The role of glutamate in neuronal ion homeostasis: A case study of spreading depolarization

Neurogenic and angiogenic poly(N-acryloylglycine)-co-(acrylamide)-co-(N-acryloyl-glutamate) hydrogel: preconditioning effect under oxidative stress and use in neuroregeneration

Traumatic injuries, neurodegenerative diseases and oxidative stress serve as the early biomarkers for neuronal damage and impede angiogenesis and subsequently neuronal growth. Considering this, the present work aimed to develop a poly(N-acryloylglycine)-co-(acrylamide)-co-(N-acryloylglutamate) hydrogel [p(NAG-Ac-NAE)] with angiogenesis/neurogenesis properties. As constituents of this polymer modulate their vital role in biological functions, inhibitory neurotransmitter glycine regulates neuronal homeostasis, and glutamatergic signalling regulates angiogenesis. The p(NAG-Ac-NAE) hydrogel is a highly branched, biodegradable and pH-responsive polymer with a very high swelling behavior of 6188%. The mechanical stability (G', 2.3-2.7 kPa) of this polymeric hydrogel is commendable in the differentiation of mature neurons. This hydrogel is biocompatible (as tested in HUVEC cells) and helps to proliferate PC12 cells (152.7 ± 13.7%), whereas it is cytotoxic towards aggressive cancers such as glioblastoma (LN229 cells) and triple negative breast cancer (TNBC; MDA-MB-231 cells) and helps to maintain the healthy cytoskeleton framework structure of primary cortical neurons by facilitating the elongation of the axonal pathway. Furthermore, FACS results revealed that the synthesized hydrogel potentiates neurogenesis by inducing the cell cycle (G0/G1) and arresting the sub-G1 phase by limiting apoptosis. Additionally, RT-PCR results revealed that this hydrogel induced an increased level of HIF-1α expression, providing preconditioning effects towards neuronal cells under oxidative stress by scavenging ROS and initiating neurogenic and angiogenic signalling. This hydrogel further exhibits more pro-angiogenic activities by increasing the expression of VEGF isoforms compared to previously reported hydrogels. In conclusion, the newly synthesized p(NAG-Ac-NAE) hydrogel can be one of the potential neuroregenerative materials for vasculogenesis-assisted neurogenic applications and paramount for the management of neurodegenerative diseases.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

Astrocytes: new evidence, new models, new roles

Astrocytes have been in the limelight of active research for about 3 decades now. Over this period, ideas about their function and role in the nervous system have evolved from simple assistance in energy supply and homeostasis maintenance to a complex informational and metabolic hub that integrates data on local neuronal activity, sensory and arousal context, and orchestrates many crucial processes in the brain. Rapid progress in experimental techniques and data analysis produces a growing body of data, which can be used as a foundation for formulation of new hypotheses, building new refined mathematical models, and ultimately should lead to a new level of understanding of the contribution of astrocytes to the cognitive tasks performed by the brain. Here, we highlight recent progress in astrocyte research, which we believe expands our understanding of how low-level signaling at a cellular level builds up to processes at the level of the whole brain and animal behavior. We start our review with revisiting data on the role of noradrenaline-mediated astrocytic signaling in locomotion, arousal, sensory integration, memory, and sleep. We then briefly review astrocyte contribution to the regulation of cerebral blood flow regulation, which is followed by a discussion of biophysical mechanisms underlying astrocyte effects on different brain processes. The experimental section is closed by an overview of recent experimental techniques available for modulation and visualization of astrocyte dynamics. We then evaluate how the new data can be potentially incorporated into the new mathematical models or where and how it already has been done. Finally, we discuss an interesting prospect that astrocytes may be key players in important processes such as the switching between sleep and wakefulness and the removal of toxic metabolites from the brain milieu.

Narrative review of roles of astrocytes in subarachnoid hemorrhage

Background and Objective

Astrocytes play an important role in healthy brain function, including the development and maintenance of blood-brain barrier (BBB), structural support, brain homeostasis, neurovascular coupling and secretion of neuroprotective factors. Reactive astrocytes participate in various pathophysiology after subarachnoid hemorrhage (SAH) including neuroinflammation, glutamate toxicity, brain edema, vasospasm, BBB disruption, cortical spreading depolarization (SD).

Methods

We searched PubMed up to 31 May, 2022 and evaluated the articles for screening and inclusion for subsequent systemic review. We found 198 articles with the searched terms. After exclusion based on the selection criteria, we selected 30 articles to start the systemic review.

