and 18 (P18) but show little further change by day 28+ (P28-P32). To identify the factors responsible, we examined the electrical responses of developing stellate cells, paying attention to two currents thought necessary for mature oscillation: the h current I(h), which provides the slow rectification required for resonance; and a persistent sodium current I(NaP), which provides amplification of resonance. Responses to injected current revealed that P14 cells were often nonresonant with a relatively high resistance. Densities of I(h) and I(NaP) both rose by about 50% from P14 to P18. However, I(h) levels fell to intermediate values by P28+. Given the nonrobust trend in I(h) expression and a previously demonstrated potency of even low levels of I(h) to sustain oscillation, we propose that resonance and MPOs are limited at P14 more by low levels of I(NaP) than of I(h). The relative importance of I(NaP) for the development of MPOs is supported by simulations of a conductance-based model, which also suggest that general shunt conductance may influence the precise age when MPOs appear. In addition to our physiological study, we analyzed spine densities at P14, P18, and P28+ and found a vigorous synaptogenesis across the whole period. Our data predict that functions that rely on theta rhythmicity in the hippocampal network are limited until at least P18.

Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach

Globus pallidus (GP) neurons recorded in brain slices show significant variability in intrinsic electrophysiological properties. To investigate how this variability arises, we manipulated the biophysical properties of GP neurons using computer simulations. Specifically, we created a GP neuron model database with 100,602 models that had varying densities of nine membrane conductances centered on a hand-tuned model that replicated typical physiological data. To test the hypothesis that the experimentally observed variability can be attributed to variations in conductance densities, we compared our model database results to a physiology database of 146 slice recordings. The electrophysiological properties of generated models and recordings were assessed with identical current injection protocols and analyzed with a uniform set of measures, allowing a systematic analysis of the effects of varying voltage-gated and calcium-gated conductance densities on the measured properties and a detailed comparison between models and recordings. Our results indicated that most of the experimental variability could be matched by varying conductance densities, which we confirmed with additional partial block experiments. Further analysis resulted in two key observations: (1) each voltage-gated conductance had effects on multiple measures such as action potential waveform and spontaneous or stimulated spike rates; and (2) the effect of each conductance was highly dependent on the background context of other conductances present. In some cases, such interactions could reverse the effect of the density of one conductance on important excitability measures. This context dependence of conductance density effects is important to understand drug and neuromodulator effects that work by affecting ion channels.

Real-time kinetic modeling of voltage-gated ion channels using dynamic clamp

We propose what to our knowledge is a new technique for modeling the kinetics of voltage-gated ion channels in a functional context, in neurons or other excitable cells. The principle is to pharmacologically block the studied channel type, and to functionally replace it with dynamic clamp, on the basis of a computational model. Then, the parameters of the model are modified in real time (manually or automatically), with the objective of matching the dynamical behavior of the cell (e.g., action potential shape and spiking frequency), but also the transient and steady-state properties of the model (e.g., those derived from voltage-clamp recordings). Through this approach, one may find a model and parameter values that explain both the observed cellular dynamics and the biophysical properties of the channel. We extensively tested the method, focusing on Na(v) models. Complex Markov models (10-12 states or more) could be accurately integrated in real time at >50 kHz using the transition probability matrix, but not the explicit Euler method. The practicality of the technique was tested with experiments in raphe pacemaker neurons. Through automated real-time fitting, a Hodgkin-Huxley model could be found that reproduced well the action potential shape and the spiking frequency. Adding a virtual axonal compartment with a high density of Na(v) channels further improved the action potential shape. The computational procedure was implemented in the free QuB software, running under Microsoft Windows and featuring a friendly graphical user interface.

Ionic channel function in action potential generation: current perspective

Over 50 years ago, Hodgkin and Huxley laid down the foundations of our current understanding of ionic channels. An impressive progress has been made during the following years that culminated in the revelation of the details of potassium channel structure. Nevertheless, even today, we cannot separate well currents recorded in central mammalian neurons. Many modern concepts about the function of sodium and potassium currents are based on experiments performed in nonmammalian cells. The recent recognition of the fast delayed rectifier current indicates that we need to reevaluate the biophysical role of sodium and potassium currents. This review will consider high quality voltage clamp data obtained from the soma of central mammalian neurons in the view of our current knowledge about proteins forming ionic channels. Fast sodium currents and three types of outward potassium currents, the delayed rectifier, the subthreshold A-type, and the D-type potassium currents, are discussed here. An updated current classification with biophysical role of each current subtype is provided. This review shows that details of kinetics of both sodium and outward potassium currents differ significantly from the classical descriptions and these differences may be of functional significance.

Persistent Na+ and K+-dominated leak currents contribute to respiratory rhythm generation in the pre-Bötzinger complex in vitro

A central problem in analyzing neural circuit function is establishing how intrinsic neuronal conductances contribute to the generation of network activity. We used real-time calcium activity imaging combined with whole-cell patch-clamp recording to analyze contributions of subthreshold conductances in the excitatory rhythm-generating network in the respiratory pre-Bötzinger complex (pre-BötC) of neonatal rat in vitro brainstem slice preparations. Voltage-clamp ramp recordings from imaged pre-BötC neurons revealed that persistent sodium (NaP) and K+-dominated leak currents primarily contribute to subthreshold I-V relations. We quantified NaP and leak conductance densities (g/C(m)) in intrinsic oscillatory bursters and intrinsically nonbursters, the two main electrophysiological phenotypes of inspiratory neurons within the pre-BötC. Densities of g(NaP) were significantly higher for intrinsic bursters, whereas leak conductance densities were not significantly different between intrinsic bursters and nonbursters. By pharmacologically manipulating g(NaP) and/or g(Leak) directly within the pre-BötC, we could modulate network oscillation frequency over a wide dynamic range and cause transitions between oscillatory and quiescent states. These results were consistent with models of the pre-BötC excitatory network consisting of heterogeneous mixtures of intrinsic bursters and nonintrinsic bursters incorporating g(NaP) and g(Leak) with parameter values found experimentally. We propose a paradigm whereby NaP and Leak represent a functional set of subthreshold conductances that endow the pre-BötC with rhythmogenic properties and represent targets for modulatory control of inspiratory rhythm generation.

