Anions Govern Cell Volume: A Case Study of Relative Astrocytic and Neuronal Swelling in Spreading Depolarization

Mechanisms of Activation of Brain's Drainage during Sleep: The Nightlife of Astrocytes

The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes-glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the "astrocytocentric" view of the BWRS function and the explanation of its activation during sleep from the viewpoint of new findings over the last decade. Our main conclusion is that the BWRS's action may be analyzed both at the systemic (whole-brain) and at the local (cellular) level. The local level means here that the neuro-glial-vascular unit can also be regarded as the smallest functional unit of sleep, and therefore, the smallest functional unit of the BWRS.

Machine Learning Technology for EEG-Forecast of the Blood-Brain Barrier Leakage and the Activation of the Brain's Drainage System during Isoflurane Anesthesia

Anesthesia enables the painless performance of complex surgical procedures. However, the effects of anesthesia on the brain may not be limited only by its duration. Also, anesthetic agents may cause long-lasting changes in the brain. There is growing evidence that anesthesia can disrupt the integrity of the blood-brain barrier (BBB), leading to neuroinflammation and neurotoxicity. However, there are no widely used methods for real-time BBB monitoring during surgery. The development of technologies for an express diagnosis of the opening of the BBB (OBBB) is a challenge for reducing post-surgical/anesthesia consequences. In this study on male rats, we demonstrate a successful application of machine learning technology, such as artificial neural networks (ANNs), to recognize the OBBB induced by isoflurane, which is widely used in surgery. The ANNs were trained on our previously presented data obtained on the sound-induced OBBB with an 85% testing accuracy. Using an optical and nonlinear analysis of the OBBB, we found that 1% isoflurane does not induce any changes in the BBB, while 4% isoflurane caused significant BBB leakage in all tested rats. Both 1% and 4% isoflurane stimulate the brain's drainage system (BDS) in a dose-related manner. We show that ANNs can recognize the OBBB induced by 4% isoflurane in 57% of rats and BDS activation induced by 1% isoflurane in 81% of rats. These results open new perspectives for the development of clinically significant bedside technologies for EEG-monitoring of OBBB and BDS.

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.

A cold and quiet brain: mechanisms of insect CNS arrest at low temperatures

Exposure to cold causes insects to enter a chill coma at species-specific temperatures and such temperature sensitivity contributes to geographic distribution and phenology. Coma results from abrupt spreading depolarization (SD) of neural tissue in the integrative centers of the CNS. SD abolishes neuronal signaling and the operation of neural circuits, like an off switch for the CNS. Turning off the CNS by allowing ion gradients to collapse will conserve energy and may offset negative consequences of temporary immobility. SD is modified by prior experience via rapid cold hardening (RCH) or cold acclimation which alter properties of K_v channels, Na⁺/K⁺-ATPase and Na⁺/K⁺/2Cl^- cotransporter. The stress hormone octopamine mediates RCH. Future progress depends on developing a more complete understanding of ion homeostasis in and of the insect CNS.

Chronic intermittent ethanol exposure disrupts stress-related tripartite communication to impact affect-related behavioral selection in male rats

Alcohol use disorder (AUD) is characterized by loss of intake control, increased anxiety, and susceptibility to relapse inducing stressors. Both astrocytes and neurons contribute to behavioral and hormonal consequences of chronic intermittent ethanol (CIE) exposure in animal models. Details on how CIE disrupts hypothalamic neuro-glial communication, which mediates stress responses are lacking. We conducted a behavioral battery (grooming, open field, reactivity to a single, uncued foot-shock, intermittent-access two-bottle choice ethanol drinking) followed by Ca²⁺ imaging in ex-vivo slices of paraventricular nucleus of the hypothalamus (PVN) from male rats exposed to CIE vapor or air-exposed controls. Ca²⁺ signals were evaluated in response to norepinephrine (NE) with or without selective α-adrenergic receptor (αAR) or GluN2B-containing N-methyl-D-aspartate receptor (NMDAR) antagonists, followed by dexamethasone (DEX) to mock a pharmacological stress response. Expectedly, CIE rats had altered anxiety-like, rearing, grooming, and drinking behaviors. Importantly, NE-mediated reductions in Ca²⁺ event frequency were blunted in both CIE neurons and astrocytes. Administration of the selective α1AR antagonist, prazosin, reversed this CIE-induced dysfunction in both cell types. Additionally, the pharmacological stress protocol reversed the altered basal Ca²⁺ signaling profile of CIE astrocytes. Signaling changes in astrocytes in response to NE were correlated with anxiety-like behaviors, such as the grooming:rearing ratio, suggesting tripartite synaptic function plays a role in switching between exploratory and stress-coping behavior. These data show how CIE exposure causes persistent changes to PVN neuro-glial function and provides the groundwork for how these physiological changes manifest in behavioral selection.

