Contribution of persistent Na+ current and M-type K+ current to somatic bursting in CA1 pyramidal cells: combined experimental and modeling study

A biophysical minimal model to investigate age-related changes in CA1 pyramidal cell electrical activity

Aging is a physiological process that is still poorly understood, especially with respect to effects on the brain. There are open questions about aging that are difficult to answer with an experimental approach. Underlying challenges include the difficulty of recording in vivo single cell and network activity simultaneously with submillisecond resolution, and brain compensatory mechanisms triggered by genetic, pharmacologic, or behavioral manipulations. Mathematical modeling can help address some of these questions by allowing us to fix parameters that cannot be controlled experimentally and investigate neural activity under different conditions. We present a biophysical minimal model of CA1 pyramidal cells (PCs) based on general expressions for transmembrane ion transport derived from thermodynamical principles. The model allows directly varying the contribution of ion channels by changing their number. By analyzing the dynamics of the model, we find parameter ranges that reproduce the variability in electrical activity seen in PCs. In addition, increasing the L-type Ca2+ channel expression in the model reproduces age-related changes in electrical activity that are qualitatively and quantitatively similar to those observed in PCs from aged animals. We also make predictions about age-related changes in PC bursting activity that, to our knowledge, have not been reported previously. We conclude that the model's biophysical nature, flexibility, and computational simplicity make it a potentially powerful complement to experimental studies of aging.

Complexity decline of hippocampal CA1 circuit model due to cholinergic deficiency associated with Alzheimer's disease

A hallmark of Alzheimer's disease (AD) is cholinergic system dysfunction, directly affecting the hippocampal neurons. Previous experiments have demonstrated that reduced complexity is one significant effect of AD on electroencephalography (EEG). Motivated by these, this study explores reduced EEG complexity of cholinergic deficiency in AD by neurocomputation. We first construct a new hippocampal CA1 circuit model with cholinergic action. M-current I M and calcium-activated potassium current I AHP are newly introduced in the model to describe cholinergic input from the medial septum. Then, by enhancing I M and I AHP to mimic cholinergic deficiency, how cholinergic deficiency influences the model complexity is investigated by sample entropy (SampEn) and approximate entropy (ApEn). Numerical results show a more severe cholinergic deficit with lower model complexity. Furthermore, we conclude that the decline of SampEn and ApEn is due to the greatly diminished excitability of model neurons. These suggest that decreased neuronal excitability due to cholinergic impairment may contribute to reduced EEG complexity in AD. Subsequently, statistical analysis between simulated AD patients and normal control (NC) groups demonstrates that SampEn and auto-mutual-information (AMI) decrease rates significantly differ. Compared to NC, AD patients have a lower SampEn and a less negative AMI decline rate. These imply a low rate of new-generation information in AD brains with cholinergic deficits. Interestingly, the statistical correlation between SampEn and AMI is analyzed, and they have a large negative Pearson correlation coefficient. Thus, AMI reduction rates may be a complementary tool for complex analysis. Our modeling and complex analysis are expected to provide a deeper understanding of the reduced EEG complexity resulting from cholinergic deficiency.

Single shot detection of alterations across multiple ionic currents from assimilation of cell membrane dynamics

The dysfunction of ion channels is a causative factor in a variety of neurological diseases, thereby defining the implicated channels as key drug targets. The detection of functional changes in multiple specific ionic currents currently presents a challenge, particularly when the neurological causes are either a priori unknown, or are unexpected. Traditional patch clamp electrophysiology is a powerful tool in this regard but is low throughput. Here, we introduce a single-shot method for detecting alterations amongst a range of ion channel types from subtle changes in membrane voltage in response to a short chaotically driven current clamp protocol. We used data assimilation to estimate the parameters of individual ion channels and from these we reconstructed ionic currents which exhibit significantly lower error than the parameter estimates. Such reconstructed currents thereby become sensitive predictors of functional alterations in biological ion channels. The technique correctly predicted which ionic current was altered, and by approximately how much, following pharmacological blockade of BK, SK, A-type K+ and HCN channels in hippocampal CA1 neurons. We anticipate this assay technique could aid in the detection of functional changes in specific ionic currents during drug screening, as well as in research targeting ion channel dysfunction.

An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons

Full-scale morphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. In this work, we propose an adaptive generalized leaky integrate-and-fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allowed (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

Theta and gamma rhythmic coding through two spike output modes in the hippocampus during spatial navigation

Hippocampal CA1 neurons generate single spikes and stereotyped bursts of spikes. However, it is unclear how individual neurons dynamically switch between these output modes and whether these two spiking outputs relay distinct information. We performed extracellular recordings in spatially navigating rats and cellular voltage imaging and optogenetics in awake mice. We found that spike bursts are preferentially linked to cellular and network theta rhythms (3-12 Hz) and encode an animal's position via theta phase precession, particularly as animals are entering a place field. In contrast, single spikes exhibit additional coupling to gamma rhythms (30-100 Hz), particularly as animals leave a place field. Biophysical modeling suggests that intracellular properties alone are sufficient to explain the observed input frequency-dependent spike coding. Thus, hippocampal neurons regulate the generation of bursts and single spikes according to frequency-specific network and intracellular dynamics, suggesting that these spiking modes perform distinct computations to support spatial behavior.

KCNQ2 channels regulate the population activity of neonatal GABAergic neurons ex vivo

Over the last decade KCNQ2 channels have arisen as fundamental and indispensable regulators of neonatal brain excitability, with KCNQ2 loss-of-function pathogenic variants being increasingly identified in patients with developmental and epileptic encephalopathy. However, the mechanisms by which KCNQ2 loss-of-function variants lead to network dysfunction are not fully known. An important remaining knowledge gap is whether loss of KCNQ2 function alters GABAergic interneuron activity early in development. To address this question, we applied mesoscale calcium imaging ex vivo in postnatal day 4-7 mice lacking KCNQ2 channels in interneurons (Vgat-ires-cre;Kcnq2f/f;GCamp5). In the presence of elevated extracellular potassium concentrations, ablation of KCNQ2 channels from GABAergic cells increased the interneuron population activity in the hippocampal formation and regions of the neocortex. We found that this increased population activity depends on fast synaptic transmission, with excitatory transmission promoting the activity and GABAergic transmission curtailing it. Together, our data show that loss of function of KCNQ2 channels from interneurons increases the network excitability of the immature GABAergic circuits, revealing a new function of KCNQ2 channels in interneuron physiology in the developing brain.

Low-dimensional models of single neurons: a review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

Comparative Effects of Domain-Specific Human Monoclonal Antibodies Against LGI1 on Neuronal Excitability

BACKGROUND AND OBJECTIVES

Autoantibodies to leucine-rich glioma inactivated protein 1 (LGI1) cause an autoimmune limbic encephalitis with frequent focal seizures and anterograde memory dysfunction. LGI1 is a neuronal secreted linker protein with 2 functional domains: the leucine-rich repeat (LRR) and epitempin (EPTP) regions. LGI1 autoantibodies are known to interfere with presynaptic function and neuronal excitability; however, their epitope-specific mechanisms are incompletely understood.

METHODS

We used patient-derived monoclonal autoantibodies (mAbs), which target either LRR or EPTP domains of LGI1 to investigate long-term antibody-induced alteration of neuronal function. LRR- and EPTP-specific effects were evaluated by patch-clamp recordings in cultured hippocampal neurons and compared with biophysical neuron modeling. K_v1.1 channel clustering at the axon initial segment (AIS) was quantified by immunocytochemistry and structured illumination microscopy techniques.

