HCN1 channels control resting and active integrative properties of stellate cells from layer II of the entorhinal cortex

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Missing Puzzle Pieces in Dementia Research: HCN Channels and Theta Oscillations

Increasing evidence indicates a role of hyperpolarization activated cation (HCN) channels in controlling the resting membrane potential, pacemaker activity, memory formation, sleep, and arousal. Their disfunction may be associated with the development of epilepsy and age-related memory decline. Neuronal hyperexcitability involved in epileptogenesis and EEG desynchronization occur in the course of dementia in human Alzheimer's Disease (AD) and animal models, nevertheless the underlying ionic and cellular mechanisms of these effects are not well understood. Some suggest that theta rhythms involved in memory formation could be used as a marker of memory disturbances in the course of neurogenerative diseases, including AD. This review focusses on the interplay between hyperpolarization HCN channels, theta oscillations, memory formation and their role(s) in dementias, including AD. While individually, each of these factors have been linked to each other with strong supportive evidence, we hope here to expand this linkage to a more inclusive picture. Thus, HCN channels could provide a molecular target for developing new therapeutic agents for preventing and/or treating dementia.

Localization of PDE4D, HCN1 channels, and mGluR3 in rhesus macaque entorhinal cortex may confer vulnerability in Alzheimer's disease

Alzheimer's disease cortical tau pathology initiates in the layer II cell clusters of entorhinal cortex, but it is not known why these specific neurons are so vulnerable. Aging macaques exhibit the same qualitative pattern of tau pathology as humans, including initial pathology in layer II entorhinal cortex clusters, and thus can inform etiological factors driving selective vulnerability. Macaque data have already shown that susceptible neurons in dorsolateral prefrontal cortex express a "signature of flexibility" near glutamate synapses on spines, where cAMP-PKA magnification of calcium signaling opens nearby potassium and hyperpolarization-activated cyclic nucleotide-gated channels to dynamically alter synapse strength. This process is regulated by PDE4A/D, mGluR3, and calbindin, to prevent toxic calcium actions; regulatory actions that are lost with age/inflammation, leading to tau phosphorylation. The current study examined whether a similar "signature of flexibility" expresses in layer II entorhinal cortex, investigating the localization of PDE4D, mGluR3, and HCN1 channels. Results showed a similar pattern to dorsolateral prefrontal cortex, with PDE4D and mGluR3 positioned to regulate internal calcium release near glutamate synapses, and HCN1 channels concentrated on spines. As layer II entorhinal cortex stellate cells do not express calbindin, even when young, they may be particularly vulnerable to magnified calcium actions and ensuing tau pathology.

Ih current stabilizes excitability in rodent DRG neurons and reverses hyperexcitability in a nociceptive neuron model of inherited neuropathic pain

We show here that hyperpolarization-activated current (Ih ) unexpectedly acts to inhibit the activity of dorsal root ganglion (DRG) neurons expressing WT Nav1.7, the largest inward current and primary driver of DRG neuronal firing, and hyperexcitable DRG neurons expressing a gain-of-function Nav1.7 mutation that causes inherited erythromelalgia (IEM), a human genetic model of neuropathic pain. In this study we created a kinetic model of Ih and used it, in combination with dynamic-clamp, to study Ih function in DRG neurons. We show, for the first time, that Ih increases rheobase and reduces the firing probability in small DRG neurons, and demonstrate that the amplitude of subthreshold oscillations is reduced by Ih . Our results show that Ih , due to slow gating, is not deactivated during action potentials (APs) and has a striking damping action, which reverses from depolarizing to hyperpolarizing, close to the threshold for AP generation. Moreover, we show that Ih reverses the hyperexcitability of DRG neurons expressing a gain-of-function Nav1.7 mutation that causes IEM. In the aggregate, our results show that Ih unexpectedly has strikingly different effects in DRG neurons as compared to previously- and well-studied cardiac cells. Within DRG neurons where Nav1.7 is present, Ih reduces depolarizing sodium current inflow due to enhancement of Nav1.7 channel fast inactivation and creates additional damping action by reversal of Ih direction from depolarizing to hyperpolarizing close to the threshold for AP generation. These actions of Ih limit the firing of DRG neurons expressing WT Nav1.7 and reverse the hyperexcitability of DRG neurons expressing a gain-of-function Nav1.7 mutation that causes IEM. KEY POINTS: Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the molecular determinants of hyperpolarization-activated current (Ih ) have been characterized as a 'pain pacemaker', and thus considered to be a potential molecular target for pain therapeutics. Dorsal root ganglion (DRG) neurons express Nav1.7, a channel that is not present in central neurons or cardiac tissue. Gain-of-function mutations (GOF) of Nav1.7 identified in inherited erythromelalgia (IEM), a human genetic model of neuropathic pain, produce DRG neuron hyperexcitability, which in turn produces severe pain. We found that Ih increases rheobase and reduces firing probability in small DRG neurons expressing WT Nav1.7, and demonstrate that the amplitude of subthreshold oscillations is reduced by Ih . We also demonstrate that Ih reverses the hyperexcitability of DRG neurons expressing a GOF Nav1.7 mutation (L858H) that causes IEM. Our results show that, in contrast to cardiac cells and CNS neurons, Ih acts to stabilize DRG neuron excitability and prevents excessive firing.

Ketamine evoked disruption of entorhinal and hippocampal spatial maps

Ketamine, a rapid-acting anesthetic and acute antidepressant, carries undesirable spatial cognition side effects including out-of-body experiences and spatial memory impairments. The neural substrates that underlie these alterations in spatial cognition however, remain incompletely understood. Here, we used electrophysiology and calcium imaging to examine ketamine's impacts on the medial entorhinal cortex and hippocampus, which contain neurons that encode an animal's spatial position, as mice navigated virtual reality and real world environments. Ketamine acutely increased firing rates, degraded cell-pair temporal firing-rate relationships, and altered oscillations, leading to longer-term remapping of spatial representations. In the reciprocally connected hippocampus, the activity of neurons that encode the position of the animal was suppressed after ketamine administration. Together, these findings demonstrate ketamine-induced dysfunction of the MEC-hippocampal circuit at the single cell, local-circuit population, and network levels, connecting previously demonstrated physiological effects of ketamine on spatial cognition to alterations in the spatial navigation circuit.