An Isotonic Model of Neuron Swelling Based on Co-Transport of Salt and Water

Neurons spend most of their energy building ion gradients across the cell membrane. During energy deprivation the neurons swell, and the concomitant mixing of their ions is commonly assumed to lead toward a Donnan equilibrium, at which the concentration gradients of all permeant ion species have the same Nernst potential. This Donnan equilibrium, however, is not isotonic, as the total concentration of solute will be greater inside than outside the neurons. The present theoretical paper, in contrast, proposes that neurons follow a path along which they swell quasi-isotonically by co-transporting water and ions. The final neuronal volume on the path is taken that at which the concentration of impermeant anions in the shrinking extracellular space equals that inside the swelling neurons. At this final state, which is also a Donnan equilibrium, all permeant ions can mix completely, and their Nernst potentials vanish. This final state is isotonic and electro-neutral, as are all intermediate states along this path. The path is in principle reversible, and maximizes the work of mixing.

I, Hramkov A, Kulminskiy D, Semenova N, Sergeev K, Slepnev A, Yu. SE, Zhuravlev M, Fedosov I, Shirokov A, Blokhina I, Dubrovski A, Terskov A, Khorovodov A, Ageev V, Elovenko D, Evsukova A, Adushkina V, Telnova V, Postnov D, Penzel T, Kurths J. EEG biomarkers of activation of the lymphatic drainage system of the brain during sleep and opening of the blood-brain barrier

The lymphatic drainage system of the brain (LDSB) is the removal of metabolites and wastes from its tissues. A dysfunction of LDSB is an important sign of aging, brain oncology, the Alzheimer's and Parkinson's diseases. The development of new strategies for diagnosis of LDSB injuries can improve prevention of age-related cerebral amyloid angiopathy, neurodegenerative and cerebrovascular diseases. There are two conditions, such as deep sleep and opening of the blood-brain-barrier (OBBB) associated with the LDSB activation. A promising candidate for measurement of LDSB could be electroencephalography (EEG). In this pilot study on rats, we tested the hypothesis, whether deep sleep and OBBB can be an informative platform for an effective extracting of information about the LDSB functions. Using the nonlinear analysis of EEG dynamics and machine learning technology, we discovered that the LDSB activation during OBBB and sleep is associated with similar changes in the EEG θ-activity. The OBBB causes the higher LDSB activation vs. sleep that is accompanied by specific changes in the low frequency EEG activity extracted by the power spectra analysis of the EEG dynamics combined with the coherence function. Thus, our findings demonstrate a link between neural activity associated with the LDSB activation during sleep and OBBB that is an important informative platform for extraction of the EEG-biomarkers of the LDSB activity. These results open new perspectives for the development of technology for the LDSB diagnostics that would open a novel era in the prognosis of brain diseases caused by the LDSB disorders, including OBBB.

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.

