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.

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 the fractality of the Freundlich adsorption isotherm in equilibrium and non-equilibrium cases.

We investigate the relationship between the Freundlich adsorption exponent and the fractal dimension of the adsorption sites for quasi-monolayer adsorption, and of the adsorbed aggregate for a simple case of multilayer adsorption. We further check whether the Freundlich adsorption mechanism may contribute to anomalous diffusion in the transport through porous materials.

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.

The role of passive calcium influx through the cell membrane in galvanotaxis.

Passive calcium influx is one of the theories to explain the cathodal galvanotaxis of cells that utilize the electric field to guide their motion. When exposed to an electric field, the intracellular fluid becomes polarized, leading to positive charge accumulation on the cathodal side and negative charge accumulation on the anodal side. The negative charge on the anodal side attracts extracellular calcium ions, increasing the anodal calcium concentration, which is supposed to decrease the mobile properties of this side. Unfortunately, this model does not capture the Ca(2+) dynamics after its presentation to the intracellular fluid. The ions cannot permanently accumulate on the anodal side because that would build a potential drop across the cytoplasm leading to an ionic current, which would carry positive ions (not only Ca(2+)) from the anodal to the cathodal part through the cytoplasm. If the cytoplasmic conductance for Ca(2+) is low enough compared to the membrane conductance, the theory could correctly predict the actual behavior. If the ions move through the cytoplasm at a faster rate, compensating for the passive influx, this theory may fail. This paper contains a discussion of the regimes of validity for this theory.

On the biophysics of cathodal galvanotaxis in rat prostate cancer cells: Poisson-Nernst-Planck equation approach.

Rat prostate cancer cells have been previously investigated using two cell lines: a highly metastatic one (Mat-Ly-Lu) and a nonmetastatic one (AT-2). It turns out that the highly metastatic Mat-Ly-Lu cells exhibit a phenomenon of cathodal galvanotaxis in an electric field which can be blocked by interrupting the voltage-gated sodium channel (VGSC) activity. The VGSC activity is postulated to be characteristic for metastatic cells and seems to be a reasonable driving force for motile behavior. However, the classical theory of cellular motion depends on calcium ions rather than sodium ions. The current research provides a theoretical connection between cellular sodium inflow and cathodal galvanotaxis of Mat-Ly-Lu cells. Electrical repulsion of intracellular calcium ions by entering sodium ions is proposed after depolarization starting from the cathodal side. The disturbance in the calcium distribution may then drive actin polymerization and myosin contraction. The presented modeling is done within a continuous one-dimensional Poisson-Nernst-Planck equation framework.

On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory.

Several approaches to ion-channel gating modelling have been proposed. Although many models describe the dwell-time distributions correctly, they are incapable of predicting and explaining the long-term correlations between the lengths of adjacent openings and closings of a channel. In this paper we propose two simple random-walk models of the gating dynamics of voltage and Ca(2+)-activated potassium channels which qualitatively reproduce the dwell-time distributions, and describe the experimentally observed long-term memory quite well. Biological interpretation of both models is presented. In particular, the origin of the correlations is associated with fluctuations of channel mass density. The long-term memory effect, as measured by Hurst R/S analysis of experimental single-channel patch-clamp recordings, is close to the behaviour predicted by our models. The flexibility of the models enables their use as templates for other types of ion channel.

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.

On the magnetic channels in polymer membranes.

In recent years we have proposed magnetic membranes (membranes with dispersed granules of a permanent magnet) for the separation of oxygen and nitrogen in the air mixture. The idea was to utilize oxygen's paramagnetic properties which are absent in the nitrogen. The experimental results were promising but they demanded a theoretical description which is given in the present paper. By a detailed analysis of the available data we arrive at four important conclusions: (1) magnetic channels are formed around the magnetic granules, (2) the channels provide high permeability "highways" for the diffusion of permeating molecules, (3) the oxygen molecules, due to their paramagnetic properties, stick to these "highways" for a longer time than the nitrogen, which is probably based on the interaction with the Weiss molecular field of the permanent magnet, (4) the magnetic field induces aggregation between oxygen and nitrogen which enhances the transport of both nitrogen and oxygen by prolonging their residence in the channel. In addition to these findings, the most suggestive theory of magnetic membrane operation is ruled out: the forcing of the oxygen molecules due to the gradients of magnetic field generated by the granules is too weak to account for the observed effects.

Characterization of the Structure and Transport Properties of Alginate/Chitosan Microparticle Membranes Utilized in the Pervaporative Dehydration of Ethanol.

