Spatial buffering of potassium ions in brain extracellular space

Melatonin protects Kir2.1 function in an oxidative stress-related model of aging neuroglia

Melatonin is a pleiotropic biofactor and an effective antioxidant and free radical scavenger and, as such, can be protective in oxidative stress-related brain conditions including epilepsy and aging. To test the potential protective effect of melatonin on brain homeostasis and identify the corresponding molecular targets, we established a new model of oxidative stress-related aging neuroglia represented by U-87 MG cells exposed to D-galactose (D-Gal). This model was characterized by a substantial elevation of markers of oxidative stress, lipid peroxidation, and protein oxidation. The function of the inward rectifying K+ channel Kir2.1, which was identified as the main Kir channel endogenously expressed in these cells, was dramatically impaired. Kir2.1 was unlikely a direct target of oxidative stress, but the loss of function resulted from a reduction of protein abundance, with no alterations in transcript levels and trafficking to the cell surface. Importantly, melatonin reverted these changes. All findings, including the melatonin antioxidant effect, were reproduced in heterologous expression systems. We conclude that the glial Kir2.1 can be a target of oxidative stress and further suggest that inhibition of its function might alter the extracellular K+ buffering in the brain, therefore contributing to neuronal hyperexcitability and epileptogenesis during aging. Melatonin can play a protective role in this context.

Mathematical Psychiatry: On Cortical Spreading Depression-A Review

The concept of migraine with aura (MwA) is a widespread condition that can affect up to 30% of migraine patients and manifests itself as a temporary visual illusion followed by a prolonged headache. It was initially pitched as a neurological disease, and observed that the spread of accompanying electrophysiological waves as part of the condition, which came to be known as cortical spreading depression (CSD). A strong theoretical basis for a link between MwA and CSD has eventually led to knowledge of the dynamics between the pair. In addition to experiment-based observations, mathematical models make an important contribution towards a numerical means of expressing codependent neural-scale manifestations. This provides alternate means of understanding and observing the phenomena while helping to visualize the links between the variables and their magnitude in contributing towards the emanation and dynamic pulsing of the condition. A number of biophysical mechanisms are believed to contribute to the MwA-CSD, spanning ion diffusion, ionic currents of membranes, osmosis, spatial buffering, neurotransmission, gap junctions, metabolic pumping, and synapse connections. As part of this review study, the various mathematical models for the description of the condition are expressed, reviewed, and contrasted, all of which vary in their depth, perspective, and level of information presented. Subsequent to this, the review looked into links between electrophysiological data-driven manifestations from measurements such as EEG and fMRI. While concluding remarks forged a structured pathway in the area on sub-themes that need to be investigated in order to strengthen and robustify the existing models, they include an accounting for inter-personal variability in models, sex and hormonal factors, and age groups, i.e., pediatrics vs. adults.

Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow

Recent studies have linked spreading depolarization (SD, an electro-chemical wave in the brain following stroke, migraine, traumatic brain injury, and more) with increase in cerebrospinal fluid (CSF) flow through the perivascular spaces (PVSs, annular channels lining the brain vasculature). We develop a novel computational model that couples SD and CSF flow. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change in cross-sectional area, pressure, and volume flow rate through the PVSs. The coupling is modelled using an empirical relationship between the excess potassium ion concentration in the extracellular space following SD and the vessel radius. We find that the CSF volumetric flow rate depends intricately on the length and width of the PVS, as well as the vessel radius and the angle of incidence of the SD wave. We derive analytical expressions for pressure and volumetric flow rates of CSF through the PVS for a given SD wave and quantify CSF flow variations when two SD waves collide. Our numerical approach is very general and could be extended in the future to obtain novel, quantitative insights into how CSF flow in the brain couples with slow waves, functional hyperemia, seizures, or externally applied neural stimulations.

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.

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.

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.

Mechanisms of the negative potential associated with Leão's spreading depolarization: A history of brain electrogenesis

Spreading depolarization (SD) is a self-propagated wave that provokes transient disorder of numerous cell and tissue functions, and that may kill neurons in metabolically compromised tissue. We examined the mechanisms underlying the main hallmark of SD, a giant extracellular potential (ΔVo) for which multiple electromotive forces have been proposed. The end-point is that neurons and not glia, dendritic channels and not spatial currents, and increased sodium conductance rather than potassium gradients, appear to be the main actors in the generation of the negative ΔVo. Neuronal currents are established by two mechanisms, a voltage independent dendritic current, and the differential polarization along the neuron membranes. Notably, despite of a marked drop of ion gradients, these evolve significantly during SD, and yet the membrane potential remains clamped at zero no matter how much inward current is present. There may be substantial inward current or none in function of the evolving portion of the neuron dendrites with SD-activated channels. We propose that the ΔVo promotes swelling-induced dendritic damage. Understanding SD electrogenesis requires all elements relevant for membrane potential, action currents, field potentials and volume conduction to be jointly considered, and it has already encouraged the search for new targets to limit SD-related pathology.

Reevaluation of Astrocyte-Neuron Energy Metabolism with Astrocyte Volume Fraction Correction: Impact on Cellular Glucose Oxidation Rates, Glutamate-Glutamine Cycle Energetics, Glycogen Levels and Utilization Rates vs. Exercising Muscle, and Na+/K+ Pumping Rates

