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

Estimation of persistent sodium-current density in rat hippocampal mossy fibre boutons: Correction of space-clamp errors

We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons. Cox's method for correcting space-clamp errors was extended to the case of an isopotential compartment with attached neurites. The method was applied to voltage-ramp experiments, in which iNaP is assumed to gate instantaneously. The raw estimates of iNaP led to predicted clamp currents that were at variance with observation, hence an algorithm was devised to improve these estimates. Optionally, the method also allows an estimate of the membrane specific capacitance, although values of the axial resistivity and seal resistance must be provided. Assuming that membrane specific capacitance and axial resistivity were constant, we conclude that seal resistance continued to fall after adding TTX to the bath. This might have been attributable to a further deterioration of the seal after baseline rather than an unlikely effect of TTX. There was an increase in the membrane specific resistance in TTX. The reason for this is unknown, but it meant that iNaP could not be determined by simple subtraction. Attempts to account for iNaP with a Hodgkin-Huxley model of the transient sodium conductance met with mixed results. One thing to emerge was the importance of voltage shifts. Also, a large variability in previously reported values of transient sodium conductance in mossy fibre boutons made comparisons with our results difficult. Various other possible sources of error are discussed. Simulations suggest a role for iNaP in modulating the axonal attenuation of EPSPs. KEY POINTS: We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons, using a KCl-based internal (pipette) solution and correcting for the liquid junction potential (2 mV). Space-clamp errors and deterioration of the patch-clamp seal during the experiment were corrected for by compartmental modelling. Attempts to account for iNaP in terms of the transient sodium conductance met with mixed results. One possibility is that the transient sodium conductance is higher in mossy fibre boutons than in the axon shaft. The analysis illustrates the need to account for various voltage shifts (Donnan potentials, liquid junction potentials and, possibly, other voltage shifts). Simulations suggest a role for iNaP in modulating the axonal attenuation of excitatory postsynaptic potentials, hence analog signalling by dentate granule cells.

Ibuprofen modulates tetrodotoxin-resistant persistent Na+ currents at acidic pH in rat trigeminal ganglion neurons

Non-steroidal anti-inflammatory drugs (NSAIDs) are widely used to relieve various symptoms such as headache, arthralgia, and dental pain. While the primary mechanism of NSAID-based pain relief is the inhibition of cyclooxygenase-2, several NSAIDs also modulate other molecular targets related to nociceptive transmission such as voltage-gated Na+ channels. In the present study, we examined the effects of NSAIDs on persistent Na+ current (INaP) mediated by tetrodotoxin-resistant (TTX-R) Na+ channels in small-to medium-sized trigeminal ganglion neurons using a whole-cell patch-clamp technique. At clinically relevant concentrations, all propionic acid derivatives tested (ibuprofen, naproxen, fenoprofen, and flurbiprofen) preferentially inhibited the TTX-R INaP. The inhibition was more potent at acidic extracellular pH (pH 6.5) than at normal pH (pH 7.4). Other NSAIDs, such as ketorolac, piroxicam, and aspirin, had a negligible effect on the TTX-R INaP. Ibuprofen both accelerated the onset of inactivation and retarded the recovery from inactivation of TTX-R Na+ channels at acidic extracellular pH. However, all NSAIDs tested in this study had minor effects on voltage-gated K+ currents, as well as hyperpolarization-activated and cyclic nucleotide-gated cation currents, at both acidic and normal extracellular pH. Under current-clamp conditions, ibuprofen decreased the number of action potentials elicited by depolarizing current stimuli at acidic (pH 6.5) extracellular pH. Considering that extracellular pH falls as low as 5.5 in inflamed tissues, TTX-R INaP inhibition could be a mechanism by which ibuprofen and propionic acid derivative NSAIDs modulate inflammatory pain.

Simulations predict differing phase responses to excitation vs. inhibition in theta-resonant pyramidal neurons

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integrating rhythmic inputs in many cortical structures. Impedance analysis has been widely used to examine frequency-dependent responses of neuronal membranes to rhythmic inputs, but it assumes that the neuronal membrane is a linear system, requiring the use of small signals to stay in a near-linear regime. However, postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). The goals of this work were to 1) develop an analysis method to evaluate membrane responses in this nonlinear domain and 2) explore phase relationships between rhythmic stimuli and subthreshold and spiking membrane potential (Vmemb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asymmetrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles. Suprathreshold theta-rhythmic stimuli produced nonstationary Vmemb responses. Sinusoidal inputs produced "phase retreat": action potentials occurred progressively later in cycles of the input stimulus, resulting from adaptation. Sinusoidal current with increasing amplitude over cycles produced "phase advance": action potentials occurred progressively earlier. Phase retreat, phase advance, and subthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responses of cortical neurons depending on the frequency of oscillatory input, which will play a role in neuronal responses to shifts in network state. We hypothesize that intrinsic cellular properties complement network properties and contribute to in vivo phase-shift phenomena such as phase precession, seen in place and grid cells, and phase roll, also observed in hippocampal CA1 neurons.NEW & NOTEWORTHY We augmented electrical impedance analysis to characterize phase shifts between large-amplitude current stimuli and nonlinear, asymmetric membrane potential responses. We predict different frequency-dependent phase shifts in response excitation vs. inhibition, as well as shifts in spike timing over multiple input cycles, in theta-resonant pyramidal neurons. We hypothesize that these effects contribute to navigation-related phenomena such as phase precession and phase roll. Our neuron-level hypothesis complements, rather than falsifies, prior network-level explanations of these phenomena.

Simulation of oscillatory dynamics induced by an approximation of grid cell output

Grid cells, in entorhinal cortex (EC) and related structures, signal animal location relative to hexagonal tilings of 2D space. A number of modeling papers have addressed the question of how grid firing behaviors emerge using (for example) ideas borrowed from dynamical systems (attractors) or from coupled oscillator theory. Here we use a different approach: instead of asking how grid behavior emerges, we take as a given the experimentally observed intracellular potentials of superficial medial EC neurons during grid firing. Employing a detailed neural circuit model modified from a lateral EC model, we then ask how the circuit responds when group of medial EC principal neurons exhibit such potentials, simultaneously with a simulated theta frequency input from the septal nuclei. The model predicts the emergence of robust theta-modulated gamma/beta oscillations, suggestive of oscillations observed in an in vitro medial EC experimental model (Cunningham, M.O., Pervouchine, D.D., Racca, C., Kopell, N.J., Davies, C.H., Jones, R.S.G., Traub, R.D., and Whittington, M.A. (2006). Neuronal metabolism governs cortical network response state. Proc. Natl. Acad. Sci. U S A 103: 5597-5601). Such oscillations result because feedback interneurons tightly synchronize with each other - despite the varying phases of the grid cells - and generate a robust inhibition-based rhythm. The lack of spatial specificity of the model interneurons is consistent with the lack of spatial periodicity in parvalbumin interneurons observed by Buetfering, C., Allen, K., and Monyer, H. (2014). Parvalbumin interneurons provide grid cell-driven recurrent inhibition in the medial entorhinal cortex. Nat. Neurosci. 17: 710-718. If in vivo EC gamma rhythms arise during exploration as our model predicts, there could be implications for interpreting disrupted spatial behavior and gamma oscillations in animal models of Alzheimer's disease and schizophrenia. Noting that experimental intracellular grid cell potentials closely resemble cortical Up states and Down states, during which fast oscillations also occur during Up states, we propose that the co-occurrence of slow principal cell depolarizations and fast network oscillations is a general property of the telencephalon, in both waking and sleep states.