Key Content and Findings

We summarized the response of astrocytes induced by SAH. Astrocytes are critical for brain edema formation, BBB reconstruction and neuroprotection in the acute stage of SAH. Astrocytes clear extracellular glutamate by increasing the uptake of glutamate and Na+/K+ ATPase activity after SAH. Neurotrophic factors released by astrocytes contribute to neurological recovery after SAH. Meanwhile, Astrocytes also form glial scars which hinder axon regeneration, produce proinflammatory cytokines, free radicals, and neurotoxic molecules.

Conclusions

Preclinical studies showed that therapeutic targeting the astrocytes response could have a beneficial effect in ameliorating neuronal injury and cognitive impairment after SAH. Clinical trials and preclinical animal studies are still urgently needed in order to determine where astrocytes stand in various pathway of brain damage and repair after SAH and, above all, to develop therapeutic approaches which benefit patient outcomes.

Plasticity of perisynaptic astroglia during ischemia-induced spreading depolarization

High astroglial capacity for glutamate and potassium clearance aids in recovering spreading depolarization (SD)-evoked disturbance of ion homeostasis during stroke. Since perisynaptic astroglia cannot be imaged with diffraction-limited light microscopy, nothing is known about the impact of SD on the ultrastructure of a tripartite synapse. We used serial section electron microscopy to assess astroglial synaptic coverage in the sensorimotor cortex of urethane-anesthetized male and female mice during and after SD evoked by transient bilateral common carotid artery occlusion. At the subcellular level, astroglial mitochondria were remarkably resilient to SD compared to dendritic mitochondria that were fragmented by SD. Overall, 482 synapses in `Sham' during `SD' and `Recovery' groups were randomly selected and analyzed in 3D. Perisynaptic astroglia was present at the axon-spine interface (ASI) during SD and after recovery. Astrocytic processes were more likely found at large synapses on mushroom spines after recovery, while the length of the ASI perimeter surrounded by astroglia has also significantly increased at large synapses. These findings suggest that as larger synapses have a bigger capacity for neurotransmitter release during SD, they attract astroglial processes to their perimeter during recovery, limiting extrasynaptic glutamate escape and further enhancing the astrocytic ability to protect synapses in stroke.

Glioma epileptiform activity and progression are driven by IGSF3-mediated potassium dysregulation

Seizures are a frequent pathophysiological feature of malignant glioma. Recent studies implicate peritumoral synaptic dysregulation as a driver of brain hyperactivity and tumor progression; however, the molecular mechanisms that govern these phenomena remain elusive. Using scRNA-seq and intraoperative patient ECoG recordings, we show that tumors from seizure patients are enriched for gene signatures regulating synapse formation. Employing a human-to-mouse in vivo functionalization pipeline to screen these genes, we identify IGSF3 as a mediator of glioma progression and dysregulated neural circuitry that manifests as spreading depolarization (SD). Mechanistically, we discover that IGSF3 interacts with Kir4.1 to suppress potassium buffering and found that seizure patients exhibit reduced expression of potassium handlers in proliferating tumor cells. In vivo imaging reveals that dysregulated synaptic activity emanates from the tumor-neuron interface, which we confirm in patients. Our studies reveal that tumor progression and seizures are enabled by ion dyshomeostasis and identify SD as a driver of disease.

Perspectives on the basis of seizure-induced respiratory dysfunction

Epilepsy is an umbrella term used to define a wide variety of seizure disorders and sudden unexpected death in epilepsy (SUDEP) is the leading cause of death in epilepsy. Although some SUDEP risk factors have been identified, it remains largely unpredictable, and underlying mechanisms remain poorly understood. Most seizures start in the cortex, but the high mortality rate associated with certain types of epilepsy indicates brainstem involvement. Therefore, to help understand SUDEP we discuss mechanisms by which seizure activity propagates to the brainstem. Specifically, we highlight clinical and pre-clinical evidence suggesting how seizure activation of: (i) descending inhibitory drive or (ii) spreading depolarization might contribute to brainstem dysfunction. Furthermore, since epilepsy is a highly heterogenous disorder, we also considered factors expected to favor or oppose mechanisms of seizure propagation. We also consider whether epilepsy-associated genetic variants directly impact brainstem function. Because respiratory failure is a leading cause of SUDEP, our discussion of brainstem dysfunction focuses on respiratory control.

Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits

Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.

Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Bursting is ubiquitous in cellular excitable rhythms and comes in a plethora of patterns, both experimentally recorded and reproduced through models. As these different patterns may reflect different coding or information properties, it is therefore crucial to develop modeling frameworks that can both capture them and understand their characteristics. In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. We complement this classical view by showing that nontrivial slow subsystem may also encode key informations important to classify bursting rhythms, due to the presence of so-called folded-node singularities. We provide minimal idealized models as well as one generic conductance-based example displaying bursting oscillations that require our extended classification in order to be fully characterized. We also highlight examples of biological data that could be suitably revisited with the lenses of this extended classifications and could lead to new models of complex cellular activity.

The Critical Role of Spreading Depolarizations in Early Brain Injury: Consensus and Contention

BACKGROUND

When a patient arrives in the emergency department following a stroke, a traumatic brain injury, or sudden cardiac arrest, there is no therapeutic drug available to help protect their jeopardized neurons. One crucial reason is that we have not identified the molecular mechanisms leading to electrical failure, neuronal swelling, and blood vessel constriction in newly injured gray matter. All three result from a process termed spreading depolarization (SD). Because we only partially understand SD, we lack molecular targets and biomarkers to help neurons survive after losing their blood flow and then undergoing recurrent SD.

METHODS

In this review, we introduce SD as a single or recurring event, generated in gray matter following lost blood flow, which compromises the Na⁺/K⁺ pump. Electrical recovery from each SD event requires so much energy that neurons often die over minutes and hours following initial injury, independent of extracellular glutamate.

RESULTS

We discuss how SD has been investigated with various pitfalls in numerous experimental preparations, how overtaxing the Na⁺/K⁺ ATPase elicits SD. Elevated K⁺ or glutamate are unlikely natural activators of SD. We then turn to the properties of SD itself, focusing on its initiation and propagation as well as on computer modeling.

CONCLUSIONS

Finally, we summarize points of consensus and contention among the authors as well as where SD research may be heading. In an accompanying review, we critique the role of the glutamate excitotoxicity theory, how it has shaped SD research, and its questionable importance to the study of early brain injury as compared with SD theory.

Surface Properties of Synaptosomes in the Presence of L-Glutamic and Kainic Acids: In Vitro Alteration of the ATPase and Acetylcholinesterase Activities

Morphologically and functionally identical to brain synapses, the nerve ending particles synaptosomes are biochemically derived membrane structures responsible for the transmission of neural information. Their surface and mechanical properties, measured in vitro, provide useful information about the functional activity of synapses in the brain in vivo. Glutamate and kainic acid are of particular interest because of their role in brain pathology (including causing seizure, migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, traumatic brain injury and stroke). The effects of the excitatory neurotransmitter L-glutamic acid and its agonist kainic acid are tested on Na⁺, K⁺-ATPase and Mg²⁺-ATPase activities in synaptic membranes prepared from the cerebral cortex of rat brain tissue. The surface parameters of synaptosome preparations from the cerebral cortex in the presence of L-glutamic and kainic acids are studied by microelectrophoresis for the first time. The studied neurotransmitters promote a significant increase in the electrophoretic mobility and surface electrical charge of synaptosomes at 1–4 h after isolation. The measured decrease in the bending modulus of model bimolecular membranes composed of monounsaturated lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine provides evidence for softer membranes in the presence of L-glutamate. Kainic acid does not affect membrane mechanical stability even at ten-fold higher concentrations. Both the L-glutamic and kainic acids reduce acetylcholinesterase activity and deviation from the normal functions of neurotransmission in synapses is presumed. The presented results regarding the modulation of the enzyme activity of synaptic membranes and surface properties of synaptosomes are expected by biochemical and biophysical studies to contribute to the elucidation of the molecular mechanisms of neurotransmitters/agonists’ action on membranes.

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.

An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain

Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.

Dysregulation of Astrocyte Ion Homeostasis and Its Relevance for Stroke-Induced Brain Damage

Ischemic stroke is a leading cause of mortality and chronic disability. Either recovery or progression towards irreversible failure of neurons and astrocytes occurs within minutes to days, depending on remaining perfusion levels. Initial damage arises from energy depletion resulting in a failure to maintain homeostasis and ion gradients between extra- and intracellular spaces. Astrocytes play a key role in these processes and are thus central players in the dynamics towards recovery or progression of stroke-induced brain damage. Here, we present a synopsis of the pivotal functions of astrocytes at the tripartite synapse, which form the basis of physiological brain functioning. We summarize the evidence of astrocytic failure and its consequences under ischemic conditions. Special emphasis is put on the homeostasis and stroke-induced dysregulation of the major monovalent ions, namely Na+, K+, H+, and Cl-, and their involvement in maintenance of cellular volume and generation of cerebral edema.