Accurate quantification of cellular contributions to rates of substrate utilization in resting, activated, and diseased brain is essential for interpretation of data from studies using [¹⁸F]fluorodeoxyglucose-positron-emission tomography (FDG-PET) and [¹³C]glucose/magnetic resonance spectroscopy (MRS). A generally-accepted dogma is that neurons have the highest energy demands of all brain cells, and calculated neuronal rates of glucose oxidation in awake, resting brain accounts for 70-80%, with astrocytes 20-30%. However, these proportions do not take cell type volume fractions into account. To evaluate the conclusion that neuron-astrocyte glucose oxidation rates are similar when adjusted for astrocytic volume fraction (Hertz, Magn Reson Imaging 2011; 29, 1319), the present study analyzed data from 31 studies. On average, astrocytes occupy 6.1, 9.6, and 15% of tissue volume in hippocampus, cerebral cortex, and cerebellum, respectively, and regional astrocytic metabolic rates are adjusted for volume fraction by multiplying by 17.6, 11.4, and 6.8, respectively. After adjustment, astrocytic glucose oxidation rates in resting awake rat brain are 4-10 fold higher than neuronal oxidation rates. Volume-fraction adjustment also increases brain glycogen concentrations and utilization rates to be similar to or exceed exercising muscle. Ion flux calculations to evaluate sodium/potassium homeostasis during neurotransmission are not correct if astrocyte-neuron volume fractions are assumed to be equal. High rates of glucose and glycogen utilization after adjustment for volume fraction indicate that astrocytic energy demands are much greater than recognized, with most of the ATP being used for functions other than glutamate processing in the glutamate-glutamine cycle, challenging the notion that astrocytes 'feed hungry neurons'.

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.

Downregulation of Astrocytic Kir4.1 Potassium Channels Is Associated with Hippocampal Neuronal Hyperexcitability in Type 2 Diabetic Mice

Epilepsy, characterized by recurrent seizures, affects 1% of the general population. Interestingly, 25% of diabetics develop seizures with a yet unknown mechanism. Hyperglycemia downregulates inwardly rectifying potassium channel 4.1 (Kir4.1) in cultured astrocytes. Therefore, the present study aims to determine if downregulation of functional astrocytic Kir4.1 channels occurs in brains of type 2 diabetic mice and could influence hippocampal neuronal hyperexcitability. Using whole-cell patch clamp recording in hippocampal brain slices from male mice, we determined the electrophysiological properties of stratum radiatum astrocytes and CA1 pyramidal neurons. In diabetic mice, astrocytic Kir4.1 channels were functionally downregulated as evidenced by multiple characteristics including depolarized membrane potential, reduced barium-sensitive Kir currents and impaired potassium uptake capabilities of hippocampal astrocytes. Furthermore, CA1 pyramidal neurons from diabetic mice displayed increased spontaneous activity: action potential frequency was ≈9 times higher in diabetic compared with non-diabetic mice and small EPSC event frequency was significantly higher in CA1 pyramidal cells of diabetics compared to non-diabetics. These differences were apparent in control conditions and largely pronounced in response to the pro-convulsant 4-aminopyridine. Our data suggest that astrocytic dysfunction due to downregulation of Kir4.1 channels may increase seizure susceptibility by impairing astrocytic ability to maintain proper extracellular homeostasis.

Diffusion magnetic resonance imaging-derived free water detects neurodegenerative pattern induced by interferon-γ

Imaging biomarkers for immune activation may be valuable for early-stage detection, therapeutic testing, and research on neurodegenerative conditions. In the present study, we determined whether diffusion magnetic resonance imaging-derived free water signal is a sensitive marker for neuroinflammatory effects of interferon-gamma (Ifn-γ). Neonatal wild-type mice were injected in the cerebral ventricles with recombinant adeno-associated viruses expressing the inflammatory cytokine Ifn-γ. Groups of mice expressing Ifn-γ and age-matched controls were imaged at 1, 5 and 8 months. Mice deficient in Ifngr1^-/- and Stat1^-/- were scanned at 5 months as controls for the signaling cascades activated by Ifn-γ. The results indicate that Ifn-γ affected fractional anisotropy (FA), mean diffusivity (MD), and free water (FW) in white matter structures, midline cortical areas, and medial thalamic areas. In these structures, FA and MD decreased progressively from 1 to 8 months of age, while FW increased significantly. The observed reductions in FA and MD and increased FW with elevated brain Ifn-γ was not observed in Ifngr1^-/- or Stat1^-/- mice. These results suggest that the observed microstructure changes involve the Ifn-gr1 and Stat1 signaling. Interestingly, increases in FW were observed in midbrain of Ifngr1^-/- mice, which suggests alternative Ifn-γ signaling in midbrain. Although initial evidence is offered in relation to the sensitivity of the FW signal to neurodegenerative and/or inflammatory patterns specific to Ifn-γ, further research is needed to determine applicability and specificity across animal models of neuroinflammatory and degenerative disorders.

A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons

Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.

Disentangling astroglial physiology with a realistic cell model in silico

Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. Our simulations suggest that currents generated by glutamate transporters or K+ channels have negligible distant effects on membrane voltage and that individual astrocytes can successfully handle extracellular K+ hotspots. We show how intracellular Ca2+ buffers affect Ca2+ waves and why the classical Ca2+ sparks-and-puffs mechanism is theoretically compatible with common readouts of astroglial Ca2+ imaging.

Breakdown of blood brain barrier as a mechanism of post-traumatic epilepsy

Traumatic brain injury (TBI) accounts for approximately 16% of acute symptomatic seizures which usually occur in the first week after trauma. Children are at higher risk for post-traumatic seizures than adults. Post-traumatic seizures are a risk factor for delayed development of epilepsy. Delayed, chronic post-traumatic epilepsy is preceded by a silent period during which therapeutic interventions may arrest, revert or prevent epileptogenesis. A number of recent review articles summarize the most important features of post-traumatic seizures and epilepsy; this review will instead focus on the link between cerebrovascular permeability, epileptogenesis and ictal events after TBI. The possibility of acting on the blood-brain barrier (BBB) and the neurovascular unit to prevent, disrupt or treat post-traumatic epilepsy is also discussed. Finally, we describe the latest quest for biomarkers of epileptogenesis which may allow for a more targeted intervention.