T-type Ca2+ and persistent Na+ currents synergistically elevate ventral, not dorsal, entorhinal cortical stellate cell excitability

Dorsal and ventral medial entorhinal cortex (mEC) regions have distinct neural network firing patterns to differentially support functions such as spatial memory. Accordingly, mEC layer II dorsal stellate neurons are less excitable than ventral neurons. This is partly because the densities of inhibitory conductances are higher in dorsal than ventral neurons. Here, we report that T-type Ca2+ currents increase 3-fold along the dorsal-ventral axis in mEC layer II stellate neurons, with twice as much CaV3.2 mRNA in ventral mEC compared with dorsal mEC. Long depolarizing stimuli trigger T-type Ca2+ currents, which interact with persistent Na+ currents to elevate the membrane voltage and spike firing in ventral, not dorsal, neurons. T-type Ca2+ currents themselves prolong excitatory postsynaptic potentials (EPSPs) to enhance their summation and spike coupling in ventral neurons only. These findings indicate that T-type Ca2+ currents critically influence the dorsal-ventral mEC stellate neuron excitability gradient and, thereby, mEC dorsal-ventral circuit activity.

Genetic mechanisms for impaired synaptic plasticity in schizophrenia revealed by computational modelling

Schizophrenia phenotypes are suggestive of impaired cortical plasticity in the disease, but the mechanisms of these deficits are unknown. Genomic association studies have implicated a large number of genes that regulate neuromodulation and plasticity, indicating that the plasticity deficits have a genetic origin. Here, we used biochemically detailed computational modelling of post-synaptic plasticity to investigate how schizophrenia-associated genes regulate long-term potentiation (LTP) and depression (LTD). We combined our model with data from post-mortem mRNA expression studies (CommonMind gene-expression datasets) to assess the consequences of altered expression of plasticity-regulating genes for the amplitude of LTP and LTD. Our results show that the expression alterations observed post mortem, especially those in anterior cingulate cortex, lead to impaired PKA-pathway-mediated LTP in synapses containing GluR1 receptors. We validated these findings using a genotyped EEG dataset where polygenic risk scores for synaptic and ion channel-encoding genes as well as modulation of visual evoked potentials (VEP) were determined for 286 healthy controls. Our results provide a possible genetic mechanism for plasticity impairments in schizophrenia, which can lead to improved understanding and, ultimately, treatment of the disorder.

Trichloroethanol, an active metabolite of chloral hydrate, modulates tetrodotoxin-resistant Na+ channels in rat nociceptive neurons

BACKGROUND

Chloral hydrate is a sedative-hypnotic drug widely used for relieving fear and anxiety in pediatric patients. However, mechanisms underlying the chloral hydrate-mediated analgesic action remain unexplored. Therefore, we investigated the effect of 2',2',2'-trichloroethanol (TCE), the active metabolite of chloral hydrate, on tetrodotoxin-resistant (TTX-R) Na⁺ channels expressed in nociceptive sensory neurons.

METHODS

The TTX-R Na⁺ current (I_Na) was recorded from acutely isolated rat trigeminal ganglion neurons using the whole-cell patch-clamp technique.

RESULTS

Trichloroethanol decreased the peak amplitude of transient TTX-R I_Na in a concentration-dependent manner and potently inhibited persistent components of transient TTX-R I_Na and slow voltage-ramp-induced I_Na at clinically relevant concentrations. Trichloroethanol exerted multiple effects on various properties of TTX-R Na⁺ channels; it (1) induced a hyperpolarizing shift on the steady-state fast inactivation relationship, (2) increased use-dependent inhibition, (3) accelerated the onset of inactivation, and (4) retarded the recovery of inactivated TTX-R Na⁺ channels. Under current-clamp conditions, TCE increased the threshold for the generation of action potentials, as well as decreased the number of action potentials elicited by depolarizing current stimuli.

CONCLUSIONS

Our findings suggest that chloral hydrate, through its active metabolite TCE, inhibits TTX-R I_Na and modulates various properties of these channels, resulting in the decreased excitability of nociceptive neurons. These pharmacological characteristics provide novel insights into the analgesic efficacy exerted by chloral hydrate.

Thalamic control of sensory processing and spindles in a biophysical somatosensory thalamoreticular circuit model of wakefulness and sleep

Thalamoreticular circuitry plays a key role in arousal, attention, cognition, and sleep spindles, and is linked to several brain disorders. A detailed computational model of mouse somatosensory thalamus and thalamic reticular nucleus has been developed to capture the properties of over 14,000 neurons connected by 6 million synapses. The model recreates the biological connectivity of these neurons, and simulations of the model reproduce multiple experimental findings in different brain states. The model shows that inhibitory rebound produces frequency-selective enhancement of thalamic responses during wakefulness. We find that thalamic interactions are responsible for the characteristic waxing and waning of spindle oscillations. In addition, we find that changes in thalamic excitability control spindle frequency and their incidence. The model is made openly available to provide a new tool for studying the function and dysfunction of the thalamoreticular circuitry in various brain states.

Processing of cell assemblies in the lateral entorhinal cortex

There is evidence that olfactory cortex responds to its afferent input with the generation of cell assemblies: collections of principal neurons that fire together over a time scale of tens of ms. If such assemblies form an odor representation, then a fundamental question is how each assembly then induces neuronal activity in downstream structures. We have addressed this question in a detailed model of superficial layers of lateral entorhinal cortex, a recipient of input from olfactory cortex and olfactory bulb. Our results predict that the response of the fan cell subpopulation can be approximated by a relatively simple Boolean process, somewhat along the lines of the McCulloch/Pitts scheme; this is the case because of the sparsity of recurrent excitation amongst fan cells. However, because of recurrent excitatory connections between layer 2 and layer 3 pyramidal cells, synaptic and probably also gap junctional, the response of pyramidal cell subnetworks cannot be so approximated. Because of the highly structured anatomy of entorhinal output projections, our model suggests that downstream targets of entorhinal cortex (dentate gyrus, hippocampal CA3, CA1, piriform cortex, olfactory bulb) receive differentially processed information.

Perinatal development of central vestibular neurons in mice

Central circuitry of the vestibular nuclei integrates sensory inputs in the adaptive control of motor behaviors such as posture, locomotion, and gaze stabilization. Thus far, such circuits have been mostly examined at mature stages, whereas their emergence and early development have remained poorly described. Here, we focused on the perinatal period of murine development, from embryonic day E14.5 to post-natal day P5, to investigate the ontogeny of two functionally distinct vestibular neuronal groups, neurons projecting to the spinal cord via the lateral vestibulospinal tract (LVST) and commissural neurons of the medial vestibular nucleus that cross the midline to the contralateral nucleus. Using transgenic mice and retrograde labeling, we found that network-constitutive GABAergic and glycinergic neurons are already established in the two vestibular groups at embryonic stages. Although incapable of repetitive firing at E14.5, neurons of both groups can generate spike trains from E15.5 onward and diverge into previously established A or B subtypes according to the absence (A) or presence (B) of a two-stage spike after hyperpolarization. Investigation of several voltage-dependent membrane properties indicated that solely LVST neurons undergo significant maturational changes in their electrophysiological characteristics during perinatal development. The proportions of A vs B subtypes also evolve in both groups, with type A neurons remaining predominant at all stages, and type B commissural neurons appearing only post-natally. Together, our results indicate that vestibular neurons acquire their distinct morpho-functional identities after E14.5 and that the early maturation of membrane properties does not emerge uniformly in the different functional subpopulations of vestibulo-motor pathways.