Dissecting cell-type-specific pathways in medial entorhinal cortical-hippocampal network for episodic memory

Episodic memory, which refers to our ability to encode and recall past events, is essential to our daily lives. Previous research has established that both the entorhinal cortex (EC) and hippocampus (HPC) play a crucial role in the formation and retrieval of episodic memories. However, to understand neural circuit mechanisms behind these processes, it has become necessary to monitor and manipulate the neural activity in a cell-type-specific manner with high temporal precision during memory formation, consolidation, and retrieval in the EC-HPC networks. Recent studies using cell-type-specific labeling, monitoring, and manipulation have demonstrated that medial EC (MEC) contains multiple excitatory neurons that have differential molecular markers, physiological properties, and anatomical features. In this review, we will comprehensively examine the complementary roles of superficial layers of neurons (II and III) and the roles of deeper layers (V and VI) in episodic memory formation and recall based on these recent findings.

Bi-directional modulation of hyperpolarization-activated cation currents (Ih) by ethanol in rat hippocampal CA3 pyramidal neurons

It is widely acknowledged that ethanol (EtOH) can alter many neuronal functions, including synaptic signaling, firing discharge, and membrane excitability, through its interaction with multiple membrane proteins and intracellular pathways. Previous work has demonstrated that EtOH enhances the firing rate of hippocampal GABAergic interneurons and thus the presynaptic GABA release at CA1 and CA3 inhibitory synapses through a positive modulation of the hyperpolarization-activated cyclic nucleotide-gated cation (HCN) channels. Activation of HCN channels produce an inward current, commonly called I_h, which plays an essential role in generating/regulating specific neuronal activities in GABAergic interneurons and principal glutamatergic pyramidal neurons such as those in the CA3 subregion. Since the direct effect of EtOH on HCN channels expressed in CA3 pyramidal neurons was not thoroughly elucidated, we investigated the possible interaction between EtOH and HCN channels and the impact on excitability and postsynaptic integration of these neurons. Patch-clamp recordings were performed in single CA3 pyramidal neurons from acute male rat coronal hippocampal slices. Our results show that EtOH modulates HCN-mediated I_h in a concentration-dependent and bi-directional manner, with a positive modulation at lower (20 mM) and an inhibitory action at higher (60-80 mM) concentrations. The modulation of I_h by EtOH was mimicked by forskolin, antagonized by different drugs that selectively interfere with the AC/cAMP/PKA intracellular pathway, as well as by the selective HCN inhibitor ZD7288. Altogether, these data further support the evidence that HCN channels may represent an important molecular target through which EtOH may regulate neuronal activity.

Ketamine evoked disruption of entorhinal and hippocampal spatial maps

Ketamine, a rapid-acting anesthetic and acute antidepressant, carries undesirable spatial cognition side effects including out-of-body experiences and spatial memory impairments. The neural substrates that underlie these alterations in spatial cognition however, remain incompletely understood. Here, we used electrophysiology and calcium imaging to examine ketamine's impacts on the medial entorhinal cortex and hippocampus, which contain neurons that encode an animal's spatial position, as mice navigated virtual reality and real world environments. Ketamine induced an acute disruption and long-term re-organization of entorhinal spatial representations. This acute ketamine-induced disruption reflected increased excitatory neuron firing rates and degradation of cell-pair temporal firing rate relationships. In the reciprocally connected hippocampus, the activity of neurons that encode the position of the animal was suppressed after ketamine administration. Together, these findings point to disruption in the spatial coding properties of the entorhinal-hippocampal circuit as a potential neural substrate for ketamine-induced changes in spatial cognition.

Heterogeneous stochastic bifurcations explain intrinsic oscillatory patterns in entorhinal cortical stellate cells

Stellate cells (SC) in the medial entorhinal cortex manifest intrinsic membrane potential oscillatory patterns. Although different theoretical frameworks have been proposed to explain these patterns, a robust unifying framework that jointly accounts for intrinsic heterogeneities and stochasticity is missing. Here, we first performed in vitro patch-clamp electrophysiological recordings from rat SCs and found pronounced cell-to-cell variability in their characteristic physiological properties, including peri-threshold oscillatory patterns. We demonstrate that noise introduced into two independent populations (endowed with deterministic or stochastic ion-channel gating kinetics) of heterogeneous biophysical models yielded activity patterns that were qualitatively similar to electrophysiological peri-threshold oscillatory activity in SCs. We developed spectrogram-based quantitative metrics for the identification of valid oscillations and confirmed that these metrics reliably captured the variable-amplitude and arhythmic oscillatory patterns observed in electrophysiological recordings. Using these quantitative metrics, we validated activity patterns from both heterogeneous populations of SC models, with each model assessed with multiple trials of different levels of noise at distinct membrane depolarizations. Our analyses unveiled the manifestation of stochastic resonance (detection of the highest number of valid oscillatory traces at an optimal level of noise) in both heterogeneous populations of SC models. Finally, we show that a generalized network motif comprised of a slow negative feedback loop amplified by a fast positive feedback loop manifested stochastic bifurcations and stochastic resonance in the emergence of oscillations. Together, through a unique convergence of the degeneracy and stochastic resonance frameworks, our unifying framework centered on heterogeneous stochastic bifurcations argues for state-dependent emergence of SC oscillations.

Activation of Dopamine D2 Receptors Alleviates Neuronal Hyperexcitability in the Lateral Entorhinal Cortex via Inhibition of HCN Current in a Rat Model of Chronic Inflammatory Pain

Functional changes in synaptic transmission from the lateral entorhinal cortex to the dentate gyrus (LEC-DG) are considered responsible for the chronification of pain. However, the underlying alterations in fan cells, which are the predominant neurons in the LEC that project to the DG, remain elusive. Here, we investigated possible mechanisms using a rat model of complete Freund's adjuvant (CFA)-induced inflammatory pain. We found a substantial increase in hyperpolarization-activated/cyclic nucleotide-gated currents (Ih), which led to the hyperexcitability of LEC fan cells of CFA slices. This phenomenon was attenuated in CFA slices by activating dopamine D2, but not D1, receptors. Chemogenetic activation of the ventral tegmental area -LEC projection had a D2 receptor-dependent analgesic effect. Intra-LEC microinjection of a D2 receptor agonist also suppressed CFA-induced behavioral hypersensitivity, and this effect was attenuated by pre-activation of the Ih. Our findings suggest that down-regulating the excitability of LEC fan cells through activation of the dopamine D2 receptor may be a strategy for treating chronic inflammatory pain.

The Contribution of HCN Channelopathies in Different Epileptic Syndromes, Mechanisms, Modulators, and Potential Treatment Targets: A Systematic Review

Background

Hyperpolarization-activated cyclic nucleotide-gated (HCN) current reduces dendritic summation, suppresses dendritic calcium spikes, and enables inhibitory GABA-mediated postsynaptic potentials, thereby suppressing epilepsy. However, it is unclear whether increased HCN current can produce epilepsy. We hypothesized that gain-of-function (GOF) and loss-of-function (LOF) variants of HCN channel genes may cause epilepsy.