Theoretical analysis of wake/sleep changes in brain solute transport suggests a flow of interstitial fluid

Clearance of protein waste products from the brain is accomplished by a combination of advection and diffusion in cerebrospinal fluid (CSF) and interstitial fluid (ISF). In the glymphatic model, there is a flow of ISF in the interstitial space, and both advection and diffusion occur there. Such a flow of ISF would be slow and difficult to detect directly, and its existence has proved controversial. Waste clearance has been shown to occur mainly during sleep, during which the volume of the interstitial space increases substantially due to ISF emitted from astrocytes. Here I show that this volume increase of the interstitial space, by itself, should lead to a slight reduction of diffusive transport, due to dilution of the waste solute, but to a significant increase in flow rate and advective transport, due to lowered hydraulic resistance. Thus, a flow of ISF together with the observed volume increase of the interstitial space might provide an important mechanism contributing to the enhanced clearance during sleep.

Migraine Aura, Transient Ischemic Attacks, Stroke, and Dying of the Brain Share the Same Key Pathophysiological Process in Neurons Driven by Gibbs–Donnan Forces, Namely Spreading Depolarization

Neuronal cytotoxic edema is the morphological correlate of the near-complete neuronal battery breakdown called spreading depolarization, or conversely, spreading depolarization is the electrophysiological correlate of the initial, still reversible phase of neuronal cytotoxic edema. Cytotoxic edema and spreading depolarization are thus different modalities of the same process, which represents a metastable universal reference state in the gray matter of the brain close to Gibbs–Donnan equilibrium. Different but merging sections of the spreading-depolarization continuum from short duration waves to intermediate duration waves to terminal waves occur in a plethora of clinical conditions, including migraine aura, ischemic stroke, traumatic brain injury, aneurysmal subarachnoid hemorrhage (aSAH) and delayed cerebral ischemia (DCI), spontaneous intracerebral hemorrhage, subdural hematoma, development of brain death, and the dying process during cardio circulatory arrest. Thus, spreading depolarization represents a prime and simultaneously the most neglected pathophysiological process in acute neurology. Aristides Leão postulated as early as the 1940s that the pathophysiological process in neurons underlying migraine aura is of the same nature as the pathophysiological process in neurons that occurs in response to cerebral circulatory arrest, because he assumed that spreading depolarization occurs in both conditions. With this in mind, it is not surprising that patients with migraine with aura have about a twofold increased risk of stroke, as some spreading depolarizations leading to the patient percept of migraine aura could be caused by cerebral ischemia. However, it is in the nature of spreading depolarization that it can have different etiologies and not all spreading depolarizations arise because of ischemia. Spreading depolarization is observed as a negative direct current (DC) shift and associated with different changes in spontaneous brain activity in the alternating current (AC) band of the electrocorticogram. These are non-spreading depression and spreading activity depression and epileptiform activity. The same spreading depolarization wave may be associated with different activity changes in adjacent brain regions. Here, we review the basal mechanism underlying spreading depolarization and the associated activity changes. Using original recordings in animals and patients, we illustrate that the associated changes in spontaneous activity are by no means trivial, but pose unsolved mechanistic puzzles and require proper scientific analysis.

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.

Increased susceptibility to quinolinic acid-induced seizures and long-term changes in brain oscillations in an animal model of glutaric acidemia type I

Glutaric acidemia type I (GA-I) is an inborn error of metabolism of lysine, hydroxylysine, and tryptophan, caused by glutaryl-CoA-dehydrogenase (GCDH) deficiency, characterized by the buildup of toxic organic acids predominantly in the brain. After acute catabolic states, patients usually develop striatal degeneration, but the mechanisms behind this damage are still unknown. Quinolinic acid (QA), a metabolite of the kynurenine pathway, increases especially during infections/inflammatory processes, and could act synergically with organic acids, contributing to the neurological features of GA-I. The aim of this study was to investigate whether QA increases seizure susceptibility and modifies brain oscillation patterns in an animal model of GA-I, the Gcdh^-/- mice taking high-lysine diet (Gcdh^-/- -Lys). Therefore, the characteristics of QA-induced seizures and changes in brain oscillatory patterns were evaluated by video-electroencephalography (EEG) analysis recorded in Gcdh^-/- -Lys, Gcdh^+/+ -Lys, and Gcdh^-/- -N (normal diet) animals. We found that the number of seizures per animal was similar for all groups receiving QA, Gcdh^-/- -Lys-QA, Gcdh^+/+ -Lys-QA, and Gcdh^-/- -N-QA. However, severe seizures were observed in the majority of Gcdh^-/- -Lys-QA mice (82%), and only in 25% of Gcdh^+/+ -Lys-QA and 44% of Gcdh^-/- -N-QA mice. All Gcdh^-/- -Lys animals developed spontaneous recurrent seizures (SRS), but Gcdh^-/- -Lys-QA animals had increased number of SRS, higher mortality rate, and significant predominance of lower frequency oscillations on EEG. Our results suggest that QA plays an important role in the neurological features of GA-I, as Gcdh^-/- -Lys mice exhibit increased susceptibility to intrastriatal QA-induced seizures and long-term changes in brain oscillations.

