Przemyslaw Borys

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.

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 Ca2+-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.

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.

Lossy dictionary-based image compression method

In this paper, we report on the new method of image compression. The method is based on LZ77 dictionary algorithm. We introduce two modifications such as quantization and noise levels. Experimental results presented in this paper prove that the new method of image compression gives promising results as compared with original LZ77 dictionary algorithm and JPEG2000.

On the Well-Posed Problems for Diffusion with Time Dependent Boundary Condition

This paper investigates a known problem of gas permeation into a finite volume. The literature treatment of this problem provides a solution, but misses the well-posedness analysis, which is of crucial importance, especially when a nonstandard problem is formulated. We have demonstrated that the Hadamard sense of well-posedness for this problem is satisfied by making use of the Duhamels theorem. The solution we have obtained using the Duhamels theorem and the solution available in the literature have different analytical representations, yet they are mathematically equivalent. In parallel, this paper provides some practical comments on the well-posedness analysis.

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 Ca2+ 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 Ca2+) from the anodal to the cathodal part through the cytoplasm. If the cytoplasmic conductance for Ca2+ 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.

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 channels 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 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.

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.

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

Abstract 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.