Multifractal Properties of BK Channel Currents in Human Glioblastoma Cells

The Functional Interaction of KATP and BK Channels with Aquaporin-4 in the U87 Glioblastoma Cell

K+ channels do play a role in cell shape changes observed during cell proliferation and apoptosis. Research suggested that the dynamics of the aggregation of Aquaporin-4 (AQP4) into AQP4-OAP isoforms can trigger cell shape changes in malignant glioma cells. Here, we investigated the relationship between AQP4 and some K+ channels in the malignant glioma U87 line. The U87 cells transfected with the human M1-AQP4 and M23-AQP4 isoforms were investigated for morphology, the gene expression of KCNJ8, KCNJ11, ABCC8, ABCC9, KCNMA1, and Cyclin genes by RT-PCR, recording the whole-cell K+ ion currents by patch-clamp experiments. AQP4 aggregation into OAPs increases the plasma membrane functional expression of the Kir6.2 and SUR2 subunits of the KATP channels and of the KCNMA1 of the BK channels in U87 cells leading to a large increase in inward and outward K+ ion currents. These changes were associated with changes in morphology, with a decrease in cell volume in the U87 cells and an increase in the ER density. These U87 cells accumulate in the mitotic and G2 cell cycle. The KATP channel blocker zoledronic acid reduced cell proliferation in both M23 AQP4-OAP and M1 AQP4-tetramer-transfected cells, leading to early and late apoptosis, respectively. The BK channel sustains the efflux of K+ ions associated with the M23 AQP4-OAP expression in the U87 cells, but it is downregulated in the M1 AQP4-tetramer cells. The KATP channels are effective in the M1 AQP4-tetramer and M23 AQP4-OAP cells. Zoledronic acid can be effective in targeting pathogenic M1 AQP4-tetramer cell phenotypes inhibiting KATP channels and inducing early apoptosis.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Ion Channels and Ionotropic Receptors in Astrocytes: Physiological Functions and Alterations in Alzheimer's Disease and Glioblastoma

The human brain is composed of nearly one hundred billion neurons and an equal number of glial cells, including macroglia, i.e., astrocytes and oligodendrocytes, and microglia, the resident immune cells of the brain. In the last few decades, compelling evidence has revealed that glial cells are far more active and complex than previously thought. In particular, astrocytes, the most abundant glial cell population, not only take part in brain development, metabolism, and defense against pathogens and insults, but they also affect sensory, motor, and cognitive functions by constantly modulating synaptic activity. Not surprisingly, astrocytes are actively involved in neurodegenerative diseases (NDs) and other neurological disorders like brain tumors, in which they rapidly become reactive and mediate neuroinflammation. Reactive astrocytes acquire or lose specific functions that differently modulate disease progression and symptoms, including cognitive impairments. Astrocytes express several types of ion channels, including K+, Na+, and Ca2+ channels, transient receptor potential channels (TRP), aquaporins, mechanoreceptors, and anion channels, whose properties and functions are only partially understood, particularly in small processes that contact synapses. In addition, astrocytes express ionotropic receptors for several neurotransmitters. Here, we provide an extensive and up-to-date review of the roles of ion channels and ionotropic receptors in astrocyte physiology and pathology. As examples of two different brain pathologies, we focus on Alzheimer's disease (AD), one of the most diffuse neurodegenerative disorders, and glioblastoma (GBM), the most common brain tumor. Understanding how ion channels and ionotropic receptors in astrocytes participate in NDs and tumors is necessary for developing new therapeutic tools for these increasingly common neurological conditions.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Multifractal Analysis of the Influence of Indole-3-Acetic Acid on Fast-Activating Vacuolar (FV) Channels of Beta vulgaris L. Taproot Cells

In this paper, the multifractal properties of the ion current time series in the fast-activating vacuolar (FV) channels of Beta vulgaris L. taproot cells were investigated. These channels are permeable for only monovalent cations and mediate K+ at very low concentrations of cytosolic Ca2+ and large voltages of either polarity. Using the patch clamp technique, the currents of the FV channels in red beet taproot vacuoles were recorded and analysed by using the multifractal detrended fluctuation analysis (MFDFA) method. The activity of the FV channels depended on the external potential and was sensitive to the auxin. It was also shown that the singularity spectrum of the ion current in the FV channels is non-singular, and the multifractal parameters, i.e., the generalised Hurst exponent and the singularity spectrum, were modified in the presence of IAA. Taking into account the obtained results, it can be suggested that the multifractal properties of fast-activating vacuolar (FV) K+ channels, indicating the existence of long-term memory, should be taken into account in the molecular mechanism of the auxin-induced growth of plant cells.

