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.

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.

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 ß 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.

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.

The distribution of information for sEMG signals in the rectal cancer treatment process.

The electrical activity of external anal sphincter can be registered with surface electromyography. This signals are known to be highly complex and nonlinear. This work aims in characterisation of the information carried in the signals by harvesting the concept of information entropy. We will focus of two classical measures of the complexity. Firstly the Shannon entropy is addressed. It is related to the probability spectrum of the possible states. Secondly the Spectral entropy is described, as a simple frequency-domain analog of the time-domain Shannon characteristics. We discuss the power spectra for separate time scales and present the characteristics which can represent the dynamics of electrical activity of this specific muscle group. We find that the rest and maximum contraction states represent rather different spectral characteristic of entropy, with close-to-normal contraction and negatively skewed rest state.

Upper extremity surface electromyography signal changes after laparoscopic training.

INTRODUCTION: Objective measures of laparoscopic skill in training are lacking. AIM: To evaluate the changes in the surface electromyography (sEMG) signal during laparoscopic training, and to link them to intracorporeal knot tying. MATERIAL AND METHODS: Ten right-handed medical students (6 female), aged 25 ±0.98, without training in laparoscopy, were enrolled in the study. With no additional training, they tied intracorporeal single knots for 15 min. Then underwent laparoscopic training and redid the knot tying exercise. During both events, sEMG was recorded from 8 measurement points on the upper extremities and neck bilaterally. We analyzed changes in sEMG resulting from training and tried to find sEMG predictive parameters for higher technical competence defined by the number of knots tied after the training. RESULTS: The average number of knots increased after the training. Significant decreases in activity after the training were visible for the non-dominant hand deltoid and trapezius muscles. Dominant and non-dominant hands had different activation patterns. Differences largely disappeared after the training. All muscles, except for the dominant forearm and non-dominant thenar, produced a negative correlation between their activities and the number of tied knots. The strongest anticorrelation occurred for the non-dominant deltoid (r = -0.863, p < 0.05). Relatively strong relationships were identified in the case of the non-dominant trapezius and forearm muscles (r = -0.587, r = -0.504). CONCLUSIONS: At least for some muscle groups there is a change in activation patterns after laparoscopic training. Proximal muscle groups tend to become more relaxed and the distal ones become more active. Changes in the non-dominant hand are more pronounced than in the dominant hand.

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.

Single measurement detection of individual cell ionic oscillations using an n-type semiconductor - electrolyte interface.

Pollen tubes are used as models in studies on the type of tip-growth in plants. They are an example of polarised and rapid growth because pollen tubes are able to quickly invade the flower pistil in order to accomplish fertilisation. How different ionic fluxes are perceived, processed or generated in the pollen tube is still not satisfactorily understood. In order to measure the H+, K+, Ca2+ and Cl- fluxes of a single pollen tube, we developed an Electrical Lab on a Photovoltaic-Chip (ELoPvC) on which the evolving cell was immersed in an electrolyte of a germination medium. Pollen from Hyacinthus orientalis L. was investigated ex vivo. We observed that the growing cell changed the (redox) potential in the medium in a periodic manner. This subtle measurement was feasible due to the effects that were taking place at the semiconductor-liquid interface. The experiment confirmed the existence of the ionic oscillations that accompany the periodic extension of pollen tubes, thereby providing - in a single run - the complete discrete frequency spectrum and phase relationships of the ion gradients and fluxes, while all of the metabolic and enzymatic functions of the cell life cycle were preserved. Furthermore, the global 1/fα characteristic of the power spectral density, which corresponds to the membrane channel noise, was found.

Multifractal characteristics of external anal sphincter based on sEMG signals.

Up to 40% of patients treated for rectal cancer suffer from therapy-related symptoms. Innervation injury is one of the suggested pathomechanisms of those symptoms hence the development of a valid, non-invasive tool for the assessment of neural systems is crucial. The aim of this work is to study the fractal properties of the surface electromyography signals obtained from patients suffering from rectal cancer. The anal sphincter activity was investigated for the group of 15 patients who underwent surgical treatment. Multifractal detrended fluctuation analysis was implemented to analyze the data, obtained at four different stages: one before treatment and three times after the surgery. The results from the standard detrended fluctuation analysis and empirical mode decomposition methods are presented and compared. The statistically significant differences between the stages of treatment were identified for the selected spectral parameters: width and maximum of the spectrum.

