Chaotic Dynamics Mediate Brain State Transitions, Driven by Changes in Extracellular Ion Concentrations

Dysregulation of extracellular potassium distinguishes healthy ageing from neurodegeneration

Progressive neuronal loss is a hallmark feature distinguishing neurodegenerative diseases from normal ageing. However, the underlying mechanisms remain unknown. Extracellular K+ homeostasis is a potential mediator of neuronal injury as K+ elevations increase excitatory activity. The dysregulation of extracellular K+ and potassium channel expressions during neurodegeneration could contribute to this distinction. Here we measured the cortical extracellular K+ concentration ([K+]e) in awake wild-type mice as well as murine models of neurodegeneration using K+-sensitive microelectrodes. Unexpectedly, aged wild-type mice exhibited significantly lower cortical [K+]e than young mice. In contrast, cortical [K+]e was consistently elevated in Alzheimer's disease (APP/PS1), amyotrophic lateral sclerosis (ALS) (SOD1G93A) and Huntington's disease (R6/2) models. Cortical resting [K+]e correlated inversely with neuronal density and the [K+]e buffering rate but correlated positively with the predicted neuronal firing rate. Screening of astrocyte-selective genomic datasets revealed a number of potassium channel genes that were downregulated in these disease models but not in normal ageing. In particular, the inwardly rectifying potassium channel Kcnj10 was downregulated in ALS and Huntington's disease models but not in normal ageing, while Fxyd1 and Slc1a3, each of which acts as a negative regulator of potassium uptake, were each upregulated by astrocytes in both Alzheimer's disease and ALS models. Chronic elevation of [K+]e in response to changes in gene expression and the attendant neuronal hyperexcitability may drive the neuronal loss characteristic of these neurodegenerative diseases. These observations suggest that the dysregulation of extracellular K+ homeostasis in a number of neurodegenerative diseases could be due to aberrant astrocytic K+ buffering and as such, highlight a fundamental role for glial dysfunction in neurodegeneration.

Fluorophore Label-Free Light-up Near Infrared Deoxyribonucleic Acid Nanosensor for Monitoring Extracellular Potassium Levels

Fluorescent DNA nanosensors have been widely used due to their unique advantages, among which the near-infrared (NIR) imaging mode can provide deeper penetration depth and lower biological background for the nanosensors. However, efficient NIR quenchers require ingenious design, complex synthesis, and modification, which severely limit the development of NIR DNA nanosensors. Label-free strategies based on G-quadruplex (G4) and NIR G4 dyes were first introduced into in situ extracellular imaging, and a novel NIR sensing strategy for the specific detection of extracellular targets is proposed. The strategy avoids complex synthesis and site-specific modification by controlling the change of the NIR signal through the formation of a G4 nanostructure. A light-up NIR DNA nanosensor based on potassium ion (K+)-sensitive G4 chain PS2.M was constructed to verify the strategy. PS2.M forms a stable G4 nanostructure in the presence of K+ and activates the NIR G4 dye CSTS, thus outputting NIR signals. The nanosensor can rapidly respond to K+ with a linear range of 5-50 mM and has good resistance to interference. The nanosensor with cholesterol can provide feedback on the changes in extracellular K+ concentration in many kinds of cells, serving as a potential tool for the study of diseases such as epilepsy and cancer, as well as the development of related drugs. The strategy can be potentially applied to the NIR detection of a variety of extracellular targets with the help of functional DNAs such as aptamer and DNAzyme.

Astrocytic chloride is brain state dependent and modulates inhibitory neurotransmission in mice

Information transfer within neuronal circuits depends on the balance and recurrent activity of excitatory and inhibitory neurotransmission. Chloride (Cl-) is the major central nervous system (CNS) anion mediating inhibitory neurotransmission. Astrocytes are key homoeostatic glial cells populating the CNS, although the role of these cells in regulating excitatory-inhibitory balance remains unexplored. Here we show that astrocytes act as a dynamic Cl- reservoir regulating Cl- homoeostasis in the CNS. We found that intracellular chloride concentration ([Cl-]i) in astrocytes is high and stable during sleep. In awake mice astrocytic [Cl-]i is lower and exhibits large fluctuation in response to both sensory input and motor activity. Optogenetic manipulation of astrocytic [Cl-]i directly modulates neuronal activity during locomotion or whisker stimulation. Astrocytes thus serve as a dynamic source of extracellular Cl- available for GABAergic transmission in awake mice, which represents a mechanism for modulation of the inhibitory tone during sustained neuronal activity.