Deconvolution of Voltage Sensor Time Series and Electro-diffusion Modeling Reveal the Role of Spine Geometry in Controlling Synaptic Strength

Most synaptic excitatory connections are made on dendritic spines. But how the voltage in spines is modulated by its geometry remains unclear. To investigate the electrical properties of spines, we combine voltage imaging data with electro-diffusion modeling. We first present a temporal deconvolution procedure for the genetically encoded voltage sensor expressed in hippocampal cultured neurons and then use electro-diffusion theory to compute the electric field and the current-voltage conversion. We extract a range for the neck resistances of 〈R〉=100±35MΩ. When a significant current is injected in a spine, the neck resistance can be inversely proportional to its radius, but not to the radius square, as predicted by Ohm's law. We conclude that the postsynaptic voltage cannot only be modulated by changing the number of receptors, but also by the spine geometry. Thus, spine morphology could be a key component in determining synaptic transduction and plasticity.

Neuroprotective potential of astroglia

Astroglia are the homoeostatic cells of the central nervous system, which participate in all essential functions of the brain. Astrocytes support neuronal networks by handling water and ion fluxes, transmitter clearance, provision of antioxidants, and metabolic precursors and growth factors. The critical dependence of neurons on constant support from the astrocytes confers astrocytes with intrinsic neuroprotective properties. On the other hand, loss of astrocytic support or their pathological transformation compromises neuronal functionality and viability. Manipulating neuroprotective functions of astrocytes is thus an important strategy to enhance neuronal survival and improve outcomes in disease states. © 2017 The Authors Journal of Neuroscience Research Published by Wiley Periodicals, Inc.

Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model

A detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ion homeostasis, thereby preventing these pathological waves. Simulations of the model illustrate how properties of spreading depolarizations, such as wave speed and duration of depolarization, depend on several factors, including the neuron and astrocyte Na(+)-K(+) ATPase pump strengths. In particular, we consider the neuroprotective role of astrocyte gap junction coupling. The model demonstrates that a syncytium of electrically coupled astrocytes can maintain a physiological membrane potential in the presence of an elevated extracellular K(+) concentration and efficiently distribute the excess K(+) across the syncytium. This provides an effective neuroprotective mechanism for delaying or preventing the initiation of spreading depolarizations.

Astrocytic modulation of neuronal excitability through K+ spatial buffering

The human brain contains two major cell populations, neurons and glia. While neurons are electrically excitable and capable of discharging short voltage pulses known as action potentials, glial cells are not. However, astrocytes, the prevailing subtype of glia in the cortex, are highly connected and can modulate the excitability of neurons by changing the concentration of potassium ions in the extracellular environment, a process called K⁺ clearance. During the past decade, astrocytes have been the focus of much research, mainly due to their close association with synapses and their modulatory impact on neuronal activity. It has been shown that astrocytes play an essential role in normal brain function including: nitrosative regulation of synaptic release in the neocortex, synaptogenesis, synaptic transmission and plasticity. Here, we discuss the role of astrocytes in network modulation through their K⁺ clearance capabilities, a theory that was first raised 50 years ago by Orkand and Kuffler. We will discuss the functional alterations in astrocytic activity that leads to aberrant modulation of network oscillations and synchronous activity.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

The neuroglial potassium cycle during neurotransmission: role of Kir4.1 channels

Neuronal excitability relies on inward sodium and outward potassium fluxes during action potentials. To prevent neuronal hyperexcitability, potassium ions have to be taken up quickly. However, the dynamics of the activity-dependent potassium fluxes and the molecular pathways underlying extracellular potassium homeostasis remain elusive. To decipher the specific and acute contribution of astroglial Kir4.1 channels in controlling potassium homeostasis and the moment to moment neurotransmission, we built a tri-compartment model accounting for potassium dynamics between neurons, astrocytes and the extracellular space. We here demonstrate that astroglial Kir4.1 channels are sufficient to account for the slow membrane depolarization of hippocampal astrocytes and crucially contribute to extracellular potassium clearance during basal and high activity. By quantifying the dynamics of potassium levels in neuron-glia-extracellular space compartments, we show that astrocytes buffer within 6 to 9 seconds more than 80% of the potassium released by neurons in response to basal, repetitive and tetanic stimulations. Astroglial Kir4.1 channels directly lead to recovery of basal extracellular potassium levels and neuronal excitability, especially during repetitive stimulation, thereby preventing the generation of epileptiform activity. Remarkably, we also show that Kir4.1 channels strongly regulate neuronal excitability for slow 3 to 10 Hz rhythmic activity resulting from probabilistic firing activity induced by sub-firing stimulation coupled to Brownian noise. Altogether, these data suggest that astroglial Kir4.1 channels are crucially involved in extracellular potassium homeostasis regulating theta rhythmic activity.

Effects of extracellular potassium diffusion on electrically coupled neuron networks

Potassium accumulation and diffusion during neuronal epileptiform activity have been observed experimentally, and potassium lateral diffusion has been suggested to play an important role in nonsynaptic neuron networks. We adopt a hippocampal CA1 pyramidal neuron network in a zero-calcium condition to better understand the influence of extracellular potassium dynamics on the stimulus-induced activity. The potassium concentration in the interstitial space for each neuron is regulated by potassium currents, Na(+)-K(+) pumps, glial buffering, and ion diffusion. In addition to potassium diffusion, nearby neurons are also coupled through gap junctions. Our results reveal that the latency of the first spike responding to stimulus monotonically decreases with increasing gap-junction conductance but is insensitive to potassium diffusive coupling. The duration of network oscillations shows a bell-like shape with increasing potassium diffusive coupling at weak gap-junction coupling. For modest electrical coupling, there is an optimal K(+) diffusion strength, at which the flow of potassium ions among the network neurons appropriately modulates interstitial potassium concentrations in a degree that provides the most favorable environment for the generation and continuance of the action potential waves in the network.