Focal seizures are organized by feedback between neural activity and ion concentration changes

Human and animal EEG data demonstrate that focal seizures start with low-voltage fast activity, evolve into rhythmic burst discharges and are followed by a period of suppressed background activity. This suggests that processes with dynamics in the range of tens of seconds govern focal seizure evolution. We investigate the processes associated with seizure dynamics by complementing the Hodgkin-Huxley mathematical model with the physical laws that dictate ion movement and maintain ionic gradients. Our biophysically realistic computational model closely replicates the electrographic pattern of a typical human focal seizure characterized by low voltage fast activity onset, tonic phase, clonic phase and postictal suppression. Our study demonstrates, for the first time in silico, the potential mechanism of seizure initiation by inhibitory interneurons via the initial build-up of extracellular K+ due to intense interneuronal spiking. The model also identifies ionic mechanisms that may underlie a key feature in seizure dynamics, i.e., progressive slowing down of ictal discharges towards the end of seizure. Our model prediction of specific scaling of inter-burst intervals is confirmed by seizure data recorded in the whole guinea pig brain in vitro and in humans, suggesting that the observed termination pattern may hold across different species. Our results emphasize ionic dynamics as elementary processes behind seizure generation and indicate targets for new therapeutic strategies.

Contribution of tetrodotoxin-resistant persistent Na+ currents to the excitability of C-type dural afferent neurons in rats

BACKGROUND

Growing evidence supports the important role of persistent sodium currents (I_NaP) in the neuronal excitability of various central neurons. However, the role of tetrodotoxin-resistant (TTX-R) Na⁺ channel-mediated I_NaP in the neuronal excitability of nociceptive neurons remains poorly understood.

METHODS

We investigated the functional role of TTX-R I_NaP in the excitability of C-type nociceptive dural afferent neurons, which was identified using a fluorescent dye, 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchloride (DiI), and a whole-cell patch-clamp technique.

RESULTS

TTX-R I_NaP were found in most DiI-positive neurons, but their density was proportional to neuronal size. Although the voltage dependence of TTX-R Na⁺ channels did not differ among DiI-positive neurons, the extent of the onset of slow inactivation, recovery from inactivation, and use-dependent inhibition of these channels was highly correlated with neuronal size and, to a great extent, the density of TTX-R I_NaP. In the presence of TTX, treatment with a specific I_NaP inhibitor, riluzole, substantially decreased the number of action potentials generated by depolarizing current injection, suggesting that TTX-R I_NaP are related to the excitability of dural afferent neurons. In animals treated chronically with inflammatory mediators, the density of TTX-R I_NaP was significantly increased, and it was difficult to inactivate TTX-R Na⁺ channels.

CONCLUSIONS

TTX-R I_NaP apparently contributes to the differential properties of TTX-R Na⁺ channels and neuronal excitability. Consequently, the selective modulation of TTX-R I_NaP could be, at least in part, a new approach for the treatment of migraine headaches.

Modeling NaV1.1/SCN1A sodium channel mutations in a microcircuit with realistic ion concentration dynamics suggests differential GABAergic mechanisms leading to hyperexcitability in epilepsy and hemiplegic migraine

Loss of function mutations of SCN1A, the gene coding for the voltage-gated sodium channel Na_V1.1, cause different types of epilepsy, whereas gain of function mutations cause sporadic and familial hemiplegic migraine type 3 (FHM-3). However, it is not clear yet how these opposite effects can induce paroxysmal pathological activities involving neuronal networks’ hyperexcitability that are specific of epilepsy (seizures) or migraine (cortical spreading depolarization, CSD). To better understand differential mechanisms leading to the initiation of these pathological activities, we used a two-neuron conductance-based model of interconnected GABAergic and pyramidal glutamatergic neurons, in which we incorporated ionic concentration dynamics in both neurons. We modeled FHM-3 mutations by increasing the persistent sodium current in the interneuron and epileptogenic mutations by decreasing the sodium conductance in the interneuron. Therefore, we studied both FHM-3 and epileptogenic mutations within the same framework, modifying only two parameters. In our model, the key effect of gain of function FHM-3 mutations is ion fluxes modification at each action potential (in particular the larger activation of voltage-gated potassium channels induced by the Na_V1.1 gain of function), and the resulting CSD-triggering extracellular potassium accumulation, which is not caused only by modifications of firing frequency. Loss of function epileptogenic mutations, on the other hand, increase GABAergic neurons’ susceptibility to depolarization block, without major modifications of firing frequency before it. Our modeling results connect qualitatively to experimental data: potassium accumulation in the case of FHM-3 mutations and facilitated depolarization block of the GABAergic neuron in the case of epileptogenic mutations. Both these effects can lead to pyramidal neuron hyperexcitability, inducing in the migraine condition depolarization block of both the GABAergic and the pyramidal neuron. Overall, our findings suggest different mechanisms of network hyperexcitability for migraine and epileptogenic Na_V1.1 mutations, implying that the modifications of firing frequency may not be the only relevant pathological mechanism.

The voltage-gated sodium channel Na_V1.1 is a major target of human mutations implicated in different pathologies. In particular, mutations identified in certain types of epilepsy cause loss of function of the channel, whereas mutations identified in certain types of migraine (in which spreading depolarizations of the cortical circuits of the brain are involved) cause instead gain of function. Here, we study dysfunctions induced by these differential effects in a two-neuron (GABAergic and pyramidal) conductance-based model with dynamic ion concentrations. We obtain results that can be related to experimental findings in both situations. Namely, extracellular potassium accumulation induced by the activity of the GABAergic neuron in the case of CSD, and higher propensity of the GABAergic neuron to depolarization block in the epileptogenic scenario, without significant modifications of its firing frequency prior to it. Both scenarios can induce hyperexcitability of the pyramidal neuron, leading in the migraine condition to depolarization block of both the GABAergic and the pyramidal neuron. Our results are successfully confronted to experimental data and suggest that modification of firing frequency is not the only key mechanism in these pathologies of neuronal excitability.

Topography in the Bursting Dynamics of Entorhinal Neurons

Medial entorhinal cortex contains neural substrates for representing space. These substrates include grid cells that fire in repeating locations and increase in scale progressively along the dorsal-to-ventral entorhinal axis, with the physical distance between grid firing nodes increasing from tens of centimeters to several meters in rodents. Whether the temporal scale of grid cell spiking dynamics shows a similar dorsal-to-ventral organization remains unknown. Here, we report the presence of a dorsal-to-ventral gradient in the temporal spiking dynamics of grid cells in behaving mice. This gradient in bursting supports the emergence of a dorsal grid cell population with a high signal-to-noise ratio. In vitro recordings combined with a computational model point to a role for gradients in non-inactivating sodium conductances in supporting the bursting gradient in vivo. Taken together, these results reveal a complementary organization in the temporal and intrinsic properties of entorhinal cells.

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.

Experimentally-constrained biophysical models of tonic and burst firing modes in thalamocortical neurons

Somatosensory thalamocortical (TC) neurons from the ventrobasal (VB) thalamus are central components in the flow of sensory information between the periphery and the cerebral cortex, and participate in the dynamic regulation of thalamocortical states including wakefulness and sleep. This property is reflected at the cellular level by the ability to generate action potentials in two distinct firing modes, called tonic firing and low-threshold bursting. Although the general properties of TC neurons are known, we still lack a detailed characterization of their morphological and electrical properties in the VB thalamus. The aim of this study was to build biophysically-detailed models of VB TC neurons explicitly constrained with experimental data from rats. We recorded the electrical activity of VB neurons (N = 49) and reconstructed morphologies in 3D (N = 50) by applying standardized protocols. After identifying distinct electrical types, we used a multi-objective optimization to fit single neuron electrical models (e-models), which yielded multiple solutions consistent with the experimental data. The models were tested for generalization using electrical stimuli and neuron morphologies not used during fitting. A local sensitivity analysis revealed that the e-models are robust to small parameter changes and that all the parameters were constrained by one or more features. The e-models, when tested in combination with different morphologies, showed that the electrical behavior is substantially preserved when changing dendritic structure and that the e-models were not overfit to a specific morphology. The models and their analysis show that automatic parameter search can be applied to capture complex firing behavior, such as co-existence of tonic firing and low-threshold bursting over a wide range of parameter sets and in combination with different neuron morphologies.