RESULTS

Both EPTP and LRR domain-specific mAbs decreased the latency of first somatic action potential firing. However, only the LRR-specific mAbs increased the number of action potential firing together with enhanced initial instantaneous frequency and promoted spike-frequency adaptation, which were less pronounced after the EPTP mAb. This also led to an effective reduction in the slope of ramp-like depolarization in the subthreshold response, suggesting K_v1 channel dysfunction. A biophysical model of a hippocampal neuron corroborated experimental results and suggests that an isolated reduction of the conductance of K_v1-mediated K⁺ currents largely accounts for the antibody-induced alterations in the initial firing phase and spike-frequency adaptation. Furthermore, K_v1.1 channel density was spatially redistributed from the distal toward the proximal site of AIS under LRR mAb treatment and, to a lesser extant, under EPTP mAb.

DISCUSSION

These findings indicate an epitope-specific pathophysiology of LGI1 autoantibodies. The pronounced neuronal hyperexcitability and SFA together with dropped slope of ramp-like depolarization after LRR-targeted interference suggest disruption of LGI1-dependent clustering of K⁺ channel complexes. Moreover, considering the effective triggering of action potentials at the distal AIS, the altered spatial distribution of K_v1.1 channel density may contribute to these effects through impairing neuronal control of action potential initiation and synaptic integration.

Theory of hierarchically organized neuronal oscillator dynamics that mediate rodent rhythmic whisking

Rodents explore their environment through coordinated orofacial motor actions, including whisking. Whisking can free-run via an oscillator of inhibitory neurons in the medulla and can be paced by breathing. Yet, the mechanics of the whisking oscillator and its interaction with breathing remain to be understood. We formulate and solve a hierarchical model of the whisking circuit. The first whisk within a breathing cycle is generated by inhalation, which resets a vibrissa oscillator circuit, while subsequent whisks are derived from the oscillator circuit. Our model posits, consistent with experiment, that there are two subpopulations of oscillator neurons. Stronger connections between the subpopulations support rhythmicity, while connections within each subpopulation induce variable spike timing that enhances the dynamic range of rhythm generation. Calculated cycle-to-cycle changes in whisking are consistent with experiment. Our model provides a computational framework to support longstanding observations of concurrent autonomous and driven rhythmic motor actions that comprise behaviors.

The role of astrocytes in place cell formation: A computational modeling study

Place cells develop spatially-tuned receptive fields during the early stages of novel environment exploration. The generative mechanism underlying these spatially-selective responses remains largely elusive, but has been associated with theta rhythmicity. An important factor implicating the transformation of silent cells to place cells is a spatially-uniform depolarization that is mediated by a persistent sodium current. This neuronal current is modulated by extracellular calcium concentration, which, in turn, is actively controlled by astrocytes. However, there is no established relationship between the neuronal depolarization and astrocytic activity. To consider this link, we designed a bioplausible computational model of a neuronal-astrocytic network, where astrocytes induced the transient emergence of place fields in silent cells, and accelerated the plasticity-induced consolidation of place cells. Interestingly, theta oscillations emerged naturally at the network level, resulting from the astrocytic modulation of subcellular neuronal properties. Our results suggest that astrocytes participate in spatial mapping and exploration, and further highlight the computational roles of these cells in the brain.

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.

Cell type-specific mechanisms of information transfer in data-driven biophysical models of hippocampal CA3 principal neurons

The transformation of synaptic input into action potential output is a fundamental single-cell computation resulting from the complex interaction of distinct cellular morphology and the unique expression profile of ion channels that define the cellular phenotype. Experimental studies aimed at uncovering the mechanisms of the transfer function have led to important insights, yet are limited in scope by technical feasibility, making biophysical simulations an attractive complementary approach to push the boundaries in our understanding of cellular computation. Here we take a data-driven approach by utilizing high-resolution morphological reconstructions and patch-clamp electrophysiology data together with a multi-objective optimization algorithm to build two populations of biophysically detailed models of murine hippocampal CA3 pyramidal neurons based on the two principal cell types that comprise this region. We evaluated the performance of these models and find that our approach quantitatively matches the cell type-specific firing phenotypes and recapitulate the intrinsic population-level variability in the data. Moreover, we confirm that the conductance values found by the optimization algorithm are consistent with differentially expressed ion channel genes in single-cell transcriptomic data for the two cell types. We then use these models to investigate the cell type-specific biophysical properties involved in the generation of complex-spiking output driven by synaptic input through an information-theoretic treatment of their respective transfer functions. Our simulations identify a host of cell type-specific biophysical mechanisms that define the morpho-functional phenotype to shape the cellular transfer function and place these findings in the context of a role for bursting in CA3 recurrent network synchronization dynamics.

The hippocampus is comprised of numerous types of neurons, which constitute the cellular substrate for its rich repertoire of network dynamics. Among these are sharp waves, sequential activations of ensembles of neurons that have been shown to be crucially involved in learning and memory. In the CA3 area of the hippocampus, two types of excitatory cells, thorny and a-thorny neurons, are preferentially active during distinct phases of a sharp wave, suggesting a differential role for these cell types in phenomena such as memory consolidation. Using a strictly data-driven approach, we built biophysically realistic models of both thorny and a-thorny cells and used them to investigate the integrative differences between these two cell types. We found that both neuron classes have the capability of integrating incoming synaptic inputs in a supralinear fashion, although only a-thorny cells respond with bursts of action potentials to spatially and temporally clustered synaptic inputs. Additionally, by using a computational approach based on information theory, we show that, owing to this propensity for bursting, a-thorny cells can encode more information in their spiking output than their thorny counterpart. These results shed new light on the computational capabilities of two types of excitatory neurons and suggest that thorny and a-thorny cells may play distinct roles in the generation of hippocampal network synchronization.

Predicting Spike Features of Hodgkin-Huxley-Type Neurons With Simple Artificial Neural Network

Hodgkin-Huxley (HH)-type model is the most famous computational model for simulating neural activity. It shows the highest accuracy in capturing neuronal spikes, and its model parameters have definite physiological meanings. However, HH-type models are computationally expensive. To address this problem, a previous study proposed a spike prediction module (SPM) to predict whether a spike will take place 1 ms later based on three voltage values with intervals of 1 ms. Although SPM does well, it fails to evaluate the informative features of the spike. In this study, the feature prediction module (FPM) based on simple artificial neural network (ANN) was proposed to predict spike features including maximum voltage, minimum voltage, and dropping interval. Nine different HH-type models were adopted whose firing patterns cover most of the firing behaviors observed in the brain. Voltage and spike feature samples under constant external input current were collected for training and testing. Experiment results illustrated that the combination of SPM and FPM can accurately predict the spiking part of different HH-type models and can generalize to unseen types of input current. The combination of SPM and FPM may offer a possible way to simulate the action potentials of biological neurons with high accuracy and efficiency.

How glutamatergic synapse loss affects the firing rhythm of DG-CA3 model related with Alzheimer's disease

As well known that synapse loss is a significant pathological feature of Alzheimer's disease (AD), meanwhile, the hippocampus is one of brain regions to be first affected in the early stage of AD. Thus, this work employs a comprehensive DG-CA3 network model of the hippocampus so as to explore the neuronal correlation between glutamatergic synapse loss and abnormal firing rhythm associated with AD from the perspective of neurocomputation. The neuropathological condition of glutamatergic synapse loss caused by the reduction of Shank3 protein in AD patients is imitated by decreasing glutamatergic excitatory synapse strength between different neurons. By means of power spectral analysis and dynamics technique, the numerical results reveal that excitability of pyramidal neuron as well as oriens lacunosum-moleculare (O-LM) cell in CA3 region is strongly degraded by the decrease of NMDA or AMPA-type glutamatergic excitatory synapse strength. Moreover, the relative power together with the peak of relative power density within alpha band is also diminished by decreasing glutamatergic synapse strength. These findings accord with the electrophysiological experiment of EEG that there is a decrease of alpha rhythm for AD patients, on the same time, they could highlight the significance of glutamatergic synapse loss in the pathogenesis of AD.