BOLD fMRI and somatosensory evoked potentials are well correlated over a broad range of frequency content of somatosensory stimulation of the rat forepaw

Electrical stimulation of the rat paw is commonly used to study the hemodynamic, metabolic and neuronal mechanisms of functional MRI (fMRI) responses in somatosensory cortex. Several groups have reported good correlation between the blood oxygenation level-dependent (BOLD) fMRI signal and somatosensory evoked potentials (SEPs) using short, typically 300 micros, square stimulation pulses. The spectral power of these short pulses is evenly distributed over a wide range of frequencies and thus the effects of the frequency content of the stimulation pulse on fMRI responses have not been previously described. Here, the effects that different stimulation pulse waveforms with a range of frequency content have on neuronal activity, as measured by SEPs, and on the amplitude of the BOLD fMRI signal in rat somatosensory cortex are investigated. The peak-to-peak SEP amplitudes increased as the power in the high frequency harmonics of the different pulse waveforms increased, using either triangular or sinusoidal stimuli waveforms from 9 Hz to 180 Hz. Similarly, BOLD fMRI response increased with increased high frequency content of the stimulation pulse. There was a linear correlation between SEPs and BOLD fMRI over the full range of frequency content in the stimulations.

Parameter estimation for bursting neural models

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preBötzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preBötzinger complex, including modulation of the persistent sodium current.

A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data

We present a novel framework for automatically constraining parameters of compartmental models of neurons, given a large set of experimentally measured responses of these neurons. In experiments, intrinsic noise gives rise to a large variability (e.g., in firing pattern) in the voltage responses to repetitions of the exact same input. Thus, the common approach of fitting models by attempting to perfectly replicate, point by point, a single chosen trace out of the spectrum of variable responses does not seem to do justice to the data. In addition, finding a single error function that faithfully characterizes the distance between two spiking traces is not a trivial pursuit. To address these issues, one can adopt a multiple objective optimization approach that allows the use of several error functions jointly. When more than one error function is available, the comparison between experimental voltage traces and model response can be performed on the basis of individual features of interest (e.g., spike rate, spike width). Each feature can be compared between model and experimental mean, in units of its experimental variability, thereby incorporating into the fitting this variability. We demonstrate the success of this approach, when used in conjunction with genetic algorithm optimization, in generating an excellent fit between model behavior and the firing pattern of two distinct electrical classes of cortical interneurons, accommodating and fast-spiking. We argue that the multiple, diverse models generated by this method could serve as the building blocks for the realistic simulation of large neuronal networks.

Analysis of resurgent sodium-current expression in rat parahippocampal cortices and hippocampal formation

The resurgent Na(+) current (I(NaR)) is a component of neuronal voltage-dependent Na(+) currents that is activated by repolarization and is believed to result from an atypical path of Na(+)-channel recovery from inactivation. So far, I(NaR) has only been identified in a small number of central neuronal populations in the cerebellum, diencephalon, and brainstem. The possible presence and roles of I(NaR) in neurons of the cerebral cortex and temporal-lobe memory system are still uncharacterized. In this study whole-cell, patch-clamp experiments were carried out in acute rat brain slices to investigate I(NaR) expression and properties in several neuronal populations of the parahippocampal region and hippocampal formation. Specifically, we examined pyramidal neurons of perirhinal cortex areas 36 and 35 (layers II and V); neurons of superficial and deep layers of medial entorhinal cortex (mEC); dentate gyrus (DG) granule cells; and pyramidal cells of the CA3 and CA1 hippocampal fields. I(NaR) was found to be thoroughly expressed in parahippocampal cortices. The most consistent and prominent I(NaR) expression was observed in mEC layer-II cells. A vast majority of areas 36 and 35 neurons (both in layers II and V) and mEC layer-III and -V neurons were also endowed with I(NaR), although at lower amplitude levels. I(NaR) was expressed by approximately 60% of DG granule cells and approximately 35% of CA1 pyramidal cells of the ventral hippocampus, whereas it was never observed in CA3 neurons (both in the ventral and dorsal hippocampus) and CA1 neurons of the dorsal hippocampus. The biophysical properties of I(NaR) were very similar in all of the neuronal types in which the current was observed, with a peak in the current-voltage relationship at -35/-40 mV. Our results show that the parahippocampal region and part of the hippocampal formation are sites of major I(NaR) expression, and provide a new basis for further studies on the molecular correlates of I(NaR).

The action potential in mammalian central neurons

The action potential of the squid giant axon is formed by just two voltage-dependent conductances in the cell membrane, yet mammalian central neurons typically express more than a dozen different types of voltage-dependent ion channels. This rich repertoire of channels allows neurons to encode information by generating action potentials with a wide range of shapes, frequencies and patterns. Recent work offers an increasingly detailed understanding of how the expression of particular channel types underlies the remarkably diverse firing behaviour of various types of neurons.