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.

Ion dynamics at the energy-deprived tripartite synapse

The anatomical and functional organization of neurons and astrocytes at 'tripartite synapses' is essential for reliable neurotransmission, which critically depends on ATP. In low energy conditions, synaptic transmission fails, accompanied by a breakdown of ion gradients, changes in membrane potentials and cell swelling. The resulting cellular damage and cell death are causal to the often devastating consequences of an ischemic stroke. The severity of ischemic damage depends on the age and the brain region in which a stroke occurs, but the reasons for this differential vulnerability are far from understood. In the present study, we address this question by developing a comprehensive biophysical model of a glutamatergic synapse to identify key determinants of synaptic failure during energy deprivation. Our model is based on fundamental biophysical principles, includes dynamics of the most relevant ions, i.e., Na+, K+, Ca2+, Cl- and glutamate, and is calibrated with experimental data. It confirms the critical role of the Na+/K+-ATPase in maintaining ion gradients, membrane potentials and cell volumes. Our simulations demonstrate that the system exhibits two stable states, one physiological and one pathological. During energy deprivation, the physiological state may disappear, forcing a transit to the pathological state, which can be reverted when blocking voltage-gated Na+ and K+ channels. Our model predicts that the transition to the pathological state is favoured if the extracellular space fraction is small. A reduction in the extracellular space volume fraction, as, e.g. observed with ageing, will thus promote the brain's susceptibility to ischemic damage. Our work provides new insights into the brain's ability to recover from energy deprivation, with translational relevance for diagnosis and treatment of ischemic strokes.

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.

Bidirectional regulation of glial potassium buffering - glioprotection versus neuroprotection

Glia modulate neuronal excitability and seizure sensitivity by maintaining potassium and water homeostasis. A salt inducible kinase 3 (SIK3)-regulated gene expression program controls the glial capacity to buffer K⁺ and water in Drosophila, however upstream regulatory mechanisms are unknown. Here, we identify an octopaminergic circuit linking neuronal activity to glial ion and water buffering. Under basal conditions, octopamine functions through the inhibitory octopaminergic G-protein-coupled receptor (GPCR) OctβR to upregulate glial buffering capacity, while under pathological K⁺ stress, octopamine signals through the stimulatory octopaminergic GPCR OAMB1 to downregulate the glial buffering program. Failure to downregulate this program leads to intracellular glia swelling and stress signaling, suggesting that turning down this pathway is glioprotective. In the eag shaker Drosophila seizure model, the SIK3-mediated buffering pathway is inactivated. Reactivation of the glial buffering program dramatically suppresses neuronal hyperactivity, seizures, and shortened life span in this mutant. These findings highlight the therapeutic potential of a glial-centric therapeutic strategy for diseases of hyperexcitability.

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.