Objectives

This systematic review aims to summarize the role of HCN channelopathies in epilepsy, update genetic findings in patients, create genotype–phenotype correlations, and discuss animal models, GOF and LOF mechanisms, and potential treatment targets.

Methods

The review was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement, for all years until August 2021.

Results

We identified pathogenic variants of HCN1 (n = 24), HCN2 (n = 8), HCN3 (n = 2), and HCN4 (n = 6) that were associated with epilepsy in 74 cases (43 HCN1, 20 HCN2, 2 HCN3, and 9 HCN4). Epilepsy was associated with GOF and LOF variants, and the mechanisms were indeterminate. Less than half of the cases became seizure-free and some developed drug-resistant epilepsy. Of the 74 cases, 12 (16.2%) died, comprising HCN1 (n = 4), HCN2 (n = 2), HCN3 (n = 2), and HCN4 (n = 4). Of the deceased cases, 10 (83%) had a sudden unexpected death in epilepsy (SUDEP) and 2 (16.7%) due to cardiopulmonary failure. SUDEP affected more adults (n = 10) than children (n = 2). HCN1 variants p.M234R, p.C329S, p.V414M, p.M153I, and p.M305L, as well as HCN2 variants p.S632W and delPPP (p.719–721), were associated with different phenotypes. HCN1 p.L157V and HCN4 p.R550C were associated with genetic generalized epilepsy. There are several HCN animal models, pharmacological targets, and modulators, but precise drugs have not been developed. Currently, there are no HCN channel openers.

Conclusion

We recommend clinicians to include HCN genes in epilepsy gene panels. Researchers should explore the possible underlying mechanisms for GOF and LOF variants by identifying the specific neuronal subtypes and neuroanatomical locations of each identified pathogenic variant. Researchers should identify specific HCN channel openers and blockers with high binding affinity. Such information will give clarity to the involvement of HCN channelopathies in epilepsy and provide the opportunity to develop targeted treatments.

Paradigm shift: new concepts for HCN4 function in cardiac pacemaking

Hyperpolarization-activated cyclic nucleotide–gated (HCN) channels are the molecular correlate of the I_f current and are critically involved in controlling neuronal excitability and the autonomous rhythm of the heart. The HCN4 isoform is the main HCN channel subtype expressed in the sinoatrial node (SAN), a tissue composed of specialized pacemaker cells responsible for generating the intrinsic heartbeat. More than 40 years ago, the I_f current was first discovered in rabbit SAN tissue. Along with this discovery, a theory was proposed that cyclic adenosine monophosphate–dependent modulation of I_f mediates heart rate regulation by the autonomic nervous system—a process called chronotropic effect. However, up to the present day, this classical theory could not be reliably validated. Recently, new concepts emerged confirming that HCN4 channels indeed play an important role in heart rate regulation. However, the cellular mechanism by which HCN4 controls heart rate turned out to be completely different than originally postulated. Here, we review the latest findings regarding the physiological role of HCN4 in the SAN. We describe a newly discovered mechanism underlying heart rate regulation by HCN4 at the tissue and single cell levels, and we discuss these observations in the context of results from previously studied HCN4 mouse models.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Fan cells in lateral entorhinal cortex directly influence medial entorhinal cortex through synaptic connections in layer 1

Standard models for spatial and episodic memory suggest that the lateral entorhinal cortex (LEC) and medial entorhinal cortex (MEC) send parallel independent inputs to the hippocampus, each carrying different types of information. Here, we evaluate the possibility that information is integrated between divisions of the entorhinal cortex prior to reaching the hippocampus. We demonstrate that, in mice, fan cells in layer 2 (L2) of LEC that receive neocortical inputs, and that project to the hippocampal dentate gyrus, also send axon collaterals to layer 1 (L1) of the MEC. Activation of inputs from fan cells evokes monosynaptic glutamatergic excitation of stellate and pyramidal cells in L2 of the MEC, typically followed by inhibition that contains fast and slow components mediated by GABA_A and GABA_B receptors, respectively. Inputs from fan cells also directly activate interneurons in L1 and L2 of MEC, with synaptic connections from L1 interneurons accounting for slow feedforward inhibition of L2 principal cell populations. The relative strength of excitation and inhibition following fan cell activation differs substantially between neurons and is largely independent of anatomical location. Our results demonstrate that the LEC, in addition to directly influencing the hippocampus, can activate or inhibit major hippocampal inputs arising from the MEC. Thus, local circuits in the superficial MEC may combine spatial information with sensory and higher order signals from the LEC, providing a substrate for integration of 'what' and 'where' components of episodic memories.

Lamotrigine Attenuates Neuronal Excitability, Depresses GABA Synaptic Inhibition, and Modulates Theta Rhythms in Rat Hippocampus

Theta oscillations generated in hippocampal (HPC) and cortical neuronal networks are involved in various aspects of brain function, including sensorimotor integration, movement planning, memory formation and attention. Disruptions of theta rhythms are present in individuals with brain disorders, including epilepsy and Alzheimer’s disease. Theta rhythm generation involves a specific interplay between cellular (ion channel) and network (synaptic) mechanisms. HCN channels are theta modulators, and several medications are known to enhance their activity. We investigated how different doses of lamotrigine (LTG), an HCN channel modulator, and antiepileptic and neuroprotective agent, would affect HPC theta rhythms in acute HPC slices (in vitro) and anaesthetized rats (in vivo). Whole-cell patch clamp recordings revealed that LTG decreased GABA_A-fast transmission in CA3 cells, in vitro. In addition, LTG directly depressed CA3 and CA1 pyramidal neuron excitability. These effects were partially blocked by ZD 7288, a selective HCN blocker, and are consistent with decreased excitability associated with antiepileptic actions. Lamotrigine depressed HPC theta oscillations in vitro, also consistent with its neuronal depressant effects. In contrast, it exerted an opposite, enhancing effect, on theta recorded in vivo. The contradictory in vivo and in vitro results indicate that LTG increases ascending theta activating medial septum/entorhinal synaptic inputs that over-power the depressant effects seen in HPC neurons. These results provide new insights into LTG actions and indicate an opportunity to develop more precise therapeutics for the treatment of dementias, memory disorders and epilepsy.

