Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space

Mathematical modeling of intracellular osmolarity and cell volume stabilization: The Donnan effect and ion transport

The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs-Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na+ out and K+ into their cytosol using the Na+/K+ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na+, K+, and Cl-), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation-chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states.

Aquaporin-4 inhibition attenuates Pentylenetetrazole-induced behavioral seizures and cognitive impairments in kindled rats

Epilepsy is a neurological condition distinguished by recurrent and unexpected seizures. Astrocytic channels and transporters are essential for maintaining normal neuronal functionality. The astrocytic water channel, aquaporin-4 (AQP4), which plays a pivotal role in regulating water homeostasis, is a potential target for epileptogenesis. In present study, we examined the effect of different doses (10, 50, 100 μM and 5 mM) of AQP4 inhibitor, 2-nicotinamide-1, 3, 4-thiadiazole (TGN-020), during kindling acquisition, on seizure parameters and seizure-induced cognitive impairments. Animals were kindled by injection of pentylenetetrazole (PTZ: 37.5 mg/kg, i.p.). TGN-020 was administered into the right lateral cerebral ventricle 30 min before PTZ every alternate day. Seizure parameters were assessed 20 min after PTZ administration. One day following the last PTZ injection, memory performance was investigated using spontaneous alternation in Y-maze and novel object recognition (NOR) tests. The inhibition of AQP4 during the kindling process significantly decreased the maximal seizure stage and seizure duration (two-way ANOVA, P = 0.0001) and increased the latency of seizure onset and the number of PTZ injections required to induce different seizure stages (one-way ANOVA, P = 0.0001). Compared to kindled rats, the results of the NOR tests showed that AQP4 inhibition during PTZ-kindling prevented recognition memory impairment. Based on these results, AQP4 could be involved in seizure development and seizure-induced cognitive impairment. More investigation is required to fully understand the complex interactions between seizure activity, water homeostasis, and cognitive dysfunction, which may help identify potential therapeutic targets for these conditions.

Effects of multiple anesthetic exposures on rhesus macaque brain development: a longitudinal structural MRI analysis

Concerns about the potential neurotoxic effects of anesthetics on developing brain exist. When making clinical decisions, the timing and dosage of anesthetic exposure are critical factors to consider due to their associated risks. In our study, we investigated the impact of repeated anesthetic exposures on the brain development trajectory of a cohort of rhesus monkeys (n = 26) over their first 2 yr of life, utilizing longitudinal magnetic resonance imaging data. We hypothesized that early or high-dose anesthesia exposure could negatively influence structural brain development. By employing the generalized additive mixed model, we traced the longitudinal trajectories of brain volume, cortical thickness, and white matter integrity. The interaction analysis revealed that age and cumulative anesthetic dose were variably linked to white matter integrity but not to morphometric measures. Early high-dose exposure was associated with increased mean, axial, and radial diffusivities across all white matter regions, compared to late-low-dose exposure. Our findings indicate that early or high-dose anesthesia exposure during infancy disrupts structural brain development in rhesus monkeys. Consequently, the timing of elective surgeries and procedures that require anesthesia for children and pregnant women should be strategically planned to account for the cumulative dose of volatile anesthetics, aiming to minimize the potential risks to brain development.

Inward Operation of Sodium-Bicarbonate Cotransporter 1 Promotes Astrocytic Na+ Loading and Loss of ATP in Mouse Neocortex during Brief Chemical Ischemia

Ischemic conditions cause an increase in the sodium concentration of astrocytes, driving the breakdown of ionic homeostasis and exacerbating cellular damage. Astrocytes express high levels of the electrogenic sodium-bicarbonate cotransporter1 (NBCe1), which couples intracellular Na+ homeostasis to regulation of pH and operates close to its reversal potential under physiological conditions. Here, we analyzed its mode of operation during transient energy deprivation via imaging astrocytic pH, Na+, and ATP in organotypic slice cultures of the mouse neocortex, complemented with patch-clamp and ion-selective microelectrode recordings and computational modeling. We found that a 2 min period of metabolic failure resulted in a transient acidosis accompanied by a Na+ increase in astrocytes. Inhibition of NBCe1 increased the acidosis while decreasing the Na+ load. Similar results were obtained when comparing ion changes in wild-type and Nbce1-deficient mice. Mathematical modeling replicated these findings and further predicted that NBCe1 activation contributes to the loss of cellular ATP under ischemic conditions, a result confirmed experimentally using FRET-based imaging of ATP. Altogether, our data demonstrate that transient energy failure stimulates the inward operation of NBCe1 in astrocytes. This causes a significant amelioration of ischemia-induced astrocytic acidification, albeit at the expense of increased Na+ influx and a decline in cellular ATP.

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.

Daily heart rate variability biofeedback training decreases locus coeruleus MRI contrast in younger adults in a randomized clinical trial

As an arousal hub region in the brain, the locus coeruleus (LC) has bidirectional connections with the autonomic nervous system. Magnetic resonance imaging (MRI)-based measures of LC structural integrity have been linked to cognition and arousal, but less is known about factors that influence LC structure and function across time. Here, we tested the effects of heart rate variability (HRV) biofeedback, an intervention targeting the autonomic nervous system, on LC MRI contrast and sympathetic activity. Younger and older participants completed daily HRV biofeedback training for five weeks. Those assigned to an experimental condition performed biofeedback involving slow, paced breathing designed to increase heart rate oscillations, whereas those assigned to a control condition performed biofeedback to decrease heart rate oscillations. At the pre- and post-training timepoints, LC contrast was assessed using turbo spin echo MRI scans, and RNA sequencing was used to assess cAMP-responsive element binding protein (CREB)-regulated gene expression in circulating blood cells, an index of sympathetic nervous system signaling. We found that left LC contrast decreased in younger participants in the experimental group, and across younger participants, decreases in left LC contrast were related to the extent to which participants increased their heart rate oscillations during training. Furthermore, decreases in left LC contrast were associated with decreased expression of CREB-associated gene transcripts. On the contrary, there were no effects of biofeedback on LC contrast among older participants in the experimental group. These findings provide novel evidence that in younger adults, HRV biofeedback involving slow, paced breathing can decrease both LC contrast and sympathetic nervous system signaling.