The role of calcium and CaMKII in sleep

Sleep is an evolutionarily conserved phenotype shared by most of the animals on the planet. Prolonged wakefulness will result in increased sleep need or sleep pressure. However, its mechanisms remain elusive. Recent findings indicate that Ca²⁺ signaling, known to control diverse physiological functions, also regulates sleep. This review intends to summarize research advances in Ca²⁺ and Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) in sleep regulation. Significant changes in sleep phenotype have been observed through calcium-related channels, receptors, and pumps. Mathematical modeling for neuronal firing patterns during NREM sleep suggests that these molecules compose a Ca²⁺-dependent hyperpolarization mechanism. The intracellular Ca²⁺ may then trigger sleep induction and maintenance through the activation of CaMKII, one of the sleep-promoting kinases. CaMKII and its multisite phosphorylation status may provide a link between transient calcium dynamics typically observed in neurons and sleep-wake dynamics observed on the long-time scale.

Biophysical Modeling of Dopaminergic Denervation Landscapes in the Striatum Reveals New Therapeutic Strategy

Parkinson’s disease (PD) results from a loss of dopaminergic neurons. What triggers the break-down of neuronal signaling, and how this might be compensated, is not understood. The age of onset, progression and symptoms vary between patients, and our understanding of the clinical variability remains incomplete. In this study, we investigate this, by characterizing the dopaminergic landscape in healthy and denervated striatum, using biophysical modeling. Based on currently proposed mechanisms, we model three distinct denervation patterns, and show how this affect the dopaminergic network. Depending on the denervation pattern, we show how local and global differences arise in the activity of striatal neurons. Finally, we use the mathematical formalism to suggest a cellular strategy for maintaining normal dopamine (DA) signaling following neuronal denervation. This strategy is characterized by dual enhancement of both the release and uptake capacity of DA in the remaining neurons. Overall, our results derive a new conceptual framework for the impaired dopaminergic signaling related to PD and offers testable predictions for future research directions.

A design principle of spindle oscillations in mammalian sleep

Neural oscillations are mainly regulated by molecular mechanisms and network connectivity of neurons. Large-scale simulations of neuronal networks have driven the population-level understanding of neural oscillations. However, cell-intrinsic mechanisms, especially a design principle, of neural oscillations remain largely elusive. Herein, we developed a minimal, Hodgkin-Huxley-type model of groups of neurons to investigate molecular mechanisms underlying spindle oscillation, which is synchronized oscillatory activity predominantly observed during mammalian sleep. We discovered that slowly inactivating potassium channels played an essential role in characterizing the firing pattern. The detailed analysis of the minimal model revealed that leak sodium and potassium channels, which controlled passive properties of the fast variable (i.e., membrane potential), competitively regulated the base value and time constant of the slow variable (i.e., cytosolic calcium concentration). Consequently, we propose a theoretical design principle of spindle oscillations that may explain intracellular mechanisms behind the flexible control over oscillation density and calcium setpoint.

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A minimal, Hodgkin-Huxley-type model of spindle oscillations is developed

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The property of delayed rectifier K⁺ channels characterizes spindle oscillations

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The combination of bifurcations specifies spindle oscillations

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Spindle oscillations are controlled by the balance of inward and outward currents

Ion concentrations in cerebrospinal fluid in wakefulness, sleep and sleep deprivation in healthy humans

