Bistable dynamics underlying excitability of ion homeostasis in neuron models

Coupled action potential and calcium dynamics underlie robust spontaneous firing in dopaminergic neurons

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillationsin-vitroandin-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

The Blood–Brain Barrier—A Key Player in Multiple Sclerosis Disease Mechanisms

Over the past decade, multiple sclerosis (MS), a chronic neuroinflammatory disease with severe personal and social consequences, has undergone a steady increase in incidence and prevalence rates worldwide. Despite ongoing research and the development of several novel therapies, MS pathology remains incompletely understood, and the prospect for a curative treatment continues to be unpromising in the near future. A sustained research effort, however, should contribute to a deeper understanding of underlying disease mechanisms, which will undoubtedly yield improved results in drug development. In recent years, the blood–brain barrier (BBB) has increasingly become the focus of many studies as it appears to be involved in both MS disease onset and progression. More specifically, neurovascular unit damage is believed to be involved in the critical process of CNS immune cell penetration, which subsequently favors the development of a CNS-specific immune response, leading to the classical pathological and clinical hallmarks of MS. The aim of the current narrative review is to merge the relevant evidence on the role of the BBB in MS pathology in a comprehensive and succinct manner. Firstly, the physiological structure and functions of the BBB as a component of the more complex neurovascular unit are presented. Subsequently, the authors review the specific alteration of the BBB encountered in different stages of MS, focusing on both the modifications of BBB cells in neuroinflammation and the CNS penetration of immune cells. Finally, the currently accepted theories on neurodegeneration in MS are summarized.

The Donnan-dominated resting state of skeletal muscle fibers contributes to resilience and longevity in dystrophic fibers

Duchenne muscular dystrophy (DMD) is an X-linked dystrophin-minus muscle-wasting disease. Ion homeostasis in skeletal muscle fibers underperforms as DMD progresses. But though DMD renders these excitable cells intolerant of exertion, sodium overloaded, depolarized, and spontaneously contractile, they can survive for several decades. We show computationally that underpinning this longevity is a strikingly frugal, robust Pump-Leak/Donnan (P-L/D) ion homeostatic process. Unlike neurons, which operate with a costly “Pump-Leak–dominated” ion homeostatic steady state, skeletal muscle fibers operate with a low-cost “Donnan-dominated” ion homeostatic steady state that combines a large chloride permeability with an exceptionally small sodium permeability. Simultaneously, this combination keeps fiber excitability low and minimizes pump expenditures. As mechanically active, long-lived multinucleate cells, skeletal muscle fibers have evolved to handle overexertion, sarcolemmal tears, ischemic bouts, etc.; the frugality of their Donnan dominated steady state lets them maintain the outsized pump reserves that make them resilient during these inevitable transient emergencies. Here, P-L/D model variants challenged with DMD-type insult/injury (low pump-strength, overstimulation, leaky Nav and cation channels) show how chronic “nonosmotic” sodium overload (observed in DMD patients) develops. Profoundly severe DMD ion homeostatic insult/injury causes spontaneous firing (and, consequently, unwanted excitation–contraction coupling) that elicits cytotoxic swelling. Therefore, boosting operational pump-strength and/or diminishing sodium and cation channel leaks should help extend DMD fiber longevity.

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.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.

Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.

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.

Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries

Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.

Regulation of CSF and Brain Tissue Sodium Levels by the Blood-CSF and Blood-Brain Barriers During Migraine

Cerebrospinal fluid (CSF) and brain tissue sodium levels increase during migraine. However, little is known regarding the underlying mechanisms of sodium homeostasis disturbance in the brain during the onset and propagation of migraine. Exploring the cause of sodium dysregulation in the brain is important, since correction of the altered sodium homeostasis could potentially treat migraine. Under the hypothesis that disturbances in sodium transport mechanisms at the blood-CSF barrier (BCSFB) and/or the blood-brain barrier (BBB) are the underlying cause of the elevated CSF and brain tissue sodium levels during migraines, we developed a mechanistic, differential equation model of a rat's brain to compare the significance of the BCSFB and the BBB in controlling CSF and brain tissue sodium levels. The model includes the ventricular system, subarachnoid space, brain tissue and blood. Sodium transport from blood to CSF across the BCSFB, and from blood to brain tissue across the BBB were modeled by influx permeability coefficients P_BCSFB and P_BBB, respectively, while sodium movement from CSF into blood across the BCSFB, and from brain tissue to blood across the BBB were modeled by efflux permeability coefficients PBCSFB′ and PBBB′, respectively. We then performed a global sensitivity analysis to investigate the sensitivity of the ventricular CSF, subarachnoid CSF and brain tissue sodium concentrations to pathophysiological variations in P_BCSFB, P_BBB, PBCSFB′ and PBBB′. Our results show that the ventricular CSF sodium concentration is highly influenced by perturbations of P_BCSFB, and to a much lesser extent by perturbations of PBCSFB′. Brain tissue and subarachnoid CSF sodium concentrations are more sensitive to pathophysiological variations of P_BBB and PBBB′ than variations of P_BCSFB and PBCSFB′ within 30 min of the onset of the perturbations. However, P_BCSFB is the most sensitive model parameter, followed by P_BBB and PBBB′, in controlling brain tissue and subarachnoid CSF sodium levels within 3 h of the perturbation onset.