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 model of neurovascular coupling and its application to cortical spreading depolarization

Cortical spreading depolarization (CSD) is a neuropathological condition involving propagating waves of neuronal silence, and is related to multiple diseases, such as migraine aura, traumatic brain injury (TBI), stroke, and cardiac arrest, as well as poor outcome of patients. While CSDs of different severity share similar roots on the ion exchange level, they can lead to different vascular responses (namely spreading hyperemia and spreading ischemia). In this paper, we propose a mathematical model relating neuronal activities to predict vascular changes as measured with near-infrared spectroscopy (NIRS) and fMRI recordings, and apply it to the extreme case of CSD, where sustained near-complete neuronal depolarization is seen. We utilize three serially connected models (namely, ion exchange, neurovascular coupling, and hemodynamic model) which are described by differential equations. Propagating waves of ion concentrations, as well as the associated vasodynamics and hemodynamics, are simulated by solving these equations. Our proposed model predicts vasodynamics and hemodynamics that agree both qualitatively and quantitatively with experimental literature. Mathematical modeling and simulation offer a powerful tool to help understand the underlying mechanisms of CSD and help interpret the data. In addition, it helps develop novel monitoring techniques prior to data collection. Our simulated results strongly suggest that fMRI is unable to reliably distinguish between spreading hyperemia and spreading ischemia, while NIRS signals are substantially distinct in the two cases.

Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study

The complex interplay between chemical, electrical, and mechanical factors is fundamental to the function and homeostasis of the brain, but the effect of electrochemical gradients on brain interstitial fluid flow, solute transport, and clearance remains poorly quantified. Here, via in-silico experiments based on biophysical modeling, we estimate water movement across astrocyte cell membranes, within astrocyte networks, and within the extracellular space (ECS) induced by neuronal activity, and quantify the relative role of different forces (osmotic, hydrostatic, and electrical) on transport and fluid flow under such conditions. We find that neuronal activity alone may induce intracellular fluid velocities in astrocyte networks of up to 14μm/min, and fluid velocities in the ECS of similar magnitude. These velocities are dominated by an osmotic contribution in the intracellular compartment; without it, the estimated fluid velocities drop by a factor of ×34-45. Further, the compartmental fluid flow has a pronounced effect on transport: advection accelerates ionic transport within astrocytic networks by a factor of ×1-5 compared to diffusion alone.

Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models

When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena.

Neurobiological reduction: From cellular explanations of behavior to interventions

Scientific reductionism, the view that higher level functions can be explained by properties at some lower-level or levels, has been an assumption of nervous system analyses since the acceptance of the neuron doctrine in the late 19th century, and became a dominant experimental approach with the development of intracellular recording techniques in the mid-20th century. Subsequent refinements of electrophysiological approaches and the continual development of molecular and genetic techniques have promoted a focus on molecular and cellular mechanisms in experimental analyses and explanations of sensory, motor, and cognitive functions. Reductionist assumptions have also influenced our views of the etiology and treatment of psychopathologies, and have more recently led to claims that we can, or even should, pharmacologically enhance the normal brain. Reductionism remains an area of active debate in the philosophy of science. In neuroscience and psychology, the debate typically focuses on the mind-brain question and the mechanisms of cognition, and how or if they can be explained in neurobiological terms. However, these debates are affected by the complexity of the phenomena being considered and the difficulty of obtaining the necessary neurobiological detail. We can instead ask whether features identified in neurobiological analyses of simpler aspects in simpler nervous systems support current molecular and cellular approaches to explaining systems or behaviors. While my view is that they do not, this does not invite the opposing view prevalent in dichotomous thinking that molecular and cellular detail is irrelevant and we should focus on computations or representations. We instead need to consider how to address the long-standing dilemma of how a nervous system that ostensibly functions through discrete cell to cell communication can generate population effects across multiple spatial and temporal scales to generate behavior.

Honey, I shrunk the extracellular space: Measurements and mechanisms of astrocyte swelling

Astrocyte volume fluctuation is a physiological phenomenon tied closely to the activation of neural circuits. Identification of underlying mechanisms has been challenging due in part to use of a wide range of experimental approaches that vary between research groups. Here, we first review the many methods that have been used to measure astrocyte volume changes directly or indirectly. While the field has recently shifted towards volume analysis using fluorescence microscopy to record cell volume changes directly, established metrics corresponding to extracellular space dynamics have also yielded valuable insights. We then turn to analysis of mechanisms of astrocyte swelling derived from many studies, with a focus on volume changes tied to increases in extracellular potassium concentration ([K+ ]o ). The diverse methods that have been utilized to generate the external [K+ ]o environment highlight multiple scenarios of astrocyte swelling mediated by different mechanisms. Classical potassium buffering theories are tempered by many recent studies that point to different swelling pathways optimized at particular [K+ ]o and that depend on local/transient versus more sustained increases in [K+ ]o .