Ion-channel degeneracy: Multiple ion channels heterogeneously regulate intrinsic physiology of rat hippocampal granule cells

Degeneracy, the ability of multiple structural components to elicit the same characteristic functional properties, constitutes an elegant mechanism for achieving biological robustness. In this study, we sought electrophysiological signatures for the expression of ion-channel degeneracy in the emergence of intrinsic properties of rat hippocampal granule cells. We measured the impact of four different ion-channel subtypes-hyperpolarization-activated cyclic-nucleotide-gated (HCN), barium-sensitive inward rectifier potassium (Kir ), tertiapin-Q-sensitive inward rectifier potassium, and persistent sodium (NaP) channels-on 21 functional measurements employing pharmacological agents, and report electrophysiological data on two characteristic signatures for the expression of ion-channel degeneracy in granule cells. First, the blockade of a specific ion-channel subtype altered several, but not all, functional measurements. Furthermore, any given functional measurement was altered by the blockade of many, but not all, ion-channel subtypes. Second, the impact of blocking each ion-channel subtype manifested neuron-to-neuron variability in the quantum of changes in the electrophysiological measurements. Specifically, we found that blocking HCN or Ba-sensitive Kir channels enhanced action potential firing rate, but blockade of NaP channels reduced firing rate of granule cells. Subthreshold measures of granule cell intrinsic excitability (input resistance, temporal summation, and impedance amplitude) were enhanced by blockade of HCN or Ba-sensitive Kir channels, but were not significantly altered by NaP channel blockade. We confirmed that the HCN and Ba-sensitive Kir channels independently altered sub- and suprathreshold properties of granule cells through sequential application of pharmacological agents that blocked these channels. Finally, we found that none of the sub- or suprathreshold measurements of granule cells were significantly altered upon treatment with tertiapin-Q. Together, the heterogeneous many-to-many mapping between ion channels and single-neuron intrinsic properties emphasizes the need to account for ion-channel degeneracy in cellular- and network-scale physiology.

Resonating neurons stabilize heterogeneous grid-cell networks

A central theme that governs the functional design of biological networks is their ability to sustain stable function despite widespread parametric variability. Here, we investigated the impact of distinct forms of biological heterogeneities on the stability of a two-dimensional continuous attractor network (CAN) implicated in grid-patterned activity generation. We show that increasing degrees of biological heterogeneities progressively disrupted the emergence of grid-patterned activity and resulted in progressively large perturbations in low-frequency neural activity. We postulated that targeted suppression of low-frequency perturbations could ameliorate heterogeneity-induced disruptions of grid-patterned activity. To test this, we introduced intrinsic resonance, a physiological mechanism to suppress low-frequency activity, either by adding an additional high-pass filter (phenomenological) or by incorporating a slow negative feedback loop (mechanistic) into our model neurons. Strikingly, CAN models with resonating neurons were resilient to the incorporation of heterogeneities and exhibited stable grid-patterned firing. We found CAN models with mechanistic resonators to be more effective in targeted suppression of low-frequency activity, with the slow kinetics of the negative feedback loop essential in stabilizing these networks. As low-frequency perturbations (1/f noise) are pervasive across biological systems, our analyses suggest a universal role for mechanisms that suppress low-frequency activity in stabilizing heterogeneous biological networks.

Membrane Resonance in Pyramidal and GABAergic Neurons of the Mouse Perirhinal Cortex

The perirhinal cortex (PRC) is a polymodal associative region of the temporal lobe that works as a gateway between cortical areas and hippocampus. In recent years, an increasing interest arose in the role played by the PRC in learning and memory processes, such as object recognition memory, in contrast with certain forms of hippocampus-dependent spatial and episodic memory. The integrative properties of the PRC should provide all necessary resources to select and enhance the information to be propagated to and from the hippocampus. Among these properties, we explore in this paper the ability of the PRC neurons to amplify the output voltage to current input at selected frequencies, known as membrane resonance. Within cerebral circuits the resonance of a neuron operates as a filter toward inputs signals at certain frequencies to coordinate network activity in the brain by affecting the rate of neuronal firing and the precision of spike timing. Furthermore, the ability of the PRC neurons to resonate could have a fundamental role in generating subthreshold oscillations and in the selection of cortical inputs directed to the hippocampus. Here, performing whole-cell patch-clamp recordings from perirhinal pyramidal neurons and GABAergic interneurons of GAD67-GFP⁺ mice, we found, for the first time, that the majority of PRC neurons are resonant at their resting potential, with a resonance frequency of 0.5–1.5 Hz at 23°C and of 1.5–2.8 Hz at 36°C. In the presence of ZD7288 (blocker of HCN channels) resonance was abolished in both pyramidal neurons and interneurons, suggesting that I_h current is critically involved in resonance generation. Otherwise, application of TTx (voltage-dependent Na⁺ channel blocker) attenuates the resonance in pyramidal neurons but not in interneurons, suggesting that only in pyramidal neurons the persistent sodium current has an amplifying effect. These experimental results have also been confirmed by a computational model. From a functional point of view, the resonance in the PRC would affect the reverberating activity between neocortex and hippocampus, especially during slow wave sleep, and could be involved in the redistribution and strengthening of memory representation in cortical regions.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism’s spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

Differential contribution of the subthreshold operating currents IT, Ih, and IKir to the resonance of thalamocortical neurons

Membrane potential oscillations of thalamocortical (TC) neurons are believed to be involved in the generation and maintenance of brain rhythms that underlie global physiological and pathological brain states. These membrane potential oscillations depend on the synaptic interactions of TC neurons and their intrinsic electrical properties. These oscillations may be also shaped by increased output responses at a preferred frequency, known as intrinsic neuronal resonance. Here, we combine electrophysiological recordings in mouse brain slices, modern pharmacological tools, dynamic clamp, and computational modeling to study the ionic mechanisms that generate and modulate TC neuron resonance. We confirm findings of pioneering studies showing that most TC neurons display resonance that results from the interaction of the slow inactivation of the low-threshold calcium current I_T with the passive properties of the membrane. We also show that the hyperpolarization-activated cationic current I_h is not involved in the generation of resonance; instead it plays a minor role in the stabilization of TC neuron impedance magnitude due to its large contribution to the steady conductance. More importantly, we also demonstrate that TC neuron resonance is amplified by the inward rectifier potassium current I_Kir by a mechanism that hinges on its strong voltage-dependent inward rectification (i.e., a negative slope conductance region). Accumulating evidence indicate that the ion channels that control the oscillatory behavior of TC neurons participate in pathophysiological processes. Results presented here points to I_Kir as a new potential target for therapeutic intervention.NEW & NOTEWORTHY Our study expands the repertoire of ionic mechanisms known to be involved in the generation and control of resonance and provides the first experimental proof of previous theoretical predictions on resonance amplification mediated by regenerative hyperpolarizing currents. In thalamocortical neurons, we confirmed that the calcium current I_T generates resonance, determined that the large steady conductance of the cationic current I_h curtails resonance, and demonstrated that the inward rectifier potassium current I_Kir amplifies resonance.