The structure and transport properties of alginate/chitosan microparticle membranes used in ethanol dehydration processes were investigated. The membranes were characterized based on images obtained from high-resolution microscopy. The following parameters were determined: the observed total amount of void space, the average size of the void domains, their length and diameter, the fractal dimension, and the generalized stochastic fractal parameters. The total amount of void space was determined to be between 54% and 64%. The average size of the void domains is smaller for alginate membranes containing neat (CS) and phosphorylated (CS-P) chitosan particles when compared to those membranes filled with glycidol-modified (CS-G) and glutaraldehyde crosslinked (CS-GA) chitosan particles. Furthermore, the transport of ethanol and water particles through the studied membranes was modelled using a random walk framework. It was observed that the results from the theoretical and experimental studies are directly correlated. The smallest values of water to ethanol diffusion coefficient ratios (i.e., 14) were obtained for Alg (sodium alginate) membranes loaded with the CS and CS-P particles, respectively. Significantly larger values (27 and 19) were noted for membranes filled with CS-G and CS-GA particles, respectively. The simulation results show that the size of channels which develop in the alginate matrix is less suited for ethanol molecules compared to water molecules because of their larger size. Such a situation facilitates the separation of water from ethanol. The comparison of the structural analysis of the membranes and random walk simulations allows one to understand the factors that influence the transport phenomena, in the studied membranes, and comment on the effect of the length, diameter, number of channels, and variations in the pore diameters on these transport parameters.

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.

On the significance of sodium ionic channels in analysis of the breast cancer metastaticity.

Using the results from previous modeling of the ball and chain inactivation of the potassium channels we try to model the inactivation of the NaV 1.5 sodium channels in adult and neonatal form. The (fast) inactivation of sodium channels differs from the inactivation of the potassium channels by the use of a inactivating hinge rather than a ball on a chain. The adult and neonatal variants of the channel differ mostly in a charged amino acid residue located on the extracellular side. We show that a drift caused by this residue is sufficient to describe the differences in inactivation between the two forms of the NaV 1.5. We use the survival probability, the patch-clamp measurable parameter, to discriminate between the cells of different metastaticity.

A Simple Methodology to Estimate the Diffusion Coefficient in Pervaporation-Based Purification Experiments.

A procedure to estimate the diffusion coefficient in solution⁻diffusion models of hydrophilic membranes used in pervaporation-based purification experiments is presented. The model is based on a series solution of the general permeation problem. It considers a membrane that can be filled with water or with the feed solution before the measurement. Furthermore, the length of the tubing between the permeation cell and the place of cold traps is also addressed. To illustrate the parameter estimation procedure, we have chosen the data for the separation of water and ethanol by chitosan membranes. It is shown that the diffusion coefficient can be estimated effectively from the time course of the transported mass and by the analysis of certain well defined time lags of the permeation curve.

Hierarchical silica monolithic tablets as novel carriers for drug delivery.

This paper proposes the use of carriers with hierarchical porous structures as novel monolithic tablets for modified drug release. The influence of pore structure on the tamsulosin release profile is presented. The hierarchical arrangement of porous structure in monolithic tablets and the deposition of tamsulosin inside the silica carrier enable to control the kinetic of release and the amount of tamsulosin released. We developed a mathematical model of tamsulosin release from two carriers with different hierarchy of meso- and macropores. A model of this nature will allow to predict the release of tamsulosin from other carriers with a similar pore structure. We hope this research will improve the design process of novel carriers, and thus, will allow to tailor the porous structure of a carrier to achieve the desired release profile.

On the role of ball and chain interactions in recovery from the inactivation of the shaker potassium channel.

We describe a new factor in the recovery from inactivation in the ball and chain model. We propose a model in which the tension from the chain may help pull the ball away from its binding site, reducing the duration of the inactivation period. A corresponding model was built and analysed.

On the mathematical reconstruction of two dimensional plants.

A set of 10, chosen medicinal plants (some of them with a reputation as remedies for tuberculosis) has been investigated through Partitioned Iterated Function Systems-Semi Fractals with Angle (PIFS-SFA) coding, Lempel, Ziv, Welch with quantization and noise (LZW-QN) compression, and surface density statistics (f(alpha)-SDS) discrimination techniques. The final outcomes of this quantitative analysis were, firstly: the linear ordering of the plants in question accompanied by the hope that it reflects their medical significance, secondly: the mathematical representation of each of the plants, and thirdly: the impressive compression achieved, leading to remarkable computer memory saving, and still permitting successful pattern recognition i.e., proper identification of the plant from the compressed image.

A diffusive model of the ball and chain inactivation.

The ball and chain mechanism is a widely accepted theory for the inactivation of the Shaker K(+)channel. In this paper we propose a diffusive model that predicts a rate of inactivation that is comparable to the experimental measurements.

Lacunarity as a novel measure of cancer cells behavior.

An important goal in many branches of science, especially in molecular biology and medicine is the quantitative analysis of the structures and their morphology. The morphology can be analyzed in many ways, in particular by the fractal analysis. Apart from the fractal dimension, an important part of the fractal analysis is the lacunarity measurement which, roughly speaking, characterizes the distribution of gaps in the fractal: a fractal with high lacunarity has large gaps. In this paper, we present an extension of the lacunarity measure to objects with nonregular shapes that enables us to provide a successful discrimination of cancer cell lines. The cell lines differ in the shape of vacuole (the gaps in their body) which is perfectly suited for the lacunarity analysis.