On the origin of ultraslow spontaneous Na+ fluctuations in neurons of the neonatal forebrain

Spontaneous neuronal and astrocytic activity in the neonate forebrain is believed to drive the maturation of individual cells and their integration into complex brain-region-specific networks. The previously reported forms include bursts of electrical activity and oscillations in intracellular Ca2+ concentration. Here, we use ratiometric Na+ imaging to demonstrate spontaneous fluctuations in the intracellular Na+ concentration of CA1 pyramidal neurons and astrocytes in tissue slices obtained from the hippocampus of mice at postnatal days 2-4 (P2-4). These occur at very low frequency (∼2/h), can last minutes with amplitudes up to several millimolar, and mostly disappear after the first postnatal week. To further investigate their mechanisms, we model a network consisting of pyramidal neurons and interneurons. Experimentally observed Na+ fluctuations are mimicked when GABAergic inhibition in the simulated network is made depolarizing. Both our experiments and computational model show that blocking voltage-gated Na+ channels or GABAergic signaling significantly diminish the neuronal Na+ fluctuations. On the other hand, blocking a variety of other ion channels, receptors, or transporters including glutamatergic pathways does not have significant effects. Our model also shows that the amplitude and duration of Na+ fluctuations decrease as we increase the strength of glial K+ uptake. Furthermore, neurons with smaller somatic volumes exhibit fluctuations with higher frequency and amplitude. As opposed to this, larger extracellular to intracellular volume ratio observed in neonatal brain exerts a dampening effect. Finally, our model predicts that these periods of spontaneous Na+ influx leave neonatal neuronal networks more vulnerable to seizure-like states when compared with mature brain.NEW & NOTEWORTHY Spontaneous activity in the neonate forebrain plays a key role in cell maturation and brain development. We report spontaneous, ultraslow, asynchronous fluctuations in the intracellular Na+ concentration of neurons and astrocytes. We show that this activity is not correlated with the previously reported synchronous neuronal population bursting or Ca2+ oscillations, both of which occur at much faster timescales. Furthermore, extracellular K+ concentration remains nearly constant. The spontaneous Na+ fluctuations disappear after the first postnatal week.

Impaired θ-γ Coupling Indicates Inhibitory Dysfunction and Seizure Risk in a Dravet Syndrome Mouse Model

Dravet syndrome (DS) is an epileptic encephalopathy that still lacks biomarkers for epileptogenesis and its treatment. Dysfunction of Na_V1.1 sodium channels, which are chiefly expressed in inhibitory interneurons, explains the epileptic phenotype. Understanding the network effects of these cellular deficits may help predict epileptogenesis. Here, we studied θ-γ coupling as a potential marker for altered inhibitory functioning and epileptogenesis in a DS mouse model. We found that cortical θ-γ coupling was reduced in both male and female juvenile DS mice and persisted only if spontaneous seizures occurred. θ-γ Coupling was partly restored by cannabidiol (CBD). Locally disrupting Na_V1.1 expression in the hippocampus or cortex yielded early attenuation of θ-γ coupling, which in the hippocampus associated with fast ripples, and which was replicated in a computational model when voltage-gated sodium currents were impaired in basket cells (BCs). Our results indicate attenuated θ-γ coupling as a promising early indicator of inhibitory dysfunction and seizure risk in DS.

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na⁺, K⁺, Ca²⁺, and Cl⁻), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

Metabolism plays a central role in the cortical spreading depression: Evidence from a mathematical model

