Brownian Aging as One of the Mechanistic Components That Shape the Single-Channel Ionic Currents through Biological and Synthetic Membranes

Semipermeable membranes enable the separation of a given system from its environment. In biological terms, they are responsible for cells' identity. In turn, the functioning of ion channels is crucial for the control of ionic fluxes across the membranes and, consequently, for the exchange of chemical and electrical signals. This paper presents a model and simulations of currents through ionic nanochannels in an attempt to better understand the physical mechanism(s) of open/closed (O/C) sequences, i.e., random interruptions of ionic flows through channels observed in all known biochannels and in some synthetic nanopores. We investigate whether aging, i.e., the changes in Brownian motion characteristics with the lapse of time, may be at least one of the sources of the O/C sequences (in addition to the gating machinery in biochannels). The simulations based on the approximated nanostructure of ion channels confirm this postulation. The results also show the possibility of changing the O/C characteristics through an appropriate alteration of the channel surroundings. This observation may be valuable in technical uses of nanochannels in synthetic membranes and allow for a better understanding of the reason for the differences between the biochannels' activity in diverse biological membranes. Proposals of experimental verification of this aging O/C hypothesis are also presented.

The cross-correlation-based analysis to digest the conformational dynamics of the mitoBK channels in terms of their modulation by flavonoids

The activity of mitochondrial large-conductance voltage- and [Formula: see text]-activated [Formula: see text] channels (mitoBK) is regulated by a number of biochemical factors, including flavonoids. In particular, naringenin (Nar) and quercetin (Que) reached reasonable scientific attention due to their well-pronounced channel-activating effects. The open-reinforcing outcomes of Nar and Que on the mitoBK channel gating have been already reported. Nevertheless, the molecular picture of the corresponding channel-ligand interactions remains still to be revealed. In this work, we investigate the effects of the Nar and Que on the conformational dynamics of the mitoBK channel. In this aim, the cross-correlation-based analysis of the single-channel signals recorded by the patch-clamp method is performed. The obtained results in the form of phase space diagrams enable us to visually monitor the effects exerted by the considered flavonoids at the level of temporal characteristics of repetitive sequences of channel conformations. It turns out that the mitoBK channel activation by naringenin and quercetin does not lead to the change in the number of clusters within the phase space diagrams, which can be related to the constant number of available channel macroconformations regardless of the flavonoid administration. The localization and occupancy of the clusters of cross-correlated sequences suggest that mitoBK channel stimulation by flavonoids affects the relative stability of channel conformations and the kinetics of switching between them. For most clusters, greater net effects are observed in terms of quercetin administration in comparison with naringenin. It indicates stronger channel interaction with Que than Nar.

Potassium Channels, Glucose Metabolism and Glycosylation in Cancer Cells

Potassium channels emerge as one of the crucial groups of proteins that shape the biology of cancer cells. Their involvement in processes like cell growth, migration, or electric signaling, seems obvious. However, the relationship between the function of K+ channels, glucose metabolism, and cancer glycome appears much more intriguing. Among the typical hallmarks of cancer, one can mention the switch to aerobic glycolysis as the most favorable mechanism for glucose metabolism and glycome alterations. This review outlines the interconnections between the expression and activity of potassium channels, carbohydrate metabolism, and altered glycosylation in cancer cells, which have not been broadly discussed in the literature hitherto. Moreover, we propose the potential mediators for the described relations (e.g., enzymes, microRNAs) and the novel promising directions (e.g., glycans-orinented drugs) for further research.

Non-Monotonic Complexity of Stochastic Model of the Channel Gating Dynamics

The simple model of an ionic current flowing through a single channel in a biological membrane is used to depict the complexity of the corresponding empirical data underlying different internal constraints and thermal fluctuations. The residence times of the channel in the open and closed states are drawn from the exponential distributions to mimic the characteristics of the real channel system. In the selected state, the dynamics are modeled by the overdamped Brownian particle moving in the quadratic potential. The simulated data allow us to directly track the effects of temperature (signal-to-noise ratio) and the channel's energetic landscape for conformational changes on the ionic currents' complexity, which are hardly controllable in the experimental case. To accurately describe the randomness, we employed four quantifiers, i.e., Shannon, spectral, sample, and slope entropies. We have found that the Shannon entropy predicts the anticipated reaction to the imposed modification of randomness by raising the temperature (an increase of entropy) or strengthening the localization (reduction of entropy). Other complexity quantifiers behave unpredictably, sometimes resulting in non-monotonic behaviour. Thus, their applicability in the analysis of the experimental time series of single-channel currents can be limited.