Potassium buffering in the neurovascular unit: models and sensitivity analysis

Astrocytes are critical regulators of neural and neurovascular network communication. Potassium transport is a central mechanism behind their many functions. Astrocytes encircle synapses with their distal processes, which express two potassium pumps (Na-K and NKCC) and an inward rectifying potassium channel (Kir), whereas the vessel-adjacent endfeet express Kir and BK potassium channels. We provide a detailed model of potassium flow throughout the neurovascular unit (synaptic region, astrocytes, and arteriole) for the cortex of the young brain. Our model reproduces several phenomena observed experimentally: functional hyperemia, in which neural activity triggers astrocytic potassium release at the perivascular endfoot, inducing arteriole dilation; K(+) undershoot in the synaptic space after periods of neural activity; neurally induced astrocyte hyperpolarization during Kir blockade. Our results suggest that the dynamics of the vascular response during functional hyperemia are governed by astrocytic Kir for the fast onset and astrocytic BK for maintaining dilation. The model supports the hypothesis that K(+) undershoot is caused by excessive astrocytic uptake through Na-K and NKCC pumps, whereas the effect is balanced by Kir. We address parametric uncertainty using high-dimensional stochastic sensitivity analysis and identify possible model limitations.

Electrodiffusive model for astrocytic and neuronal ion concentration dynamics

The cable equation is a proper framework for modeling electrical neural signalling that takes place at a timescale at which the ionic concentrations vary little. However, in neural tissue there are also key dynamic processes that occur at longer timescales. For example, endured periods of intense neural signaling may cause the local extracellular K⁺-concentration to increase by several millimolars. The clearance of this excess K⁺ depends partly on diffusion in the extracellular space, partly on local uptake by astrocytes, and partly on intracellular transport (spatial buffering) within astrocytes. These processes, that take place at the time scale of seconds, demand a mathematical description able to account for the spatiotemporal variations in ion concentrations as well as the subsequent effects of these variations on the membrane potential. Here, we present a general electrodiffusive formalism for modeling of ion concentration dynamics in a one-dimensional geometry, including both the intra- and extracellular domains. Based on the Nernst-Planck equations, this formalism ensures that the membrane potential and ion concentrations are in consistency, it ensures global particle/charge conservation and it accounts for diffusion and concentration dependent variations in resistivity. We apply the formalism to a model of astrocytes exchanging ions with the extracellular space. The simulations show that K⁺-removal from high-concentration regions is driven by a local depolarization of the astrocyte membrane, which concertedly (i) increases the local astrocytic uptake of K⁺, (ii) suppresses extracellular transport of K⁺, (iii) increases axial transport of K⁺ within astrocytes, and (iv) facilitates astrocytic relase of K⁺ in regions where the extracellular concentration is low. Together, these mechanisms seem to provide a robust regulatory scheme for shielding the extracellular space from excess K⁺.

When neurons generate electrical signals they release potassium ions (K⁺) into the extracellular space. During periods of intense neural activity, the local extracellular K⁺ may increase drastically. If it becomes too high, it can lead to neural dysfunction. Astrocytes (a kind of glial cells) are involved in preventing this from happening. Astrocytes can take up excess K⁺, transport it intracellularly, and release it in regions where the concentration is lower. This process is called spatial buffering, and a full mechanistic understanding of it is currently lacking. The aim of this work is twofold: First, we develop a formalism for modeling ion concentration dynamics in the intra- and extracellular space. The formalism is general, and could be used to simulate many cellular processes. It accounts for ion transports due to diffusion (along concentration gradients) as well as electrical migration (along voltage gradients). It extends previous, related formalisms, which have focused only on intracellular dynamics. Secondly, we apply the formalism to model how astrocytes exchange ions with the extracellular space. We conclude that the membrane mechanisms possessed by astrocytes seem optimal for shielding the extracellular space from excess K⁺, and provide a full mechanistic description of the spatial (K⁺) buffering process.

Mathematical approaches to modeling of cortical spreading depression

Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by a sustained headache. MwA was conjectured by Lashley to be related to some neurological phenomenon. A few years later, Leão observed electrophysiological waves in the brain that are now known as cortical spreading depression (CSD). CSD waves were soon conjectured to be the neurological phenomenon underlying MwA that had been suggested by Lashley. However, the confirmation of the link between MwA and CSD was not made until 2001 by Hadjikhani et al. [Proc. Natl. Acad. Sci. U.S.A. 98, 4687-4692 (2001)] using functional MRI techniques. Despite the fact that CSD has been studied continuously since its discovery in 1944, our detailed understandings of the interactions between the mechanisms underlying CSD waves have remained elusive. The connection between MwA and CSD makes the understanding of CSD even more compelling and urgent. In addition to all of the information gleaned from the many experimental studies on CSD since its discovery, mathematical modeling studies provide a general and in some sense more precise alternative method for exploring a variety of mechanisms, which may be important to develop a comprehensive picture of the diverse mechanisms leading to CSD wave instigation and propagation. Some of the mechanisms that are believed to be important include ion diffusion, membrane ionic currents, osmotic effects, spatial buffering, neurotransmitter substances, gap junctions, metabolic pumps, and synaptic connections. Discrete and continuum models of CSD consist of coupled nonlinear differential equations for the ion concentrations. In this review of the current quantitative understanding of CSD, we focus on these modeling paradigms and various mechanisms that are felt to be important for CSD.

Aquaporin-4-dependent K(+) and water transport modeled in brain extracellular space following neuroexcitation

Potassium (K(+)) ions released into brain extracellular space (ECS) during neuroexcitation are efficiently taken up by astrocytes. Deletion of astrocyte water channel aquaporin-4 (AQP4) in mice alters neuroexcitation by reducing ECS [K(+)] accumulation and slowing K(+) reuptake. These effects could involve AQP4-dependent: (a) K(+) permeability, (b) resting ECS volume, (c) ECS contraction during K(+) reuptake, and (d) diffusion-limited water/K(+) transport coupling. To investigate the role of these mechanisms, we compared experimental data to predictions of a model of K(+) and water uptake into astrocytes after neuronal release of K(+) into the ECS. The model computed the kinetics of ECS [K(+)] and volume, with input parameters including initial ECS volume, astrocyte K(+) conductance and water permeability, and diffusion in astrocyte cytoplasm. Numerical methods were developed to compute transport and diffusion for a nonstationary astrocyte-ECS interface. The modeling showed that mechanisms b-d, together, can predict experimentally observed impairment in K(+) reuptake from the ECS in AQP4 deficiency, as well as altered K(+) accumulation in the ECS after neuroexcitation, provided that astrocyte water permeability is sufficiently reduced in AQP4 deficiency and that solute diffusion in astrocyte cytoplasm is sufficiently low. The modeling thus provides a potential explanation for AQP4-dependent K(+)/water coupling in the ECS without requiring AQP4-dependent astrocyte K(+) permeability. Our model links the physical and ion/water transport properties of brain cells with the dynamics of neuroexcitation, and supports the conclusion that reduced AQP4-dependent water transport is responsible for defective neuroexcitation in AQP4 deficiency.