The slow propagating waves of strong depolarization of neural cells characterizing cortical spreading depression, or depolarization, (SD) are known to break cerebral homeostasis and induce significant hemodynamic and electro-metabolic alterations. Mathematical models of cortical spreading depression found in the literature tend to focus on the changes occurring at the electrophysiological level rather than on the ensuing metabolic changes. In this paper, we propose a novel mathematical model which is able to simulate the coupled electrophysiology and metabolism dynamics of SD events, including the swelling of neurons and astrocytes and the concomitant shrinkage of extracellular space. The simulations show that the metabolic coupling leads to spontaneous repetitions of the SD events, which the electrophysiological model alone is not capable to produce. The model predictions, which corroborate experimental findings from the literature, show a strong disruption in metabolism accompanying each wave of spreading depression in the form of a sharp decrease of glucose and oxygen concentrations, with a simultaneous increase in lactate concentration which, in turn, delays the clearing of excess potassium in extracellular space. Our model suggests that the depletion of glucose and oxygen concentration is more pronounced in astrocyte than neuron, in line with the partitioning of the energetic cost of potassium clearing. The model suggests that the repeated SD events are electro-metabolic oscillations that cannot be explained by the electrophysiology alone. The model highlights the crucial role of astrocytes in cleaning the excess potassium flooding extracellular space during a spreading depression event: further, if the ratio of glial/neuron density increases, the frequency of cortical SD events decreases, and the peak potassium concentration in extracellular space is lower than with equal volume fractions.

Mitochondrial dysfunction and role in spreading depolarization and seizure

The effect of pathological phenomena such as epileptic seizures and spreading depolarization (SD) on mitochondria and the potential feedback of mitochondrial dysfunction into the dynamics of those phenomena are complex and difficult to study experimentally due to the simultaneous changes in many variables governing neuronal behavior. By combining a model that accounts for a wide range of neuronal behaviors including seizures, normoxic SD, and hypoxic SD (HSD), together with a detailed model of mitochondrial function and intracellular Ca²⁺ dynamics, we investigate mitochondrial dysfunction and its potential role in recovery of the neuron from seizures, HSD, and SD. Our results demonstrate that HSD leads to the collapse of mitochondrial membrane potential and cellular ATP levels that recover only when normal oxygen supply is restored. Mitochondrial organic phosphate and pH gradients determine the strength of the depolarization block during HSD and SD, how quickly the cell enters the depolarization block when the oxygen supply is disrupted or potassium in the bath solution is raised beyond the physiological value, and how fast the cell recovers from SD and HSD when normal potassium concentration and oxygen supply are restored. Although not as dramatic as phosphate and pH gradients, mitochondrial Ca²⁺ uptake has a similar effect on neuronal behavior during these conditions.

Cytotoxic Swelling of Sick Excitable Cells - Impaired Ion Homeostasis and Membrane Tension Homeostasis in Muscle and Neuron

When they become simultaneously leaky to both Na⁺ and Cl^-, excitable cells are vulnerable to potentially lethal cytotoxic swelling. Swelling ensues in spite of an isosmotic milieu because the entering ions add osmolytes to the cytoplasm's high concentration of impermeant anionic osmolytes. An influx of osmotically-obliged water is unavoidable. A cell that cannot stanch at least one the leaks will succumb to death by Donnan effect. "Sick excitable cells" are those injured through ischemia, trauma, inflammation, hyperactivity, genetically-impaired membrane skeletons and other insults, all of which foster bleb-damage to regions of the plasma membrane. Nav channels resident in damaged membrane exhibit left-shifted kinetics; the corresponding Nav window conductance constitutes a Na⁺-leak. In cortical neurons, sustained depolarization to ∼-20mV elicits a sustained lethal gCl. Underlying V_rest in skeletal muscle is a constitutively active gCl; not surprisingly therefore, dystrophic muscle fibers, which are prone to bleb damage and which exhibit Nav-leak and Na⁺-overload, are prone to cytotoxic swelling. To restore viability in cytotoxically swelling neurons and muscle, the imperative of fully functional ion homeostasis is well-recognized. However, as emphasized here, in a healthy excitable cell, fully functional membrane tension homeostasis is also imperative. ATPase-pumps keep plasma membrane batteries charged, and ATPase-motor proteins maintain membrane tone. In sick excitable cells, neither condition prevails.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. The extracellular medium of neural tissue is an active medium of neuromodulators, ions, inflammatory cells, oxygen, NO and other gases, with additional physiological, pharmacological and pathological agents. These extracellular agents influence, and are influenced by, cellular electrophysiology, and cellular chemophysiology-the complex internal cellular milieu of second-messenger signaling and cascades. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction-the proportion of space in which species are able to diffuse, and tortuosity-the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke. Simulation results were verified against analytic results and against the extracellular portion of the simulation run under FiPy. The creation of this NEURON interface provides a pathway for interoperability that can be used to automatically export this class of models into complex intracellular/extracellular simulations and future cross-simulator standardization.