Neocortex saves energy by reducing coding precision during food scarcity

Information processing is energetically expensive. In the mammalian brain, it is unclear how information coding and energy use are regulated during food scarcity. Using whole-cell recordings and two-photon imaging in layer 2/3 mouse visual cortex, we found that food restriction reduced AMPA receptor conductance, reducing synaptic ATP use by 29%. Neuronal excitability was nonetheless preserved by a compensatory increase in input resistance and a depolarized resting potential. Consequently, neurons spiked at similar rates as controls but spent less ATP on underlying excitatory currents. This energy-saving strategy had a cost because it amplified the variability of visually-evoked subthreshold responses, leading to a 32% broadening of orientation tuning and impaired fine visual discrimination. This reduction in coding precision was associated with reduced levels of the fat mass-regulated hormone leptin and was restored by exogenous leptin supplementation. Our findings reveal that metabolic state dynamically regulates the energy spent on coding precision in neocortex.

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Kcnq2/Kv7.2 controls the threshold and bi-hemispheric symmetry of cortical spreading depolarization

Spreading depolarization is a slowly propagating wave of massive cellular depolarization associated with acute brain injury and migraine aura. Genetic studies link depolarizing molecular defects in Ca2+ flux, Na+ current in interneurons, and glial Na+-K+ ATPase with spreading depolarization susceptibility, emphasizing the important roles of synaptic activity and extracellular ionic homeostasis in determining spreading depolarization threshold. In contrast, although gene mutations in voltage-gated potassium ion channels that shape intrinsic membrane excitability are frequently associated with epilepsy susceptibility, it is not known whether epileptogenic mutations that regulate membrane repolarization also modify spreading depolarization threshold and propagation. Here we report that the Kcnq2/Kv7.2 potassium channel subunit, frequently mutated in developmental epilepsy, is a spreading depolarization modulatory gene with significant control over the seizure-spreading depolarization transition threshold, bi-hemispheric cortical expression, and diurnal temporal susceptibility. Chronic DC-band cortical EEG recording from behaving conditional Kcnq2 deletion mice (Emx1cre/+::Kcnq2flox/flox) revealed spontaneous cortical seizures and spreading depolarization. In contrast to the related potassium channel deficient model, Kv1.1-KO mice, spontaneous cortical spreading depolarizations in Kcnq2 cKO mice are tightly coupled to the terminal phase of seizures, arise bilaterally, and are observed predominantly during the dark phase. Administration of the non-selective Kv7.2 inhibitor XE991 to Kv1.1-KO mice partly reproduced the Kcnq2 cKO-like spreading depolarization phenotype (tight seizure coupling and bilateral symmetry) in these mice, indicating that Kv7.2 currents can directly and actively modulate spreading depolarization properties. In vitro brain slice studies confirmed that Kcnq2/Kv7.2 depletion or pharmacological inhibition intrinsically lowers the cortical spreading depolarization threshold, whereas pharmacological Kv7.2 activators elevate the threshold to multiple depolarizing and hypometabolic spreading depolarization triggers. Together these results identify Kcnq2/Kv7.2 as a distinctive spreading depolarization regulatory gene, and point to spreading depolarization as a potentially significant pathophysiological component of KCNQ2-linked epileptic encephalopathy syndromes. Our results also implicate KCNQ2/Kv7.2 channel activation as a potential adjunctive therapeutic target to inhibit spreading depolarization incidence.

Fast-slow analysis as a technique for understanding the neuronal response to current ramps

The standard protocol for studying the spiking properties of single neurons is the application of current steps while monitoring the voltage response. Although this is informative, the jump in applied current is artificial. A more physiological input is where the applied current is ramped up, reflecting chemosensory input. Unsurprisingly, neurons can respond differently to the two protocols, since ion channel activation and inactivation are affected differently. Understanding the effects of current ramps, and changes in their slopes, is facilitated by mathematical models. However, techniques for analyzing current ramps are under-developed. In this article, we demonstrate how current ramps can be analyzed in single neuron models. The primary issue is the presence of gating variables that activate on slow time scales and are therefore far from equilibrium throughout the ramp. The use of an appropriate fast-slow analysis technique allows one to fully understand the neural response to ramps of different slopes. This study is motivated by data from olfactory bulb dopamine neurons, where both fast ramp (tens of milliseconds) and slow ramp (tens of seconds) protocols are used to understand the spiking profiles of the cells. The slow ramps generate experimental bifurcation diagrams with the applied current as a bifurcation parameter, thereby establishing asymptotic spiking activity patterns. The faster ramps elicit purely transient behavior that is of relevance to most physiological inputs, which are short in duration. The two protocols together provide a broader understanding of the neuron's spiking profile and the role that slowly activating ion channels can play.

A computational model of dopaminergic modulation of hippocampal Schaffer collateral-CA1 long-term plasticity

Dopamine plays a critical role in modulating the long-term synaptic plasticity of the hippocampal Schaffer collateral-CA1 pyramidal neuron synapses (SC-CA1), a widely accepted cellular model of learning and memory. Limited results from hippocampal slice experiments over the last four decades have shown that the timing of the activation of dopamine D1/D5 receptors relative to a high/low-frequency stimulation (HFS/LFS) in SC-CA1 synapses regulates the modulation of HFS/LFS-induced long-term potentiation/depression (LTP/LTD) in these synapses. However, the existing literature lacks a complete picture of how various concentrations of D1/D5 agonists and the relative timing between the activation of D1/D5 receptors and LTP/LTD induction by HFS/LFS, affect the spatiotemporal modulation of SC-CA1 synaptic dynamics. In this paper, we have developed a computational model, a first of its kind, to make quantitative predictions of the temporal dose-dependent modulation of the HFS/LFS induced LTP/LTD in SC-CA1 synapses by various D1/D5 agonists. Our model combines the biochemical effects with the electrical effects at the electrophysiological level. We have estimated the model parameters from the published electrophysiological data, available from diverse hippocampal CA1 slice experiments, in a Bayesian framework. Our modeling results demonstrate the capability of our model in making quantitative predictions of the available experimental results under diverse HFS/LFS protocols. The predictions from our model show a strong nonlinear dependency of the modulated LTP/LTD by D1/D5 agonists on the relative timing between the activated D1/D5 receptors and the HFS/LFS protocol and the applied concentration of D1/D5 agonists.

Place fields of single spikes in hippocampus involve Kcnq3 channel-dependent entrainment of complex spike bursts

Hippocampal pyramidal cells encode an animal's location by single action potentials and complex spike bursts. These elementary signals are believed to play distinct roles in memory consolidation. The timing of single spikes and bursts is determined by intrinsic excitability and theta oscillations (5-10 Hz). Yet contributions of these dynamics to place fields remain elusive due to the lack of methods for specific modification of burst discharge. In mice lacking Kcnq3-containing M-type K+ channels, we find that pyramidal cell bursts are less coordinated by the theta rhythm than in controls during spatial navigation, but not alert immobility. Less modulated bursts are followed by an intact post-burst pause of single spike firing, resulting in a temporal discoordination of network oscillatory and intrinsic excitability. Place fields of single spikes in one- and two-dimensional environments are smaller in the mutant. Optogenetic manipulations of upstream signals reveal that neither medial septal GABA-ergic nor cholinergic inputs alone, but rather their joint activity, is required for entrainment of bursts. Our results suggest that altered representations by bursts and single spikes may contribute to deficits underlying cognitive disabilities associated with KCNQ3-mutations in humans.