Resurgent Na+ current in pyramidal neurones of rat perirhinal cortex: axonal location of channels and contribution to depolarizing drive during repetitive firing

The perirhinal cortex (PRC) is a supra-modal cortical area that collects and integrates information originating from uni- and multi-modal neocortical regions and directed to the hippocampus. The mechanisms that underlie the specific excitable properties of the different PRC neuronal types are still largely unknown, and their elucidation may be important in understanding the integrative functions of PRC. In this study we investigated the expression and properties of resurgent Na(+) current (I(NaR)) in pyramidal neurones of rat PRC area 35 (layer II). Patch-clamp experiments in acute PRC slices were first carried out. A measurable I(NaR) was expressed by a large majority of neurones (31 out of 35 cells). I(NaR) appeared as an inward, slowly decaying current elicited upon step repolarization after depolarizations sufficient to induce nearly complete inactivation of the transient Na(+) current (I(NaT)). I(NaR) had a peak amplitude of approximately 2.5% that of I(NaT), and showed the typical biophysical properties also observed in other neuronal types (i.e. cerebellar Purkinje and granule cells), including a bell-shaped current-voltage relationship with a peak at approximately -40 mV, and a characteristic acceleration of activation and decay speed at potentials negative to -45 mV. Current-clamp experiments were then carried out in which repetitive action-potential discharge at various frequencies was induced with depolarizing current injection. The voltage signals thus obtained were then used as command waveforms for voltage-clamp recordings. These experiments showed that a Na(+) current identifiable as I(NaR) activates in the early interspike phase even at relatively high firing frequencies (20 Hz), thereby contributing to the depolarizing drive and possibly enhancing repetitive discharge. In acutely dissociated area 35 layer II neurones, as well as in nucleated patches from the same neurones, I(NaR) was never observed, despite the presence of typical I(NaT)s. Since in both preparations neuronal processes are lost, we carried out experiments of focal tetrodotoxin (TTX) application in slices to verify whether the channels responsible for I(NaR) are located in compartment(s) different from the soma. We found that TTX preferentially inhibited I(NaR) when applied close to the site of axon emergence from soma, whereas application to the apical pole of the soma had a significantly smaller effect on I(NaR). Our results indicate that in area 35 pyramidal cells I(NaR) is largely generated in the axon initial segment, where it may participate in setting the coding properties of these neurones.

Theta phase coding in a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections

We investigated successive firing of the stellate cells within a theta cycle, which replicates the phase coding of place information, using a network model of the entorhinal cortex layer II with loop connections. Layer II of the entorhinal cortex (ECII) sends signals to the hippocampus, and the hippocampus sends signals back to layer V of the entorhinal cortex (ECV). In addition to this major pathway, projection from ECV to ECII also exists. It is, therefore, inferred that reverberation activity readily appears if projections from ECV to ECII are potentiated. The frequency of the reverberation would be in a gamma range because it takes signals 20-30 ms to go around the entorhinal-hippocampal loop circuits. On the other hand, it has been suggested that ECII is a theta rhythm generator. If the reverberation activity appears in the entorhinal-hippocampal loop circuits, gamma oscillation would be superimposed on a theta rhythm in ECII like a gamma-theta oscillation. This is a reminiscence of the theta phase coding of place information. In this paper, first, a network model of ECII will be developed in order to reproduce a theta rhythm. Secondly, we will show that loop connections from one stellate cell to the other one are selectively potentiated by afferent signals to ECII. Frequencies of those afferent signals are different, and transmission delay of the loop connections is 20 ms. As a result, stellate cells fire successively within one cycle of the theta rhythm. This resembles gamma-theta oscillation underlying the phase coding. Our model also replicates the phase precession of stellate cell firing within a cycle of subthreshold oscillation (theta rhythm).

Active and passive membrane properties and intrinsic kinetics shape synaptic inhibition in hippocampal CA1 pyramidal neurons

The impact of synaptic inhibition depends on the passive and active properties of the neuronal membrane as well as on the characteristics of the underlying synaptic conductances. Here, we evaluated the contributions of these different factors to the IPSPs produced by two kinetically and anatomically distinct inhibitory synapses onto hippocampal CA1 pyramidal neurons: somatic GABA(A,fast) and dendritic GABA(A,slow). Using combined current-clamp and voltage-clamp recordings from neurons in hippocampal brain slices, we found that despite pronounced differences in kinetics and only weak voltage dependence of the underlying synaptic conductances, there were much smaller differences in duration but strong voltage dependence of IPSPs arising from somatic and dendritic synapses. Pharmacologic tests and compartmental modeling showed that these effects were produced by the hyperpolarization-activated cation current, I(H), which accelerated IPSP decay over a broad range of membrane potentials and reduced IPSP amplitudes at hyperpolarized potentials, and the persistent sodium current, I(NaP), which prolonged and amplified IPSPs at depolarized subthreshold potentials. The relative magnitudes of their influences depended on the kinetics of the underlying synaptic conductances: the effect on duration was greater for GABA(A,fast) and on amplitude was greater for GABA(A,slow). Passive and active factors thus influence the impact of synaptic inhibition in a location- and voltage-dependent manner.