Noise-sustained patterns in a model of volume-coupled neural tissue

Computational neuroscience operates on models based on several important paradigms. Among them is the assumption that coupling in neural ensembles is provided by chemical or electrical synapses. This assumption works well under normal conditions. However, there is a growing body of data that show the importance of other communication pathways caused by bi-directional transport of substances between the cells and the intercellular space. This type of interaction is called "volume transmission" and has not been rarely addressed in the model studies. The volume transmission pathway naturally appears in multidimensional quantitative models of cellular processes, but is not sufficiently represented at the level of lumped and computationally effective neural models. In this paper, we propose a simple model that allows one to study the features of volume transmission coupling at various spatial scales and taking into account various inhomogeneities. This model is obtained by the extension of the well-known FitzHugh-Nagumo system by the addition of the nonlinear terms and equations to describe, at a qualitative level, the release of potassium into the intercellular space, its diffusion, and the reverse effect on the neurons. The study of model dynamics in various spatial configurations has revealed a number of characteristic spatio-temporal types of behavior that include self-organizing bursting and phase-locked firing patterns, different scenarios of excitation spreading, noise-sustained target patterns, and long-living slow moving wave segments.

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

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

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

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

A mathematical model of recurrent spreading depolarizations

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

Comparative approximations of criticality in a neural and quantum regime

Under a variety of conditions, stochastic and non-linear systems with many degrees of freedom tend to evolve towards complexity and criticality. Over the last decades, a steady proliferation of models re: far-from-equilibrium thermodynamics of metastable, many-valued systems arose, serving as attributes of a 'critical' attractor landscape. Building off recent data citing trademark aspects of criticality in the brain-including: power-laws, scale-free (1/f) behavior (scale invariance, or scale independence), critical slowing, and avalanches-it has been conjectured that operating at criticality entails functional advantages such as: optimized neural computation and information processing; boosted memory; large dynamical ranges; long-range communication; and an increased ability to react to highly diverse stimuli. In short, critical dynamics provide a necessary condition for neurobiologically significant elements of brain dynamics. Theoretical predictions have been verified in specific models such as Boolean networks, liquid state machines, and neural networks. These findings inspired the neural criticality hypothesis, proposing that the brain operates in a critical state because the associated optimal computational capabilities provide an evolutionarily advantage. This paper develops in three parts: after developing the critical landscape, we will then shift gears to rediscover another inroad to criticality via stochastic quantum field theory and dissipative dynamics. The existence of these two approaches deserves some consideration, given both neural and quantum criticality hypotheses propose specific mechanisms that leverage the same phenomena. This suggests that understanding the quantum approach could help to shed light on brain-based modeling. In the third part, we will turn to Whitehead's actual entities and modes of perception in order to demonstrate a concomitant logic underwriting both models. In the discussion, I briefly motivate a reading of criticality and its properties as responsive to the characterization of tenets from Eastern wisdom traditions.

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

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

A Biophysical Model for Cytotoxic Cell Swelling

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

SIGNIFICANCE STATEMENT

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

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.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Mechanisms of spreading depolarization in vertebrate and insect central nervous systems

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

Near-Infrared Spectroscopy - Electroencephalography-Based Brain-State-Dependent Electrotherapy: A Computational Approach Based on Excitation-Inhibition Balance Hypothesis