Parametric exploration of cellular swelling in a computational model of cortical spreading depression

Cortical spreading depression (CSD) is a slowly propagating wave of depolarization of brain cells, followed by temporary silenced electrical brain activity. Major structural changes during CSD are linked to neuronal and possibly glial swelling. However, basic questions still remain unanswered. In particular, there are open questions regarding whether neurons or glial cells swell more, and how the cellular swelling affects the CSD wave propagation.In this study, we computationally explore how different parameters affect the swelling of neurons and astrocytes (starshaped glial cells) during CSD and how the cell swelling alters the CSD wave spatial distribution. We apply a homogenized mathematical model that describes electrodiffusion in the intraand extracellular space, and discretize the equations using a finite element method. The simulations are run with a twocompartment (extracellular space and neurons) and a threecompartment version of the model with astrocytes added. We consider cell swelling during CSD in four scenarios: (A) incorporating aquaporin-4 channels in the astrocytic membrane, (B) increasing the neuron/astrocyte ratio to 2:1, (C) blocking and increasing the Na⁺/K⁺-ATPase rate in the astrocytic compartment, and (D) blocking the Cl^- channels in astrocytes. Our results show that increasing the water permeability in the astrocytes results in a higher astrocytic swelling and a lower neuronal swelling than in the default case. Further, elevated neuronal density increases the swelling in both neurons and astrocytes. Blocking the Na⁺/K⁺-ATPase in the astrocytes leads to an increased wave width and swelling in both compartments, which instead decreases when the pump rate is raised. Blocking the Cl^- channels in the astrocytes results in neuronal swelling, and a shrinkage in the astrocytes. Our results suggest a supporting role of astrocytes in preventing cellular swelling and CSD, as well as highlighting how dysfunctions in astrocytes might elicit CSD.

Sleep as a Novel Biomarker and a Promising Therapeutic Target for Cerebral Small Vessel Disease: A Review Focusing on Alzheimer's Disease and the Blood-Brain Barrier

Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep plays a crucial role in keeping health of the central nervous system and in resistance to CSVD. The deficit of sleep contributes to accumulation of metabolites and toxins such as beta-amyloid in the brain and can lead to BBB disruption. Currently, sleep is considered as an important informative platform for diagnosis and therapy of AD. However, there are no effective methods for extracting of diagnostic information from sleep characteristics. In this review, we show strong evidence that slow wave activity (SWA) (0–0.5 Hz) during deep sleep reflects glymphatic pathology, the BBB leakage and memory deficit in AD. We also discuss that diagnostic and therapeutic targeting of SWA in AD might lead to be a novel era in effective therapy of AD. Moreover, we demonstrate that SWA can be pioneering non-invasive and bed–side technology for express diagnosis of the BBB permeability. Finally, we review the novel data about the methods of detection and enhancement of SWA that can be biomarker and a promising therapy of amyloidal CSVD and CSVD associated with the BBB disorders.

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.

Cell Volume Control in Healthy Brain and Neuropathologies

Regulation of cellular volume is a critical homeostatic process that is intimately linked to ionic and osmotic balance in the brain tissue. Because the brain is encased in the rigid skull and has a very complex cellular architecture, even minute changes in the volume of extracellular and intracellular compartments have a very strong impact on tissue excitability and function. The failure of cell volume control is a major feature of several neuropathologies, such as hyponatremia, stroke, epilepsy, hyperammonemia, and others. There is strong evidence that such dysregulation, especially uncontrolled cell swelling, plays a major role in adverse pathological outcomes. To protect themselves, brain cells utilize a variety of mechanisms to maintain their optimal volume, primarily by releasing or taking in ions and small organic molecules through diverse volume-sensitive ion channels and transporters. In principle, the mechanisms of cell volume regulation are not unique to the brain and share many commonalities with other tissues. However, because ions and some organic osmolytes (e.g., major amino acid neurotransmitters) have a strong impact on neuronal excitability, cell volume regulation in the brain is a surprisingly treacherous process, which may cause more harm than good. This topical review covers the established and emerging information in this rapidly developing area of physiology.

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.

Spiking patterns of a neuron model to stimulus: Rich dynamics and oxygen's role

Neuronal spiking patterns, which are of fundamental importance for the understanding of information processing in neural systems, can be generated in response to different stimuli. We here investigate in detail the stimulus-induced spiking patterns in a biologically plausible neuron model in which the oxygen concentration and the dynamical concentrations of potassium, sodium, and chloride are considered. Various types of spiking patterns can be induced by the different external potassium accumulations in response to the stimulus, including two different types of epileptic seizure (SZ) and spreading depression (SD) states, two different mixed states of SD and SZ, SZ state with multi-burst, and tonic firing behaviors. Interestingly, we show that these rich spiking patterns can also be induced by the current stimulus with a low oxygen concentration. Furthermore, we reveal that the stimulus can induce two different phase transitions from the SD state to the SZ state according to the phase transition theory, which results in the different electrical activities. All these findings may provide insight into information processing in neural systems.