Metabotropic glutamate receptor subtype 1 regulates sodium currents in rat neocortical pyramidal neurons

Brain sodium channels (NaChs) are regulated by various neurotransmitters such as acetylcholine, serotonin and dopamine. However, it is not known whether NaCh activity is regulated by glutamate, the principal brain neurotransmitter. We show here that activation of metabotropic glutamate receptor (mGluR) subtype 1 regulates fast transient (I(NaT)) and persistent Na(+) currents (I(NaP)) in cortical pyramidal neurons. A selective agonist of group I mGluR, (S)-3,5-dihydroxyphenylglycine (DHPG), reduced action potential amplitude and decreased I(NaT). This reduction was blocked when DHPG was applied in the presence of selective mGluR1 antagonists. The DHPG-induced reduction of the current was accompanied by a shift of both the inactivation curve of I(NaT) and the activation curve of I(NaP). These effects were dependent on the activation of PKC. The respective role of these two regulatory processes on neuronal excitability was determined by simulating transient and persistent Na(+) conductances (G(NaT) and G(NaP)) with fast dynamic-clamp techniques. The facilitated activation of G(NaP) increased excitability near the threshold, but, when combined with the down-regulation of G(NaT), repetitive firing was strongly decreased. Consistent with this finding, the mGluR1 antagonist LY367385 increased neuronal excitability when glutamatergic synaptic activity was stimulated with high external K(+). We conclude that mGluR1-dependent regulation of Na(+) current depresses neuronal excitability, which thus might constitute a novel mechanism of homeostatic regulation acting during intense glutamatergic synaptic activity.

The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.

Ankyrin-G regulates inactivation gating of the neuronal sodium channel, Nav1.6

Ankyrin-G, a modular protein, plays a critical role in clustering voltage-gated sodium channels (Nav channels) in nodes of Ranvier and initial segments of mammalian neurons. However, direct effects of ankyrin-G on electrophysiological properties of Nav channels remain elusive. In this study, we explored whether ankyrin-G has a role in modifying gating properties of the neuronal Nav1.6 channel that is predominantly localized at nodes of Ranvier and initial segments. TsA201 cells transfected with the human Nav1.6 cDNA alone exhibited significant persistent sodium current (Ina-p). On the other hand, Ina-p was barely detected on co-expression with ankyrin-G. Ankyrin-B, another ankyrin, did not show such an effect. Expression of chimeras between the two isoforms of ankyrin suggests that the membrane-binding domain of ankyrin-G is critical for reducing the Ina-p of Nav1.6. These results suggest that ankyrin-G regulates neuronal excitability not only through clustering Nav channels but also by directly modifying their channel gating.

Dynamical mechanisms of odor processing in olfactory bulb mitral cells

In the olfactory system, the contribution of dynamical properties such as neuronal oscillations and spike synchronization to the representation of odor stimuli is a matter of substantial debate. While relatively simple computational models have sufficed to guide current research in large-scale network dynamics, less attention has been paid to modeling the membrane dynamics in bulbar neurons that may be equally essential to sensory processing. We here present a reduced, conductance-based compartmental model of olfactory bulb mitral cells that exhibits the complex dynamical properties observed in these neurons. Specifically, model neurons exhibit intrinsic subthreshold oscillations with voltage-dependent frequencies that shape the timing of stimulus-evoked action potentials. These oscillations rely on a persistent sodium conductance, an inactivating potassium conductance, and a calcium-dependent potassium conductance and are reset via inhibitory input such as that delivered by periglomerular cell shunt inhibition. Mitral cells fire bursts, or clusters, of spikes when continuously stimulated. Burst properties depend critically on multiple currents, but a progressive deinactivation of I(A) over the course of a burst is an important regulator of burst termination. Each of these complex properties exhibits appropriate dynamics and pharmacology as determined by electrophysiological studies. Additionally, we propose that a second, inconsistently observed form of infrathreshold bistability in mitral cells may derive from the activation of ATP-activated potassium currents responding to hypoxic conditions. We discuss the integration of these cellular properties in the larger context of olfactory bulb network operations.

Realistic modeling of entorhinal cortex field potentials and interpretation of epileptic activity in the guinea pig isolated brain preparation

Mechanisms underlying epileptic activities recorded from entorhinal cortex (EC) were studied through a computational model based on review of cytoarchitectonic and neurobiological data about this structure. The purpose of this study is to describe and use this model to interpret epileptiform discharge patterns recorded in an experimental model of ictogenesis (guinea pig isolated brain perfused with bicuculline). A macroscopic modeling approach representing synaptic interactions between cells subpopulations in the EC was chosen for its adequacy to mimic field potentials reflecting overall dynamics rising from interconnected cells populations. Therefore intrinsic properties of neurons were not included in the modeling design. Model parameters were adjusted from an identification procedure based on quantitative comparison between real and simulated signals. For both EC deep and superficial layers, results show that the model generates very realistic signals regarding temporal dynamics, spectral features, and cross-correlation values. These simulations allowed us to infer information about the evolution of synaptic transmission between principal cell and interneuronal populations and about connectivity between deep and superficial layers during the transition from background to ictal activity. In the model, this transition was obtained for increased excitation in deep versus superficial layers. Transitions between epileptiform activities [interictal spikes, fast onset activity (25 Hz), ictal bursting activity] were explained by changes of parameters mainly related to GABAergic interactions. Notably, the model predicted an important role of GABAa,fast- and GABAb-receptor-mediated inhibition in the generation of ictal fast onset and burst activities, respectively. These findings are discussed with respect to experimental data.