Thalamocortical neurons are one of the main components of the thalamocortical system, which is implicated in key functions including sensory transmission and the transition between brain states. These functions are reflected at the cellular level by the ability to generate action potentials in two distinct modes, called burst and tonic firing. Biophysically-detailed computational modeling of these cells can provide a tool to understand the role of these neurons within thalamocortical circuitry. We started by collecting single cell experimental data by applying standardized experimental procedures in brain slices of the rat. Prior work has demonstrated that biological constraints can be integrated using multi-objective optimization to build biologically realistic models of neurons. Here, we employed similar techniques, but extended them to capture the multiple firing modes of thalamic neurons. We compared the model results with additional experimental data, test their generalization and quantitatively reject those that deviated significantly from the experimental variability. These models can be readily integrated in a data-driven pipeline to reconstruct and simulate circuit activity in the thalamocortical system.

Kinetic properties of persistent Na+ current orchestrate oscillatory bursting in respiratory neurons

The rhythmic pattern of breathing depends on the pre-Bötzinger complex (preBötC) in the brainstem, a vital circuit that contains a population of neurons with intrinsic oscillatory bursting behavior. Here, we investigate the specific kinetic properties that enable voltage-gated sodium channels to establish oscillatory bursting in preBötC inspiratory neurons, which exhibit an unusually large persistent Na⁺ current (I_NaP). We first characterize the kinetics of I_NaP in neonatal rat brainstem slices in vitro, using whole-cell patch-clamp and computational modeling, and then test the contribution of I_NaP to rhythmic bursting in live neurons, using the dynamic clamp technique. We provide evidence that subthreshold activation, persistence at suprathreshold potentials, slow inactivation, and slow recovery from inactivation are kinetic features of I_NaP that regulate all aspects of intrinsic rhythmic bursting in preBötC neurons. The slow and cumulative inactivation of I_NaP during the burst active phase controls burst duration and termination, while the slow recovery from inactivation controls the duration of the interburst interval. To demonstrate this mechanism, we develop a Markov state model of I_NaP that explains a comprehensive set of voltage clamp data. By adding or subtracting a computer-generated I_NaP from a live neuron via dynamic clamp, we are able to convert nonbursters into intrinsic bursters, and vice versa. As a control, we test a model with inactivation features removed. Adding noninactivating I_NaP into nonbursters results in a pattern of random transitions between sustained firing and quiescence. The relative amplitude of I_NaP is the key factor that separates intrinsic bursters from nonbursters and can change the fraction of intrinsic bursters in the preBötC. I_NaP could thus be an important target for regulating network rhythmogenic properties.

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Biological heterogeneities are ubiquitous and play critical roles in the emergence of physiology at multiple scales. Although neurons in layer II (LII) of the medial entorhinal cortex (MEC) express heterogeneities in channel properties, the impact of such heterogeneities on the robustness of their cellular-scale physiology has not been assessed. Here, we performed a 55-parameter stochastic search spanning nine voltage- or calcium-activated channels to assess the impact of channel heterogeneities on the concomitant emergence of 10 in vitro electrophysiological characteristics of LII stellate cells (SCs). We generated 150,000 models and found a heterogeneous subpopulation of 449 valid models to robustly match all electrophysiological signatures. We employed this heterogeneous population to demonstrate the emergence of cellular-scale degeneracy in SCs, whereby disparate parametric combinations expressing weak pairwise correlations resulted in similar models. We then assessed the impact of virtually knocking out each channel from all valid models and demonstrate that the mapping between channels and measurements was many-to-many, a critical requirement for the expression of degeneracy. Finally, we quantitatively predict that the spike-triggered average of SCs should be endowed with theta-frequency spectral selectivity and coincidence detection capabilities in the fast gamma-band. We postulate this fast gamma-band coincidence detection as an instance of cellular-scale-efficient coding, whereby SC response characteristics match the dominant oscillatory signals in LII MEC. The heterogeneous population of valid SC models built here unveils the robust emergence of cellular-scale physiology despite significant channel heterogeneities, and forms an efficacious substrate for evaluating the impact of biological heterogeneities on entorhinal network function.

NEW & NOTEWORTHY We assessed the impact of heterogeneities in channel properties on the robustness of cellular-scale physiology of medial entorhinal cortical stellate neurons. We demonstrate that neuronal models with disparate channel combinations were endowed with similar physiological characteristics, as a consequence of the many-to-many mapping between channel properties and the physiological characteristics that they modulate. We predict that the spike-triggered average of stellate cells should be endowed with theta-frequency spectral selectivity and fast gamma-band coincidence detection capabilities.

Mutations in SCN3A cause early infantile epileptic encephalopathy

OBJECTIVE

Voltage-gated sodium (Na⁺ ) channels underlie action potential generation and propagation and hence are central to the regulation of excitability in the nervous system. Mutations in the genes SCN1A, SCN2A, and SCN8A, encoding the Na⁺ channel pore-forming (α) subunits Nav1.1, 1.2, and 1.6, respectively, and SCN1B, encoding the accessory subunit β₁ , are established causes of genetic epilepsies. SCN3A, encoding Nav1.3, is known to be highly expressed in brain, but has not previously been linked to early infantile epileptic encephalopathy. Here, we describe a cohort of 4 patients with epileptic encephalopathy and heterozygous de novo missense variants in SCN3A (p.Ile875Thr in 2 cases, p.Pro1333Leu, and p.Val1769Ala).

METHODS

All patients presented with treatment-resistant epilepsy in the first year of life, severe to profound intellectual disability, and in 2 cases (both with the variant p.Ile875Thr), diffuse polymicrogyria.

RESULTS

Electrophysiological recordings of mutant channels revealed prominent gain of channel function, with a markedly increased amplitude of the slowly inactivating current component, and for 2 of 3 mutants (p.Ile875Thr and p.Pro1333Leu), a leftward shift in the voltage dependence of activation to more hyperpolarized potentials. Gain of function was not observed for Nav1.3 variants known or presumed to be inherited (p.Arg1642Cys and p.Lys1799Gln). The antiseizure medications phenytoin and lacosamide selectively blocked slowly inactivating over transient current in wild-type and mutant Nav1.3 channels.

INTERPRETATION

These findings establish SCN3A as a new gene for infantile epileptic encephalopathy and suggest a potential pharmacologic intervention. These findings also reinforce the role of Nav1.3 as an important regulator of neuronal excitability in the developing brain, while providing additional insight into mechanisms of slow inactivation of Nav1.3. Ann Neurol 2018;83:703-717.

Systematic generation of biophysically detailed models for diverse cortical neuron types

The cellular components of mammalian neocortical circuits are diverse, and capturing this diversity in computational models is challenging. Here we report an approach for generating biophysically detailed models of 170 individual neurons in the Allen Cell Types Database to link the systematic experimental characterization of cell types to the construction of cortical models. We build models from 3D morphologies and somatic electrophysiological responses measured in the same cells. Densities of active somatic conductances and additional parameters are optimized with a genetic algorithm to match electrophysiological features. We evaluate the models by applying additional stimuli and comparing model responses to experimental data. Applying this technique across a diverse set of neurons from adult mouse primary visual cortex, we verify that models preserve the distinctiveness of intrinsic properties between subsets of cells observed in experiments. The optimized models are accessible online alongside the experimental data. Code for optimization and simulation is also openly distributed.