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.

Astroglial Modulation of Hydromineral Balance and Cerebral Edema

Maintenance of hydromineral balance (HB) is an essential condition for life activity at cellular, tissue, organ and system levels. This activity has been considered as a function of the osmotic regulatory system that focuses on hypothalamic vasopressin (VP) neurons, which can reflexively release VP into the brain and blood to meet the demand of HB. Recently, astrocytes have emerged as an essential component of the osmotic regulatory system in addition to functioning as a regulator of the HB at cellular and tissue levels. Astrocytes express all the components of osmoreceptors, including aquaporins, molecules of the extracellular matrix, integrins and transient receptor potential channels, with an operational dynamic range allowing them to detect and respond to osmotic changes, perhaps more efficiently than neurons. The resultant responses, i.e., astroglial morphological and functional plasticity in the supraoptic and paraventricular nuclei, can be conveyed, physically and chemically, to adjacent VP neurons, thereby influencing HB at the system level. In addition, astrocytes, particularly those in the circumventricular organs, are involved not only in VP-mediated osmotic regulation, but also in regulation of other osmolality-modulating hormones, including natriuretic peptides and angiotensin. Thus, astrocytes play a role in local/brain and systemic HB. The adaptive astrocytic reactions to osmotic challenges are associated with signaling events related to the expression of glial fibrillary acidic protein and aquaporin 4 to promote cell survival and repair. However, prolonged osmotic stress can initiate inflammatory and apoptotic signaling processes, leading to glial dysfunction and a variety of brain diseases. Among many diseases of brain injury and hydromineral disorders, cytotoxic and osmotic cerebral edemas are the most common pathological manifestation. Hyponatremia is the most common cause of osmotic cerebral edema. Overly fast correction of hyponatremia could lead to central pontine myelinolysis. Ischemic stroke exemplifies cytotoxic cerebral edema. In this review, we summarize and analyze the osmosensory functions of astrocytes and their implications in cerebral edema.

Astrocytic Kir4.1 channels and gap junctions account for spontaneous epileptic seizure

Experimental recordings in hippocampal slices indicate that astrocytic dysfunction may cause neuronal hyper-excitation or seizures. Considering that astrocytes play important roles in mediating local uptake and spatial buffering of K⁺ in the extracellular space of the cortical circuit, we constructed a novel model of an astrocyte-neuron network module consisting of a single compartment neuron and 4 surrounding connected astrocytes and including extracellular potassium dynamics. Next, we developed a new model function for the astrocyte gap junctions, connecting two astrocyte-neuron network modules. The function form and parameters of the gap junction were based on nonlinear regression fitting of a set of experimental data published in previous studies. Moreover, we have created numerical simulations using the above single astrocyte-neuron network module and the coupled astrocyte-neuron network modules. Our model validates previous experimental observations that both Kir4.1 channels and gap junctions play important roles in regulating the concentration of extracellular potassium. In addition, we also observe that changes in Kir4.1 channel conductance and gap junction strength induce spontaneous epileptic activity in the absence of external stimuli.

Astrocytes are critical regulators of normal physiological activity in the central nervous system, and one of their key functions is removing extracellular K⁺. In recent years, numerous biological studies have shown that astrocytic Kir4.1 channels and gap junctions between astrocytes act as major K⁺ clearance mechanisms. Dysfunction of either of these regulatory mechanisms may cause generation of K⁺-induced seizures. However, it is unclear how and to what extent these two K⁺-regulating processes lead to spontaneous epileptic activity. These questions were addressed in the present study by constructing novel single astrocyte-neuron network models and a coupled astrocyte-neuron module network connected by an astrocyte gap junction based on existing experimental observations and previous theoretical reports. Simulation results first verified that either down-regulation of astrocytic Kir4.1 channels or a decrease of the gap junction strength between astrocytes causes neuropathological hyper-excitability and spontaneous epileptic activity. These results imply that dysfunctional astrocytes should be considered as targets for therapeutic strategies in epilepsy.