The extracellular space and epileptic activity in the adult brain: explaining the antiepileptic effects of furosemide and bumetanide

Treatments that modulate the size of the extracellular space (ECS) also block epileptiform activity in adult brain tissue. This includes the loop diuretics furosemide and bumetanide, and alterations of the osmolarity of the ECS. These treatments block epileptiform activity in a variety of laboratory adult seizure models regardless of the underlying synaptic and physiologic mechanisms generating the seizure activity. Optical imaging studies on adult hippocampal slices show that the blockade of epileptiform activity by these treatments is concomitant with their blockade of activity-driven changes of the ECS. Here we develop and analyze the hypothesis that activity-driven changes in the size of the ECS are necessary for the maintenance of hypersynchronous epileptiform activity. In support of this hypothesis is an accumulation of data from a number of studies suggesting that furosemide and bumetanide mediate antiepileptic effects through their blockade of cell swelling, dependent on their antagonism of the glial Na+-K-2Cl cotransporter (NKCC1).

Expression of olfactory-type cyclic nucleotide-gated channels in rat cortical astrocytes

Cyclic nucleotide-gated (CNG) channels are nonselective cation channels activated by cyclic AMP (cAMP) or cyclic GMP (cGMP). They were originally identified in retinal and olfactory receptors, but evidence has also emerged for their expression in several mammalian brain areas. Because cGMP and cAMP control important aspects of glial cell physiology, we wondered whether CNG channels are expressed in astrocytes, the most functionally relevant glial cells in the CNS. Immunoblot and immunofluorescence experiments demonstrated expression of the CNG channel olfactory-type A subunit, CNGA2, in cultured rat cortical astrocytes. In patch-clamp experiments, currents elicited in these cells by voltage ramps from -100 to +100 mV in the presence of the cGMP analogue, dB-cGMP, were significantly reduced by the CNG channel blockers, L-cis-diltiazem (LCD) and Cd(2+) . The reversal potentials of the LCD- and Cd(2+) -sensitive currents were more positive than that of K(+) , as expected for a mixed cation current. Noninactivating, voltage-independent currents were also elicited by extracellular application of the membrane permeant cGMP analogue, 8-Br-cGMP. These effects were blocked by LCD and were mimicked by natriuretic peptide receptor activation and inhibition of phosphodiesterase activity. Voltage-independent, LCD-sensitive currents were also elicited by 8-Br-cGMP in astrocytes of hippocampal and neocortical brain slices. Immunohistochemistry confirmed a broad distribution of CNG channels in astrocytes of the rat forebrain, midbrain, and hindbrain. These findings suggest that CNG channels are downstream targets of cyclic nucleotides in astrocytes, and they may be involved in the glial-mediated regulation of CNS functions under physiological and pathological conditions.

Extracellular K⁺ and astrocyte signaling via connexin and pannexin channels

Astrocytes utilize two major pathways to achieve long distance intercellular communication. One pathway involves direct gap junction mediated signal transmission and the other consists of release of ATP through pannexin channels and excitation of purinergic receptors on nearby cells. Elevated extracellular potassium to levels occurring around hyperactive neurons affects both gap junction and pannexin1 channels. The action on Cx43 gap junctions is to increase intercellular coupling for a period that long outlasts the stimulus. This long term increase in coupling, termed "LINC", is mediated through calcium and calmodulin dependent activation of calmodulin dependent kinase (CaMK). Pannexin1 can be activated by elevations in extracellular potassium through a mechanism that is quite different. In this case, potassium shifts activation potentials to more physiological range, thereby allowing channel opening at resting or slightly depolarized potentials. Enhanced activity of both these channel types by elevations in extracellular potassium of the magnitude occurring during periods of high neuronal activity likely has profound effects on intercellular signaling among astrocytes in the nervous system.

In vitro effect of adenosine on the mRNA expression of Kir 2.1 and Kir 4.1 channels in rat retinal Müller cells at elevated hydrostatic pressure

The aim of this study was to investigate the expression of Kir 2.1 and Kir 4.1 channels at an elevated hydrostatic pressure in vitro, and to determine whether adenosine may modulate the mRNA expression of Kir 2.1 and Kir 4.1 channels in retinal Müller cells at an elevated hydrostatic pressure in vitro. Müller cells treated with 1 μM adenosine at 40 mmHg/24 h, and mRNA expression of Kir 2.1 and Kir 4.1 channels were examined using real-time PCR. Müller cells significantly increased the mRNA expression of Kir 2.1 and Kir 4.1 channels at 40 mmHg/24 h. When further treated with 1 μM adenosine at 40 mmHg/24 h, the mRNA expression of the Kir 2.1 channels decreased, while the mRNA expression of the Kir 4.1 channels continued to increase. When the pressure was elevated, Müller cells were still able to take up K(+) and mediate the potassium concentration of the retina. Adenosine upregulated the expression of the Kir 4.1 channels, but weakly affected the expression of the Kir 2.1 channels.