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations’ interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront’s propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID’s speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na⁺/K⁺ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

During an epileptic seizure, neuronal excitation spreads across the brain tissue and is accompanied by significant changes in ionic concentrations. Ictal discharge front spreads at low speeds, less than 1 mm/s. Mechanisms underlying this phenomenon are not yet well understood. We study these mechanisms using electrophysiological recordings in brain slices and computer simulations. Our detailed biophysical model describing neuronal populations’ interaction, spatial propagation, and ionic dynamics reproduces the generation and propagation of spontaneously repeating ictal discharges. The simulations are consistent with our recordings of the electrical activity and the extracellular potassium ion concentration. We distinguished between the two alternative mechanisms of the ictal wavefront propagation: (i) the diffusion of potassium ions released from excited neurons, which depolarizes distant neurons and thus supports excitation, and (ii) the axonal spread of excitation followed by the local extracellular potassium ion accumulation that supports the excitation. Our simulations provide evidence in favor of the latter mechanism. Our experiment-based modeling contributes to a mathematical description of brain tissue functioning and potentially contributes to developing new treatments against epilepsy.

Accurate numerical simulation of electrodiffusion and water movement in brain tissue

Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide a new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution.

Astrocyte Role in Temporal Lobe Epilepsy and Development of Mossy Fiber Sprouting

Epilepsy affects approximately 50 million people worldwide, with 60% of adult epilepsies presenting an onset of focal origin. The most common focal epilepsy is temporal lobe epilepsy (TLE). The role of astrocytes in the presentation and development of TLE has been increasingly studied and discussed within the literature. The most common histopathological diagnosis of TLE is hippocampal sclerosis. Hippocampal sclerosis is characterized by neuronal cell loss within the Cornu ammonis and reactive astrogliosis. In some cases, mossy fiber sprouting may be observed. Mossy fiber sprouting has been controversial in its contribution to epileptogenesis in TLE patients, and the mechanisms surrounding the phenomenon have yet to be elucidated. Several studies have reported that mossy fiber sprouting has an almost certain co-existence with reactive astrogliosis within the hippocampus under epileptic conditions. Astrocytes are known to play an important role in the survival and axonal outgrowth of central and peripheral nervous system neurons, pointing to a potential role of astrocytes in TLE and associated cellular alterations. Herein, we review the recent developments surrounding the role of astrocytes in the pathogenic process of TLE and mossy fiber sprouting, with a focus on proposed signaling pathways and cellular mechanisms, histological observations, and clinical correlations in human patients.

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.

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.

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.

Transient changes in white matter microstructure during general anesthesia

Cognitive dysfunction after surgery under general anesthesia is a well-recognized clinical phenomenon in the elderly. Physiological effects of various anesthetic agents have been studied at length. Very little is known about potential effects of anesthesia on brain structure. In this study we used Diffusion Tensor Imaging to compare the white matter microstructure of healthy control subjects under sevoflurane anesthesia with their awake state. Fractional Anisotropy, a white mater integrity index, transiently decreases throughout the brain during sevoflurane anesthesia and then returns back to baseline. Other DTI metrics such as mean diffusivity, axial diffusivity and radial diffusivity were increased under sevoflurane anesthesia. Although DTI metrics are age dependent, the transient changes due to sevoflurane were independent of age and sex. Volumetric analysis shows various white matter volumes decreased whereas some gray matter volumes increased during sevoflurane anesthesia. These results suggest that sevoflurane anesthesia has a significant, but transient, effect on white matter microstructure. In spite of the transient effects of sevoflurane anesthesia there were no measurable effects on brain white matter as determined by the DTI metrics at 2 days and 7 days following anesthesia. The role of white matter in the loss of consciousness under anesthesia will need to be studied and MRI studies with subjects under anesthesia will need to take these results into account.

The Role of Astrogliosis in Formation of the Syrinx in Spinal Cord Injury

A massive localized trauma to the spinal cord results in complex pathologic events driven by necrosis and vascular damage which in turn leads to hemorrhage and edema. Severe, destructive and very protracted inflammatory response is characterized by infiltration by phagocytic macrophages of a site of injury which is converted into a cavity of injury (COI) surrounded by astroglial reaction mounted by the spinal cord. The tissue response to the spinal cord injury (SCI) has been poorly understood but the final outcome appears to be a mature syrinx filled with the cerebrospinal fluid with related neural tissue loss and permanent neurologic deficits. This paper reviews known pathologic mechanisms involved in the formation of the COI after SCI and discusses the integrative role of reactive astrogliosis in mechanisms involved in the removal of edema after the injury. A large proportion of edema fluid originating from the trauma and then from vasogenic edema related to persistent severe inflammation, may be moved into the COI in an active process involving astrogliosis and specifically over-expressed aquaporins.

Astrocytes as Guardians of Neuronal Excitability: Mechanisms Underlying Epileptogenesis

Astrocytes are key homeostatic regulators in the central nervous system and play important roles in physiology. After brain damage caused by e.g., status epilepticus, traumatic brain injury, or stroke, astrocytes may adopt a reactive phenotype. This process of reactive astrogliosis is important to restore brain homeostasis. However, persistent reactive astrogliosis can be detrimental for the brain and contributes to the development of epilepsy. In this review, we will focus on physiological functions of astrocytes in the normal brain as well as pathophysiological functions in the epileptogenic brain, with a focus on acquired epilepsy. We will discuss the role of astrocyte-related processes in epileptogenesis, including reactive astrogliosis, disturbances in energy supply and metabolism, gliotransmission, and extracellular ion concentrations, as well as blood-brain barrier dysfunction and dysregulation of blood flow. Since dysfunction of astrocytes can contribute to epilepsy, we will also discuss their role as potential targets for new therapeutic strategies.

Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study

In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters.