Stroke is the leading cause of severe chronic disability and the second cause of death worldwide with 15 million new cases and 50 million stroke survivors. The poststroke chronic disability may be ameliorated with early neuro rehabilitation where non-invasive brain stimulation (NIBS) techniques can be used as an adjuvant treatment to hasten the effects. However, the heterogeneity in the lesioned brain will require individualized NIBS intervention where innovative neuroimaging technologies of portable electroencephalography (EEG) and functional-near-infrared spectroscopy (fNIRS) can be leveraged for Brain State Dependent Electrotherapy (BSDE). In this hypothesis and theory article, we propose a computational approach based on excitation–inhibition (E–I) balance hypothesis to objectively quantify the poststroke individual brain state using online fNIRS–EEG joint imaging. One of the key events that occurs following Stroke is the imbalance in local E–I (that is the ratio of Glutamate/GABA), which may be targeted with NIBS using a computational pipeline that includes individual “forward models” to predict current flow patterns through the lesioned brain or brain target region. The current flow will polarize the neurons, which can be captured with E–I-based brain models. Furthermore, E–I balance hypothesis can be used to find the consequences of cellular polarization on neuronal information processing, which can then be implicated in changes in function. We first review the evidence that shows how this local imbalance between E–I leading to functional dysfunction can be restored in targeted sites with NIBS (motor cortex and somatosensory cortex) resulting in large-scale plastic reorganization over the cortex, and probably facilitating recovery of functions. Second, we show evidence how BSDE based on E–I balance hypothesis may target a specific brain site or network as an adjuvant treatment. Hence, computational neural mass model-based integration of neurostimulation with online neuroimaging systems may provide less ambiguous, robust optimization of NIBS, and its application in neurological conditions and disorders across individual patients.

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.

Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K+ pumps-dependent manner

The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region-specific neuronal damage. Neurons in higher brain regions exhibiting nonreversible, strong AD are more susceptible to ischemic injury as compared to cells in lower brain regions that exhibit reversible, weak AD. While the contrasting ADs in different brain regions in response to oxygen-glucose deprivation (OGD) is well established, the mechanism leading to such differences is not clear. Here we use computational modeling to elucidate the mechanism behind the brain region-specific recovery from AD. Our extended Hodgkin-Huxley (HH) framework consisting of neural spiking dynamics, processes of ion accumulation, and ion homeostatic mechanisms unveils that glial-vascular K(+) clearance and Na(+)/K(+)-exchange pumps are key to the cell's recovery from AD. Our phase space analysis reveals that the large extracellular space in the upper brain regions leads to impaired Na(+)/K(+)-exchange pumps so that they function at lower than normal capacity and are unable to bring the cell out of AD after oxygen and glucose is restored.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

EEG-NIRS based assessment of neurovascular coupling during anodal transcranial direct current stimulation--a stroke case series

A method for electroencephalography (EEG) - near-infrared spectroscopy (NIRS) based assessment of neurovascular coupling (NVC) during anodal transcranial direct current stimulation (tDCS). Anodal tDCS modulates cortical neural activity leading to a hemodynamic response, which was used to identify impaired NVC functionality. In this study, the hemodynamic response was estimated with NIRS. NIRS recorded changes in oxy-hemoglobin (HbO2) and deoxy-hemoglobin (Hb) concentrations during anodal tDCS-induced activation of the cortical region located under the electrode and in-between the light sources and detectors. Anodal tDCS-induced alterations in the underlying neuronal current generators were also captured with EEG. Then, a method for the assessment of NVC underlying the site of anodal tDCS was proposed that leverages the Hilbert-Huang Transform. The case series including four chronic (>6 months) ischemic stroke survivors (3 males, 1 female from age 31 to 76) showed non-stationary effects of anodal tDCS on EEG that correlated with the HbO2 response. Here, the initial dip in HbO2 at the beginning of anodal tDCS corresponded with an increase in the log-transformed mean-power of EEG within 0.5Hz-11.25Hz frequency band. The cross-correlation coefficient changed signs but was comparable across subjects during and after anodal tDCS. The log-transformed mean-power of EEG lagged HbO2 response during tDCS but then led post-tDCS. This case series demonstrated changes in the degree of neurovascular coupling to a 0.526 A/m(2) square-pulse (0-30 s) of anodal tDCS. The initial dip in HbO2 needs to be carefully investigated in a larger cohort, for example in patients with small vessel disease.

Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.

Linking a genetic defect in migraine to spreading depression in a computational model

Familial hemiplegic migraine (FHM) is a rare subtype of migraine with aura. A mutation causing FHM type 3 (FHM3) has been identified in SCN1A encoding the Nav1.1 Na⁺ channel. This genetic defect affects the inactivation gate. While the Na⁺ tail currents following voltage steps are consistent with both hyperexcitability and hypoexcitability, in this computational study, we investigate functional consequences beyond these isolated events. Our extended Hodgkin–Huxley framework establishes a connection between genotype and cellular phenotype, i.e., the pathophysiological dynamics that spans over multiple time scales and is relevant to migraine with aura. In particular, we investigate the dynamical repertoire from normal spiking (milliseconds) to spreading depression and anoxic depolarization (tens of seconds) and show that FHM3 mutations render gray matter tissue more vulnerable to spreading depression despite opposing effects associated with action potential generation. We conclude that the classification in terms of hypoexcitability vs. hyperexcitability is too simple a scheme. Our mathematical analysis provides further basic insight into also previously discussed criticisms against this scheme based on psychophysical and clinical data.