Flavonoids as Modulators of Potassium Channels

Potassium channels are widely distributed integral proteins responsible for the effective and selective transport of K+ ions through the biological membranes. According to the existing structural and mechanistic differences, they are divided into several groups. All of them are considered important molecular drug targets due to their physiological roles, including the regulation of membrane potential or cell signaling. One of the recent trends in molecular pharmacology is the evaluation of the therapeutic potential of natural compounds and their derivatives, which can exhibit high specificity and effectiveness. Among the pharmaceuticals of plant origin, which are potassium channel modulators, flavonoids appear as a powerful group of biologically active substances. It is caused by their well-documented anti-oxidative, anti-inflammatory, anti-mutagenic, anti-carcinogenic, and antidiabetic effects on human health. Here, we focus on presenting the current state of knowledge about the possibilities of modulation of particular types of potassium channels by different flavonoids. Additionally, the biological meaning of the flavonoid-mediated changes in the activity of K+ channels will be outlined. Finally, novel promising directions for further research in this area will be proposed.

A New Method of Identifying Characteristic Points in the Impedance Cardiography Signal Based on Empirical Mode Decomposition

The accurate detection of fiducial points in the impedance cardiography signal (ICG) has a decisive impact on the proper estimation of diagnostic parameters such as stroke volume or cardiac output. It is, therefore, necessary to find an algorithm that is able to assess their positions with great precision. The solution to this problem is, however, quite challenging with regard to the high sensitivity of the ICG technique to the noise and varying morphology of the acquired signals. The aim of this study is to propose a novel method that allows us to overcome these limitations. The developed algorithm is based on Empirical Mode Decomposition (EMD)-an effective technique for processing and analyzing various types of non-stationary signals. We find high correlations between the results obtained from the algorithm and annotated by an expert. This, in turn, implies that the difference in estimation of the diagnostic-relevant parameters is small, which suggests that the method can automatically provide precise clinical information.

New Diagnostic Tool for Ion Channel Activity Hidden Behind the Dwell-Time Correlations

The patch-clamp technique is a powerful tool that allows for a long observation of transport protein activity in real time. Experimental traces of single-channel currents can be considered as a record of the channel's conformational switching related to its activation and gating. In this work, we present a mathematically simple method of patch-clamp data analysis that assesses the connectivity and occupancy of distinct conformational substates of the channel. The proposed approach appears to be a big step forward due to its possible applications in the determination of channel substates related to disease and in the analysis of drug-channel interactions on the level of repetitive sequences of channel conformations. This is especially important in cases when molecular dynamics docking is impossible and Markovian modeling requires ambiguous optimization tasks.

Recent Update on the Molecular Mechanisms of Gonadal Steroids Action in Adipose Tissue

The gonadal steroids, including androgens, estrogens and progestogens, are involved in the control of body fat distribution in humans. Nevertheless, not only the size and localization of the fat depots depend on the sex steroids levels, but they can also highly affect the functioning of adipose tissue. Namely, the gonadocorticoids can directly influence insulin signaling, lipid metabolism, fatty acid uptake and adipokine production. They may also alter energy balance and glucose homeostasis in adipocytes in an indirect way, e.g., by changing the expression level of aquaglyceroporins. This work presents the recent advances in understanding the molecular mechanism of how the gonadal steroids influence the functioning of adipose tissue leading to a set of detrimental metabolic consequences. Special attention is given here to highlighting the sexual dimorphism of adipocyte functioning in terms of health and disease. Particularly, we discuss the molecular background of metabolic disturbances occurring in consequence of hormonal imbalance which is characteristic of some common endocrinopathies such as the polycystic ovary syndrome. From this perspective, we highlight the potential drug targets and the active substances which can be used in personalized sex-specific management of metabolic diseases, in accord with the patient's hormonal status.

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.