Kinetic and functional analysis of transient, persistent and resurgent sodium currents in rat cerebellar granule cells in situ: an electrophysiological and modelling study

Cerebellar neurones show complex and differentiated mechanisms of action potential generation that have been proposed to depend on peculiar properties of their voltage-dependent Na+ currents. In this study we analysed voltage-dependent Na(+) currents of rat cerebellar granule cells (GCs) by performing whole-cell, patch-clamp experiments in acute rat cerebellar slices. A transient Na+ current (I(NaT)) was always present and had the properties of a typical fast-activating/inactivating Na+ current. In addition to I(NaT), robust persistent (I(NaP)) and resurgent (I(NaR)) Na+ currents were observed. I(NaP) peaked at approximately -40 mV, showed half-maximal activation at approximately -55 mV, and its maximal amplitude was about 1.5% of that of I(NaT). I(NaR) was elicited by repolarizing pulses applied following step depolarizations able to activate/inactivate I(NaT), and showed voltage- and time-dependent activation and voltage-dependent decay kinetics. The conductance underlying I(NaR) showed a bell-shaped voltage dependence, with peak at -35 mV. A significant correlation was found between GC I(NaR) and I(NaT) peak amplitudes; however, GCs expressing I(NaT) of similar size showed marked variability in terms of I(NaR) amplitude, and in a fraction of cells I(NaR) was undetectable. I(NaT), I(NaP) and I(NaR) could be accounted for by a 13-state kinetic scheme comprising closed, open, inactivated and blocked states. Current-clamp experiments carried out to identify possible functional correlates of I(NaP) and/or I(NaR) revealed that in GCs single action potentials were followed by depolarizing afterpotentials (DAPs). In a majority of cells, DAPs showed properties consistent with I(NaR) playing a role in their generation. Computer modelling showed that I(NaR) promotes DAP generation and enhances high-frequency firing, whereas I(NaP) boosts near-threshold firing activity. Our findings suggest that special properties of voltage-dependent Na+ currents provides GCs with mechanisms suitable for shaping activity patterns, with potentially important consequences for cerebellar information transfer and computation.

Sodium currents in medullary neurons isolated from the pre-Bötzinger complex region

The pre-Bötzinger complex (preBötC) in the ventrolateral medulla contains interneurons important for respiratory rhythm generation. Voltage-dependent sodium channels mediate transient current (I(NaT)), underlying action potentials, and persistent current (I(NaP)), contributing to repetitive firing, pacemaker properties, and the amplification of synaptic inputs. Voltage-clamp studies of the biophysical properties of these sodium currents were conducted on acutely dissociated preBötC region neurons. Reverse transcription-PCR demonstrated the presence of mRNA for Nav1.1, Nav1.2, and Nav1.6 alpha-subunits in individual neurons. A TTX-sensitive I(NaP) was evoked in all tested neurons by ramp depolarization from -80 to 0 mV. Including a constant in the Boltzmann equation for inactivation by estimating the steady-state fraction of Na+ channels available for inactivation allowed prediction of a window current that did not decay to 0 at voltages positive to -20 mV and closely matched the measured I(NaP). Riluzole (3 microM), a putative I(NaP) antagonist, reduced both I(NaP) and I(NaT) and produced a hyperpolarizing shift in the voltage dependence of steady-state inactivation. The latter decreased the predicted window current by an amount equivalent to the decrease in I(NaP). Riluzole also decreased the inactivation time constant at potentials in which the peak window/persistent currents are generated. Together, these findings imply that I(NaP) and I(NaT) arise from the same channels and that a simple modification of the Hodgkin-Huxley model can satisfactorily account for both currents. In the rostral ventral respiratory group (immediately caudal to preBötC), I(NaP) was also detected, but peak conductance, current density, and input resistance were smaller than in preBötC region cells.

Layer-specific properties of the persistent sodium current in sensorimotor cortex

We evaluated the characteristics of the persistent sodium current (I(NaP)) in pyramidal neurons of layers II/III and V in slices of rat sensorimotor cortex using whole cell patch-clamp recordings. In both layers, I(NaP) began activating around -60 mV and was half-activated at -43 mV. The I(NaP) peak amplitude and density were significantly higher in layer V. The voltage-dependent I(NaP) steady-state inactivation occurred at potentials that were significantly more positive in layer V (V(1/2): -42.3 +/- 1.1 mV) than in layer II/III (V(1/2): -46.8 +/- 1.6 mV). In both layers, a current fraction corresponding to about 25% of the maximal peak amplitude did not inactivate. The time course of I(NaP) inactivation and recovery from inactivation could be fitted with a biexponential function. In layer V pyramidal neurons the faster time constant of development of inactivation had variable values, ranging from 158.0 to 1,133.8 ms, but it was on average significantly slower than that in layer II/III (425.9 +/- 80.5 vs. 145.8 +/- 18.2 ms). In both layers, I(NaP) did not completely inactivate even with very long conditioning depolarizations (40 s at -10 mV). Recovery from inactivation was similar in the two layers. Layer V intrinsically bursting and regular spiking nonadapting neurons showed particularly prolonged depolarized plateau potentials when Ca2+ and K+ currents were blocked and slower early phase of I(NaP) development of inactivation. The biexponential kinetics characterizing the time-dependent inactivation of I(NaP) in layers II/III and V indicates a complex inactivating process that is incomplete, allowing a residual "persistent" current fraction that does not inactivate. Moreover, our data indicate that I(NaP) has uneven inactivation properties in pyramidal neurons of different layers of rat sensorimotor cortex. The higher current density, the rightward shifted voltage dependency of inactivation as well the slower kinetics of inactivation characterizing I(NaP) in layer V with respect to layer II/III pyramidal neurons may play a significant role in their ability to fire recurrent action potential bursts, as well in the high susceptibility to generate epileptic events.