A Computational Study of Astrocytic GABA Release at the Glutamatergic Synapse: EAAT-2 and GAT-3 Coupled Dynamics

Neurotransmitter dynamics within neuronal synapses can be controlled by astrocytes and reflect key contributors to neuronal activity. In particular, Glutamate (Glu) released by activated neurons is predominantly removed from the synaptic space by perisynaptic astrocytic transporters EAAT-2 (GLT-1). In previous work, we showed that the time course of Glu transport is affected by ionic concentration gradients either side of the astrocytic membrane and has the propensity for influencing postsynaptic neuronal excitability. Experimental findings co-localize GABA transporters GAT-3 with EAAT-2 on the perisynaptic astrocytic membrane. While these transporters are unlikely to facilitate the uptake of synaptic GABA, this paper presents simulation results which demonstrate the coupling of EAAT-2 and GAT-3, giving rise to the ionic-dependent reversed transport of GAT-3. The resulting efflux of GABA from the astrocyte to the synaptic space reflects an important astrocytic mechanism for modulation of hyperexcitability. Key results also illustrate an astrocytic-mediated modulation of synaptic neuronal excitation by released GABA at the glutamatergic synapse.

Muscarinic regulation of the neuronal Na+ /K+ -ATPase in rat hippocampus

KEY POINTS

Stimulation of postsynaptic muscarinic receptors was shown to excite principal hippocampal neurons by modulating several membrane ion conductances. We show here that activation of postsynaptic muscarinic receptors also causes neuronal excitation by inhibiting Na⁺ /K⁺ -ATPase activity. Muscarinic Na⁺ /K⁺ -ATPase inhibition is mediated by two separate signalling pathways that lead downstream to enhanced Na⁺ /K⁺ -ATPase phosphorylation by activating protein kinase C and protein kinase G. Muscarinic excitation through Na⁺ /K⁺ -ATPase inhibition is probably involved in cholinergic modulation of hippocampal activity and may turn out to be a widespread mechanism of neuronal excitation in the brain.

ABSTRACT

Stimulation of muscarinic cholinergic receptors on principal hippocampal neurons enhances intrinsic neuronal excitability by modulating several membrane ion conductances. The electrogenic Na⁺ /K⁺ -ATPase (NKA; the 'Na⁺ pump') is a ubiquitous regulator of intrinsic neuronal excitability, generating a hyperpolarizing current to thwart excessive neuronal firing. Using electrophysiological and pharmacological methodologies in rat hippocampal slices, we show that neuronal NKA pumping activity is also subjected to cholinergic regulation. Stimulation of postsynaptic muscarinic, but not nicotinic, cholinergic receptors activates membrane-bound phospholipase C and hydrolysis of membrane-integral phosphatidylinositol 4,5-bisphosphate into diacylglycerol (DAG) and inositol 1,4,5-triphosphate (IP₃ ). Along one signalling pathway, DAG activates protein kinase C (PKC). Along a second signalling pathway, IP₃ causes Ca²⁺ release from the endoplasmic reticulum, facilitating nitric oxide (NO) production. The rise in NO levels stimulates cGMP synthesis by guanylate-cyclase, activating protein kinase G (PKG). The two pathways converge to cause partial NKA inhibition through enzyme phosphorylation by PKC and PKG, leading to a marked increase in intrinsic neuronal excitability. This novel mechanism of neuronal NKA regulation probably contributes to the cholinergic modulation of hippocampal activity in spatial navigation, learning and memory.

Two opposite voltage-dependent currents control the unusual early development pattern of embryonic Renshaw cell electrical activity

Renshaw cells (V1^R) are excitable as soon as they reach their final location next to the spinal motoneurons and are functionally heterogeneous. Using multiple experimental approaches, in combination with biophysical modeling and dynamical systems theory, we analyzed, for the first time, the mechanisms underlying the electrophysiological properties of V1^R during early embryonic development of the mouse spinal cord locomotor networks (E11.5–E16.5). We found that these interneurons are subdivided into several functional clusters from E11.5 and then display an unexpected transitory involution process during which they lose their ability to sustain tonic firing. We demonstrated that the essential factor controlling the diversity of the discharge pattern of embryonic V1^R is the ratio of a persistent sodium conductance to a delayed rectifier potassium conductance. Taken together, our results reveal how a simple mechanism, based on the synergy of two voltage-dependent conductances that are ubiquitous in neurons, can produce functional diversity in embryonic V1^R and control their early developmental trajectory.

The Integrated Effects of Brivaracetam, a Selective Analog of Levetiracetam, on Ionic Currents and Neuronal Excitability

Brivaracetam (BRV) is recognized as a novel third-generation antiepileptic drug approved for the treatment of epilepsy. Emerging evidence has demonstrated that it has potentially better efficacy and tolerability than its analog, Levetiracetam (LEV). This, however, cannot be explained by their common synaptic vesicle-binding mechanism. Whether BRV can affect different ionic currents and concert these effects to alter neuronal excitability remains unclear. With the aid of patch clamp technology, we found that BRV concentration dependently inhibited the depolarization-induced M-type K⁺ current (I_K(M)), decreased the delayed-rectifier K⁺ current (I_K(DR)), and decreased the hyperpolarization-activated cation current in GH3 neurons. However, it had a concentration-dependent inhibition on voltage-gated Na⁺ current (I_Na). Under an inside-out patch configuration, a bath application of BRV increased the open probability of large-conductance Ca²⁺-activated K⁺ channels. Furthermore, in mHippoE-14 hippocampal neurons, the whole-cell I_Na was effectively depressed by BRV. In simulated modeling of hippocampal neurons, BRV was observed to reduce the firing of the action potentials (APs) concurrently with decreases in the AP amplitude. In animal models, BRV ameliorated acute seizures in both OD-1 and lithium-pilocarpine epilepsy models. However, LEV had effects in the latter only. Collectively, our study demonstrated BRV’s multiple ionic mechanism in electrically excitable cells and a potential concerted effect on neuronal excitability and hyperexcitability disorders.

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

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

Dynamics analysis of the hippocampal neuronal model subjected to cholinergic action related with Alzheimer's disease

There are evidences that the region of hippocampus is affected in the early stage of Alzheimer's disease (AD). Moreover, the hippocampal pyramidal neurons receive cholinergic input from the medial septum. Thus, this study, based on the results of electrophysiological experiments, first constructs a modified hippocampal CA1 pyramidal neuronal model by introducing two new currents of M-current and calcium ion-activated potassium ion current to depict the cholinergic input receiving from the medial septum, and then explores how acetylcholine deficiency and beta-amyloid accumulation under the pathological condition of AD influence the neuronal dynamics in terms of theta band power and spiking frequency using computational approach. By simulating acetylcholine potentiated M-current and calcium ion-activated potassium ion current, numerical results reveal that the relative theta band power increases significantly and the firing rate decreases obviously when acetylcholine is deficient. Similarly, by simulating beta-amyloid enhanced delay rectification potassium ion current, we also detect that the relative theta band power increases as well as the firing rate decreases remarkably as beta-amyloid is accumulated. In addition, the mechanism underlying these dynamical changes in theta rhythm and firing behavior is investigated by nonlinear behavioral analysis, which demonstrates that both deficiency in acetylcholine and accumulation in beta-amyloid can promote the emergence of stable equilibrium state in this modified hippocampal neuronal model. Note that acetylcholine deficiency together with beta-amyloid deposition plays key role in the pathogenesis of AD. We expect these findings could have important implications on better understanding pathogenesis and expounding potential biomarkers for AD.

