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

Long-term memory in Staphylococcus aureus α-hemolysin ion channel kinetics

The kinetics of an ion channel are classically understood as a random process. However, studies have shown that in complex ion channels, formed by multiple subunits, this process can be deterministic, presenting long-term memory. Staphylococcus aureus α-hemolysin (α-HL) is a toxin that acts as the major factor in Staphylococcus aureus virulence. α-HL is a water-soluble protein capable of forming ion channels into lipid bilayers, by insertion of an amphipathic  β-barrel. Here, the α-HL was used as an experimental model to study memory in ion channel kinetics. We applied the approximate entropy (ApEn) approach to analyze randomness and the Detrended Fluctuation Analysis (DFA) to investigate the existence of long memory in α-HL channel kinetics. Single-channel currents were measured through experiments with α-HL channels incorporated in planar lipid bilayers. All experiments were carried out under the following conditions: 1 M NaCl solution, pH 4.5; transmembrane potential of + 40 mV and temperature 25 ± 1 °C. Single-channel currents were recorded in real-time in the memory of a microcomputer coupled to an A/D converter and a patch-clamp amplifier. The conductance value of the α-HL channels was 0.82 ± 0.0025 nS (n = 128). The DFA analysis showed that the kinetics of α-HL channels presents long-term memory ([Formula: see text] = 0.63 ± 0.04). The ApEn outcomes showed low complexity to dwell times when open (ApEno = 0.5514 ± 0.28) and closed (ApEnc = 0.1145 ± 0.08), corroborating the results of the DFA method.

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.

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.

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.

BK in Double-Membrane Organelles: A Biophysical, Pharmacological, and Functional Survey

In the 1970s, calcium-activated potassium currents were recorded for the first time. In 10years, this Ca²⁺-activated potassium channel was identified in rat skeletal muscle, chromaffin cells and characterized in skeletal muscle membranes reconstituted in lipid bilayers. This calcium- and voltage-activated potassium channel, dubbed BK for “Big K” due to its large ionic conductance between 130 and 300 pS in symmetric K⁺. The BK channel is a tetramer where the pore-forming α subunit contains seven transmembrane segments. It has a modular architecture containing a pore domain with a highly potassium-selective filter, a voltage-sensor domain and two intracellular Ca²⁺ binding sites in the C-terminus. BK is found in the plasma membrane of different cell types, the inner mitochondrial membrane (mitoBK) and the nuclear envelope’s outer membrane (nBK). Like BK channels in the plasma membrane (pmBK), the open probability of mitoBK and nBK channels are regulated by Ca²⁺ and voltage and modulated by auxiliary subunits. BK channels share common pharmacology to toxins such as iberiotoxin, charybdotoxin, paxilline, and agonists of the benzimidazole family. However, the precise role of mitoBK and nBK remains largely unknown. To date, mitoBK has been reported to play a role in protecting the heart from ischemic injury. At the same time, pharmacology suggests that nBK has a role in regulating nuclear Ca²⁺, membrane potential and expression of eNOS. Here, we will discuss at the biophysical level the properties and differences of mitoBK and nBK compared to those of pmBK and their pharmacology and function.

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).