Computational Model for Cross-Depolarization in DRG Neurons via Satellite Glial Cells using [K]o: Role of Kir4.1 Channels and Extracellular Leakage

Satellite glial cells (SGCs) are glial cells found in the peripheral nervous system where they tightly envelop the somata of the primary sensory neurons such as dorsal root ganglion (DRG) neurons and nodose ganglion (NG) neurons. The somata of these neurons are generally compactly packed in their respective ganglia (DRG and NG). SGCs covering a neuron behave as an insulator of electrical activity from neighbouring neurons within the ganglion. Several studies have however shown that the somata show "cross-depolarization" (CD). Origin of CDs has been hypothesized to be chemical in nature: either from neurotransmitter release from both SGCs and somata or from elevation of extracellular potassium concentration ([K]_o) in the vicinity of somata. Here, we investigate the role of Kir4.1 channels on SGC and diffusion/clearance factor (β) of [K]_o from the space between SGC and DRG neuron somata to the bulk extracellular space in ganglion. We show using two "Soma-SGC Units" interacting via gap junction that a combination of Kir4.1 and β could be responsible for CD between DRG neuron somata in pathological conditions.

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.

Roles of glial ion transporters in brain diseases

Glial ion transporters are important in regulation of ionic homeostasis, cell volume, and cellular signal transduction under physiological conditions of the central nervous system (CNS). In response to acute or chronic brain injuries, these ion transporters can be activated and differentially regulate glial functions, which has subsequent impact on brain injury or tissue repair and functional recovery. In this review, we summarized the current knowledge about major glial ion transporters, including Na⁺ /H⁺ exchangers (NHE), Na⁺ /Ca²⁺ exchangers (NCX), Na⁺ -K⁺ -Cl^- cotransporters (NKCC), and Na⁺ -HCO₃ ^- cotransporters (NBC). In acute neurological diseases, such as ischemic stroke and traumatic brain injury (TBI), these ion transporters are rapidly activated and play significant roles in regulation of the intra- and extracellular pH, Na⁺ , K⁺ , and Ca²⁺ homeostasis, synaptic plasticity, and myelin formation. However, overstimulation of these ion transporters can contribute to glial apoptosis, demyelination, inflammation, and excitotoxicity. In chronic brain diseases, such as glioma, Alzheimer's disease (AD), Parkinson's disease (PD), and multiple sclerosis (MS), glial ion transporters are involved in the glioma Warburg effect, glial activation, neuroinflammation, and neuronal damages. These findings suggest that glial ion transporters are involved in tissue structural and functional restoration, or brain injury and neurological disease development and progression. A better understanding of these ion transporters in acute and chronic neurological diseases will provide insights for their potential as therapeutic targets.

Computational Modeling of Glucose Uptake in the Enterocyte

Absorption of glucose across the epithelial cells of the small intestine is a key process in human nutrition and initiates signaling cascades that regulate metabolic homeostasis. Validated and predictive mathematical models of glucose transport in intestinal epithelial cells are essential for interpreting experimental data, generating hypotheses, and understanding the contributions of and interactions between transport pathways. Here we report on the development of such a model that, in contrast to existing models, incorporates mechanistic descriptions of all relevant transport proteins and is implemented in the CellML framework. The model is validated against experimental and simulation data from the literature. It is then used to elucidate the relative contributions of the sodium-glucose cotransporter (SGLT1) and the glucose transporter type 2 (GLUT2) proteins in published measurements of glucose absorption from human intestinal epithelial cell lines. The model predicts that the contribution of SGLT1 dominates at low extracellular glucose concentrations (<20 mM) and short exposure times (<60 s) while the GLUT2 contribution is more significant at high glucose concentrations and long durations. Implementation in CellML permitted a modular structure in which the model was composed by reusing existing models of the individual transporters. The final structure also permits transparent changes of the model components and parameter values in order to facilitate model reuse, extension, and customization (for example, to simplify, or add complexity to specific transporter/pathway models, or reuse the model as a component of a larger framework) and carry out parameter sensitivity studies.

Off-Label Use of Bumetanide for Brain Disorders: An Overview

Bumetanide (BTN or BUM) is a FDA-approved potent loop diuretic (LD) that acts by antagonizing sodium-potassium-chloride (Na-K-Cl) cotransporters, NKCC1 (SLc12a2) and NKCC2. While NKCC1 is expressed both in the CNS and in systemic organs, NKCC2 is kidney-specific. The off-label use of BTN to modulate neuronal transmembrane Cl⁻ gradients by blocking NKCC1 in the CNS has now been tested as an anti-seizure agent and as an intervention for neurological disorders in pre-clinical studies with varying results. BTN safety and efficacy for its off-label use has also been tested in several clinical trials for neonates, children, adolescents, and adults. It failed to meet efficacy criteria for hypoxic-ischemic encephalopathy (HIE) neonatal seizures. In contrast, positive outcomes in temporal lobe epilepsy (TLE), autism, and schizophrenia trials have been attributed to BTN in studies evaluating its off-label use. NKCC1 is an electroneutral neuronal Cl⁻ importer and the dominance of NKCC1 function has been proposed as the common pathology for HIE seizures, TLE, autism, and schizophrenia. Therefore, the use of BTN to antagonize neuronal NKCC1 with the goal to lower internal Cl⁻ levels and promote GABAergic mediated hyperpolarization has been proposed. In this review, we summarize the data and results for pre-clinical and clinical studies that have tested off-label BTN interventions and report variable outcomes. We also compare the data underlying the developmental expression profile of NKCC1 and KCC2, highlight the limitations of BTN’s brain-availability and consider its actions on non-neuronal cells.

Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges

Despite big experimental data on the phenomena and mechanisms of the generation of ictal and interictal discharges (IDs and IIDs), mathematical models that can describe the synaptic interactions of neurons and the ionic dynamics in biophysical detail are not well-established. Based on experimental recordings of combined hippocampal-entorhinal cortex slices from rats in a high-potassium and a low-magnesium solution containing 4-aminopyridine as well as previous observations of similar experimental models, this type of mathematical model has been developed. The model describes neuronal excitation through the application of the conductance-based refractory density approach for three neuronal populations: two populations of glutamatergic neurons with hyperpolarizing and depolarizing GABAergic synapses and one GABAergic population. The ionic dynamics account for the contributions of voltage-gated and synaptic channels, active and passive transporters, and diffusion. The relatively slow dynamics of potassium, chloride, and sodium ion concentrations determine the transitions from pure GABAergic IIDs to IDs and GABA-glutamatergic IIDs. The model reproduces different types of IIDs, including those initiated by interneurons; repetitive IDs; tonic and bursting modes of an ID composed of clustered IID-like events. The simulations revealed contributions from different ionic channels to the ion concentration dynamics before and during ID generation. The proposed model is a step forward to an optimal mathematical description of the mechanisms of epileptic discharges.