A mathematical model of recurrent spreading depolarizations

A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for the initiation and propagation of recurrent cortical spreading depolarizations. The model incorporates biophysical processes not considered in the earlier models. This includes a model for the Na⁺-glutamate transporter, which allows for a detailed description of reverse glutamate uptake. In particular, we consider the specific roles of elevated extracellular glutamate and K⁺ in the initiation, propagation and recurrence of spreading depolarizations.

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

Simultaneous changes in ion concentrations, glutamate, and cell volume together with exchange of matter between cell network and vasculature are ubiquitous in numerous brain pathologies. A complete understanding of pathological conditions as well as normal brain function, therefore, hinges on elucidating the molecular and cellular pathways involved in these mostly interdependent variations. In this paper, we develop the first computational framework that combines the Hodgkin-Huxley type spiking dynamics, dynamic ion concentrations and glutamate homeostasis, neuronal and astroglial volume changes, and ion exchange with vasculature into a comprehensive model to elucidate the role of glutamate uptake in the dynamics of spreading depolarization (SD)-the electrophysiological event underlying numerous pathologies including migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, and trauma. We are particularly interested in investigating the role of glutamate in the duration and termination of SD caused by K+ perfusion and oxygen-glucose deprivation. Our results demonstrate that glutamate signaling plays a key role in the dynamics of SD, and that impaired glutamate uptake leads to recovery failure of neurons from SD. We confirm predictions from our model experimentally by showing that inhibiting astrocytic glutamate uptake using TFB-TBOA nearly quadruples the duration of SD in layers 2-3 of visual cortical slices from juvenile rats. The model equations are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles or a combination of these principles and known physiological facts. Accordingly, we claim that our approach can be used as a future guide to investigate the role of glutamate, ion concentrations, and dynamics cell volume in other brain pathologies and normal brain function.

A Biophysical Model for Cytotoxic Cell Swelling

We present a dynamic biophysical model to explain neuronal swelling underlying cytotoxic edema in conditions of low energy supply, as observed in cerebral ischemia. Our model contains Hodgkin-Huxley-type ion currents, a recently discovered voltage-gated chloride flux through the ion exchanger SLC26A11, active KCC2-mediated chloride extrusion, and ATP-dependent pumps. The model predicts changes in ion gradients and cell swelling during ischemia of various severity or channel blockage with realistic timescales. We theoretically substantiate experimental observations of chloride influx generating cytotoxic edema, while sodium entry alone does not. We show a tipping point of Na⁺/K⁺-ATPase functioning, where below cell volume rapidly increases as a function of the remaining pump activity, and a Gibbs-Donnan-like equilibrium state is reached. This precludes a return to physiological conditions even when pump strength returns to baseline. However, when voltage-gated sodium channels are temporarily blocked, cell volume and membrane potential normalize, yielding a potential therapeutic strategy.

SIGNIFICANCE STATEMENT

Cytotoxic edema most commonly results from energy shortage, such as in cerebral ischemia, and refers to the swelling of brain cells due to the entry of water from the extracellular space. We show that the principle of electroneutrality explains why chloride influx is essential for the development of cytotoxic edema. With the help of a biophysical model of a single neuron, we show that a tipping point of the energy supply exists, below which the cell volume rapidly increases. We simulate realistic time courses to and reveal critical components of neuronal swelling in conditions of low energy supply. Furthermore, we show that, after transient blockade of the energy supply, cytotoxic edema may be reversed by temporary blockade of Na⁺ channels.

Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells

Two features common to diverse sick excitable cells are "leaky" Nav channels and bleb damage-damaged membranes. The bleb damage, we have argued, causes a channel kinetics based "leakiness." Recombinant (node of Ranvier type) Nav1.6 channels voltage-clamped in mechanically-blebbed cell-attached patches undergo a damage intensity dependent kinetic change. Specifically, they experience a coupled hyperpolarizing (left) shift of the activation and inactivation processes. The biophysical observations on Nav1.6 currents formed the basis of Nav-Coupled Left Shift (Nav-CLS) theory. Node of Ranvier excitability can be modeled with Nav-CLS imposed at varying LS intensities and with varying fractions of total nodal membrane affected. Mild damage from which sick excitable cells might recover is of most interest pathologically. Accordingly, Na⁺/K⁺ ATPase (pump) activity was included in the modeling. As we described more fully in our other recent reviews, Nav-CLS in nodes with pumps proves sufficient to predict many of the pathological excitability phenomena reported for sick excitable cells. This review explains how the model came about and outlines how we have used it. Briefly, we direct the reader to studies in which Nav-CLS is being implemented in larger scale models of damaged excitable tissue. For those who might find it useful for teaching or research purposes, we coded the Nav-CLS/node of Ranvier model (with pumps) in NEURON. We include, here, the resulting "Regimes" plot of classes of excitability dysfunction.

Analyzing and Modeling the Dysfunction of Inhibitory Neurons in Alzheimer's Disease

Alzheimer's disease (AD) is characterized by the abnormal proteolytic processing of amyloid precursor protein, resulting in increased production of a self-aggregating form of beta amyloid (Aβ). Several lines of work on AD patients and transgenic mice with high Aβ levels exhibit altered rhythmicity, aberrant neuronal network activity and hyperexcitability reflected in clusters of hyperactive neurons, and spontaneous epileptic activity. Recent studies highlight that abnormal accumulation of Aβ changes intrinsic properties of inhibitory neurons, which is one of the main reasons underlying the impaired network activity. However, specific cellular mechanisms leading to interneuronal dysfunction are not completely understood. Using extended Hodgkin-Huxley (HH) formalism in conjunction with patch-clamp experiments, we investigate the mechanisms leading to the impaired activity of interneurons. Our detailed analysis indicates that increased Na+ leak explains several observations in inhibitory neurons, including their failure to reliably produce action potentials, smaller action potential amplitude, increased resting membrane potential, and higher membrane depolarization in response to a range of stimuli in a model of APPSWE/PSEN1DeltaE9 (APdE9) AD mice as compared to age-matched control mice. While increasing the conductance of hyperpolarization activated cyclic nucleotide-gated (HCN) ion channel could account for most of the observations, the extent of increase required to reproduce these observations render such changes unrealistic. Furthermore, increasing the conductance of HCN does not account for the observed changes in depolarizability of interneurons from APdE9 mice as compared to those from NTG mice. None of the other pathways tested could lead to all observations about interneuronal dysfunction. Thus we conclude that upregulated sodium leak is the most likely source of impaired interneuronal function.

Mechanisms of spreading depolarization in vertebrate and insect central nervous systems

Spreading depolarization (SD) is generated in the central nervous systems of both vertebrates and invertebrates. SD manifests as a propagating wave of electrical depression caused by a massive redistribution of ions. Mammalian SD underlies a continuum of human pathologies from migraine to stroke damage, whereas insect SD is associated with environmental stress-induced neural shutdown. The general cellular mechanisms underlying SD seem to be evolutionarily conserved throughout the animal kingdom. In particular, SD in the central nervous system of Locusta migratoria and Drosophila melanogaster has all the hallmarks of mammalian SD. Locust SD is easily induced and monitored within the metathoracic ganglion (MTG) and can be modulated both pharmacologically and by preconditioning treatments. The finding that the fly brain supports repetitive waves of SD is relatively recent but noteworthy, since it provides a genetically tractable model system. Due to the human suffering caused by SD manifestations, elucidating control mechanisms that could ultimately attenuate brain susceptibility is essential. Here we review mechanisms of SD focusing on the similarities between mammalian and insect systems. Additionally we discuss advantages of using invertebrate model systems and propose insect SD as a valuable model for providing new insights to mammalian SD.