Models of neurovascular coupling via potassium and EET signalling

Functional hyperemia is an important metabolic autoregulation mechanism by which increased neuronal activity is matched by a rapid and regional increase in blood supply. This mechanism is facilitated by a process known as "neurovascular coupling"--the orchestrated communication system involving neurons, astrocytes and arterioles. Important steps in this process are the production of EETs in the astrocyte and the release of potassium, via two potassium channels (BK and KIR), into the perivascular space. We provide a model which successfully accounts for several observations seen in experiment. The model is capable of simulating the approximate 15% arteriolar dilation caused by a 60-s neuronal activation (modelled as a release of potassium and glutamate into the synaptic cleft). This model also successfully emulates the paradoxical experimental finding that vasoconstriction follows vasodilation when the astrocytic calcium concentration (or perivascular potassium concentration) is increased further. We suggest that the interaction of the changing smooth muscle cell membrane potential and the changing potassium-dependent resting potential of the KIR channel are responsible for this effect. Finally, we demonstrate that a well-controlled mechanism of potassium buffering is potentially important for successful neurovascular coupling.

The impact of the glial spatial buffering on the K(+) Nernst potential

Astrocytes play a critical role in CNS metabolism, regulation of volume and ion homeostasis of the interstitial space. Of special relevance is their clearance of K(+) that is released by active neurons into the extracellular space. Mathematical analysis of a modified Nernst equation for the electrochemical equilibrium of neuronal plasma membranes, suggests that K(+) uptake by glial cells is not only relevant during neuronal activity but also has a non-neglectable impact on the basic electrical membrane properties, specifically the resting membrane potential, of neurons and might be clinically valuable as a factor in the genetics and epigenetics of the epilepsy and tuberous sclerosis complex.

Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms

Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation ('depolarisation block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K( + )]₀ causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K( + )](o) conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin-Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K( + )]₀-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.

HPMA-RGD hydrogels seeded with mesenchymal stem cells improve functional outcome in chronic spinal cord injury

Chronic spinal cord injury (SCI) is characterized by tissue loss and a stable functional deficit. While several experimental therapies have proven to be partly successful for the treatment of acute SCI, treatment of chronic SCI is still challenging. We studied whether we can bridge a chronic spinal cord lesion by implantation of our newly developed hydrogel based on 2-hydroxypropyl methacrylamide, either alone or seeded with mesenchymal stem cells (MSCs), and whether this treatment leads to functional improvement. A balloon-induced compression lesion was performed in adult 2-month-old male Wistar rats. Five weeks after injury, HPMA-RGD hydrogels [N-(2-hydroxypropyl)-methacrylamide with attached amino acid sequences--Arg-Gly-Asp] were implanted into the lesion, either with or without seeded MSCs. Animals with chronic SCI served as controls. The animals were behaviorally tested using the Basso–Beattie-Breshnahan (BBB) (motor) and plantar (sensory) tests once a week for 6 months. Behavioral analysis showed a statistically significant improvement in rats with combined treatment, hydrogel and MSCs, compared with the control group (P < 0.05). Although a tendency toward improvement was found in rats treated with hydrogel only, this was not significant. Subsequently, the animals were sacrificed 6 months after SCI, and the spinal cord lesions evaluated histologically. The combined therapy (hydrogel with MSCs) prevented tissue atrophy (P < 0.05), and the hydrogels were infiltrated with axons myelinated with Schwann cells. Blood vessels and astrocytes also grew inside the implant. MSCs were present in the hydrogels even 5 months after implantation. We conclude that 5 weeks after injury, HPMA-RGD hydrogels seeded with MSCs can successfully bridge a spinal cord cavity and provide a scaffold for tissue regeneration. This treatment leads to functional improvement even in chronic SCI.

Temporary sequestration of potassium by mitochondria in astrocytes

Increases in extracellular potassium concentration ([K(+)](o)), which can occur during neuronal activity and under pathological conditions such as ischemia, lead to a variety of potentially detrimental effects on neuronal function. Although astrocytes are known to contribute to the clearance of excess K(+)(o), the mechanisms are not fully understood. We examined the potential role of mitochondria in sequestering K(+) in astrocytes. Astrocytes were loaded with the fluorescent K(+) indicator PBFI and release of K(+) from mitochondria into the cytoplasm was examined after uncoupling the mitochondrial membrane potential with carbonyl cyanide m-chlorophenylhydrazone (CCCP). Under the experimental conditions employed, transient applications of elevated [K(+)](o) led to increases in K(+) within mitochondria, as assessed by increases in the magnitudes of cytoplasmic [K(+)] ([K(+)](i)) transients evoked by brief exposures to CCCP. When mitochondrial K(+) sequestration was impaired by prolonged application of CCCP, there was a robust increase in [K(+)](i) upon exposure to elevated [K(+)](o). Blockade of plasmalemmal K(+) uptake routes by ouabain, Ba(2+), or a mixture of voltage-activated K(+) channel inhibitors reduced K(+) uptake into mitochondria. Also, reductions in mitochondrial K(+) uptake occurred in the presence of mito-K(ATP) channel inhibitors. Rises in [K(+)](i) evoked by brief applications of CCCP following exposure to high [K(+)](o) were also reduced by gap junction blockers and in astrocytes isolated from connexin43-null mice, suggesting that connexins also play a role in K(+) uptake into astrocyte mitochondria. We conclude that mitochondria play a key role in K(+)(o) handling by astrocytes.

TASK channels contribute to the K+-dominated leak current regulating respiratory rhythm generation in vitro

Leak channels regulate neuronal activity and excitability. Determining which leak channels exist in neurons and how they control electrophysiological behavior is fundamental. Here we investigated TASK channels, members of the two-pore domain K(+) channel family, as a component of the K(+)-dominated leak conductance that controls and modulates rhythm generation at cellular and network levels in the mammalian pre-Bötzinger complex (pre-BötC), an excitatory network of neurons in the medulla critically involved in respiratory rhythmogenesis. By voltage-clamp analyses of pre-BötC neuronal current-voltage (I-V) relations in neonatal rat medullary slices in vitro, we demonstrated that pre-BötC inspiratory neurons have a weakly outward-rectifying total leak conductance with reversal potential that was depolarized by approximately 4 mV from the K(+) equilibrium potential, indicating that background K(+) channels are dominant contributors to leak. This K(+) channel component had I-V relations described by constant field theory, and the conductance was reduced by acid and was augmented by the volatile anesthetic halothane, which are all hallmarks of TASK. We established by single-cell RT-PCR that pre-BötC inspiratory neurons express TASK-1 and in some cases also TASK-3 mRNA. Furthermore, acid depolarized and augmented bursting frequency of pre-BötC inspiratory neurons with intrinsic bursting properties. Microinfusion of acidified solutions into the rhythmically active pre-BötC network increased network bursting frequency, halothane decreased bursting frequency, and acid reversed the depressant effects of halothane, consistent with modulation of network activity by TASK channels. We conclude that TASK-like channels play a major functional role in chemosensory modulation of respiratory rhythm generation in the pre-Bötzinger complex in vitro.