General Principles of Neuronal Co-transmission: Insights From Multiple Model Systems

It is now accepted that neurons contain and release multiple transmitter substances. However, we still have only limited insight into the regulation and functional effects of this co-transmission. Given that there are 200 or more neurotransmitters, the chemical complexity of the nervous system is daunting. This is made more-so by the fact that their interacting effects can generate diverse non-linear and novel consequences. The relatively poor history of pharmacological approaches likely reflects the fact that manipulating a transmitter system will not necessarily mimic its roles within the normal chemical environment of the nervous system (e.g., when it acts in parallel with co-transmitters). In this article, co-transmission is discussed in a range of systems [from invertebrate and lower vertebrate models, up to the mammalian peripheral and central nervous system (CNS)] to highlight approaches used, degree of understanding, and open questions and future directions. Finally, we offer some outlines of what we consider to be the general principles of co-transmission, as well as what we think are the most pressing general aspects that need to be addressed to move forward in our understanding of co-transmission.

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.

Combination Therapy for Multi-Target Manipulation of Secondary Brain Injury Mechanisms

Traumatic brain injury (TBI) is a major healthcare problem that affects millions of people worldwide. Despite advances in understanding and developing preventative and treatment strategies using preclinical animal models, clinical trials to date have failed, and a 'magic bullet' for effectively treating TBI-induced damage does not exist. Thus, novel pharmacological strategies to effectively manipulate the complex and heterogeneous pathophysiology of secondary injury mechanisms are needed. Given that goal, this paper discusses the relevance and advantages of combination therapies (COMTs) for 'multi-target manipulation' of the secondary injury cascade by administering multiple drugs to achieve an optimal therapeutic window of opportunity (e.g., temporally broad window) and compares these regimens to monotherapies that manipulate a single target with a single drug at a given time. Furthermore, we posit that integrated mechanistic multiscale models that combine primary injury biomechanics, secondary injury mechanobiology/neurobiology, physiology, pharmacology and mathematical programming techniques could account for vast differences in the biological space and time scales and help to accelerate drug development, to optimize pharmacological COMT protocols and to improve treatment outcomes.

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

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

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 mathematical model of cellular swelling in Neuromyelitis optica

Neuromyelitis Optica (NMO) is a severe neuro-inflammatory disease of the central nervous system characterized by predominant damage to the optic nerve and of the spinal cord. The pathogenic antibody found in the majority of patients targets the AQP4 channels on astrocytic endfeet and causes the cells to swell. Although, the pathophysiology of the disease is broadly known, there are no specific targeted treatments for this process clinically available nor accurate prognostic markers both during attacks and for predicting long term neuronal damage. This lack is, in part, due to the rarity of the disease and its relatively recent pathogenic clarity. Hence, the ability to mathematically model the progress of the condition to test prospective therapies in silico would be a step forward. This paper combines state of the art models of cellular metabolism and cytotoxic oedema in neurons and astrocytes and augments it with a detailed characterization of water transport across the cellular membrane. In particular, we capture the process of perforation of the cell through the human complement cascade and resulting water and ionic fluxes. Simulating NMO by injecting its antibody and human complement into the extracellular space showed a 25% increase of the astrocytic volume after 12 h from onset. Most of the volume change occurred during the first 30 min of simulation with a peak volume change of 38%. The model was further adapted to simulate the therapeutic potential of CD59. It was found that there is a threshold of CD59 concentration that can prevent the swelling of astrocytes. Since the astrocyte volume changes mostly during the first hour, further experimental work should focus on this time scale to provide data for further model refinement and validation.

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.

The Influence of Fluorine on the Disturbances of Homeostasis in the Central Nervous System

Fluorides occur naturally in the environment, the daily exposure of human organism to fluorine mainly depends on the intake of this element with drinking water and it is connected with the geographical region. In some countries, we can observe the endemic fluorosis-the damage of hard and soft tissues caused by the excessive intake of fluorine. Recent studies showed that fluorine is toxic to the central nervous system (CNS). There are several known mechanisms which lead to structural brain damage caused by the excessive intake of fluorine. This element is able to cross the blood-brain barrier, and it accumulates in neurons affecting cytological changes, cell activity and ion transport (e.g. chlorine transport). Additionally, fluorine changes the concentration of non-enzymatic advanced glycation end products (AGEs), the metabolism of neurotransmitters (influencing mainly glutamatergic neurotransmission) and the energy metabolism of neurons by the impaired glucose transporter-GLUT1. It can also change activity and lead to dysfunction of important proteins which are part of the respiratory chain. Fluorine also affects oxidative stress, glial activation and inflammation in the CNS which leads to neurodegeneration. All of those changes lead to abnormal cell differentiation and the activation of apoptosis through the changes in the expression of neural cell adhesion molecules (NCAM), glial fibrillary acidic protein (GFAP), brain-derived neurotrophic factor (BDNF) and MAP kinases. Excessive exposure to this element can cause harmful effects such as permanent damage of all brain structures, impaired learning ability, memory dysfunction and behavioural problems. This paper provides an overview of the fluoride neurotoxicity in juveniles and adults.