Ih from synapses to networks: HCN channel functions and modulation in neurons

Hyperpolarization-activated cyclic nucleotide gated (HCN) channels and the current they carry, I_h, are widely and diversely distributed in the central nervous system (CNS). The distribution of the four subunits of HCN channels is variable within the CNS, within brain regions, and often within subcellular compartments. The precise function of I_h can depend heavily on what other channels are co-expressed. In this review, we give an overview of HCN channel structure, distribution, and modulation by cyclic adenosine monophosphate (cAMP). We then discuss HCN channel and I_h functions, where we have parsed the roles into two main effects: a steady effect on maintaining the resting membrane potential at relatively depolarized values, and slow channel dynamics. Within this framework, we discuss I_h involvement in resonance, synaptic integration, transmitter release, plasticity, and point out a special case, where the effects of I_h on the membrane potential and its slow channel dynamics have dual roles in thalamic neurons.

Loss of HCN2 in Dorsal Hippocampus of Young Adult Mice Induces Specific Apoptosis of the CA1 Pyramidal Neuron Layer

Neurons inevitably rely on a proper repertoire and distribution of membrane-bound ion-conducting channels. Among these proteins, the family of hyperpolarization-activated and cyclic nucleotide-gated (HCN) channels possesses unique properties giving rise to the corresponding I_h-current that contributes to various aspects of neural signaling. In mammals, four genes (hcn1-4) encode subunits of HCN channels. These subunits can assemble as hetero- or homotetrameric ion-conducting channels. In order to elaborate on the specific role of the HCN2 subunit in shaping electrical properties of neurons, we applied an Adeno-associated virus (AAV)-mediated, RNAi-based knock-down strategy of hcn2 gene expression both in vitro and in vivo. Electrophysiological measurements showed that HCN2 subunit knock-down resulted in specific yet anticipated changes in I_h-current properties in primary hippocampal neurons and, in addition, corroborated that the HCN2 subunit participates in postsynaptic signal integration. To further address the role of the HCN2 subunit in vivo, we injected recombinant (r)AAVs into the dorsal hippocampus of young adult male mice. Behavioral and biochemical analyses were conducted to assess the contribution of HCN2-containing channels in shaping hippocampal network properties. Surprisingly, knock-down of hcn2 expression resulted in a severe degeneration of the CA1 pyramidal cell layer, which did not occur in mice injected with control rAAV constructs. This finding might pinpoint to a vital and yet unknown contribution of HCN2 channels in establishing or maintaining the proper function of CA1 pyramidal neurons of the dorsal hippocampus.

Protective effect of HCN2-induced SON sensitization on chronic visceral hypersensitivity in neonatal-CRD rat model

Abnormal brain-gut interactions contribute to the development of chronic visceral hypersensitivity (CVH), which is the pivotal feature of irritable bowel syndrome (IBS). Despite the consensus with respect to the vital role of hyperpolarization-activated cyclic nucleotide-gated 2 (HCN2) channels in promoting painful symptoms in the peripheral nervous system, we identified that the upregulation of HCN2 in supraoptic nucleus (SON) was involved in the modulation of CVH in rat model of neonatal colorectal distention (n-CRD). Specifically, colorectal distention (CRD) upregulated the expression of c-Fos in SON in adult CVH rats, indicating the involvement of SON sensitazation in visceral sensation. Moreover, the administration of ZD7288 (the pan-HCN channel inhibitor) rather than 8-Br-cAMP (the non-specific HCN channel agonist) aggravated the CVH symptoms and reduced the phosphorylation level of CaMKII-CREB cascade. Together, the findings indicated that the upregulation of supraoptic HCN2 contributed to the sensitization of SON, which had protective effects on the modulation of CVH with the involvement of CaMKII-CREB cascade in n-CRD rat model.

AAV-Mediated CRISPRi and RNAi Based Gene Silencing in Mouse Hippocampal Neurons

Uncovering the physiological role of individual proteins that are part of the intricate process of cellular signaling is often a complex and challenging task. A straightforward strategy of studying a protein's function is by manipulating the expression rate of its gene. In recent years, the Clustered Regularly Interspaced Short Palindromic Repeat (CRISPR)/Cas9-based technology was established as a powerful gene-editing tool for generating sequence specific changes in proliferating cells. However, obtaining homogeneous populations of transgenic post-mitotic neurons by CRISPR/Cas9 turned out to be challenging. These constraints can be partially overcome by CRISPR interference (CRISPRi), which mediates the inhibition of gene expression by competing with the transcription machinery for promoter binding and, thus, transcription initiation. Notably, CRISPR/Cas is only one of several described approaches for the manipulation of gene expression. Here, we targeted neurons with recombinant Adeno-associated viruses to induce either CRISPRi or RNA interference (RNAi), a well-established method for impairing de novo protein biosynthesis by using cellular regulatory mechanisms that induce the degradation of pre-existing mRNA. We specifically targeted hyperpolarization-activated and cyclic nucleotide-gated (HCN) channels, which are widely expressed in neuronal tissues and play essential physiological roles in maintaining biophysical characteristics in neurons. Both of the strategies reduced the expression levels of three HCN isoforms (HCN1, 2, and 4) with high specificity. Furthermore, detailed analysis revealed that the knock-down of just a single HCN isoform (HCN4) in hippocampal neurons did not affect basic electrical parameters of transduced neurons, whereas substantial changes emerged in HCN-current specific properties.

Kv11 (ether-à-go-go-related gene) voltage-dependent K+ channels promote resonance and oscillation of subthreshold membrane potentials

Key points

Some ion channels are known to behave as inductors and make up the parallel resonant circuit in the plasma membrane of neurons, which enables neurons to respond to current inputs with a specific frequency (so‐called ‘resonant properties’).

Here, we report that heterologous expression of mouse Kv11 voltage‐dependent K⁺ channels generate resonance and oscillation at depolarized membrane potentials in HEK293 cells; expressions of individual Kv11 subtypes generate resonance and oscillation with different frequency properties.

Kv11.3‐expressing HEK293 cells exhibited transient conductance changes that opposed the current changes induced by voltage steps; this probably enables Kv11 channels to behave like an inductor.

The resonance and oscillation of inferior olivary neurons were impaired at the resting membrane potential in Kv11.3 knockout mice.

This study helps to elucidate basic ion channel properties that are crucial for the frequency responses of neurons.