Linearization of excitatory synaptic integration at no extra cost

In many theories of neural computation, linearly summed synaptic activation is a pervasive assumption for the computations performed by individual neurons. Indeed, for certain nominally optimal models, linear summation is required. However, the biophysical mechanisms needed to produce linear summation may add to the energy-cost of neural processing. Thus, the benefits provided by linear summation may be outweighed by the energy-costs. Using voltage-gated conductances in a relatively simple neuron model, this paper quantifies the cost of linearizing dendritically localized synaptic activation. Different combinations of voltage-gated conductances were examined, and many are found to produce linearization; here, four of these models are presented. Comparing the energy-costs to a purely passive model, reveals minimal or even no additional costs in some cases.

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model

Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar'e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.

Changes of Ionic Concentrations During Seizure Transitions - A Modeling Study

Traditionally, it is considered that neuronal synchronization in epilepsy is caused by a chain reaction of synaptic excitation. However, it has been shown that synchronous epileptiform activity may also arise without synaptic transmission. In order to investigate the respective roles of synaptic interactions and nonsynaptic mechanisms in seizure transitions, we developed a computational model of hippocampal cells, involving the extracellular space, realistic dynamics of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] ions, glial uptake and extracellular diffusion mechanisms. We show that the network behavior with fixed ionic concentrations may be quite different from the neurons' behavior when more detailed modeling of ionic dynamics is included. In particular, we show that in the extended model strong discharge of inhibitory interneurons may result in long lasting accumulation of extracellular [Formula: see text], which sustains the depolarization of the principal cells and causes their pathological discharges. This effect is not present in a reduced, purely synaptic network. These results point to the importance of nonsynaptic mechanisms in the transition to seizure.

Competition between Persistent Na+ and Muscarine-Sensitive K+ Currents Shapes Perithreshold Resonance and Spike Tuning in CA1 Pyramidal Neurons

Neurons from many brain regions display intrinsic subthreshold theta-resonance, responding preferentially to theta-frequency oscillatory stimuli. Resonance may contribute to selective communication among neurons and to orchestrate brain rhythms. CA1 pyramidal neurons receive theta activity, generating place fields. In these neurons the expression of perithreshold frequency preference is controversial, particularly in the spiking regime, with evidence favoring either non-resonant (integrator-like) or resonant behavior. Perithreshold dynamics depends on the persistent Na⁺ current I_NaP developing above −70 mV and the muscarine-sensitive K⁺ current I_M activating above −60 mV. We conducted current and voltage clamp experiments in slices to investigate perithreshold excitability of CA1 neurons under oscillatory stimulation. Around 20% of neurons displayed perithreshold resonance that is expressed in spiking. The remaining neurons (~80%) acted as low-pass filters lacking frequency preference. Paired voltage clamp measurement of I_NaP and I_M showed that perithreshold activation of I_M is in general low while I_NaP is high enough to depolarize neurons toward threshold before resonance expression, explaining the most abundant non-resonant perithreshold behavior. Partial blockade of I_NaP by pharmacological tools or dynamic clamp changed non-resonant to resonant behavior. Furthermore, shifting I_M activation toward hyperpolarized potentials by dynamic clamp also transformed non-resonant neurons into resonant ones. We propose that the relative levels of I_NaP and I_M control perithreshold behavior of CA1 neurons constituting a gating mechanism for theta resonance in the spiking regime. Both currents are regulated by intracellular signaling and neuromodulators which may allow dynamic switching of perithreshold behavior between resonant and non-resonant.

Ranolazine vs phenytoin: greater effect of ranolazine on the transient Na(+) current than on the persistent Na(+) current in central neurons

Voltage-gated Na(+) channels (NaV) are involved in pathologies and are important targets of drugs (NaV-blockers), e.g. some anti-epileptic drugs (AEDs). Besides the fast inactivating transient Na(+) current (INaT), they generate a slowly inactivating "persistent" current (INaP). Ranolazine, a NaV-blocker approved for treatment of angina pectoris, is considered a preferential inhibitor of INaP and has been proposed as a novel AED. Although it is thought that classic NaV-blockers used as AEDs target mainly INaT, they can also reduce INaP. It is important to disclose specific features of novel NaV-blockers, which could be necessary for their effect as AEDs in drug resistant patients. We have compared the action of ranolazine and of the classic AED phenytoin in transfected cells expressing the neuronal NaV1.1 Na(+) channel and in neurons of neocortical slices. Our results show that the relative block of INaT versus INaP of ranolazine and phenytoin is variable and depends on Na(+) current activation conditions. Strikingly, ranolazine blocks with less efficacy INaP and more efficacy INaT than phenytoin in conditions mimicking pathological states (i.e. high frequency firing and long lasting depolarizations). The effects are consistent with binding of ranolazine to both open/pre-open and inactivated states; larger INaT block at high stimulation frequencies is caused by the induction of a slow inactivated state. Thus, contrary than expected, ranolazine is not a better INaP blocker than phenytoin in central neurons, and phenytoin is not a better INaT blocker than ranolazine. Nevertheless, they show a complementary action and could differentially target specific pathological dysfunctions.

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca(2+) current I s, and the Ca(2+) -activated K(+) current I KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.

Two distinct types of depolarizing afterpotentials are differentially expressed in stellate and pyramidal-like neurons of entorhinal-cortex layer II

Two types of principal neurons, stellate cells and pyramidal-like cells, are found in medial entorhinal-cortex (mEC) layer II, and are believed to represent two distinct channels of information processing and transmission in the entorhinal cortex-hippocampus network. In this study, we found that depolarizing afterpotentials (DAPs) that follow single action potentials (APs) evoked from various levels of holding membrane voltage (Vh ) show distinct properties in the two cells types. In both, an evident DAP followed the AP at near-threshold Vh levels, and was accompanied by an enhancement of excitability and spike-timing precision. This DAP was sensitive to voltage-gated Na(+)-channel block with TTx, but not to partial removal of extracellular Ca(2+). Application of 5-μM anandamide, which inhibited the resurgent and persistent Na(+) -current components in a relatively selective way, significantly reduced the amplitude of this particular DAP while exerting poor effects on the foregoing AP. In the presence of background hyperpolarization, DAPs showed an opposite behavior in the two cell types, as in stellate cells they became even more prominent, whereas in pyramidal-like cells their amplitude was markedly reduced. The DAP observed in stellate cells under this condition was strongly inhibited by partial extracellular-Ca(2+) removal, and was sensitive to the low-voltage-activated Ca(2+)-channel blocker, NNC55-0396. This Ca(2+) dependence was not observed in the residual DAP evoked in pyramidal-like cells from likewise negative Vh levels. These results demonstrate that two distinct mechanism of DAP generation operate in mEC layer-II neurons, one Na(+)-dependent and active at near-threshold Vh levels in both stellate and-pyramidal-like cells, the other Ca(2+)-dependent and only expressed by stellate cells in the presence of background membrane hyperpolarization.