TRPC6 interacted with KCa1.1 channels to regulate the proliferation and apoptosis of glioma cells

Malignant glioma is the most aggressive and deadliest brain malignancy. TRPC6 and K_Ca1.1, two ion channels, have been considered as potential therapeutic targets for malignant glioma treatment. TRPC6, a Ca²⁺-permeable channel, plays a vital role in promoting tumorigenesis and the progression of glioma. K_Ca1.1, a large-conductance Ca²⁺-activated channel, is also involved in growth and migration of glioma. However, the underlying mechanism by which these two ion channels promote glioma progression was unclear. In our study, we found that TRPC6 upregulated the expression of K_Ca1.1, while the immunoprecipitation analysis also showed that TRPC6 interacts with K_Ca1.1 channels in glioma cells. The currents of K_Ca1.1 recorded by the whole-cell patch clamp technique were increased by TRPC6 in glioma cells, suggesting that TRPC6 can provide a Ca²⁺ source for the activation of K_Ca1.1 channels. It was also suggested that TRPC6 regulates the proliferation and apoptosis of glioma cells through K_Ca1.1 channels in vitro. Therefore, C6-bearing glioma rats were established to validate the results in vitro. After the administration of paxilline (a specific inhibitor of K_Ca1.1 channels), TRPC6-dependent growth of glioma was inhibited in vivo. We also found that TRPC6 enhanced co-expression with K_Ca1.1 in glioma. These all suggested that TRPC6/K_Ca1.1 signal plays a role in promoting the growth of glioma. Our results provided new evidence for TRPC6 and K_Ca1.1 as potential targets for glioma treatment.

Memory in Ion Channel Kinetics

Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

Dynamical diversity of mitochondrial BK channels located in different cell types

Mitochondrial large-conductance voltage- and Ca²⁺-activated potassium channels (mitoBK) exhibit substantial similarities in their physiology regardless of the channel's location. Nevertheless, depending on the cell type, composition of membranes can vary, and mitoBK channels can be expressed in different splice variants as well as they can be co-assembled with different types of auxiliary β subunits. These factors can modulate their voltage- and Ca²⁺-sensitivity, and single-channel current kinetics. It is still an open question to what extent the mentioned factors can affect the complexity of the conformational dynamics of the mitoBK channel gating. In this work the dynamical diversity of mitoBK channels from different cell types was unraveled by the use of nonlinear methods of analysis: multifractal detrended fluctuation analysis (MFDFA) and multiscale entropy (MSE). These techniques were applied to the experimental series of single channel currents. It turns out that the differences in the mitoBK expression systems influence gating machinery by changing the scheme of switching between the stable channel conformations, and affecting the average number of available channel conformations (this effect is visible for mitoBK channels in glioblastoma cells). The obtained results suggest also that a pathological dynamics can be represented by signals of relatively low complexity (low MSE of the mitoBK channel gating in glioblastoma).

Differences in Gating Dynamics of BK Channels in Cellular and Mitochondrial Membranes from Human Glioblastoma Cells Unraveled by Short- and Long-Range Correlations Analysis

The large-conductance voltage- and Ca2+-activated K+ channels (BK) are encoded in humans by the Kcnma1 gene. Nevertheless, BK channel isoforms in different locations can exhibit functional heterogeneity mainly due to the alternative splicing during the Kcnma1 gene transcription. Here, we would like to examine the existence of dynamic diversity of BK channels from the inner mitochondrial and cellular membrane from human glioblastoma (U-87 MG). Not only the standard characteristics of the spontaneous switching between the functional states of the channel is discussed, but we put a special emphasis on the presence and strength of correlations within the signal describing the single-channel activity. The considered short- and long-range memory effects are here analyzed as they can be interpreted in terms of the complexity of the switching mechanism between stable conformational states of the channel. We calculate the dependencies of mean dwell-times of (conducting/non-conducting) states on the duration of the previous state, Hurst exponents by the rescaled range R/S method and detrended fluctuation analysis (DFA), and use the multifractal extension of the DFA (MFDFA) for the series describing single-channel activity. The obtained results unraveled statistically significant diversity in gating machinery between the mitochondrial and cellular BK channels.

Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.