How Cells Can Control Their Size by Pumping Ions

The ability of all cells to set and regulate their size is a fundamental aspect of cellular physiology. It has been known for sometime but not widely so, that size stability in animal cells is dependent upon the operation of the sodium pump, through the so-called pump-leak mechanism (Tosteson and Hoffman, 1960). Impermeant molecules in cells establish an unstable osmotic condition, the Donnan effect, which is counteracted by the operation of the sodium pump, creating an asymmetry in the distribution of Na⁺ and K⁺ staving off water inundation. In this paper, which is in part a tutorial, I show how to model quantitatively the ion and water fluxes in a cell that determine the cell volume and membrane potential. The movement of water and ions is constrained by both osmotic and charge balance, and is driven by ion and voltage gradients and active ion transport. Transforming these constraints and forces into a set of coupled differential equations allows us to model how the ion distributions, volume and voltage change with time. I introduce an analytical solution to these equations that clarifies the influence of ion conductances, pump rates and water permeability in this multidimensional system. I show that the number of impermeant ions (x) and their average charge have a powerful influence on the distribution of ions and voltage in a cell. Moreover, I demonstrate that in a cell where the operation of active ion transport eliminates an osmotic gradient, the size of the cell is directly proportional to x. In addition, I use graphics to reveal how the physico-chemical constraints and chemical forces interact with one another in apportioning ions inside the cell. The form of model used here is applicable to all membrane systems, including mitochondria and bacteria, and I show how pumps other than the sodium pump can be used to stabilize cells. Cell biologists may think of electrophysiology as the exclusive domain of neuroscience, however the electrical effects of ion fluxes need to become an intimate part of cell biology if we are to understand a fundamental process like cell size regulation.

Spreading depolarization triggered by elevated potassium is weak or absent in the rodent lower brain

We examined in live coronal slices from rat and mouse which brain regions generate potassium-triggered spreading depolarization (SD_Kt). This technique simulates cortical spreading depression, which underlies migraine aura in the intact brain. An SD_Kt episode was evoked by increasing bath [K⁺]_o and recorded as a propagating front of elevated light transmittance representing transient neuronal swelling in gray matter of neocortex, hippocampus, striatum, and thalamus. In contrast, SD_Kt was not imaged in hypothalamic nuclei or brainstem with exception of those nuclei near the dorsal brainstem surface. In rat slices, single neurons were whole-cell current clamped during SD_Kt. "Higher" neurons depolarized to near zero millivolts indicating SD_Kt generation. In contrast, seven types of neurons in hypothalamus and brainstem only slowly depolarized without generating SD_Kt, supporting our imaging findings. Therefore, SD_Kt is not a default of CNS neurons but rather displays a region-specific susceptibility, similar to anoxic depolarization, which we have proposed is correlated with a region's vulnerability to traumatic brain injury. In the higher brain, SD_Kt may be a vestigial spreading depolarization that originally evolved to shut down and vasoconstrict gray matter regions more exposed to impact and contusion.

Spatial separation of two different pathways accounting for the generation of calcium signals in astrocytes

Astrocytes integrate and process synaptic information and exhibit calcium (Ca2+) signals in response to incoming information from neighboring synapses. The generation of Ca2+ signals is mostly attributed to Ca2+ release from internal Ca2+ stores evoked by an elevated metabotropic glutamate receptor (mGluR) activity. Different experimental results associated the generation of Ca2+ signals to the activity of the glutamate transporter (GluT). The GluT itself does not influence the intracellular Ca2+ concentration, but it indirectly activates Ca2+ entry over the membrane. A closer look into Ca2+ signaling in different astrocytic compartments revealed a spatial separation of those two pathways. Ca2+ signals in the soma are mainly generated by Ca2+ release from internal Ca2+ stores (mGluR-dependent pathway). In astrocytic compartments close to the synapse most Ca2+ signals are evoked by Ca2+ entry over the plasma membrane (GluT-dependent pathway). This assumption is supported by the finding, that the volume ratio between the internal Ca2+ store and the intracellular space decreases from the soma towards the synapse. We extended a model for mGluR-dependent Ca2+ signals in astrocytes with the GluT-dependent pathway. Additionally, we included the volume ratio between the internal Ca2+ store and the intracellular compartment into the model in order to analyze Ca2+ signals either in the soma or close to the synapse. Our model results confirm the spatial separation of the mGluR- and GluT-dependent pathways along the astrocytic process. The model allows to study the binary Ca2+ response during a block of either of both pathways. Moreover, the model contributes to a better understanding of the impact of channel densities on the interaction of both pathways and on the Ca2+ signal.

A model of neurovascular coupling and the BOLD response: PART I

The mechanisms with which neurons communicate with the vasculature to increase blood flow, termed neurovascular coupling is still unclear primarily due to the complex interactions between many parameters and the difficulty in accessing, monitoring and measuring them in the highly heterogeneous brain. Hence a solid theoretical framework based on existing experimental knowledge is necessary to study the relation between neural activity, the associated vasoactive factors released and their effects on the vasculature. Such a framework should also be related to experimental data so that it can be validated against repetitive experiments and generate verifiable hypothesis. We have developed a mathematical model which describes a signaling mechanism of neurovascular coupling with a model of pyramidal neuron and its corresponding fMRI BOLD response. In the first part of two papers we describe the integration of the neurovascular coupling unit extended to include a complex neuron model, which includes the important Na/K ATPase pump, with a model that provides a BOLD signal taking its input from the cerebral blood flow and the metabolic rate of oxygen consumption. We show that this produces a viable signal in terms of initial dip, positive and negative BOLD signals.