M-Current Inhibition in Hippocampal Excitatory Neurons Triggers Intrinsic and Synaptic Homeostatic Responses at Different Temporal Scales

Persistent alterations in neuronal activity elicit homeostatic plastic changes in synaptic transmission and/or intrinsic excitability. However, it is unknown whether these homeostatic processes operate in concert or at different temporal scales to maintain network activity around a set-point value. Here we show that chronic neuronal hyperactivity, induced by M-channel inhibition, triggered intrinsic and synaptic homeostatic plasticity at different timescales in cultured hippocampal pyramidal neurons from mice of either sex. Homeostatic changes of intrinsic excitability occurred at a fast timescale (1-4 h) and depended on ongoing spiking activity. This fast intrinsic adaptation included plastic changes in the threshold current and a distal relocation of FGF14, a protein physically bridging Na_v1.6 and K_v7.2 channels along the axon initial segment. In contrast, synaptic adaptations occurred at a slower timescale (∼2 d) and involved decreases in miniature EPSC amplitude. To examine how these temporally distinct homeostatic responses influenced hippocampal network activity, we quantified the rate of spontaneous spiking measured by multielectrode arrays at extended timescales. M-Channel blockade triggered slow homeostatic renormalization of the mean firing rate (MFR), concomitantly accompanied by a slow synaptic adaptation. Thus, the fast intrinsic adaptation of excitatory neurons is not sufficient to account for the homeostatic normalization of the MFR. In striking contrast, homeostatic adaptations of intrinsic excitability and spontaneous MFR failed in hippocampal GABAergic inhibitory neurons, which remained hyperexcitable following chronic M-channel blockage. Our results indicate that a single perturbation such as M-channel inhibition triggers multiple homeostatic mechanisms that operate at different timescales to maintain network mean firing rate.SIGNIFICANCE STATEMENT Persistent alterations in synaptic input elicit homeostatic plastic changes in neuronal activity. Here we show that chronic neuronal hyperexcitability, induced by M-type potassium channel inhibition, triggered intrinsic and synaptic homeostatic plasticity at different timescales in hippocampal excitatory neurons. The data indicate that the fast adaptation of intrinsic excitability depends on ongoing spiking activity but is not sufficient to provide homeostasis of the mean firing rate. Our results show that a single perturbation such as M-channel inhibition can trigger multiple homeostatic processes that operate at different timescales to maintain network mean firing rate.

Optimal solid state neurons

Bioelectronic medicine is driving the need for neuromorphic microcircuits that integrate raw nervous stimuli and respond identically to biological neurons. However, designing such circuits remains a challenge. Here we estimate the parameters of highly nonlinear conductance models and derive the ab initio equations of intracellular currents and membrane voltages embodied in analog solid-state electronics. By configuring individual ion channels of solid-state neurons with parameters estimated from large-scale assimilation of electrophysiological recordings, we successfully transfer the complete dynamics of hippocampal and respiratory neurons in silico. The solid-state neurons are found to respond nearly identically to biological neurons under stimulation by a wide range of current injection protocols. The optimization of nonlinear models demonstrates a powerful method for programming analog electronic circuits. This approach offers a route for repairing diseased biocircuits and emulating their function with biomedical implants that can adapt to biofeedback.

Quantitative firing pattern phenotyping of hippocampal neuron types

Systematically organizing the anatomical, molecular, and physiological properties of cortical neurons is important for understanding their computational functions. Hippocampome.org defines 122 neuron types in the rodent hippocampal formation based on their somatic, axonal, and dendritic locations, putative excitatory/inhibitory outputs, molecular marker expression, and biophysical properties. We augmented the electrophysiological data of this knowledge base by collecting, quantifying, and analyzing the firing responses to depolarizing current injections for every hippocampal neuron type from published experiments. We designed and implemented objective protocols to classify firing patterns based on 5 transients (delay, adapting spiking, rapidly adapting spiking, transient stuttering, and transient slow-wave bursting) and 4 steady states (non-adapting spiking, persistent stuttering, persistent slow-wave bursting, and silence). This automated approach revealed 9 unique (plus one spurious) families of firing pattern phenotypes while distinguishing potential new neuronal subtypes. Novel statistical associations emerged between firing responses and other electrophysiological properties, morphological features, and molecular marker expression. The firing pattern parameters, experimental conditions, spike times, references to the original empirical evidences, and analysis scripts are released open-source through Hippocampome.org for all neuron types, greatly enhancing the existing search and browse capabilities. This information, collated online in human- and machine-accessible form, will help design and interpret both experiments and model simulations.

Data-Driven Predictive Modeling of Neuronal Dynamics Using Long Short-Term Memory

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions have been of interest to engineers, mathematicians and physicists over the last several decades. With the motivation of developing computationally efficient models of brain dynamics to use in designing control-theoretic neurostimulation strategies, we have developed a novel data-driven approach in a long short-term memory (LSTM) neural network architecture to predict the temporal dynamics of complex systems over an extended long time-horizon in future. In contrast to recent LSTM-based dynamical modeling approaches that make use of multi-layer perceptrons or linear combination layers as output layers, our architecture uses a single fully connected output layer and reversed-order sequence-to-sequence mapping to improve short time-horizon prediction accuracy and to make multi-timestep predictions of dynamical behaviors. We demonstrate the efficacy of our approach in reconstructing the regular spiking to bursting dynamics exhibited by an experimentally-validated 9-dimensional Hodgkin-Huxley model of hippocampal CA1 pyramidal neurons. Through simulations, we show that our LSTM neural network can predict the multi-time scale temporal dynamics underlying various spiking patterns with reasonable accuracy. Moreover, our results show that the predictions improve with increasing predictive time-horizon in the multi-timestep deep LSTM neural network.

The role of relative membrane capacitance and time delay in cerebellar Purkinje cells

The membrane capacitance of a neuron can influence the synaptic efficacy and the speed of electrical signal propagation. Exploring the role of membrane capacitance will help facilitate a deeper understanding of the electrical properties of neurons. Thus, in this paper, we investigated the neuronal firing behaviors of a two-compartment model in Purkinje cells. We evaluated the influence of membrane capacitance under two different circumstances: in the absence of time delay and in the presence of time delay. Firstly, we separately studied the influence of somatic membrane capacitance Cs and dendritic membrane capacitance Cd on neuronal firing patterns. Through numerical simulation, we observed that they had two different types of period-adding scenarios, i.e. with and without chaotic bursting. Secondly, our results indicated that when the time delay was included in the model, periodic motions were more inclined to be destroyed, while at the same time, corresponding new chaotic motions were induced. These findings suggested that membrane capacitance and time delay play a pivotal functional role in modulating dynamical firing properties of neurons, especially aspects which lead to behaviors which result in changes to bursting patterns.