Channel noise is essential for perithreshold oscillations in entorhinal stellate neurons

Previous experimental and computational work (for review, see White et al., 2000) has suggested that channel noise, generated by the stochastic flicker of voltage-gated ion channels, can be a major contributor to electrical membrane noise in neurons. In spiny stellate neurons of the entorhinal cortex, we remove the primary source of channel noise by pharmacologically blocking the native persistent Na+ conductance. Via the dynamic-clamp technique (Robinson and Kawai, 1993; Sharp et al., 1993), we then introduce virtual persistent Na+ channels into the membranes of the stellate neurons. By altering the mathematical properties of these virtual "knock-ins," we demonstrate that stochastic flicker of persistent Na+ channels is necessary for the existence of slow perithreshold oscillations that characterize stellate neurons. Channel noise also alters the ability of stellate neurons to phase lock to weak sinusoidal stimuli. These results provide the first direct demonstration that physiological levels of channel noise can produce qualitative changes in the integrative properties of neurons.

Contrasting Effects of the Persistent Na+ Current on Neuronal Excitability and Spike Timing

The persistent Na+ current, INaP, is known to amplify subthreshold oscillations and synaptic potentials, but its impact on action potential generation remains enigmatic. Using computational modeling, whole-cell recording, and dynamic clamp of CA1 hippocampal pyramidal cells in brain slices, we examined how INaP changes the transduction of excitatory current into action potentials. Model simulations predicted that INaP increases afterhyperpolarizations, and, although it increases excitability by reducing rheobase, INaP also reduces the gain in discharge frequency in response to depolarizing current (f/I gain). These predictions were experimentally confirmed by using dynamic clamp, thus circumventing the longstanding problem that INaP cannot be selectively blocked. Furthermore, we found that INaP increased firing regularity in response to sustained depolarization, although it decreased spike time precision in response to single evoked EPSPs. Finally, model simulations demonstrated that I(NaP) increased the relative refractory period and decreased interspike-interval variability under conditions resembling an active network in vivo.

NMDA/AMPA ratio impacts state transitions and entrainment to oscillations in a computational model of the nucleus accumbens medium spiny projection neuron

We describe a computational model of the principal cell in the nucleus accumbens (NAcb), the medium spiny projection (MSP) neuron. The model neuron, constructed in NEURON, includes all of the known ionic currents in these cells and receives synaptic input from simulated spike trains via NMDA, AMPA, and GABAA receptors. After tuning the model by adjusting maximal current conductances in each compartment, the model cell closely matched whole-cell recordings from an adult rat NAcb slice preparation. Synaptic inputs in the range of 1000-1300 Hz are required to maintain an "up" state in the model. Cell firing in the model required concurrent depolarization of several dendritic branches, which responded independently to afferent input. Depolarization from action potentials traveled to the tips of the dendritic branches and increased Ca2+ influx through voltage-gated Ca2+ channels. As NMDA/AMPA current ratios were increased, the membrane showed an increase in hysteresis of "up" and "down" state dwell times, but intrinsic bistability was not observed. The number of oscillatory inputs required to entrain the model cell was determined to be approximately 20% of the "up" state inputs. Altering the NMDA/AMPA ratio had a profound effect on processing of afferent input, including the ability to entrain to oscillations in afferent input in the theta range (4-12 Hz). These results suggest that afferent information integration by the NAcb MSP cell may be compromised by pathology in which the NMDA current is altered or modulated, as has been proposed in both schizophrenia and addiction.

Fast Pseudo-Periodic Oscillation in the Rat Brain Voltage-gated Sodium Channel α Subunit

In the work reported here, we have investigated the changes in the activation and fast inactivation properties of the rat brain voltage-gated sodium channel (rNa(v) 1.2a) alpha subunit, expressed heterologously in the Chinese Hamster Ovary (CHO) cells, by short depolarizing prepulses (10-1000 ms). The time constant of recovery from fast inactivation (tau(fast)) and steady-state parameters for activation and inactivation varied in a pseudo-oscillatory fashion with the duration and amplitude of a sustained prepulse. A consistent oscillation was observed in most of the steady-state and non-inactivating current parameters with a time period close to 225 ms, although a faster oscillation of time period 125 ms was observed in the tau(fast). The studies on the non-inactivating current and steady-state activation indicate that the phase of oscillation varies from cell to cell. Co-expression of the beta1 subunit with the alpha subunit channel suppressed the oscillation in the charge movement per single channel and free energy of steady-state inactivation, although the oscillation in the half steady-state inactivation potential remained unaltered. Incidentally, the frequencies of oscillation in the sodium channel parameters (4-8 Hz) correspond to the theta component of network oscillation. This fast pseudo-oscillatory mechanism, together with the slow pseudo-oscillatory mechanism found in these channels earlier, may contribute to the oscillations in the firing properties observed in various neuronal subtypes and many pathological conditions.