In Search of New Therapeutics-Molecular Aspects of the PCOS Pathophysiology: Genetics, Hormones, Metabolism and Beyond

In a healthy female reproductive system, a subtle hormonal and metabolic dance leads to repetitive cyclic changes in the ovaries and uterus, which make an effective ovulation and potential implantation of an embryo possible. However, that is not so in the case of polycystic ovary syndrome (PCOS), in which case the central mechanism responsible for entraining hormonal and metabolic rhythms during the menstrual cycle is notably disrupted. In this review we provide a detailed description of the possible scenario of PCOS pathogenesis. We begin from the analysis of how a set of genetic disorders related to PCOS leads to particular malfunctions at a molecular level (e.g., increased enzyme activities of cytochrome P450 (CYP) type 17A1 (17α-hydroxylase), 3β-HSD type II and CYP type 11A1 (side-chain cleavage enzyme) in theca cells, or changes in the expression of aquaporins in granulosa cells) and discuss further cellular- and tissue-level consequences (e.g., anovulation, elevated levels of the advanced glycation end products in ovaries), which in turn lead to the observed subsequent systemic symptoms. Since gene-editing therapy is currently out of reach, herein special emphasis is placed on discussing what kinds of drug targets and which potentially active substances seem promising for an effective medication, acting on the primary causes of PCOS on a molecular level.

Multifractal Properties of BK Channel Currents in Human Glioblastoma Cells

Potassium channels play an important physiological role in glioma cells. In particular, voltage- and Ca2+-activated large-conductance BK channels (gBK in gliomas) are involved in the intensive growth and extensive migrating behavior of the mentioned tumor cells; thus, they may be considered as a drug target for the therapeutic treatment of glioblastoma. To enable appropriate drug design, molecular mechanisms of gBK channel activation by diverse stimuli should be unraveled as well as the way that the specific conformational states of the channel relate to its functional properties (conducting/nonconducting). There is an open debate about the actual mechanism of BK channel gating, including the question of how the channel proteins undergo a range of conformational transitions when they flicker between nonconducting (functionally closed) and conducting (open) states. The details of channel conformational diffusion ought to have its representation in the properties of the experimental signal that describes the ion-channel activity. Nonlinear methods of analysis of experimental nonstationary series can be useful for observing the changes in the number of channel substates available from geometrical and energetic points of view at given external conditions. In this work, we analyze whether the multifractal properties of the activity of glioblastoma BK channels depend on membrane potential, and which states, conducting or nonconducting, affect the total signal to a larger extent. With this aim, we carried out patch-clamp experiments at different levels of membrane hyper- and depolarization. The obtained time series of single channel currents were analyzed using the multifractal detrended fluctuation analysis (MFDFA) method in a standard form and incorporating focus-based multifractal (FMF) formalism. Thus, we show the applicability of a modified MFDFA technique in the analysis of an experimental patch-clamp time series. The obtained results suggest that membrane potential strongly affects the conformational space of the gBK channel proteins and the considered process has nonlinear multifractal characteristics. These properties are the inherent features of the analyzed signals due to the fact that the main tendencies vanish after shuffling the data.

Mechanosensitivity of the BK Channels in Human Glioblastoma Cells: Kinetics and Dynamical Complexity

BK channels are potassium selective and exhibit large single-channel conductance. They play an important physiological role in glioma cells: they are involved in cell growth and extensive migrating behavior. Due to the fact that these processes are accompanied by changes in membrane stress, here, we examine mechanosensitive properties of BK channels from human glioblastoma cells (gBK channels). Experiments were performed by the use of patch-clamp method on excised patches under membrane suction (0-40 mmHg) at membrane hyper- and depolarization. We have also checked whether channel's activity is affected by possible changes of membrane morphology after a series of long impulses of suction. Unconventionally, we also analyzed internal structure of the experimental signal to make inferences about conformational dynamics of the channel in stressed membranes. We examined the fractal long-range memory effect (by R/S Hurst analysis), the rate of changes in information by sample entropy, or correlation dimension, and characterize its complexity over a range of scales by the use of Multiscale Entropy method. The obtained results indicate that gBK channels are mechanosensitive at membrane depolarization and hyperpolarization. Prolonged suction of membrane also influences open-closed fluctuations-it decreases channel's activity at membrane hyperpolarization and, in contrary, increases channel's activity at high voltages. Both membrane strain and its "fatigue" reduce dynamical complexity of channel gating, which suggest decrease in the number of available open conformations of channel protein in stressed membranes.