Oxytocin Transforms Firing Mode of CA2 Hippocampal Neurons

Oxytocin is an important neuromodulator in the mammalian brain that increases information salience and circuit plasticity, but its signaling mechanisms and circuit effect are not fully understood. Here we report robust oxytocinergic modulation of intrinsic properties and circuit operations in hippocampal area CA2, a region of emerging importance for hippocampal function and social behavior. Upon oxytocin receptor activation, CA2 pyramidal cells depolarize and fire bursts of action potentials, a consequence of phospholipase C signaling to modify two separate voltage-dependent ionic processes. A reduction of potassium current carried by KCNQ-based M channels depolarizes the cell; protein kinase C activity attenuates spike rate of rise and overshoot, dampening after-hyperpolarizations. These actions, in concert with activation of fast-spiking interneurons, promote repetitive firing and CA2 bursting; bursting then governs short-term plasticity of CA2 synaptic transmission onto CA1 and, thus, efficacy of information transfer in the hippocampal network.

Leak potassium channels regulate sleep duration

A primary goal of sleep research is to understand the molecular basis of sleep. Although some sleep/wake-promoting circuits and secreted substances have been identified, the detailed molecular mechanisms underlying the regulation of sleep duration have been elusive. Here, to address these mechanisms, we developed a simple computational model of a cortical neuron with five channels and a pump, which recapitulates the cortical electrophysiological characteristics of slow-wave sleep (SWS) and wakefulness. Comprehensive bifurcation and detailed mathematical analyses predicted that leak K⁺ channels play a role in generating the electrophysiological characteristics of SWS, leading to a hypothesis that leak K⁺ channels play a role in the regulation of sleep duration. To test this hypothesis experimentally, we comprehensively generated and analyzed 14 KO mice, and found that impairment of the leak K⁺ channel (Kcnk9) decreased sleep duration. Based on these results, we hypothesize that leak K⁺ channels regulate sleep duration in mammals.

Maintenance of postsynaptic neuronal excitability by a positive feedback loop of postsynaptic BDNF expression

Experiments have demonstrated that in mice, the PVT strongly projects to the CeL and participates in the formation of fear memories by synaptic potentiation in the amygdala. Herein, we propose a mathematical model based on a positive feedback loop of BDNF expression and signaling to investigate PVT manipulation of synaptic potentiation. The model is validated by comparisons with experimental observations. We find that a high postsynaptic firing frequency after stimulation is induced by presynaptic Ca2+ when the rates of BDNF secretion from PVT and LA neurons to the CeL are above a threshold value. Moreover, the positive feedback of postsynaptic BDNF production is important for the maintenance of the high excitability of the SOM+ CeL neuron after stimulation. The model brings insight into the underlying mechanisms of PVT modulation of synaptic potentiation at LA-CeL synapses and provides a framework of understanding other similar processes associated with synaptic plasticity.

Persistent sodium current modulates axonal excitability in CA1 pyramidal neurons

Axonal excitability is an important determinant for the accuracy, direction, and velocity of neuronal signaling. The mechanisms underlying spike generation in the axonal initial segment and transmitter release from presynaptic terminals have been intensely studied and revealed a role for several specific ionic conductances, including the persistent sodium current (I_NaP ). Recent evidence indicates that action potentials can also be generated at remote locations along the axonal fiber, giving rise to ectopic action potentials during physiological states (e.g., fast network oscillations) or in pathological situations (e.g., following demyelination). Here, we investigated how ectopic axonal excitability of mouse hippocampal CA1 pyramidal neurons is regulated by I_NaP . Recordings of field potentials and intracellular voltage in brain slices revealed that electrically evoked antidromic spikes were readily suppressed by two different blockers of I_NaP , riluzole and phenytoin. The effect was mediated by a reduction of the probability of ectopic spike generation while latency was unaffected. Interestingly, the contribution of I_NaP to excitability was much more pronounced in axonal branches heading toward the entorhinal cortex compared with the opposite fiber direction toward fimbria. Thus, excitability of distal CA1 pyramidal cell axons is affected by persistent sodium currents in a direction-selective manner. This mechanism may be of importance for ectopic spike generation in oscillating network states as well as in pathological situations.

M current regulates firing mode and spike reliability in a collision-detecting neuron

All animals must detect impending collisions to escape and reliably discriminate them from nonthreatening stimuli, thus preventing false alarms. Therefore, it is no surprise that animals have evolved highly selective and sensitive neurons dedicated to such tasks. We examined a well-studied collision-detection neuron in the grasshopper ( Schistocerca americana) using in vivo electrophysiology, pharmacology, and computational modeling. This lobula giant movement detector (LGMD) neuron is excitable by inputs originating from each ommatidia of the compound eye. It possesses many intrinsic properties that increase its selectivity to objects approaching on a collision course, including switching between burst and nonburst firing. In this study, we demonstrate that the LGMD neuron exhibits a large M current, generated by noninactivating K⁺ channels, that shortens the temporal window of dendritic integration, regulates a firing mode switch between burst and isolated spiking, increases the precision of spike timing, and increases the reliability of spike propagation to downstream motor centers. By revealing how the M current increases the LGMD's ability to detect impending collisions, our results suggest that similar channels may play an analogous role in other collision detection circuits. NEW & NOTEWORTHY The ability to reliably detect impending collisions is a critical survival skill. The nervous systems of many animals have developed dedicated neurons for accomplishing this task. We used a mix of in vivo electrophysiology and computational modeling to investigate the role of M potassium channels within one such collision-detecting neuron and show that through regulation of burst firing and enhancement of spiking reliability, the M current increases the ability to detect impending collisions.

A computational study of astrocytic glutamate influence on post-synaptic neuronal excitability

The ability of astrocytes to rapidly clear synaptic glutamate and purposefully release the excitatory transmitter is critical in the functioning of synapses and neuronal circuits. Dysfunctions of these homeostatic functions have been implicated in the pathology of brain disorders such as mesial temporal lobe epilepsy. However, the reasons for these dysfunctions are not clear from experimental data and computational models have been developed to provide further understanding of the implications of glutamate clearance from the extracellular space, as a result of EAAT2 downregulation: although they only partially account for the glutamate clearance process. In this work, we develop an explicit model of the astrocytic glutamate transporters, providing a more complete description of the glutamate chemical potential across the astrocytic membrane and its contribution to glutamate transporter driving force based on thermodynamic principles and experimental data. Analysis of our model demonstrates that increased astrocytic glutamate content due to glutamine synthetase downregulation also results in increased postsynaptic quantal size due to gliotransmission. Moreover, the proposed model demonstrates that increased astrocytic glutamate could prolong the time course of glutamate in the synaptic cleft and enhances astrocyte-induced slow inward currents, causing a disruption to the clarity of synaptic signalling and the occurrence of intervals of higher frequency postsynaptic firing. Overall, our work distilled the necessity of a low astrocytic glutamate concentration for reliable synaptic transmission of information and the possible implications of enhanced glutamate levels as in epilepsy.

The role of astrocytes in the excitability and hyperexcitability of neurons is a subject which has gained a lot of attention, particularly in the pathology of neurological disorders including epilepsy. Although not completely understood, the control of glutamate homeostasis is believed to play a role in paroxysmal neuronal hyperexcitability known to precede seizure activity. We have developed a computational model which explores two of the astrocytic homeostatic mechanisms, namely glutamate clearance and gliotransmission, and connect them with a common controlling factor, astrocytic cytoplasmic glutamate concentration. In our model simulations we demonstrate both a slower clearance rate of synaptic glutamate and enhanced astrocytic glutamate release where cytoplasmic glutamate is elevated, both of which contribute to high frequency neuronal firing and conditions for seizure generation. We also describe a viable role for astrocytes as a “high pass” filter, where astrocytic activation in the form of intracellular calcium oscillations is possible for only a certain range of presynaptic neuronal firing rates, the lower bound of the range being reduced where astrocytic glutamate is elevated. In physiological terms this perhaps indicates not only neuronal but also astrocytic glutamate-mediated excitation in the neural-astrocytic network.