The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus

Experiments on hippocampal slices have recorded that a novel pattern of epileptic seizures with alternating excitatory and inhibitory activities in the CA1 region can be induced by an elevated potassium ion (K(+)) concentration in the extracellular space between neurons and astrocytes (ECS-NA). To explore the intrinsic effects of the factors (such as glial K(+) uptake, Na(+)-K(+)-ATPase, the K(+) concentration of the bath solution, and K(+) lateral diffusion) influencing K(+) concentration in the ECS-NA on the epileptic seizures recorded in previous experiments, we present a coupled model composed of excitatory and inhibitory neurons and glia in the CA1 region. Bifurcation diagrams showing the glial K(+) uptake strength with either the Na(+)-K(+)-ATPase pump strength or the bath solution K(+) concentration are obtained for neural epileptic seizures. The K(+) lateral diffusion leads to epileptic seizure in neurons only when the synaptic conductance values of the excitatory and inhibitory neurons are within an appropriate range. Finally, we propose an energy factor to measure the metabolic demand during neuron firing, and the results show that different energy demands for the normal discharges and the pathological epileptic seizures of the coupled neurons.

Unified model of brain tissue microstructure dynamically binds diffusion and osmosis with extracellular space geometry

We present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS). Our model robustly describes and predicts the nonlinear time dependency of tortuosity (λ=sqrt[D/D^{*}]) changes with very high precision in various media with uniform and nonuniform osmolarity distribution, as demonstrated by previously published experimental data (D = free diffusion coefficient, D^{*} = effective diffusion coefficient). To construct this model, we first developed a multiscale technique for computationally effective modeling of osmolarity in the brain tissue. Osmolarity differences across cell membranes lead to changes in the ECS dynamics. The evolution of the underlying dynamics is then captured by a level set method. Subsequently, using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of cells and their associated ECS. Our modeling results in very accurate analytical approximation of tortuosity based on time, space, osmolarity differences across cell membranes, and water permeability of cell membranes. Our model provides a unique platform for studying ECS dynamics not only in physiologic conditions such as sleep-wake cycles and aging but also in pathologic conditions such as stroke, seizure, and neoplasia, as well as in predictive pharmacokinetic modeling such as predicting medication biodistribution and efficacy and novel biomolecule development and testing.

Expanding Spectrum of Sodium Potassium Chloride Co-transporters in the Pathophysiology of Diseases

Sodium potassium chloride co-transporter (NKCC) belongs to cation-dependent chloride co-transporter family, whose activation allows the entry of Na(+), K(+) and 2Cl(-) inside the cell. It acts in concert with K(+) Cl(-) co-transporter (KCC), which extrudes K(+) and Cl(-) ions from cell. NKCC1 is widely distributed throughout the body, while NKCC2 is exclusively present in kidney. Protein kinase A, protein kinase C, Ste20-related proline-alanine-rich kinase, oxidative stress responsive kinases, With No K=lysine kinase and protein phosphatase type 1 control the phosphorylation/dephosphorylation of key threonine residues of in regulatory domain of NKCC1. The selective inhibitors of NKCC1 including bumetanide and furosemide are conventionally employed as diuretics. However, recent studies have indicated that NKCC1 may be involved in the pathophysiology of anxiety, cerebral ischemia, epilepsy, neuropathic pain, fragile X syndrome, autism and schizophrenia. The inhibitors of NKCC1 are shown to produce anxiolytic effects; attenuate cerebral ischemia-induced neuronal injury; produce antiepileptic effects and attenuate neuropathic pain. In the early developing brain, GABAA activation primarily produces excitatory actions due to high NKCC1/KCC2 ratio. However, as the development progresses, the ratio of NKCC1/KCC2 ratio reverses and there is switch in the polarity of GABAA actions and latter acquires the inhibitory actions. The recapitulation of developmental-like state during pathological state may be associated with increase in the expression and functioning of NKCC1, which decreases the strength of inhibitory GABAergic neurotransmission. The present review describes the expanding role and mechanism of NKCC1 in the pathophysiology of different diseases.

Glial Na(+) -dependent ion transporters in pathophysiological conditions

Sodium dynamics are essential for regulating functional processes in glial cells. Indeed, glial Na(+) signaling influences and regulates important glial activities, and plays a role in neuron-glia interaction under physiological conditions or in response to injury of the central nervous system (CNS). Emerging studies indicate that Na(+) pumps and Na(+) -dependent ion transporters in astrocytes, microglia, and oligodendrocytes regulate Na(+) homeostasis and play a fundamental role in modulating glial activities in neurological diseases. In this review, we first briefly introduced the emerging roles of each glial cell type in the pathophysiology of cerebral ischemia, Alzheimer's disease, epilepsy, Parkinson's disease, Amyotrophic Lateral Sclerosis, and myelin diseases. Then, we discussed the current knowledge on the main roles played by the different glial Na(+) -dependent ion transporters, including Na(+) /K(+) ATPase, Na(+) /Ca(2+) exchangers, Na(+) /H(+) exchangers, Na(+) -K(+) -Cl(-) cotransporters, and Na(+) - HCO3- cotransporter in the pathophysiology of the diverse CNS diseases. We highlighted their contributions in cell survival, synaptic pathology, gliotransmission, pH homeostasis, and their role in glial activation, migration, gliosis, inflammation, and tissue repair processes. Therefore, this review summarizes the foundation work for targeting Na(+) -dependent ion transporters in glia as a novel strategy to control important glial activities associated with Na(+) dynamics in different neurological disorders. GLIA 2016;64:1677-1697.