Abstract

The plasma membranes of some neurons preferentially respond to current inputs with a specific frequency, and output as large voltage changes. This property is called resonance, and is thought to be mediated by ion channels that show inductor‐like behaviour. However, details of the candidate ion channels remain unclear. In this study, we mainly focused on the functional roles of Kv11 potassium (K⁺) channels, encoded by ether‐á‐go‐go‐related genes, in resonance in mouse inferior olivary (IO) neurons. We transfected HEK293 cells with long or short splice variants of Kv11.1 (Merg1a and Merg1b) or Kv11.3, and examined membrane properties using whole‐cell recording. Transfection with Kv11 channels reproduced resonance at membrane potentials depolarized from the resting state. Frequency ranges of Kv11.3‐, Kv11.1(Merg1b)‐ and Kv11.1(Merg1a)‐expressing cells were 2–6 Hz, 2–4 Hz, and 0.6–0.8 Hz, respectively. Responses of Kv11.3 currents to step voltage changes were essentially similar to those of inductor currents in the resistor–inductor–capacitor circuit. Furthermore, Kv11 transfections generated membrane potential oscillations. We also confirmed the contribution of HCN1 channels as a major mediator of resonance at more hyperpolarized potentials by transfection into HEK293 cells. The Kv11 current kinetics and properties of Kv11‐dependent resonance suggested that Kv11.3 mediated resonance in IO neurons. This finding was confirmed by the impairment of resonance and oscillation at –30 to –60 mV in Kcnh7 (Kv11.3) knockout mice. These results suggest that Kv11 channels have important roles in inducing frequency‐dependent responses in a subtype‐dependent manner from resting to depolarized membrane potentials.

Some ion channels are known to behave as inductors and make up the parallel resonant circuit in the plasma membrane of neurons, which enables neurons to respond to current inputs with a specific frequency (so‐called ‘resonant properties’).

Here, we report that heterologous expression of mouse Kv11 voltage‐dependent K⁺ channels generate resonance and oscillation at depolarized membrane potentials in HEK293 cells; expressions of individual Kv11 subtypes generate resonance and oscillation with different frequency properties.

Kv11.3‐expressing HEK293 cells exhibited transient conductance changes that opposed the current changes induced by voltage steps; this probably enables Kv11 channels to behave like an inductor.

The resonance and oscillation of inferior olivary neurons were impaired at the resting membrane potential in Kv11.3 knockout mice.

This study helps to elucidate basic ion channel properties that are crucial for the frequency responses of neurons.

Hyperpolarization-Activated Cyclic Nucleotide-Gated Channels as Drug Targets for Neurological Disorders

The hyperpolarization-activated cyclic nucleotide-gated (HCN) channels are voltage-gated ion channels that critically modulate neuronal activity. Four HCN subunits (HCN1-4) have been cloned, each having a unique expression profile and distinctive effects on neuronal excitability within the brain. Consistent with this, the expression and function of these subunits are altered in diverse ways in neurological disorders. Here, we review current knowledge on the structure and distribution of the individual HCN channel isoforms, their effects on neuronal activity under physiological conditions, and how their expression and function are altered in neurological disorders, particularly epilepsy, neuropathic pain, and affective disorders. We discuss the suitability of HCN channels as therapeutic targets and how drugs might be strategically designed to specifically act on particular isoforms. We conclude that medicines that target individual HCN isoforms and/or their auxiliary subunit, TRIP8b, may provide valuable means of treating distinct neurological conditions.

Grid cells are modulated by local head direction

Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directional modulation is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. We suggest that local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

Theta resonance and synaptic modulation scale activity patterns in the medial entorhinal cortex stellate cells

Stellate cells (SCs) of the medial entorhinal cortex (MEC) are rich in hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are known to effectively shape their activity patterns. The explanatory mechanisms, however, have remained elusive. One important but previously unassessed possibility is that HCN channels control the gain of synaptic inputs to these cells. Here, we test this possibility in rat brain slices, while subjecting SCs to a stochastic synaptic bombardment using the dynamic clamp. We show that in the presence of synaptic noise, HCN channels mainly exert their influence by increasing the relative signal gain in the theta frequency through the theta modulation of stochastic synaptic inputs. This subthreshold synaptic modulation then translates into a spiking resonance, which steepens with excitation in the presence of HCN channels. We present here a systematic assessment of synaptic theta modulation and trace its implications to the suprathreshold control of firing rate motifs. Such analysis was yet lacking in the SC literature. Furthermore, we assess the impact of noise statistics on this gain modulation and indicate possible mechanisms for the emergence of membrane theta oscillations and synaptic ramps, as observed in vivo. We support the data with a computational model that further unveils a competing role of inhibition, suggesting important implications for MEC computations.

Temperature effects on synaptic transmission and neuronal function in the visual thalamus

Numerous neuronal properties including the synaptic vesicle release process, neurotransmitter receptor complement, and postsynaptic ion channels are involved in transforming synaptic inputs into postsynaptic spiking. Temperature is a significant influencer of neuronal function and synaptic integration. Changing temperature can affect neuronal physiology in a diversity of ways depending on how it affects different members of the cell’s ion channel complement. Temperature’s effects on neuronal function are critical for pathological states such as fever, which can trigger seizure activity, but are also important in interpreting and comparing results of experiments conducted at room vs physiological temperature. The goal of this study was to examine the influence of temperature on synaptic properties and ion channel function in thalamocortical (TC) relay neurons in acute brain slices of the dorsal lateral geniculate nucleus, a key synaptic target of retinal ganglion cells in the thalamus. Warming the superfusate in patch clamp experiments with acutely-prepared brain slices led to an overall inhibition of synaptically-driven spiking behavior in TC neurons in response to a retinal ganglion cell spike train. Further study revealed that this was associated with an increase in presynaptic synaptic vesicle release probability and synaptic depression and altered passive and active membrane properties. Additionally, warming the superfusate triggered activation of an inwardly rectifying potassium current and altered the voltage-dependence of voltage-gated Na⁺ currents and T-type calcium currents. This study highlights the importance of careful temperature control in ex vivo physiological experiments and illustrates how numerous properties such as synaptic inputs, active conductances, and passive membrane properties converge to determine spike output.

Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal cortex

Distinctions between cell types underpin organizational principles for nervous system function. Functional variation also exists between neurons of the same type. This is exemplified by correspondence between grid cell spatial scales and the synaptic integrative properties of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about how functional variability is structured either within or between individuals. Using ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative properties vary between mice and, in contrast to the modularity of grid cell spatial scales, have a continuous dorsoventral organization. Our results constrain mechanisms for modular grid firing and provide evidence for inter-animal phenotypic variability among neurons of the same type. We suggest that neuron type properties are tuned to circuit-level set points that vary within and between animals.