Membrane potential-dependent integration of synaptic inputs in entorhinal stellate neurons

Stellate cells (SCs) of the medial entorhinal cortex exhibit robust spontaneous membrane-potential oscillations (MPOs) in the theta (4-12 Hz) frequency band as well as theta-frequency resonance in their membrane impedance spectra. Past experimental and modeling work suggests that these features may contribute to the phase-locking of SCs to the entorhinal theta rhythm and may be important for forming the hexagonally tiled grid cell place fields exhibited by these neurons in vivo. Among the major biophysical mechanisms contributing to MPOs is a population of persistent (non-inactivating or slowly inactivating) sodium channels. The resulting persistent sodium conductance (GNaP ) gives rise to an apparent increase in input resistance as the cell approaches threshold. In this study, we used dynamic clamp to test the hypothesis that this increased input resistance gives rise to voltage-dependent, and thus MPO phase-dependent, changes in the amplitude of excitatory and inhibitory post-synaptic potential (PSP) amplitudes. We find that PSP amplitude depends on membrane potential, exhibiting a 5-10% increase in amplitude per mV depolarization. The effect is larger than-and sums quasi-linearly with-the effect of the synaptic driving force, V - Esyn . Given that input-driven MPOs 10 mV in amplitude are commonly observed in MEC stellate cells in vivo, this voltage- and phase-dependent synaptic gain is large enough to modulate PSP amplitude by over 50% during theta-frequency MPOs. Phase-dependent synaptic gain may therefore impact the phase locking and phase precession of grid cells in vivo to ongoing network oscillations. © 2014 Wiley Periodicals, Inc.

The effects of eslicarbazepine on persistent Na⁺ current and the role of the Na⁺ channel β subunits

Eslicarbazepine is the major active metabolite of eslicarbazepine acetate, a once-daily antiepileptic drug approved in Europe as adjunctive therapy for refractory partial-onset seizures in adults. This study was aimed to determine the effects of eslicarbazepine on persistent Na(+) currents (INaP) and the role of β subunits in modulating these effects. To study the role of β subunits of the Na(+) channel we used a mouse line genetically lacking either the β1 or β2 subunit, encoded by the SCN1B or SCN2B gene, respectively. Whole cell patch-clamp recordings were performed on CA1 neurons in hippocampal slices under control conditions and application of 300 μM eslicarbazepine. We examined INaP in acutely isolated CA1 neurons and repetitive firing in hippocampal slices of mice lacking β subunits and corresponding wild-type littermates. We found that eslicarbazepine caused a significant reduction of maximal INaP conductance and an efficient reduction of the firing rate in wild-type mice. We have shown previously a paradoxical increase of conductance of INaP caused by carbamazepine in mice lacking β1 subunits in the subthreshold range, leading to a failure in affecting neuronal firing (Uebachs et al., 2010). In contrast, eslicarbazepine did not cause this paradoxical effect on INaP in SCN1B null mice. Consequently, the effects of eslicarbazepine on repetitive firing were maintained in these animals. These results indicate that eslicarbazepine exerts effects on INaP similar to those known for carbamazepine. However, in animals lacking the β1 Na(+) channel subunit these effects are maintained. Therefore, eslicarbazepine potentially overcomes a previously described putative mechanism of resistance to established Na(+) channel acting antiepileptic drugs.

The cellular building blocks of breathing

Respiratory brainstem neurons fulfill critical roles in controlling breathing: they generate the activity patterns for breathing and contribute to various sensory responses including changes in O2 and CO2. These complex sensorimotor tasks depend on the dynamic interplay between numerous cellular building blocks that consist of voltage-, calcium-, and ATP-dependent ionic conductances, various ionotropic and metabotropic synaptic mechanisms, as well as neuromodulators acting on G-protein coupled receptors and second messenger systems. As described in this review, the sensorimotor responses of the respiratory network emerge through the state-dependent integration of all these building blocks. There is no known respiratory function that involves only a small number of intrinsic, synaptic, or modulatory properties. Because of the complex integration of numerous intrinsic, synaptic, and modulatory mechanisms, the respiratory network is capable of continuously adapting to changes in the external and internal environment, which makes breathing one of the most integrated behaviors. Not surprisingly, inspiration is critical not only in the control of ventilation, but also in the context of "inspiring behaviors" such as arousal of the mind and even creativity. Far-reaching implications apply also to the underlying network mechanisms, as lessons learned from the respiratory network apply to network functions in general.

From lamprey to salamander: an exploratory modeling study on the architecture of the spinal locomotor networks in the salamander

The evolutionary transition from water to land required new locomotor modes and corresponding adjustments of the spinal "central pattern generators" for locomotion. Salamanders resemble the first terrestrial tetrapods and represent a key animal for the study of these changes. Based on recent physiological data from salamanders, and previous work on the swimming, limbless lamprey, we present a model of the basic oscillatory network in the salamander spinal cord, the spinal segment. Model neurons are of the Hodgkin-Huxley type. Spinal hemisegments contain sparsely connected excitatory and inhibitory neuron populations, and are coupled to a contralateral hemisegment. The model yields a large range of experimental findings, especially the NMDA-induced oscillations observed in isolated axial hemisegments and segments of the salamander Pleurodeles waltlii. The model reproduces most of the effects of the blockade of AMPA synapses, glycinergic synapses, calcium-activated potassium current, persistent sodium current, and [Formula: see text]-current. Driving segments with a population of brainstem neurons yields fast oscillations in the in vivo swimming frequency range. A minimal modification to the conductances involved in burst-termination yields the slower stepping frequency range. Slow oscillators can impose their frequency on fast oscillators, as is likely the case during gait transitions from swimming to stepping. Our study shows that a lamprey-like network can potentially serve as a building block of axial and limb oscillators for swimming and stepping in salamanders.

Slowly inactivating component of Na+ current in peri-somatic region of hippocampal CA1 pyramidal neurons

The properties of voltage-gated ion channels on the neuronal membrane shape electrical activity such as generation and backpropagation of action potentials, initiation of dendritic spikes, and integration of synaptic inputs. Subthreshold currents mediated by sodium channels are of interest because of their activation near rest, slow inactivation kinetics, and consequent effects on excitability. Modulation of these currents can also perturb physiological responses of a neuron that might underlie pathological states such as epilepsy. Using nucleated patches from the peri-somatic region of hippocampal CA1 neurons, we recorded a slowly inactivating component of the macroscopic Na(+) current (which we have called INaS) that shared many biophysical properties with the persistent Na(+) current, INaP, but showed distinctively faster inactivating kinetics. Ramp voltage commands with a velocity of 400 mV/s were found to elicit this component of Na(+) current reliably. INaS also showed a more hyperpolarized I-V relationship and slower inactivation than those of the fast transient Na(+) current (INaT) recorded in the same patches. The peak amplitude of INaS was proportional to the peak amplitude of INaT but was much smaller in amplitude. Hexanol, riluzole, and ranolazine, known Na(+) channel blockers, were tested to compare their effects on both INaS and INaT. The peak conductance of INaS was preferentially blocked by hexanol and riluzole, but the shift of half-inactivation voltage (V1/2) was only observed in the presence of riluzole. Current-clamp measurements with hexanol suggested that INaS was involved in generation of an action potential and in upregulation of neuronal excitability.

Phenytoin inhibits the persistent sodium current in neocortical neurons by modifying its inactivation properties

The persistent Na⁺ current (I_NaP) is important for neuronal functions and can play a role in several pathologies, although it is small compared to the transient Na⁺ current (I_NaT). Notably, I_NaP is not a real persistent current because it undergoes inactivation with kinetics in the order of tens of seconds, but this property has often been overlooked. Na⁺ channel blockers, drugs used for treating epilepsy and other diseases, can inhibit I_NaP, but the mechanism of this action and the conditions in which I_NaP can be actually inhibited have not been completely clarified yet. We evaluated the action of phenytoin (PHT), a prototype anti-epileptic Na⁺ channel blocker, on I_NaP inactivation in pyramidal neurons of rat sensorimotor cortical slices at different concentrations, from 5 to 100 µM. PHT did not modify I_NaP evoked with depolarizing voltage ramps of 50 or 100 mVs⁻¹, but decreased I_NaP evoked by slower voltage ramps (10 mVs⁻¹). However, at all of the tested concentrations, PHT decreased I_NaP evoked by faster ramps when they were preceded by inactivating pre-pulses. Moreover, PHT shifted towards negative potentials the voltage-dependence of I_NaP inactivation and accelerated its kinetics of development also at depolarized potentials (+40 mV), not consistently with a simple inactivated state stabilizer. Therefore, our study shows a prominent PHT effect on I_NaP inactivation rather than an open channel block, which is instead often implied. I_NaP is inhibited by PHT only in conditions that induce major I_NaP inactivation. These results highlight the importance of I_NaP inactivation not only for physiological functions but also as drug target, which could be shared by other therapeutic drugs. Through this action PHT can reduce I_NaP-induced long-lasting pathological depolarisations and intracellular sodium overload, whereas shorter I_NaP actions should not be modified. These properties set the conditions of efficacy and the limits of PHT as I_NaP inhibitor.