Sleep is controlled by a circadian rhythmicity, via a reduction of arousal-promoting neuromodulatory activity, and by accumulation of somnogenic factors in the interstitial fluid of the brain. Recent experiments in mice suggest that a reduced neuronal excitability caused by a reduced concentration of potassium in the brain, concomitant with an increased concentration of calcium and magnesium, constitutes an important mediator of sleep. In the present study, we examined whether such changes in ion concentrations could be detected in the cerebrospinal fluid of healthy humans. Each subject underwent cerebrospinal fluid collection at three occasions in a randomized order: at 15:00 hours-17:00 hours during waking, at 06:00 hours-07:00 hours immediately following 1 night of sleep, and at 06:00 hours-07:00 hours following 1 night of sleep deprivation. When compared with wakefulness, both sleep and sleep deprivation produced the same effect of a small (0.1 mm, about 3%), but robust and highly significant, reduction in potassium concentration. Calcium and magnesium concentrations were unchanged. Our results support a circadian modulation of neuronal excitability in the brain mediated via changes of the interstitial potassium concentration.

Epileptiform activity in mouse hippocampal slices induced by moderate changes in extracellular Mg2+, Ca2+, and K. BMC Neurosci 2021;22:46. [PMID: 34301200 PMCID: PMC8305515 DOI: 10.1186/s12868-021-00650-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

BACKGROUND

Rodent brain slices-particularly hippocampal slices-are widely used in experimental investigations of epileptiform activity. Oxygenated artificial cerebrospinal fluid (ACSF) is used to maintain slices in vitro. Physiological or standard ACSF containing 3-3.5 mM K⁺, 1-2 mM Mg²⁺, and 1-3 mM Ca²⁺ generally does not induce population epileptiform activity, which can be induced by ACSF with high K⁺ (8-10 mM), low Mg²⁺, or low Ca²⁺ alone or in combination. While low-Mg²⁺ ACSF without intentionally added Mg salt but with contaminating Mg²⁺ (≤ 50-80 µM) from other salts can induce robust epileptiform activity in slices, it is unclear whether such epileptiform activity can be achieved using ACSF with moderately decreased Mg²⁺. To explore this issue, we examined the effects of moderately modified (m)ACSF with 0.8 mM Mg²⁺, 1.3 mM Ca²⁺, and 5.7 mM K⁺ on induction of epileptiform discharges in mouse hippocampal slices.

RESULTS

Hippocampal slices were prepared from young (21-28 days old), middle-aged (13-14 months old), and aged (24-26 months old) C57/BL6 mice. Conventional thin (0.4 mm) and thick (0.6 mm) slices were obtained using a vibratome and pretreated with mACSF at 35-36 °C for 1 h prior to recordings. During perfusion with mACSF at 35-36 °C, spontaneous or self-sustained epileptiform field potentials following high-frequency stimulation were frequently recorded in slices pretreated with mACSF but not in those without the pretreatment. Seizure-like ictal discharges were more common in thick slices than in thin slices.

CONCLUSIONS

Prolonged exposure to mACSF by pretreatment and subsequent perfusion can induce epileptiform field potentials in mouse hippocampal slices.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

A design principle for posttranslational chaotic oscillators

Chaos behavior has been observed in various cellular and molecular processes. Here, we modeled reversible phosphorylation dynamics to elucidate a design principle for autonomous chaos generation that may arise from generic enzymatic reactions. A comprehensive parameter search demonstrated that the reaction system composed of a set of kinases and phosphatases and two substrates with two modification sites exhibits chaos behavior. All reactions are described according to the Michaelis-Menten reaction scheme without exotic functions being applied to enzymes and substrates. Clustering analysis of parameter sets that can generate chaos behavior revealed the existence of motif structures. These chaos motifs allow the two-substrate species to interact via enzyme availability and constrain the two substrates' dynamic changes in phosphorylation status so that they occur at different timescales. This chaos motif structure is found in several enzymatic reactions, suggesting that chaos behavior may underlie cellular autonomy in a variety of biochemical systems.

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Two substrates with reversible two-site phosphorylation can exhibit chaos behavior

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The chaos does not require autocatalysis or allosteric regulation of enzymes

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The chaos is a result of the coupling of two substrates via enzyme availability

Interstitial ions: A key regulator of state-dependent neural activity?