Understanding the Generation of Network Bursts by Adaptive Oscillatory Neurons

Experimental and numerical studies have revealed that isolated populations of oscillatory neurons can spontaneously synchronize and generate periodic bursts involving the whole network. Such a behavior has notably been observed for cultured neurons in rodent's cortex or hippocampus. We show here that a sufficient condition for this network bursting is the presence of an excitatory population of oscillatory neurons which displays spike-driven adaptation. We provide an analytic model to analyze network bursts generated by coupled adaptive exponential integrate-and-fire neurons. We show that, for strong synaptic coupling, intrinsically tonic spiking neurons evolve to reach a synchronized intermittent bursting state. The presence of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. Thanks to a simple self-consistent equation, our model gives an intuitive and semi-quantitative tool to understand the bursting behavior. Furthermore, it suggests that after-hyperpolarization currents are sufficient to explain bursting termination. Through a thorough mapping between the theoretical parameters and ion-channel properties, we discuss the biological mechanisms that could be involved and the relevance of the explored parameter-space. Such an insight enables us to propose experimentally-testable predictions regarding how blocking fast, medium or slow after-hyperpolarization channels would affect the firing rate and burst duration, as well as the interburst interval.

Slow moving neural source in the epileptic hippocampus can mimic progression of human seizures

Fast and slow neural waves have been observed to propagate in the human brain during seizures. Yet the nature of these waves is difficult to study in a surgical setting. Here, we report an observation of two different traveling waves propagating in the in-vitro epileptic hippocampus at speeds similar to those in the human brain. A fast traveling spike and a slow moving wave were recorded simultaneously with a genetically encoded voltage sensitive fluorescent protein (VSFP Butterfly 1.2) and a high speed camera. The results of this study indicate that the fast traveling spike is NMDA-sensitive but the slow moving wave is not. Image analysis and model simulation demonstrate that the slow moving wave is moving slowly, generating the fast traveling spike and is, therefore, a moving source of the epileptiform activity. This slow moving wave is associated with a propagating neural calcium wave detected with calcium dye (OGB-1) but is independent of NMDA receptors, not related to ATP release, and much faster than those previously recorded potassium waves. Computer modeling suggests that the slow moving wave can propagate by the ephaptic effect like epileptiform activity. These findings provide an alternative explanation for slow propagation seizure wavefronts associated with fast propagating spikes.

A computational model for how the fast afterhyperpolarization paradoxically increases gain in regularly firing neurons

The gain of a neuron, the number and frequency of action potentials triggered in response to a given amount of depolarizing injection, is an important behavior underlying a neuron's function. Variations in action potential waveform can influence neuronal discharges by the differential activation of voltage- and ion-gated channels long after the end of a spike. One component of the action potential waveform, the afterhyperpolarization (AHP), is generally considered an inhibitory mechanism for limiting firing rates. In dentate gyrus granule cells (DGCs) expressing fast-gated BK channels, large fast AHPs (fAHP) are paradoxically associated with increased gain. In this article, we describe a mechanism for this behavior using a computational model. Hyperpolarization provided by the fAHP enhances activation of a dendritic inward current (a T-type Ca²⁺ channel is suggested) that, in turn, boosts rebound depolarization at the soma. The model suggests that the fAHP may both reduce Ca²⁺ channel inactivation and, counterintuitively, enhance its activation. The magnitude of the rebound depolarization, in turn, determines the activation of a subsequent, slower inward current (a persistent Na⁺ current is suggested) limiting the interspike interval. Simulations also show that the effect of AHP on gain is also effective for physiologically relevant stimulation; varying AHP amplitude affects interspike interval across a range of "noisy" stimulus frequency and amplitudes. The mechanism proposed suggests that small fAHPs in DGCs may contribute to their limited excitability. NEW & NOTEWORTHY The afterhyperpolarization (AHP) is canonically viewed as a major factor underlying the refractory period, serving to limit neuronal firing rate. We recently reported that enhancing the amplitude of the fast AHP (fAHP) in a relatively slowly firing neuron (vs. fast spiking neurons) expressing fast-gated BK channels augments neuronal excitability. In this computational study, we present a novel, quantitative hypothesis for how varying the amplitude of the fAHP can, paradoxically, influence a subsequent spike tens of milliseconds later.

Epilepsy-associated alterations in hippocampal excitability

The hippocampus exhibits a wide range of epilepsy-related abnormalities and is situated in the mesial temporal lobe, where limbic seizures begin. These abnormalities could affect membrane excitability and lead to overstimulation of neurons. Multiple overlapping processes refer to neural homeostatic responses develop in neurons that work together to restore neuronal firing rates to control levels. Nevertheless, homeostatic mechanisms are unable to restore normal neuronal excitability, and the epileptic hippocampus becomes hyperexcitable or hypoexcitable. Studies show that there is hyperexcitability even before starting recurrent spontaneous seizures, suggesting although hippocampal hyperexcitability may contribute to epileptogenesis, it alone is insufficient to produce epileptic seizures. This supports the concept that the hippocampus is not the only substrate for limbic seizure onset, and a broader hyperexcitable limbic structure may contribute to temporal lobe epilepsy (TLE) seizures. Nevertheless, seizures also occur in conditions where the hippocampus shows a hypoexcitable phenotype. Since TLE seizures most often originate in the hippocampus, it could therefore be assumed that both hippocampal hypoexcitability and hyperexcitability are undesirable states that make the epileptic hippocampal network less stable and may, under certain conditions, trigger seizures.

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed "slow" because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. NEW & NOTEWORTHY Nervous system functions rely on the modulation of neuronal activity between different rhythmic patterns. The mechanisms of this modulation are still poorly understood. Using computational modeling, we show the critical role of currents that provide slow negative conductance, distinct from the fast negative conductance necessary for spike generation. The significance of the slow negative conductance for neuromodulation is often overlooked, leading to computational models that are rigid and fragile.

Brain extracellular space, hyaluronan, and the prevention of epileptic seizures

Mutant mice deficient in hyaluronan (HA) have an epileptic phenotype. HA is one of the major constituents of the brain extracellular matrix. HA has a remarkable hydration capacity, and a lack of HA causes reduced extracellular space (ECS) volume in the brain. Reducing ECS volume can initiate or exacerbate epileptiform activity in many in vitro models of epilepsy. There is both in vitro and in vivo evidence of a positive feedback loop between reduced ECS volume and synchronous neuronal activity. Reduced ECS volume promotes epileptiform activity primarily via enhanced ephaptic interactions and increased extracellular potassium concentration; however, the epileptiform activity in many models, including the brain slices from HA synthase-3 knockout mice, may still require glutamate-mediated synaptic activity. In brain slice epilepsy models, hyperosmotic solution can effectively shrink cells and thus increase ECS volume and block epileptiform activity. However, in vivo, the intravenous administration of hyperosmotic solution shrinks both brain cells and brain ECS volume. Instead, manipulations that increase the synthesis of high-molecular-weight HA or decrease its breakdown may be used in the future to increase brain ECS volume and prevent seizures in patients with epilepsy. The prevention of epileptogenesis is also a future target of HA manipulation. Head trauma, ischemic stroke, and other brain insults that initiate epileptogenesis are known to be associated with an early decrease in high-molecular-weight HA, and preventing that decrease in HA may prevent the epileptogenesis.