MAPK induces AQP1 expression in astrocytes following injury

Aquaporin-4 (AQP4) is the principle water channel and the primary route for water transport across astrocytic membranes. AQP4 co-localizes with Kir4.1 channels at astrocytic endfeet, and it has been suggested that these channels cooperate in K(+) and water homeostasis. In response to injury, two additional aquaporins, AQP1 and AQP9, can be detected in astrocytes, yet neither is found in cultured astrocytes, and therefore their contribution to astrocyte water uptake and biology is poorly investigated. In this study, we used a cortical stab wound assay to demonstrate an upregulation of AQP1 following injury in reactive glia. We were able to mimic such injury in astrocytic cultures and show that AQP1 expression is induced within 16 h following injury in vitro. This induction could be blocked by inhibition of MEK1/2 using U0126, and suggests that AQP1 is specifically induced in reactive astrocytes via the mitogen-activated protein kinases signaling pathway.

Astrocytic dysfunction in epileptogenesis: consequence of altered potassium and glutamate homeostasis?

Focal epilepsy often develops following traumatic, ischemic, or infectious brain injury. While the electrical activity of the epileptic brain is well characterized, the mechanisms underlying epileptogenesis are poorly understood. We have recently shown that in the rat neocortex, long-lasting breakdown of the blood-brain barrier (BBB) or direct exposure of the neocortex to serum-derived albumin leads to rapid upregulation of the astrocytic marker GFAP (glial fibrillary acidic protein), followed by delayed (within 4-7 d) development of an epileptic focus. We investigated the role of astrocytes in epileptogenesis in the BBB-breakdown and albumin models of epileptogenesis. We found similar, robust changes in astrocytic gene expression in the neocortex within hours following treatment with deoxycholic acid (BBB breakdown) or albumin. These changes predict reduced clearance capacity for both extracellular glutamate and potassium. Electrophysiological recordings in vitro confirmed the reduced clearance of activity-dependent accumulation of both potassium and glutamate 24 h following exposure to albumin. We used a NEURON model to simulate the consequences of reduced astrocytic uptake of potassium and glutamate on EPSPs. The model predicted that the accumulation of glutamate is associated with frequency-dependent (>100 Hz) decreased facilitation of EPSPs, while potassium accumulation leads to frequency-dependent (10-50 Hz) and NMDA-dependent synaptic facilitation. In vitro electrophysiological recordings during epileptogenesis confirmed frequency-dependent synaptic facilitation leading to seizure-like activity. Our data indicate a transcription-mediated astrocytic transformation early during epileptogenesis. We suggest that the resulting reduction in the clearance of extracellular potassium underlies frequency-dependent neuronal hyperexcitability and network synchronization.

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

Neuronal stimulation causes ∼30% shrinkage of the extracellular space (ECS) between neurons and surrounding astrocytes in grey and white matter under experimental conditions. Despite its possible implications for a proper understanding of basic aspects of potassium clearance and astrocyte function, the phenomenon remains unexplained. Here we present a dynamic model that accounts for current experimental data related to the shrinkage phenomenon in wild-type as well as in gene knockout individuals. We find that neuronal release of potassium and uptake of sodium during stimulation, astrocyte uptake of potassium, sodium, and chloride in passive channels, action of the Na/K/ATPase pump, and osmotically driven transport of water through the astrocyte membrane together seem sufficient for generating ECS shrinkage as such. However, when taking into account ECS and astrocyte ion concentrations observed in connection with neuronal stimulation, the actions of the Na⁺/K⁺/Cl⁻ (NKCC1) and the Na⁺/HCO₃⁻ (NBC) cotransporters appear to be critical determinants for achieving observed quantitative levels of ECS shrinkage. Considering the current state of knowledge, the model framework appears sufficiently detailed and constrained to guide future key experiments and pave the way for more comprehensive astroglia–neuron interaction models for normal as well as pathophysiological situations.

A key experimental observation associated with the astroglia–neuron interaction is the shrinkage of the extracellular space (ECS) that occurs in response to enhanced neuronal activation. Although well documented to be present in mammalian brains, this phenomenon has resisted a proper explanation since it was first reported. We present here a mathematical conceptualization that may explain the main mechanisms behind ECS shrinkage and provide a framework for a theoretical-experimental research programme that may help to reach a consensus explanation. Effective clearance of K⁺ is essential for normal brain function because an inappropriate increase in extracellular K⁺ will enhance neuronal excitability and promote neuronal afterdischarges and increase the probability of epileptic episodes. The shrinkage of the ECS usually appears in conjunction with K⁺ clearance and must be taken into account in a model of how astrocytes clear excess K⁺ following trains of action potentials. The present model allows us to make several clear and testable predictions addressing the relationship among potassium clearance, water transport, and ECS shrinkage. Among these are predictions concerning water transport functions of aquaporins in astrocytes, involvement of cotransporters in potassium clearance, and effects of particular knockouts on ECS shrinkage and ion concentrations.

Cellular automata approach of transmembrane ionic currents

Ionic currents across neuron and glial cells membranes lie at the origin of the entire brain electrophysiology. They are the common root of functional brain dynamics and mesoscopic or macroscopic phenomena such as extracellular fields. In particular, they provide the relevant basis to relate cellular electrophysiology and macroscopic dipole models. In order to derive robust features and to envision the multi-scale approaches required to connect the different levels of observation, an essential prerequisite is to have minimal model of elementary ionic motions. In this paper, we propose a general cellular automata framework allowing to investigate the distribution of ionic currents in heterogeneous media interspersed with membranes, from which follows the local electromagnetic field.