Throughout the nervous system, ion gradients drive fundamental processes. Yet, the roles of interstitial ions in brain functioning is largely forgotten. Emerging literature is now revitalizing this area of neuroscience by showing that interstitial cations (K+, Ca2+ and Mg2+) are not static quantities but change dynamically across states such as sleep and locomotion. In turn, these state-dependent changes are capable of sculpting neuronal activity; for example, changing the local interstitial ion composition in the cortex is sufficient for modulating the prevalence of slow-frequency neuronal oscillations, or potentiating the gain of visually evoked responses. Disturbances in interstitial ionic homeostasis may also play a central role in the pathogenesis of central nervous system diseases. For example, impairments in K+ buffering occur in a number of neurodegenerative diseases, and abnormalities in neuronal activity in disease models disappear when interstitial K+ is normalized. Here we provide an overview of the roles of interstitial ions in physiology and pathology. We propose the brain uses interstitial ion signaling as a global mechanism to coordinate its complex activity patterns, and ion homeostasis failure contributes to central nervous system diseases affecting cognitive functions and behavior.

Astrocytes-The Ultimate Effectors of Long-Range Neuromodulatory Networks?

It was long thought that astrocytes, given their lack of electrical signaling, were not involved in communication with neurons. However, we now know that one astrocyte on average maintains and regulates the extracellular neurotransmitter and potassium levels of more than 140,000 synapses, both excitatory and inhibitory, within their individual domains, and form a syncytium that can propagate calcium waves to affect distant cells via release of “gliotransmitters” such as glutamate, ATP, or adenosine. Neuromodulators can affect signal-to-noise and frequency transmission within cortical circuits by effects on inhibition, allowing for the filtering of relevant vs. irrelevant stimuli. Moreover, synchronized “resting” and desynchronized “activated” brain states are gated by short bursts of high-frequency neuromodulatory activity, highlighting the need for neuromodulation that is robust, rapid, and far-reaching. As many neuromodulators are released in a volume manner where degradation/uptake and the confines of the complex CNS limit diffusion distance, we ask the question—are astrocytes responsible for rapidly extending neuromodulator actions to every synapse? Neuromodulators are known to influence transitions between brain states, leading to control over plasticity, responses to salient stimuli, wakefulness, and sleep. These rapid and wide-spread state transitions demand that neuromodulators can simultaneously influence large and diverse regions in a manner that should be impossible given the limitations of simple diffusion. Intriguingly, astrocytes are ideally situated to amplify/extend neuromodulator effects over large populations of synapses given that each astrocyte can: (1) ensheath a large number of synapses; (2) release gliotransmitters (glutamate/ATP/adenosine) known to affect inhibition; (3) regulate extracellular potassium that can affect excitability and excitation/inhibition balance; and (4) express receptors for all neuromodulators. In this review article, we explore the hypothesis that astrocytes extend and amplify neuromodulatory influences on neuronal networks via alterations in calcium dynamics, the release of gliotransmitters, and potassium homeostasis. Given that neuromodulatory networks are at the core of our sleep-wake cycle and behavioral states, and determine how we interact with our environment, this review article highlights the importance of basic astrocyte function in homeostasis, general cognition, and psychiatric disorders.

Effect of potassium channel noise on nerve discharge based on the Chay model

BACKGROUND:

The nervous system senses and transmits information through the firing behavior of neurons, and this process is affected by various noises. However, in the previous study of the influence of noise on nerve discharge, the channel of some noise effects is not clear, and the difference from other noises was not examined.

OBJECTIVE:

To construct ion channel noise which is more biologically significant, and to clarify the basic characteristics of the random firing rhythm of neurons generated by different types of noise acting on ion channels.

Method:

Based on the dynamics of the ion channel, we constructed ion channel noise. We simulated the nerve discharge based on the Chay model of potassium ion channel noise, and used the nonlinear time series analysis method to measure the certainty and randomness of nerve discharge.

RESULTS:

In the Chay model with potassium ion noise, the chaotic rhythm defined by the original model could be effectively unified with the random rhythm simulated by the previous random Chay model into a periodic bifurcation process.

CONCLUSION:

This method clarified the influence of ion channel noise on nerve discharge, better understood the randomness of nerve discharge and provided a more reasonable explanation for the mechanism of nerve discharge.