Neuronal Intrinsic Physiology Changes During Development of a Learned Behavior

Juvenile male zebra finches learn their songs over distinct auditory and sensorimotor stages, the former requiring exposure to an adult tutor song pattern. The cortical premotor nucleus HVC (acronym is name) plays a necessary role in both learning stages, as well as the production of adult song. Consistent with neural network models where synaptic plasticity mediates developmental forms of learning, exposure to tutor song drives changes in the turnover, density, and morphology of HVC synapses during vocal development. A network's output, however, is also influenced by the intrinsic properties (e.g., ion channels) of the component neurons, which could change over development. Here, we use patch clamp recordings to show cell-type-specific changes in the intrinsic physiology of HVC projection neurons as a function of vocal development. Developmental changes in HVC neurons that project to the basal ganglia include an increased voltage sag response to hyperpolarizing currents and an increased rebound depolarization following hyperpolarization. Developmental changes in HVC neurons that project to vocal-motor cortex include a decreased resting membrane potential and an increased spike amplitude. HVC interneurons, however, show a relatively stable range of intrinsic features across vocal development. We used mathematical models to deduce possible changes in ionic currents that underlie the physiological changes and to show that the magnitude of the observed changes could alter HVC circuit function. The results demonstrate developmental plasticity in the intrinsic physiology of HVC projection neurons and suggest that intrinsic plasticity may have a role in the process of song learning.

CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging

Neuron types (e.g., pyramidal cells) within one area of the brain are often considered homogeneous, despite variability in their biophysical properties. Here we review literature demonstrating variability in the electrical activity of CA1 hippocampal pyramidal cells (PCs), including responses to somatic current injection, synaptic stimulation, and spontaneous network-related activity. In addition, we describe how responses of CA1 PCs vary with development, experience, and aging, and some of the underlying ionic currents responsible. Finally, we suggest directions that may be the most impactful in expanding this knowledge, including the use of text and data mining to systematically study cellular heterogeneity in more depth; dynamical systems theory to understand and potentially classify neuron firing patterns; and mathematical modeling to study the interaction between cellular properties and network output. Our goals are to provide a synthesis of the literature for experimentalists studying CA1 PCs, to give theorists an idea of the rich diversity of behaviors models may need to reproduce to accurately represent these cells, and to provide suggestions for future research.

Epilepsy-Associated KCNQ2 Channels Regulate Multiple Intrinsic Properties of Layer 2/3 Pyramidal Neurons

KCNQ2 potassium channels are critical for normal brain function, as both loss-of-function and gain-of-function KCNQ2 variants can lead to various forms of neonatal epilepsy. Despite recent progress, the full spectrum of consequences as a result of KCNQ2 dysfunction in neocortical pyramidal neurons is still unknown. Here, we report that conditional ablation of Kcnq2 from mouse neocortex leads to hyperexcitability of layer 2/3 (L2/3) pyramidal neurons, exhibiting an increased input resistance and action potential frequency, as well as a reduced medium afterhyperpolarization (mAHP), a conductance partly mediated by KCNQ2 channels. Importantly, we show that introducing the KCNQ2 loss-of-function variant KCNQ2I205V into L2/3 pyramidal neurons using in utero electroporation also results in a hyperexcitable phenotype similar to the conditional knock-out. KCNQ2I205V has a right-shifted conductance-to-voltage relationship, suggesting loss of KCNQ2 channel activity at subthreshold membrane potentials is sufficient to drive large changes in L2/3 pyramidal neuronal excitability even in the presence of an intact mAHP. We also found that the changes in excitability following Kcnq2 ablation are accompanied by alterations at action potential properties, including action potential amplitude in Kcnq2-null neurons. Importantly, partial inhibition of Nav1.6 channels was sufficient to counteract the hyperexcitability of Kcnq2-null neurons. Therefore, our work shows that loss of KCNQ2 channels alters the intrinsic neuronal excitability and action potential properties of L2/3 pyramidal neurons, and identifies Nav1.6 as a new potential molecular target to reduce excitability in patients with KCNQ2 encephalopathy.

SIGNIFICANCE STATEMENT

KCNQ2 channels are critical for the development of normal brain function, as KCNQ2 variants could lead to epileptic encephalopathy. However, the role of KCNQ2 channels in regulating the properties of neocortical neurons is largely unexplored. Here, we find that Kcnq2 ablation or loss-of-function at subthreshold membrane potentials leads to increased neuronal excitability of neocortical layer 2/3 (L2/3) pyramidal neurons. We also demonstrate that Kcnq2 ablation unexpectedly leads to a larger action potential amplitude. Importantly, we propose the Nav1.6 channel as a new molecular target for patients with KCNQ2 encephalopathy, as partial inhibition of these channels counteracts the increased L2/3 pyramidal neuron hyperexcitability of Kcnq2-null neurons.

Bifurcation analysis of a two-compartment hippocampal pyramidal cell model

The Pinsky-Rinzel model is a non-smooth 2-compartmental CA3 pyramidal cell model that has been used widely within the field of neuroscience. Here we propose a modified (smooth) system that captures the qualitative behaviour of the original model, while allowing the use of available, numerical continuation methods to perform full-system bifurcation and fast-slow analysis. We study the bifurcation structure of the full system as a function of the applied current and the maximal calcium conductance. We identify the bifurcations that shape the transitions between resting, bursting and spiking behaviours, and which lead to the disappearance of bursting when the calcium conductance is reduced. Insights gained from this analysis, are then used to firstly illustrate how the irregular spiking activity found between bursting and stable spiking states, can be influenced by phase differences in the calcium and dendritic voltage, which lead to corresponding changes in the calcium-sensitive potassium current. Furthermore, we use fast-slow analysis to investigate the mechanisms of bursting and show that bursting in the model is dependent on the intermediately slow variable, calcium, while the other slow variable, the activation gate of the afterhyperpolarisation current, does not contribute to setting the intraburst dynamics but participates in setting the interburst interval. Finally, we discuss how some of the described bifurcations affect spiking behaviour, during sharp-wave ripples, in a larger network of Pinsky-Rinzel cells.

Can Neural Activity Propagate by Endogenous Electrical Field?

It is widely accepted that synaptic transmissions and gap junctions are the major governing mechanisms for signal traveling in the neural system. Yet, a group of neural waves, either physiological or pathological, share the same speed of ∼0.1 m/s without synaptic transmission or gap junctions, and this speed is not consistent with axonal conduction or ionic diffusion. The only explanation left is an electrical field effect. We tested the hypothesis that endogenous electric fields are sufficient to explain the propagation with in silico and in vitro experiments. Simulation results show that field effects alone can indeed mediate propagation across layers of neurons with speeds of 0.12 ± 0.09 m/s with pathological kinetics, and 0.11 ± 0.03 m/s with physiologic kinetics, both generating weak field amplitudes of ∼2-6 mV/mm. Further, the model predicted that propagation speed values are inversely proportional to the cell-to-cell distances, but do not significantly change with extracellular resistivity, membrane capacitance, or membrane resistance. In vitro recordings in mice hippocampi produced similar speeds (0.10 ± 0.03 m/s) and field amplitudes (2.5-5 mV/mm), and by applying a blocking field, the propagation speed was greatly reduced. Finally, osmolarity experiments confirmed the model's prediction that cell-to-cell distance inversely affects propagation speed. Together, these results show that despite their weak amplitude, electric fields can be solely responsible for spike propagation at ∼0.1 m/s. This phenomenon could be important to explain the slow propagation of epileptic activity and other normal propagations at similar speeds.