Sample Entropy of sEMG Signals at Different Stages of Rectal Cancer Treatment.

Information theory provides a spectrum of nonlinear methods capable of grasping an internal structure of a signal together with an insight into its complex nature. In this work, we discuss the usefulness of the selected entropy techniques for a description of the information carried by the surface electromyography signals during colorectal cancer treatment. The electrical activity of the external anal sphincter can serve as a potential source of knowledge of the actual state of the patient who underwent a common surgery for rectal cancer in the form of anterior or lower anterior resection. The calculation of Sample entropy parameters has been extended to multiple time scales in terms of the Multiscale Sample Entropy. The specific values of the entropy measures and their dependence on the time scales were analyzed with regard to the time elapsed since the operation, the type of surgical treatment and also the different depths of the rectum canal. The Mann-Whitney U test and Anova Friedman statistics indicate the statistically significant differences among all of stages of treatment and for all consecutive depths of rectum area for the estimated Sample Entropy. The further analysis at the multiple time scales signify the substantial differences among compared stages of treatment in the group of patients who underwent the lower anterior resection.

Correlation based analysis of sEMG signals during complex muscle activity. Feasibility study of new methodology.

Assessment of complex motor task (CMT) competency is still very prone to bias. Objective assessment is based either on outcomes leaving the process out of the equitation or on checklists with all their limitations. We tested the hypothesis that muscular recruitment patterns assessed with surface Electromyography (sEMG) will be different between novices and skilled trainees. sEMG signals of the muscles that potentially are characterized by the highest level of engagement at complex motor task were submitted to comprehensive correlation analysis. Standard methods of estimating the correlation coefficients were compared with more advanced analysis including cross-wavelet coherence and calculation of mutual information. We conclude that with appropriate analytical tools it is possible to compare sEMG signals during complex motor tasks and that at least on our very small sample it differs between individuals.

Sensitivity and specificity of multichannel surface electromyography in diagnosing fecal incontinence.

BACKGROUND: Assessment of the neurocontrol of the external anal sphincter has long been restricted to investigating patients by invasive tools. Less invasive techniques have been regarded less suitable for diagnosis. OBJECTIVE: The aim was to develop a surface electromyography-based algorithm to facilitate fecal incontinence diagnosis, and to assess its sensitivity and specificity. DESIGN: Data analysis from a single center prospective study. PATIENTS: All patients from colorectal surgery office were considered. They underwent a structured interview, a general physical and proctologic examination. Patients with diagnosed fecal incontinence (Fecal Incontinence Severity Index >10) were included into the study group. The control group consisted of healthy volunteers that scored 5 or less and had negative history and physical exam. Both groups underwent the same tests (rectoscopy, anorectal manometry, transanal ultrasonography, multichannel surface electromyography and assessment of anal reflexes). METHODS: EMG results were analyzed to find parameters that would facilitate fecal incontinence diagnosis. OUTCOME MEASURES: Sensitivity and specificity of surface electromyography, to diagnose fecal incontinence, were assessed. RESULTS: A total of 49 patients were included in the study group (mean age ± SD 58.9 ± 13.8). The control group (n = 49) gender matched the study group (mean age ± SD 45.4 ± 15.1). The constructed classification tree, based on surface electromyography results, correctly classified 97% of cases. Thee sensitivity and specificity of this classification tree, to diagnose FI, was 96% and 98% respectively. LIMITATIONS: The age of women in the control group differs significantly from mean age of other groups. CONCLUSIONS: Surface electromyography is an good tool to facilitate diagnosing of fecal incontinence.

Transport characteristics of molecular motors.

Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically studied with respect to its energetic efficiency and quality expressed by an effective diffusion coefficient. We demonstrate the role of friction and non-equilibrium driving on the transport quantifiers and identify regions of a parameter space where motors are optimally transported.

Optimal strategy for controlling transport in inertial Brownian motors.

In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green-Kubo type.