D2 dopamine receptor-mediated modulation of voltage-dependent Na+ channels reduces autonomous activity in striatal cholinergic interneurons

Striatal cholinergic interneurons are critical elements of the striatal circuitry controlling motor planning, movement, and associative learning. Intrastriatal release of dopamine and inhibition of interneuron activity is thought to be a critical link between behaviorally relevant events, such as reward, and alterations in striatal function. However, the mechanisms mediating this modulation are unclear. Using a combination of electrophysiological, molecular, and computational approaches, the studies reported here show that D2 dopamine receptor modulation of Na+ currents underlying autonomous spiking contributes to a slowing of discharge rate, such as that seen in vivo. Four lines of evidence support this conclusion. First, D2 receptor stimulation in tissue slices reduced the autonomous spiking in the presence of synaptic blockers. Second, in acutely isolated neurons, D2 receptor activation led to a reduction in Na+ currents underlying pacemaking. The modulation was mediated by a protein kinase C-dependent enhancement of channel entry into a slow-inactivated state at depolarized potentials. Third, the sodium channel blocker TTX mimicked the effects of D2 receptor agonists on pacemaking. Fourth, simulation of cholinergic interneuron pacemaking revealed that a modest increase in the entry of Na+ channels into the slow-inactivated state was sufficient to account for the slowing of pacemaker discharge. These studies establish a cellular mechanism linking dopamine and the reduction in striatal cholinergic interneuron activity seen in the initial stages of associative learning.

Persistent Sodium Currents in Mesencephalic V Neurons Participate in Burst Generation and Control of Membrane Excitability

The functional and biophysical properties of a persistent sodium current ( INaP) previously proposed to participate in the generation of subthreshold oscillations and burst discharge in mesencephalic trigeminal sensory neurons (Mes V) were investigated in brain stem slices (rats, p7–p12) using whole cell patch-clamp methods. INaPactivated around −76 mV and peaked at −48 mV, with V1/2of −58.7 mV. Ramp voltage-clamp protocols showed that INaPundergoes time- as well as voltage-dependent inactivation and recovery from inactivation in the range of several seconds (τonset= 2.04 s, τrecov= 2.21 s). Riluzole (≤5 μM) substantially reduced INaP, membrane resonance, postinhibitory rebound (PIR), and subthreshold oscillations, and completely blocked bursting, but produced modest effects on the fast transient Na+current ( INaT). Before complete cessation, burst cycle duration was increased substantially, while modest and inconsistent changes in burst duration were observed. The properties of the INaTwere obtained and revealed that the amplitude and voltage dependence of the resulting “window current” were not consistent with those of the observed INaPrecorded in the same neurons. This suggests an additional mechanism for the origin of INaP. A neuronal model was constructed using Hodgkin-Huxley parameters obtained experimentally for Na+and K+currents that simulated the experimentally observed membrane resonance, subthreshold oscillations, bursting, and PIR. Alterations in the model gNaPparameters indicate that INaPis critical for control of subthreshold and suprathreshold Mes V neuron membrane excitability and burst generation.

Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold

Neurones generate intrinsic subthreshold membrane potential oscillations (MPOs) under various physiological and behavioural conditions. These oscillations influence neural responses and coding properties on many levels. On the single-cell level, MPOs modulate the temporal precision of action potentials; they also have a pronounced impact on large-scale cortical activity. Recent studies have described a close association between the MPOs of a given neurone and its electrical resonance properties. Using intracellular sharp microelectrode recordings we examine both dynamical characteristics in layers II and III of the entorhinal cortex (EC). Our data from EC layer II stellate cells show strong membrane potential resonances and oscillations, both in the range of 5-15 Hz. At the resonance maximum, the membrane impedance can be more than twice as large as the input resistance. In EC layer III cells, MPOs could not be elicited, and frequency-resolved impedances decay monotonically with increasing frequency or has only a small peak followed by a subsequent decay. To quantify and compare the resonance and oscillation properties, we use a simple mathematical model that includes stochastic components to capture channel noise. Based on this model we demonstrate that electrical resonance is closely related though not equivalent to the occurrence of sag-potentials and MPOs. MPO frequencies can be predicted from the membrane impedance curve for stellate cells. The model also explains the broad-band nature of the observed MPOs. This underscores the importance of intrinsic noise sources for subthreshold phenomena and rules out a deterministic description of MPOs. In addition, our results show that the two identified cell classes in the superficial EC layers, which are known to target different areas in the hippocampus, also have different preferred frequency ranges and dynamic characteristics. Intrinsic cell properties may thus play a major role for the frequency-dependent information flow in the hippocampal formation.

Kinetic diversity of single-channel burst openings underlying persistent Na(+) current in entorhinal cortex neurons

The kinetic diversity of burst openings responsible for the persistent Na(+) current (I(NaP)) in entorhinal cortex neurons was examined by separately analyzing single bursts. Although remarkable kinetic variability was observed among bursts in terms of intraburst opening probability and mean open and closed times, the values of time constants describing intraburst open times (tau(o(b))s) and closed times (tau(c(b))s) were distributed around well-defined peaks. At -40 mV, tau(o(b)) peaks were found at approximately 0.34 (tau(o(b))1) and 0.77 (tau(o(b))2) ms, and major tau(c(b)) peaks were found at approximately 0.24 (tau(c(b))1) and 0.54 (tau(c(b))2) ms. In approximately 80% of the bursts two preferential gating modes were found that consisted of a combination of either tau(o(b))1 and tau(c(b))2 ("intraburst mode 1"), or tau(o(b))2 and tau(c(b))1 ("intraburst mode 2"). Individual channels could switch between different gating modalities, but normally tended to maintain a specific gating mode for long periods. Mean burst duration also displayed considerable variability. At least three time constants were found to describe burst duration, and the frequencies at which each of the corresponding "bursting states" occurred varied in different channels. Short-lasting bursting states were preferentially associated with intraburst mode 1, whereas very-long-lasting bursts tended to gate according to mode 2 only or other modes that included considerably longer mean open times. These results show that I(NaP) channels can generate multiple intraburst open and closed states and bursting states, but these different kinetic states tend to combine in definite ways to produce a limited number of prevalent, well-defined gating modalities. Modulation of distinct gating modalities in individual Na(+) channels may be a powerful form of plasticity to influence neuronal excitability and function.

Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons

A multicompartmental biophysical model of entorhinal cortex layer II stellate cells was developed to analyze the ionic basis of physiological properties, such as subthreshold membrane potential oscillations, action potential clustering, and the medium afterhyperpolarization. In particular, the simulation illustrates the interaction of the persistent sodium current (I(Nap)) and the hyperpolarization activated inward current (Ih) in the generation of subthreshold membrane potential oscillations. The potential role of Ih in contributing to the medium hyperpolarization (mAHP) and rebound spiking was studied. The role of Ih and the slow calcium-activated potassium current Ikappa(AHP) in action potential clustering was also studied. Representations of Ih and I(Nap) were developed with parameters based on voltage-clamp data from whole-cell patch and single channel recordings of stellate cells (Dickson et al., J Neurophysiol 83:2562-2579, 2000; Magistretti and Alonso, J Gen Physiol 114:491-509, 1999; Magistretti et al., J Physiol 521:629-636, 1999a; J Neurosci 19:7334-7341, 1999b). These currents interacted to generate robust subthreshold membrane potentials with amplitude and frequency corresponding to data observed in the whole cell patch recordings. The model was also able to account for effects of pharmacological manipulations, including blockade of Ih with ZD7288, partial blockade with cesium, and the influence of barium on oscillations. In a model with a wider range of currents, the transition from oscillations to single spiking, to spike clustering, and finally tonic firing could be replicated. In agreement with experiment, blockade of calcium channels in the model strongly reduced clustering. In the voltage interval during which no data are available, the model predicts that the slow component of Ih does not follow the fast component down to very short time constants. The model also predicts that the fast component of Ih is responsible for the involvement in the generation of subthreshold oscillations, and the slow component dominates in the generation of spike clusters.

Riluzole-Sensitive Slowly Inactivating Sodium Current in Rat Suprachiasmatic Nucleus Neurons

The persistent (i.e., slowly inactivating) fraction of the Na current ( INa,P) regulates excitability of CNS neurons. In isolated rat suprachiasmatic nucleus (SCN) neurons with a ramp-type voltage-clamp protocol, we have studied the properties of a robust current that has the general properties of INa,P but exhibits a slow inactivation ( INa,S). The time dependence of the development of the inactivation was also studied by clamping of the membrane potential at different levels: time constants ranging from ∼50 to ∼700 ms, depending on the voltage level, were revealed. The INa,S (50–150 pA) was present in both spontaneously active and silent neurons. The neurons exhibited INa,S without visible rundown during ∼1-h recordings. INa,S had a threshold between –65 and –60 mV and was maximal at about –45 mV. Tetrodotoxin (TTX; 1 μM) completely and reversibly blocked INa,S. Riluzole, an effective blocker of INa,P, inhibited reversibly INa,S with an EC50 of 1–2 μM. Microapplication of 10 μM riluzole during either extracellular or intracellular recording suppressed spontaneous activity in isolated SCN neurons. In the slice preparation, bath application of 20 μM riluzole resulted in decreased firing rate or complete suppression of spontaneous activity in some neurons (9/14) but had no effect on other neurons (5/14). In riluzole-resistant neurons in cell-attached experiments, low-amplitude current spikes were present in 1 μM TTX. We concluded that INa,S is ubiquitously expressed by all SCN neurons and that this current is a necessary but not sufficient depolarizing component of the mechanism for spontaneous firing.

Modulation of neuronal activity by the endogenous pentapeptide QYNAD

Inflammation and demyelination both contribute to the neurological deficits characteristic of multiple sclerosis. Neurological dysfunctions are attributable to inflammatory demyelination and, in addition, to soluble factors such as nitric oxide, cytokines and antibodies. QYNAD, an endogenous pentapeptide identified in the cerebrospinal fluid of patients with demyelinating disorders, has been proposed to promote axonal dysfunction by blocking sodium channels. The present study aimed at characterizing the properties of QYNAD in acutely isolated thalamic neurons in vitro. QYNAD, but not a scrambled peptide (NYDQA), blocked sodium channels in neurons by shifting the steady-state inactivation to more negative potentials. Blocking properties followed a dose-response curve with a maximum effect at 10 microm. A fluorescently labelled QYNAD analogue with retained biological activity specifically stained thalamic neurons, positive for type II sodium channels, thus demonstrating the specificity of QYNAD binding. Our study confirms and extends previous observations describing QYNAD as a potent sodium channel-blocking agent. These data as well as our preliminary observations in in vivo experiments in an animal model of inflammatory CNS demyelination warrant further in vivo studies in order to clarify the exact pathogenetic role of QYNAD in inflammatory neurological diseases.