Fan Cells in Layer 2 of the Lateral Entorhinal Cortex Are Critical for Episodic-like Memory

Episodic memory requires different types of information to be bound together to generate representations of experiences. The lateral entorhinal cortex (LEC) and hippocampus are required for episodic-like memory in rodents [1, 2]. The LEC is critical for integrating spatial and contextual information about objects [2, 3, 4, 5, 6]. Further, LEC neurons encode objects in the environment and the locations where objects were previously experienced and generate representations of time during the encoding and retrieval of episodes [7, 8, 9, 10, 11, 12]. However, it remains unclear how specific populations of cells within the LEC contribute to the integration of episodic memory components. Layer 2 (L2) of LEC manifests early pathology in Alzheimer’s disease (AD) and related animal models [13, 14, 15, 16]. Projections to the hippocampus from L2 of LEC arise from fan cells in a superficial sub-layer (L2a) that are immunoreactive for reelin and project to the dentate gyrus [17, 18]. Here, we establish an approach for selectively targeting fan cells using Sim1:Cre mice. Whereas complete lesions of the LEC were previously found to abolish associative recognition memory [2, 3], we report that, after selective suppression of synaptic output from fan cells, mice can discriminate novel object-context configurations but are impaired in recognition of novel object-place-context associations. Our results suggest that memory functions are segregated between distinct LEC networks.

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Sim1:Cre mice provide access to DG-projecting fan cells in lateral entorhinal cortex

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Fan cells are not required for novel object or object-context recognition

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Fan cells are required to discriminate novel object-place-context configurations

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Episodic-like memory impairment is correlated with extent of fan-cell inactivation

Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp

Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential ([Formula: see text]) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording [Formula: see text] in response to a sinusoidal current ([Formula: see text]), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control [Formula: see text] with a sinusoidal input at different frequencies [[Formula: see text]] and measure the total membrane current ([Formula: see text]). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [[Formula: see text]], V-clamp measures admittance [[Formula: see text]]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: [Formula: see text]. However, nonlinear model neurons produce different values for Z and [Formula: see text]. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

Hyperpolarization-Activated Cyclic Nucleotide-Gated Channels: An Emerging Role in Neurodegenerative Diseases

Neurodegenerative diseases such as Parkinson's disease (PD), Alzheimer's disease (AD), amyotrophic lateral sclerosis (ALS), and spinal muscular atrophy (SMA) are chronic, progressive, and age-associated neurological disorders characterized by neuronal deterioration in specific brain regions. Although the specific pathological mechanisms underlying these disorders have remained elusive, ion channel dysfunction has become increasingly accepted as a potential mechanism for neurodegenerative diseases. Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels are encoded by the HCN1-4 gene family and conduct the hyperpolarization-activated current (I h). These channels play important roles in modulating cellular excitability, rhythmic activity, dendritic integration, and synaptic transmission. In the present review, we first provide a comprehensive picture of the role of HCN channels in PD by summarizing their role in the regulation of neuronal activity in PD-related brain regions. Dysfunction of I h may participate in 1-methyl-4-phenylpyridinium (MPP+)-induced toxicity and represent a pathogenic mechanism in PD. Given current reports of the critical role of HCN channels in neuroinflammation and depression, we also discussed the putative contribution of HCN channels in inflammatory processes and non-motor symptoms in PD. In the second section, we summarize how HCN channels regulate the formation of β-amyloid peptide in AD and the role of these channels in learning and memory. Finally, we briefly discuss the effects of HCN channels in ALS and SMA based on existing discoveries.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

HCN4 knockdown in dorsal hippocampus promotes anxiety-like behavior in mice

Hyperpolarization‐activated and cyclic nucleotide‐gated (HCN) channels mediate the I_h current in the murine hippocampus. Disruption of the I_h current by knockout of HCN1, HCN2 or tetratricopeptide repeat‐containing Rab8b‐interacting protein has been shown to affect physiological processes such as synaptic integration and maintenance of resting membrane potentials as well as several behaviors in mice, including depressive‐like and anxiety‐like behaviors. However, the potential involvement of the HCN4 isoform in these processes is unknown. Here, we assessed the contribution of the HCN4 isoform to neuronal processing and hippocampus‐based behaviors in mice. We show that HCN4 is expressed in various regions of the hippocampus, with distinct expression patterns that partially overlapped with other HCN isoforms. For behavioral analysis, we specifically modulated HCN4 expression by injecting recombinant adeno‐associated viral (rAAV) vectors mediating expression of short hairpin RNA against hcn4 (shHcn4) into the dorsal hippocampus of mice. HCN4 knockdown produced no effect on contextual fear conditioning or spatial memory. However, a pronounced anxiogenic effect was evident in mice treated with shHcn4 compared to control littermates. Our findings suggest that HCN4 specifically contributes to anxiety‐like behaviors in mice.

HCN channels in the hippocampus regulate active coping behavior

Active coping is an adaptive stress response that improves outcomes in medical and neuropsychiatric diseases. To date, most research into coping style has focused on neurotransmitter activity and little is known about the intrinsic excitability of neurons in the associated brain regions that facilitate coping. Previous studies have shown that HCN channels regulate neuronal excitability in pyramidal cells and that HCN channel current (Ih ) in the CA1 area increases with chronic mild stress. Reduction of Ih in the CA1 area leads to antidepressant-like behavior, and this region has been implicated in the regulation of coping style. We hypothesized that the antidepressant-like behavior achieved with CA1 knockdown of Ih is accompanied by increases in active coping. In this report, we found that global loss of TRIP8b, a necessary subunit for proper HCN channel localization in pyramidal cells, led to active coping behavior in numerous assays specific to coping style. We next employed a viral strategy using a dominant negative TRIP8b isoform to alter coping behavior by reducing HCN channel expression. This approach led to a robust reduction in Ih in CA1 pyramidal neurons and an increase in active coping. Together, these results establish that changes in HCN channel function in CA1 influences coping style.

Anticonvulsant effect of dipropofol by enhancing native GABA currents in cortical neurons in mice

Temporal lobe epilepsy (TLE), the most common pharmacoresistant focal epilepsy disorder, remains a major unmet medical need. Propofol is used as a short-acting medication for general anesthesia and refractory status epilepticus with issues of decreased consciousness and memory loss. Dipropofol, a derivative of propofol, has been reported to exert antioxidative and antibacterial activities. Here we report that dipropofol exerted anticonvulsant activity in a mouse model of kainic acid-induced seizures. Whole cell patch-clamp recordings of brain slices from the medial entorhinal cortex (mEC) revealed that dipropofol hyperpolarized the resting membrane potential and reduced the number of action potential firings, resulting in suppression of cortical neuronal excitability. Furthermore, dipropofol activated native tonic GABAA currents of mEC layer II stellate neurons in a dose-dependent manner with an EC50 value of 9.3 ± 1.6 μM (mean ± SE). Taken together, our findings show that dipropofol activated GABAA currents and exerted anticonvulsant activities in mice, thus possessing developmental potential for new anticonvulsant therapy.

NEW & NOTEWORTHY The anticonvulsant effect of dipropofol was shown in a mouse model of kainic acid-induced seizures. Whole cell patch-clamp recordings of brain slices showed suppression of cortical neuronal excitability by dipropofol. Dipropofol activated the native tonic GABAA currents in a dose-dependent manner.

