Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long time limit describing non-uniform distribution due to a space dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution.Comment: arXiv admin note: text overlap with arXiv:1902.0308

Abstract P-41: Contribution of Matrix-bound Vesicles Produced by Mesenchymal Stromal Cells in the Differentiation of Multipotent Stem Cells in vitro

Background: According to the current view on the extracellular matrix (ECM) composition and functions, it includes not only structural proteins and components of cell adhesion, but also various deposited components, including enzymes involved in ECM remodeling, growth factors, and matrix-bound vesicles (MBV). MBV can presumably participate in the formation of a specific microenvironment for stem cells and regulate their differentiation. However, the contribution of MBV to these processes remains poorly understood. In our work, we evaluated the effects of MBV within native ECM produced by mesenchymal stromal cells (MSCs) cultured in cell sheet on multipotent stem cell differentiation. Methods: We isolated MBV from decellularized MSC-produced ECM by treatment with the following enzymes: collagenase, hyaluronidase, or trypsin, and centrifugation on 1000 kDa filters. The nanostructure and relative size in each sample were observed using TEM. The particle size and concentration were also studied with NTA. In addition, the obtained MBV were examined for the presence of key exosome markers using Western blot. Then we investigated the effect of MBV on the formation of capillary-like structures by endothelial cells (in vitro model of angiogenesis) as well as on the differentiation of primary MSCs isolated from human adipose tissue in the adipogenic, osteogenic, and chondrogenic directions. Results: As a result of comparative analysis of isolation protocols, it was shown that all MBV samples had the characteristics of extracellular vesicles (EV), but differed in size and representation of exosomal markers. The MBV isolated from ECM did not stimulate the formation of capillary-like structures by endothelial cells, in contrast to EV secreted by MSCs to the conditioned medium, but maintained the viability of the endothelium. Isolated MBV stimulated osteogenic and adipogenic differentiation of MSCs similar to secreted EV. On the other hand, preincubation of MSCs with MBV leads to reorganization of cell monolayer to spheroid-like structures during chondrogenic differentiation. Conclusion: Here, we developed the protocol of isolation of MBV from ECM that have distinguished characteristics and functional activity

On the theory of the magnetic deformation of ferrogels

The paper deals with theoretical study of deformation of a ferrogel sample under the action of an applied magnetic field. The main goal of this work is to determine the type of deformation - either elongation or contraction in the field direction. To answer this question and to avoid artificial conclusions, we have estimated the free energy of the deformed sample by using standard methods of statistical physics. The analysis shows that the type of magnetically induced deformation significantly depends on initial shape of the sample, the applied magnetic field, as well as on the concentration and magnetic properties of the magnetic particles embedded in the gel. © 2012 The Royal Society of Chemistry

Effect of ferromagnetic nanoparticles aggregation on magnetic hyperthermia

We present the results of mathematical modeling and theoretical study of the magnetic hyperthermia effect in a system of ferromagnetic nanoparticles, united in two-particle aggregates. The heat effect is produced by a linearly polarized oscillating magnetic field. The influence of the coupling of the particles on the thermal effect is analyzed. The results show that particle aggregation decreases the hyperthermia effect

Effect of ferroparticles clustering on magnetic hyperthermia in non-liquid systems

The paper deals with theoretical study of effect of ferromagnetic nanoparticles clustering on the intensity of heat production (magnetic hyperthermia) under an alternating magnetic field in non-liquid systems. To be determined, we consider four-particle clusters with two types of the ferroparticle’s spatial disposition. Internal magnetic anisotropy of the ferroparticles is supposed strong. Our results demonstrate that, first, the particles clustering significantly reduce the produced thermal effect. Second, the cluster morphology influences this effect

Gradient diffusion in ferrofluids with chain aggregates

The paper deals with the theoretical study of the effect of chain-like aggregates on the diffusion of magnetic particles in ferrofluids. Our analysis shows that the appearance of the chains leads to strong anisotropy of the diffusion transport—the diffusion coefficient in the direction of an applied magnetic field is significantly more than that in the perpendicular direction. Effects of the interchain interaction are taken into account

To the theory of ferrohydrodynamic circulating flow induced by running magnetic field

We present results of theoretical modeling of macroscopic circulating flow induced in a drop of ferrofluid by oscillating running magnetic field. The drop is placed in a narrow flat channel filled by a nonmagnetic liquid. The aim of this work is development of a scientific basis for a progressive method of address drug delivery to thrombus clots in blood vessels with the help of the magnetically induced circulation flow. Our results show that the oscillating running field allows inducing the carrier fluid flow with velocity amplitude 1–10 cm/s. This is the range of values, presenting interest from the point of view of the drug delivery

Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long time limit describing non-uniform distribution due to a space dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution.Comment: arXiv admin note: text overlap with arXiv:1902.0308

In silico study of magnetic nanoparticles transport in channels of various diameters in the presence of a constant magnetic field

In general, this study is concerned with the development of theoretical basis for the use of magnetic nanoparticles (MNPs) for the needs of cardiology. A mathematical model reflecting the fundamental features of MNPs motion and transport in a liquid that flows in a channel modeling a stenotic blood vessel is introduced. The obtained results of computational simulations of MNPs transport revealed the presence of stagnant zones with vortices of the host liquid that appear near the stenosis. The application of a magnetic field to the channel provokes the accumulation of MNPs in these zones. An increased MNPs concentration near the stenosis makes it possible to determine the position and size of the stenosis using an external magnetic sensor

In-silico study of hemodynamic effects in a coronary artery with stenosis

The paper presents a study of hemodynamic processes in an artery with stenosis. The Navier–Stokes model and the Carreau model for a non-Newtonian fluid are proposed for computer simulations. Computational experiments were performed using the FlowVision© software. The results of a test simulation for blood flow in the 2D tube, as well as a simulation for the native artery model, based on medical research data, are presented. The simulation results show that in a native artery with a stenosis, the distribution of blood velocity and viscosity may be asymmetric, and their local values differ significantly from the average values observed in the artery after the presumed revascularization. The results have great potential importance for diagnosing and treating arterial stenosis