Fluoride Induces a Volume Reduction in CA1 Hippocampal Slices Via MAP Kinase Pathway Through Volume Regulated Anion Channels

Regulation of cell volume is an important aspect of cellular homeostasis during neural activity. This volume regulation is thought to be mediated by activation of specific transporters, aquaporin, and volume regulated anion channels (VRAC). In cultured astrocytes, it was reported that swelling-induced mitogen-activated protein (MAP) kinase activation is required to open VRAC, which are thought to be important in regulatory volume decrease and in the response of CNS to trauma and excitotoxicity. It has been also described that sodium fluoride (NaF), a recognized G-protein activator and protein phosphatase inhibitor, leads to a significant MAP kinase activation in endothelial cells. However, NaF's effect in volume regulation in the brain is not known yet. Here, we investigated the mechanism of NaF-induced volume change in rat and mouse hippocampal slices using intrinsic optical signal (IOS) recording, in which we measured relative changes in intracellular and extracellular volume as changes in light transmittance through brain slices. We found that NaF (1~5 mM) application induced a reduction in light transmittance (decreased volume) in CA1 hippocampus, which was completely reversed by MAP kinase inhibitor U0126 (10 µM). We also observed that NaF-induced volume reduction was blocked by anion channel blockers, suggesting that NaF-induced volume reduction could be mediated by VRAC. Overall, our results propose a novel molecular mechanism of NaF-induced volume reduction via MAP kinase signaling pathway by activation of VRAC.

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

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little about the dynamics of cell and tissue swelling, and the differential changes in the volumes of neurons and glia during pathological states such as spreading depolarizations (SD) under ischemic and non–ischemic conditions, and epileptic seizures. By combining the Hodgkin–Huxley type spiking dynamics, dynamic ion concentrations, and simultaneous neuronal and astroglial volume changes into a comprehensive model, we elucidate why glial cells swell more than neurons in SD and the special case of anoxic depolarization (AD), and explore the relative contributions of the two cell types to tissue swelling. Our results demonstrate that anion channels, particularly Cl⁻, are intrinsically connected to cell swelling and blocking these currents prevents changes in cell volume. The model is based on a simple and physiologically realistic description. We introduce model extensions that are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles, or by a phenomenological combination of these principles and known physiological facts. This work provides insights into numerous studies related to neuronal and glial volume changes in SD that otherwise seem contradictory, and is broadly applicable to swelling in other cell types and conditions.

Mechanisms of astrocytic K(+) clearance and swelling under high extracellular K(+) concentrations

In response to the elevation of extracellular K(+) concentration ([K(+)]out), astrocytes clear excessive K(+) to maintain conditions necessary for neural activity. K(+) clearance in astrocytes occurs via two processes: K(+) uptake and K(+) spatial buffering. High [K(+)]out also induces swelling in astrocytes, leading to edema and cell death in the brain. Despite the importance of astrocytic K(+) clearance and swelling, the underlying mechanisms remain unclear. Here, we report results from a simulation analysis of astrocytic K(+) clearance and swelling. Astrocyte models were constructed by incorporating various mechanisms such as intra/extracellular ion concentrations of Na(+), K(+), and Cl(-), cell volume, and models of Na,K-ATPase, Na-K-Cl cotransporter (NKCC), K-Cl cotransporter, inwardly-rectifying K(+) (KIR) channel, passive Cl(-) current, and aquaporin channel. The simulated response of astrocyte models under the uniform distribution of high [K(+)]out revealed significant contributions of NKCC and Na,K-ATPase to increases of intracellular K(+) and Cl(-) concentrations, and swelling. Moreover, we found that, under the non-uniform distribution of high [K(+)]out, KIR channels localized at synaptic clefts absorbed excess K(+) by depolarizing the equivalent potential of K(+) (E K) above membrane potential, while K(+) released through perivascular KIR channels was enhanced by hyperpolarizing E K and depolarizing membrane potential. Further analysis of simulated drug effects revealed that astrocyte swelling was modulated by blocking each of the ion channels and transporters. Our simulation analysis revealed controversial mechanisms of astrocytic K(+) clearance and swelling resulting from complex interactions among ion channels and transporters.

Maximum-likelihood q-estimator uncovers the role of potassium at neuromuscular junctions

Recently, we demonstrated the existence of nonextensive behavior in neuromuscular transmission (da Silva et al. in Phys Rev E 84:041925, 2011). In this letter, we first obtain a maximum-likelihood q-estimator to calculate the scale factor ([Formula: see text]) and the q-index of q-Gaussian distributions. Next, we use the indexes to analyze spontaneous miniature end plate potentials in electrophysiological recordings from neuromuscular junctions. These calculations were performed assuming both normal and high extracellular potassium concentrations [Formula: see text]. This protocol was used to test the validity of Tsallis statistics under electrophysiological conditions closely resembling physiological stimuli. The analysis shows that q-indexes are distinct depending on the extracellular potassium concentration. Our letter provides a general way to obtain the best estimate of parameters from a q-Gaussian distribution function. It also expands the validity of Tsallis statistics in realistic physiological stimulus conditions. In addition, we discuss the physical and physiological implications of these findings.

Perinodal glial swelling mitigates axonal degradation in a model of axonal injury

Mild traumatic brain injury (mTBI) has been associated with the damage to myelinated axons in white matter tracts. Animal models and in vitro studies suggest that axonal degradation develops during a latent period following a traumatic event. This delay has been attributed to slowly developing axonal membrane depolarization that is initiated by injury-induced ionic imbalance and in turn, leads to the activation of Ca(2+) proteases via pathological accumulation of Ca(2+). However, the mechanisms mitigating the transition to axonal degradation after injury remain elusive. We addressed this question in a detailed biophysical model of axonal injury that incorporated ion exchange and glial swelling mechanisms. We show that glial swelling, which often co-occurs with mTBI, promotes axonal survival by regulating extracellular K(+) dynamics, extending the range of injury parameters in which axons exhibit stable membrane potential postinjury. In addition, glial swelling was instrumental in reducing axonal sensitivity to repetitive stretch injury that occurred several minutes following the first one. Results of this study suggest that acute post-traumatic swelling of perinodal astrocytes helps prevent or postpone axonal degradation by maintaining physiologically relevant levels of extracellular K(+).