Complex rectification of Müller cell Kir currents

Although Kir4.1 channels are the major inwardly rectifying channels in glial cells and are widely accepted to support K+- and glutamate-uptake in the nervous system, the properties of Kir4.1 channels during vital changes of K+ and polyamines remain poorly understood. Therefore, the present study examined the voltage-dependence of K+ conductance with varying physiological and pathophysiological external [K+] and intrapipette spermine ([SP]) concentrations in Müller glial cells and in tsA201 cells expressing recombinant Kir4.1 channels. Two different types of [SP] block were characterized: "fast" and "slow." Fast block was steeply voltage-dependent, with only a low sensitivity to spermine and strong dependence on extracellular potassium concentration, [K+]o. Slow block had a strong voltage sensitivity that begins closer to resting membrane potential and was essentially [K+]o-independent, but with a higher spermine- and [K+]i-sensitivity. Using a modified Woodhull model and fitting i/V curves from whole cell recordings, we have calculated free [SP](in) in Müller glial cells as 0.81 +/- 0.24 mM. This is much higher than has been estimated previously in neurons. Biphasic block properties underlie a significantly varying extent of rectification with [K+] and [SP]. While confirming similar properties of glial Kir and recombinant Kir4.1, the results also suggest mechanisms underlying K+ buffering in glial cells: When [K+]o is rapidly increased, as would occur during neuronal excitation, "fast block" would be relieved, promoting potassium influx to glial cells. Increase in [K+]in would then lead to relief of "slow block," further promoting K+-influx.

Seizure-like afterdischarges simulated in a model neuron

To explore non-synaptic mechanisms in paroxysmal discharges, we used a computer model of a simplified hippocampal pyramidal cell, surrounded by interstitial space and a "glial-endothelial" buffer system. Ion channels for Na+, K+, Ca2+ and Cl- ion antiport 3Na/Ca, and "active" ion pumps were represented in the neuron membrane. The glia had "leak" conductances and an ion pump. Fluxes, concentration changes and cell swelling were computed. The neuron was stimulated by injecting current. Afterdischarge (AD) followed stimulation if depolarization due to rising interstitial K+ concentration ([K+]o) activated persistent Na+ current (INa.P). AD was either simple or self-regenerating; either regular (tonic) or burst-type (clonic); and always self-limiting. Self-regenerating AD required sufficient INa.P to ensure re-excitation. Burst firing depended on activation of dendritic Ca2+ currents and Ca-dependent K+ current. Varying glial buffer function influenced [K+]o accumulation and afterdischarge duration. Variations in Na+ and K+ currents influenced the threshold and the duration of AD. The data show that high [K+]o and intrinsic membrane currents can produce the feedback of self-regenerating afterdischarges without synaptic input. The simulated discharge resembles neuron behavior during paroxysmal firing in living brain tissue.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

Role of potassium lateral diffusion in non-synaptic epilepsy: A computational study

An increase of extracellular potassium ion concentration can result in neuronal hyperexcitability, and thus contribute to non-synaptic epileptiform activity. It has been shown that potassium lateral diffusion alone is sufficient for synchronization in the low-calcium epilepsy in-vitro model. However, it is not yet known whether the lateral diffusion can, by itself, induce seizure activity. We hypothesize that spontaneous sustained neuronal activity can be generated by potassium coupling between neurons. To test this hypothesis, neuronal simulations with 2-cell or 4-cell models were used. Each model neuron was embedded in a bath of K+ and surrounded by interstitial space. Interstitial potassium concentration was regulated by both K+-pump and glial buffer mechanisms. Simulations performed with two coupled neurons with parameter values within physiological range show that, without chemical and electrical synapses, potassium lateral diffusion alone can generate and synchronize zero-Ca2+ non-synaptic epileptiform activity. Simulations performed with a network of four zero-Ca2+ CA1 pyramidal neurons modeled in zero-calcium conditions also show that spontaneous sustained activity can propagate by potassium lateral diffusion alone with a velocity of approximately 0.93 mm/sec. This diffusion model used for the simulations is based on physiological parameters, is robust for various kinetics, and is able to reproduce both the spontaneous triplet bursting of non-synaptic activity and speed of propagation in low-Ca2+ non-synaptic epilepsy experiments. These simulations suggest that potassium lateral diffusion can play an important role in the synchronization and generation on non-synaptic epilepsy.

Transforming growth factor-beta3 increases gap-junctional communication among folliculostellate cells to release basic fibroblast growth factor

Folliculostellate (FS) cells are known to communicate with each other and with endocrine cells via gap junctions in the anterior pituitary. We investigated whether TGFbeta3 and estradiol, known to regulate FS cell production and secretion of basic fibroblast growth factor (bFGF), increases gap junctional communication to alter bFGF secretion from FS cells. FS cells in monolayer cultures were treated with TGFbeta3 or vehicle alone for 24 h and then microinjected with Lucifer Yellow and high-molecular-weight Texas Red dextran. Ten minutes later the transfer of dye among adjacent cells was recorded with a digital microscope. TGFbeta3 increased the transfer of dye. The TGFbeta3-neutralizing antibody and the gap junction inhibitor octanol reduced the effect of TGFbeta3 on the transfer of dye. The TGFbeta3-induced transfer of dye was unaltered by simultaneous treatment with estradiol. The steroid alone also had no effect. TGFbeta3 increased total and phosphorylated levels of connexin 43. Estradiol treatment did not produce any significant changes on basal or TGFbeta3-induced increases in connexin 43 levels. The gap-junction inhibitor octanol reduced TGFbeta3-increased levels of bFGF in FS cells. Taken together, these results suggest that TGFbeta3 may act on FS cells to increase gap-junctional communication to maximize its effect on bFGF secretion.