Cortex-wide Changes in Extracellular Potassium Ions Parallel Brain State Transitions in Awake Behaving Mice

Brain state fluctuations modulate sensory processing, but the factors governing state-dependent neural activity remain unclear. Here, we tracked the dynamics of cortical extracellular K+ concentrations ([K+]o) during awake state transitions and manipulated [K+]o in slices, during visual processing, and during skilled motor execution. When mice transitioned from quiescence to locomotion, [K+]o increased by 0.6-1.0 mM in all cortical areas analyzed, and this preceded locomotion by 1 s. Emulating the state-dependent [K+]o increase in cortical slices caused neuronal depolarization and enhanced input-output transformation. In vivo, locomotion increased the gain of visually evoked responses in layer 2/3 of visual cortex; this effect was recreated by imposing a [K+]o increase. Elevating [K+]o in the motor cortex increased movement-induced neuronal spiking in layer 5 and improved motor performance. Thus, [K+]o increases in a cortex-wide state-dependent manner, and this [K+]o increase affects both sensory and motor processing through the dynamic modulation of neural activity.

Neuromodulatory Influences on Integration and Segregation in the Brain

Cognitive function relies on the dynamic cooperation of specialized regions of the brain; however, the elements of the system responsible for coordinating this interaction remain poorly understood. In this Opinion article I argue that this capacity is mediated in part by competitive and cooperative dynamic interactions between two prominent metabotropic neuromodulatory systems - the cholinergic basal forebrain and the noradrenergic locus coeruleus (LC). I assert that activity in these projection nuclei regulates the amount of segregation and integration within the whole brain network by modulating the activity of a diverse set of specialized regions of the brain on a timescale relevant for cognition and attention.

Introducing chaotic codes for the modulation of code modulated visual evoked potentials (c-VEP) in normal adults for visual fatigue reduction

Code modulated Visual Evoked Potentials (c-VEP) based BCI studies usually employ m-sequences as a modulating codes for their broadband spectrum and correlation property. However, subjective fatigue of the presented codes has been a problem. In this study, we introduce chaotic codes containing broadband spectrum and similar correlation property. We examined whether the introduced chaotic codes could be decoded from EEG signals and also compared the subjective fatigue level with m-sequence codes in normal subjects. We generated chaotic code from one-dimensional logistic map and used it with conventional 31-bit m-sequence code. In a c-VEP based study in normal subjects (n = 44, 21 females) we presented these codes visually and recorded EEG signals from the corresponding codes for their four lagged versions. Canonical correlation analysis (CCA) and spatiotemporal beamforming (STB) methods were used for target identification and comparison of responses. Additionally, we compared the subjective self-declared fatigue using VAS caused by presented m-sequence and chaotic codes. The introduced chaotic code was decoded from EEG responses with CCA and STB methods. The maximum total accuracy values of 93.6 ± 11.9% and 94 ± 14.4% were achieved with STB method for chaotic and m-sequence codes for all subjects respectively. The achieved accuracies in all subjects were not significantly different in m-sequence and chaotic codes. There was significant reduction in subjective fatigue caused by chaotic codes compared to the m-sequence codes. Both m-sequence and chaotic codes were similar in their accuracies as evaluated by CCA and STB methods. The chaotic codes significantly reduced subjective fatigue compared to the m-sequence codes.

Leak potassium channels regulate sleep duration

A primary goal of sleep research is to understand the molecular basis of sleep. Although some sleep/wake-promoting circuits and secreted substances have been identified, the detailed molecular mechanisms underlying the regulation of sleep duration have been elusive. Here, to address these mechanisms, we developed a simple computational model of a cortical neuron with five channels and a pump, which recapitulates the cortical electrophysiological characteristics of slow-wave sleep (SWS) and wakefulness. Comprehensive bifurcation and detailed mathematical analyses predicted that leak K⁺ channels play a role in generating the electrophysiological characteristics of SWS, leading to a hypothesis that leak K⁺ channels play a role in the regulation of sleep duration. To test this hypothesis experimentally, we comprehensively generated and analyzed 14 KO mice, and found that impairment of the leak K⁺ channel (Kcnk9) decreased sleep duration. Based on these results, we hypothesize that leak K⁺ channels regulate sleep duration in mammals.