The role of entropic potential in voltage activation and K+ transport through Kv 1.2 channels

We analyze the entropic effects of inner pore geometry changes of Kv 1.2 channel during membrane depolarization and their implications for the rate of transmembrane transport of potassium ions. We base this on the idea that spatial confinements within the channel pore give rise to entropic barriers which can both effectively affect the stability of open macroconformation and influence channel's ability to conduct the potassium ions through the membrane. First, we calculate the differences in entropy between voltage-activated and resting states of the channel. As a template, we take a set of structures of channel pore in an open state at different membrane potentials generated in our previous research. The obtained results indicate that tendency to occupy open states at membrane depolarization is entropy facilitated. Second, we describe the differences in rates of K⁺ transport through the channel pore at different voltages based on the results of appropriate random walk simulations in entropic and electric potentials. The simulated single channel currents (I) suggest that the geometry changes during membrane depolarization are an important factor contributing to the observed flow of potassium ions through the channel. Nevertheless, the charge distribution within the channel pore (especially at the extracellular entrance) seems most prominent for the observed I/I_max relation at a qualitative level at analyzed voltages.

The role of aquaporins in polycystic ovary syndrome - A way towards a novel drug target in PCOS

Aquaporins (AQPs) are transmembrane proteins, able to transport water (and in some cases also small solutes, e. g. glycerol) through the cell membrane. There are twelve types of aquaporins (AQP1-AQP12) expressed in mammalian reproductive systems. According to literature, many diseases of the reproductive organs are correlated with changes of AQPs expression and their malfunction. That is the case in the polycystic ovary syndrome (PCOS), where dysfunctions of AQPs 7-9 and alterations in its levels occur. In this work, we postulate how AQPs are involved in PCOS-related disorders, in order to emphasize their potential therapeutic meaning as a drug target. Our research allows for a surprising inference, that genetic mutation causing malfunction and/or decreased expression of aquaporins, may be incorporated in the popular insulin-dependent hypothesis of PCOS pathogenesis. What is more, changes in AQP's expression may affect the folliculogenesis and follicular atresia in PCOS.

Impact of geometry changes in the channel pore by the gating movements on the channel's conductance

Kv 1.2 are voltage-dependent potassium channels of great biological importance. Despite the existence of many reports considering structure - function relations of the Kv 1.2 channel's quantitative domains, some details of the voltage gating remain ambiguous, or even unknown. One of the examples is the range of the S4-S6 domains motions involved in channel activation and gating. Another important question is to what extent the channel geometry influences the observable channel conductance at different voltages, and what mechanism stands behind. Does the narrowing of the pore reduce the conductance by ohmic resistance growth? The answer is surprisingly negative. But it can be explained in an alternative way by considering the fluctuations. To address these problems, we formulate geometric models that mimic the generic features of voltage sensor movement and trigger the movement of the other domains involved in gating. We carry out a complete simulation of S4-S6 domains translations and tilts. The obtained pore profiles allow to estimate the (ohmic) conductance dependency on the voltage. From a family of analysed models, we choose the one most concurring with the experimental data. The results allow to suggest the most probable scenario of S4-S6 domains movement during channel activation by membrane depolarization.

On Application Of Langevin Dynamics In Logarithmic Potential To Model Ion Channel Gate Activity

We model the activity of an ion channel gate by Langevin dynamics in a logarithmic potential. This approach enables one to describe the power-law dwell-time distributions of the considered system, and the long-term correlations between the durations of the subsequent channel states, or fractal scaling of statistical characteristics of the gate's movement with time. Activity of an ion channel gate is described as an overdamped motion of the reaction coordinate in a confining logarithmic potential, which ensures great flexibility of the model. Depending on the chosen parameters, it allows one to reproduce many types of gate dynamics within the family of non-Markovian, anomalous conformational diffusion processes. In this study we apply the constructed model to largeconductance voltage and Ca2+-activated potassium channels (BKCa). The interpretation of model assumptions and parameters is provided in terms of this biological system. Our results show good agreement with the experimental data.