The response of NaV1.3 sodium channels to ramp stimuli: multiple components and mechanisms

NaV1.3 voltage-gated sodium channels have been shown to be expressed at increased levels within axotomized dorsal root ganglion neurons and within injured axons within neuromas and have been implicated in neuropathic pain. Like a number of other sodium channel isoforms, NaV1.3 channels produce a robust response to slow ramplike stimuli. Here we show that the response of NaV1.3 to ramp stimuli consists of two components: an early component, dependent upon ramp rate, that corresponds to a window current that is dependent upon closed-state inactivation; and a second component at more depolarized potentials that is correlated with persistent current which is detected for many tens of milliseconds after the start of a depolarizing pulse. We also assessed the K354Q NaV1.3 epilepsy-associated mutant channel, which is known to display an enhanced persistent current and demonstrate a strong correlation with the second component of the ramp response. Our results show that a single sodium channel isoform can produce a ramp response with multiple components, reflecting multiple mechanisms, and suggest that the upregulated expression of NaV1.3 in axotomized dorsal root ganglion neurons and enhanced ramp current in K354Q mutant channels can contribute in several ways to hyperexcitability and abnormal spontaneous firing that contribute to hyperexcitability disorders, such as epilepsy and neuropathic pain.

Transient sodium current at subthreshold voltages: activation by EPSP waveforms

Tetrodotoxin (TTX)-sensitive sodium channels carry large transient currents during action potentials and also "persistent" sodium current, a noninactivating TTX-sensitive current present at subthreshold voltages. We examined gating of subthreshold sodium current in dissociated cerebellar Purkinje neurons and hippocampal CA1 neurons, studied at 37°C with near-physiological ionic conditions. Unexpectedly, in both cell types small voltage steps at subthreshold voltages activated a substantial component of transient sodium current as well as persistent current. Subthreshold EPSP-like waveforms also activated a large component of transient sodium current, but IPSP-like waveforms engaged primarily persistent sodium current with only a small additional transient component. Activation of transient as well as persistent sodium current at subthreshold voltages produces amplification of EPSPs that is sensitive to the rate of depolarization and can help account for the dependence of spike threshold on depolarization rate, as previously observed in vivo.

Contribution of near-threshold currents to intrinsic oscillatory activity in rat medial entorhinal cortex layer II stellate cells

The temporal lobe is well known for its oscillatory activity associated with exploration, navigation, and learning. Intrinsic membrane potential oscillations (MPOs) and resonance of stellate cells (SCs) in layer II of the entorhinal cortex are thought to contribute to network oscillations and thereby to the encoding of spatial information. Generation of both MPOs and resonance relies on the expression of specific voltage-dependent ion currents such as the hyperpolarization-activated cation current (I(H)), the persistent sodium current (I(NaP)), and the noninactivating muscarine-modulated potassium current (I(M)). However, the differential contributions of these currents remain a matter of debate. We therefore examined how they modify neuronal excitability near threshold and generation of near-threshold MPOs and resonance in vitro. We found that resonance mainly relied on I(H) and was reduced by I(H) blockers and modulated by cAMP and an I(M) enhancer but that neither of the currents exhibited full control over MPOs in these cells. As previously reported, I(H) controlled a theta-frequency component of MPOs such that blockade of I(H) resulted in fewer regular oscillations that retained low-frequency components and high peak amplitude. However, pharmacological inhibition and augmentation of I(M) also affected MPO frequencies and amplitudes. In contrast to other cell types, inhibition of I(NaP) did not result in suppression of MPOs but only in a moderation of their properties. We reproduced the experimentally observed effects in a single-compartment stochastic model of SCs, providing further insight into the interactions between different ionic conductances.

Distinct developmental patterns in the expression of transient, persistent, and resurgent Na+ currents in entorhinal cortex layer-II neurons

Sub- and near-threshold voltage-dependent Na+ currents (VDSCs) are of major importance in determining the electrical properties of medial entorhinal cortex (mEC) layer-II neurons. Developmental changes in the ability of mEC layer-II stellate cells (SCs) to generate Na+ -dependent, subthreshold electrical events have been reported between P14 and P18. In this study we examined the modifications occurring in the various components of VDSCs during postnatal development of mEC SCs. The transient, resurgent, and persistent Na+ currents (I(NaT), I(NaR), and I(NaP), respectively) showed distinct patterns of developmental expression in the time window considered (P5 to P24-27). All three currents prominently and steeply increased in absolute amplitude and conductance from P5 to at least P16. However, capacitive charge accumulation, an index of membrane surface area, also markedly increased in the same time window, and in the case of I(NaT) the specific conductance per unit of accumulated capacitive charge remained relatively constant. By contrast, specific I(NaR) and I(NaP) conductances showed a significant tendency to increase, especially from P5 to P18. Neither I(NaR) nor I(NaP) represented a constant fraction of the total Na+ current at all developmental ages. Indeed, detectable levels of I(NaR) and I(NaP) were present in only ~20% and ~70%, respectively, of the cells on P5, and were observed in all cells only from P10 onwards. Moreover, the average I(NaR)-to-I(NaT) conductance ratio increased steadily from ~0.004 (P5) up to a plateau level of ~0.05 (P22+), whereas the I(NaP)-to-I(NaT) conductance ratio increased only from ~0.009 on P5 to ~0.02 on P22+. The relative increase in conductance ratio from P5 to P22 was significantly greater for I(NaR) than for I(NaP), indicating that I(NaR) expression starts later than that of I(NaP). These findings show that in mEC layer-II SCs the single functional components of the VDSC are regulated differentially from each other as far as their developmental expression is concerned.

Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields.

Frequency of subthreshold oscillations at different membrane potential voltages in neurons at different anatomical positions on the dorsoventral axis in the rat medial entorhinal cortex

Neurons from layer II of the medial entorhinal cortex show subthreshold membrane potential oscillations (SMPOs) which could contribute to theta-rhythm generation in the entorhinal cortex and to generation of grid cell firing patterns. However, it is unclear whether single neurons have a fixed unique oscillation frequency or whether their frequency varies depending on the mean membrane potential in a cell. We therefore examined the frequency of SMPOs at different membrane potentials in layer II stellate-like cells of the rat medial entorhinal cortex in vitro. Using whole-cell patch recordings, we found that the fluctuations in membrane potential show a broad band of low power frequencies near resting potential that transition to more narrowband oscillation frequencies with depolarization. The transition from broadband to narrowband frequencies depends on the location of the neuron along the dorsoventral axis in the entorhinal cortex, with dorsal neurons transitioning to higher-frequency oscillations relative to ventral neurons transitioning to lower-frequency oscillations. Once SMPOs showed a narrowband frequency, systematic frequency changes were not observed with further depolarization. Using a Hodgkin-Huxley-style model of membrane currents, we show that differences in the influence of depolarization on the frequency of SMPOs at different dorsal to ventral positions could arise from differences in the properties of the h current. The properties of frequency changes in this data are important for evaluating models of the generation of grid cell firing fields with different spacings along the dorsal-to-ventral axis of medial entorhinal cortex.

Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active properties

The thick-tufted layer 5b pyramidal cell extends its dendritic tree to all six layers of the mammalian neocortex and serves as a major building block for the cortical column. L5b pyramidal cells have been the subject of extensive experimental and modeling studies, yet conductance-based models of these cells that faithfully reproduce both their perisomatic Na(+)-spiking behavior as well as key dendritic active properties, including Ca(2+) spikes and back-propagating action potentials, are still lacking. Based on a large body of experimental recordings from both the soma and dendrites of L5b pyramidal cells in adult rats, we characterized key features of the somatic and dendritic firing and quantified their statistics. We used these features to constrain the density of a set of ion channels over the soma and dendritic surface via multi-objective optimization with an evolutionary algorithm, thus generating a set of detailed conductance-based models that faithfully replicate the back-propagating action potential activated Ca(2+) spike firing and the perisomatic firing response to current steps, as well as the experimental variability of the properties. Furthermore, we show a useful way to analyze model parameters with our sets of models, which enabled us to identify some of the mechanisms responsible for the dynamic properties of L5b pyramidal cells as well as mechanisms that are sensitive to morphological changes. This automated framework can be used to develop a database of faithful models for other neuron types. The models we present provide several experimentally-testable predictions and can serve as a powerful tool for theoretical investigations of the contribution of single-cell dynamics to network activity and its computational capabilities.

Multiple T-type Ca2+ current subtypes in electrophysiologically characterized hamster dorsal horn neurons: possible role in spinal sensory integration

Whole cell patch-clamp recordings were used to investigate the contribution of transient, low-threshold calcium currents (I(T)) to firing properties of hamster spinal dorsal horn neurons. I(T) was widely, though not uniformly, expressed by cells in Rexed's laminae I-IV and correlated with the pattern of action potential discharge evoked under current-clamp conditions: I(T) in neurons responding to constant membrane depolarization with one or two action potentials was nearly threefold larger than I(T) in cells responding to the same activation with continuous firing. I(T) was evoked by depolarizing voltage ramps exceeding 46 mV/s and increased with ramp slope (240-2,400 mV/s). Bath application of 200 μM Ni(2+) depressed ramp-activated I(T). Phasic firing recorded in current clamp could only be activated by membrane depolarizations exceeding ∼43-46 mV/s and was blocked by Ni(2+) and mibefradil, suggesting I(T) as an underlying mechanism. Two components of I(T), "fast" and "slow," were isolated based on a difference in time constant of inactivation (12 ms and 177 ms, respectively). The amplitude of the fast subtype depended on the slope of membrane depolarization and was twice as great in burst-firing cells than in cells having a tonic discharge. Post hoc single-cell RT-PCR analyses suggested that the fast component is associated with the Ca(V)3.1 channel subtype. I(T) may enhance responses of phasic-firing dorsal horn neurons to rapid membrane depolarizations and contribute to an ability to discriminate between afferent sensory inputs that encode high- and low-frequency stimulus information.

Na/K ATPase activity is coordinated with the persistent sodium current amplitude

It is known that the Na+/K+ ATPase may control the frequency of slow action potential bursts that can be found in motor patterns generating neurons. Thus, Na+/K+ ATPase can participate in the formation of firing patterns in neurons and it is likely that the ATPase activity is coordinated with the expression of ionic channels. However, so far, there is no such evidence. Here it is shown that, in pyramidal neurons of the rat prefrontal cortex, the density of electrogenic sodium-potassium ATPase current was correlated with the density of the persistent sodium current (R2=0.62, P<0.002). It is speculated that such coordination may improve the control of the firing patterns in prefrontal cortex pyramidal neurons.

Differential effects of Zn2+ on activation, deactivation, and inactivation kinetics in neuronal voltage-gated Na+ channels

Whole-cell, patch-clamp recordings were carried out in acutely dissociated neurons from entorhinal cortex (EC) layer II to study the effects of Zn(2+) on Na(+) current kinetics and voltage dependence. In the presence of 200 μM extracellular Cd(2+) to abolish voltage-dependent Ca(2+) currents, and 100 mM extracellular Na(+), 1 mM Zn(2+) inhibited the transient Na(+) current, I (NaT), only to a modest degree (~17% on average). A more pronounced inhibition (~36%) was induced by Zn(2+) when extracellular Na(+) was lowered to 40 mM. Zn(2+) also proved to modify I (NaT) voltage-dependent and kinetic properties in multiple ways. Zn(2+) (1 mM) shifted the voltage dependence of I (NaT) activation and that of I (NaT) onset speed in the positive direction by ~5 mV. The voltage dependence of I (NaT) steady-state inactivation and that of I (NaT) inactivation kinetics were markedly less affected by Zn(2+). By contrast, I (NaT) deactivation speed was prominently accelerated, and its voltage dependence was shifted by a significantly greater amount (~8 mV on average) than that of I (NaT) activation. In addition, the kinetics of I (NaT) recovery from inactivation were significantly slowed by Zn(2+). Zn(2+) inhibition of I (NaT) showed no signs of voltage dependence over the explored membrane-voltage window, indicating that the above effects cannot be explained by voltage dependence of Zn(2+)-induced channel-pore block. These findings suggest that the multiple, voltage-dependent state transitions that the Na(+) channel undergoes through its activation path are differentially sensitive to the gating-modifying effects of Zn(2+), thus resulting in differential modifications of the macroscopic current's activation, inactivation, and deactivation. Computer modeling provided support to this hypothesis.

The role of spiking and bursting pacemakers in the neuronal control of breathing

Breathing is controlled by a distributed network involving areas in the neocortex, cerebellum, pons, medulla, spinal cord, and various other subcortical regions. However, only one area seems to be essential and sufficient for generating the respiratory rhythm: the preBötzinger complex (preBötC). Lesioning this area abolishes breathing and following isolation in a brain slice the preBötC continues to generate different forms of respiratory activities. The use of slice preparations led to a thorough understanding of the cellular mechanisms that underlie the generation of inspiratory activity within this network. Two types of inward currents, the persistent sodium current (I(NaP)) and the calcium-activated non-specific cation current (I(CAN)), play important roles in respiratory rhythm generation. These currents give rise to autonomous pacemaker activity within respiratory neurons, leading to the generation of intrinsic spiking and bursting activity. These membrane properties amplify as well as activate synaptic mechanisms that are critical for the initiation and maintenance of inspiratory activity. In this review, we describe the dynamic interplay between synaptic and intrinsic membrane properties in the generation of the respiratory rhythm and we relate these mechanisms to rhythm generating networks involved in other behaviors.

Persistent sodium current decreases transient gain in turtle motoneurons

Voltage dependent ion channels can influence signal integration in neurons dramatically. In addition to the classical fast-inactivating Na(+) current that mediates action potentials, many neurons also express persistent sodium current (I(NaP)). Activating at membrane potentials below the threshold for action potentials, this current may amplify excitatory postsynaptic potentials and shape the firing patterns. To determine the qualitative contribution of I(NaP) to the intrinsic firing properties of motoneurons, we eliminated this current by dynamic clamp. As expected, we found that elimination of I(NaP) shifted the rheobase to more positive currents. More interestingly, elimination of I(NaP) increased the steepness of initial frequency-to-current (fI) relation. This suggests that I(NaP) decreases the transient gain and broadens the integration window for short synaptic inputs in spinal motoneurons.