A Loss-of-Function HCN4 Mutation Associated With Familial Benign Myoclonic Epilepsy in Infancy Causes Increased Neuronal Excitability

HCN channels are highly expressed and functionally relevant in neurons and increasing evidence demonstrates their involvement in the etiology of human epilepsies. Among HCN isoforms, HCN4 is important in cardiac tissue, where it underlies pacemaker activity. Despite being expressed also in deep structures of the brain, mutations of this channel functionally shown to be associated with epilepsy have not been reported yet. Using Next Generation Sequencing for the screening of patients with idiopathic epilepsy, we identified the p.Arg550Cys (c.1648C>T) heterozygous mutation on HCN4 in two brothers affected by benign myoclonic epilepsy of infancy. Functional characterization in heterologous expression system and in neurons showed that the mutation determines a loss of function of HCN4 contribution to activity and an increase of neuronal discharge, potentially predisposing to epilepsy. Expressed in cardiomyocytes, mutant channels activate at slightly more negative voltages than wild-type (WT), in accordance with borderline bradycardia. While HCN4 variants have been frequently associated with cardiac arrhythmias, these data represent the first experimental evidence that functional alteration of HCN4 can also be involved in human epilepsy through a loss-of-function effect and associated increased neuronal excitability. Since HCN4 appears to be highly expressed in deep brain structures only early during development, our data provide a potential explanation for a link between dysfunctional HCN4 and infantile epilepsy. These findings suggest that it may be useful to include HCN4 screening to extend the knowledge of the genetic causes of infantile epilepsies, potentially paving the way for the identification of innovative therapeutic strategies.

Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells

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An SDE model of entorhinal cortex (EC) stellate cells is proposed.

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Experimentally observed action potential clustering is investigated in the model.

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Clusters are generated by subcritical-Hopf/homoclinic type bursting.

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Potential mechanisms underlying changes in EC dynamics in dementia are presented.

The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer’s disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4–12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing.

To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.

Interaction of Intrinsic and Synaptic Currents Mediate Network Resonance Driven by Layer V Pyramidal Cells

Cortical oscillations modulate cellular excitability and facilitate neuronal communication and information processing. Layer 5 pyramidal cells (L5 PYs) drive low-frequency oscillations (<4 Hz) in neocortical networks in vivo. In vitro, individual L5 PYs exhibit subthreshold resonance in the theta band (4-8 Hz). This bandpass filtering of periodic input is mediated by h-current (Ih) and m-current (IM) that selectively suppress low-frequency input. It has remained unclear how these intrinsic properties of cells contribute to the emergent, network oscillation dynamics. To begin to close this gap, we studied the link between cellular and network mechanisms of network resonance driven by L5 PYs. We performed multielectrode array recordings of network activity in slices of medial prefrontal cortex from the Thy1-ChR2-eYFP line and activated the network by temporally patterned optogenetic suprathreshold stimulation. Networks driven by stimulation of L5 PYs exhibited resonance in the theta band. We found that Ih and IM play a role in resonant suprathreshold network response to depolarizing stimuli. The action of Ih in mediating resonance was dependent on synaptic transmission while that of IM was not. These results demonstrate how synergistic interaction of synaptic and intrinsic ion channels contribute to the response of networks driven by L5 PYs.

Long-term high-intensity sound stimulation inhibits h current (Ih ) in CA1 pyramidal neurons

Afferent neurotransmission to hippocampal pyramidal cells can lead to long-term changes to their intrinsic membrane properties and affect many ion currents. One of the most plastic neuronal currents is the hyperpolarization-activated cationic current (I_h ), which changes in CA1 pyramidal cells in response to many types of physiological and pathological processes, including auditory stimulation. Recently, we demonstrated that long-term potentiation (LTP) in rat hippocampal Schaffer-CA1 synapses is depressed by high-intensity sound stimulation. Here, we investigated whether a long-term high-intensity sound stimulation could affect intrinsic membrane properties of rat CA1 pyramidal neurons. Our results showed that I_h is depressed by long-term high-intensity sound exposure (1 min of 110 dB sound, applied two times per day for 10 days). This resulted in a decreased resting membrane potential, increased membrane input resistance and time constant, and decreased action potential threshold. In addition, CA1 pyramidal neurons from sound-exposed animals fired more action potentials than neurons from control animals; however, this effect was not caused by a decreased I_h . On the other hand, a single episode (1 min) of 110 dB sound stimulation which also inhibits hippocampal LTP did not affect I_h and firing in pyramidal neurons, suggesting that effects on I_h are long-term responses to high-intensity sound exposure. Our results show that prolonged exposure to high-intensity sound affects intrinsic membrane properties of hippocampal pyramidal neurons, mainly by decreasing the amplitude of I_h .

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.

NeuroMatic: An Integrated Open-Source Software Toolkit for Acquisition, Analysis and Simulation of Electrophysiological Data

Acquisition, analysis and simulation of electrophysiological properties of the nervous system require multiple software packages. This makes it difficult to conserve experimental metadata and track the analysis performed. It also complicates certain experimental approaches such as online analysis. To address this, we developed NeuroMatic, an open-source software toolkit that performs data acquisition (episodic, continuous and triggered recordings), data analysis (spike rasters, spontaneous event detection, curve fitting, stationarity) and simulations (stochastic synaptic transmission, synaptic short-term plasticity, integrate-and-fire and Hodgkin-Huxley-like single-compartment models). The merging of a wide range of tools into a single package facilitates a more integrated style of research, from the development of online analysis functions during data acquisition, to the simulation of synaptic conductance trains during dynamic-clamp experiments. Moreover, NeuroMatic has the advantage of working within Igor Pro, a platform-independent environment that includes an extensive library of built-in functions, a history window for reviewing the user's workflow and the ability to produce publication-quality graphics. Since its original release, NeuroMatic has been used in a wide range of scientific studies and its user base has grown considerably. NeuroMatic version 3.0 can be found at http://www.neuromatic.thinkrandom.com and https://github.com/SilverLabUCL/NeuroMatic.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (I_h) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold I_h-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by I_h conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of I_h in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (I_h) and cell morphology cooperatively shape the response to applied alternating electric fields.

Synaptic integrative mechanisms for spatial cognition

Synaptic integrative mechanisms have profound effects on electrical signaling in the brain that, although largely hidden from recording methods that observe the spiking activity of neurons, may be critical for the encoding, storage and retrieval of information. Here we review roles for synaptic integrative mechanisms in the selection, generation and plasticity of place and grid fields, and in related temporal codes for the representation of space. We outline outstanding questions and challenges in the testing of hypothesized models for spatial computation and memory.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

A single-cell spiking model for the origin of grid-cell patterns

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.