Dmitry Bratsun

Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue

We propose a multiscale chemo-mechanical model of cancer tumor development in epithelial tissue. The model is based on the transformation of normal cells into a cancerous state triggered by a local failure of spatial synchronization of the circadian rhythm. The model includes mechanical interactions and a chemical signal exchange between neighboring cells, as well as a division of cells and intercalation that allows for modification of the respective parameters following transformation into the cancerous state. The numerical simulations reproduce different dephasing patterns—spiral waves and quasistationary clustering, with the latter being conducive to cancer formation. Modification of mechanical properties reproduces a distinct behavior of invasive and localized carcinoma.

Deterministic Modeling Spatio-Temporal Dynamics of Delay-Induced Circadian Oscillations in Neurospora crassa

We propose a spatially extended deterministic model with time delay for the circadian oscillations in the fungal species Neurospora crassa. The temporal behavior of the system is governed by a two variable model based on the nonlinear interplay between the FRQ and WCC proteins which are products of transcription of frequency and white collar genes. We show numerically that the model accounts for various features observed in experiments. Spatio-temporal protein patterns excited in Neurospora in complete darkness are studied for different initial conditions. It is shown that basal activation of transcription factors has a strong effect on pattern formation.

Synchronization of Circadian Rhythms at Scale of Gene, Cell and Whole Organism

Three characteristic scales of a biological system are distinguished in the chapter: microscopic (gene’s size), mesoscopic (cell’s size) and macroscopic (organism’s size). For each case the approach to modeling of the circadian rhythms is discussed on the base of a time-delay model. The stochastic description has been used at the gene’s scale. The deterministic description within the spatially extended model has been suggested on the mesoscopic scale. Macroscopic effects have been analyzed within the discrete model describing the collective behaviour of large amount of cells. The effect of collective rhythms synchronization for each case has been studied. The problem of cross-linking of the results obtained at different scales is discussed.

Chemo-mechanical modeling of tumor growth in elastic epithelial tissue

We propose a multiscale chemo-mechanical model of the cancer tumor development in the epithelial tissue. The epithelium is represented by an elastic 2D array of polygonal cells with its own gene regulation dynamics. The model allows the simulation of the evolution of multiple cells interacting via the chemical signaling or mechanically induced strain. The algorithm includes the division and intercalation of cells as well as the transformation of normal cells into a cancerous state triggered by a local failure of the spatial synchronization of the cellular rhythms driven by transcription/translation processes. Both deterministic and stochastic descriptions of the system are given for chemical signaling. The transformation of cells means the modification of their respective parameters responsible for chemo-mechanical interactions. The simulations reproduce a distinct behavior of invasive and localized carcinoma. Generally, the model is designed in such a way that it can be readily modified to take account o...

Modeling of Tumour Growth Induced by Circadian Rhythm Disruption in Epithelial Tissue

We propose a multiscale model of cancer tumour growth in a quasi epithelial tissue. Basic model of the epithelium growth describes the appearance of intensive movement and growth of tissue via mechanisms of division and intercalation of cells. It is assumed that the movement of cells is caused by the wave of mitogen-activated protein kinase (MAPK), which in turn activated by the chemo-mechanical signal propagating along tissue due to its local damage. It is assumed also that cancer cells can arise from local failure of a spatial synchronization of circadian rhythms. We hope that the subsequent study of the dynamic properties of the model could determine the relationship between the occurrence of the cancer cells and development of the entire tissue coordinating its evolution through the exchange of chemical and mechanical signals.

On the efficiency of active control of thermal convection in a thermosyphon with time-delayed controller

The paper deals with the problem of automatic control of the motion of an inhomogeneously heated liquid in long vertical channels connected at the ends. Such a rectangular loop (a non-simply connected thermosyphon) makes it easy to maintain the mechanical equilibrium of a liquid with a vertical temperature gradient. The fluid flow is controlled by small discrete channel orientation changes with respect to the static component of the inertial field, for example, gravity. Such changes are made by the computer according to the law of proportional negative feedback. The effect of a time delay, which naturally arises in the controllers commands, is considered. To study the effect in detail, an artificial time delay has been also added. A mathematical model of the phenomenon is developed. Dynamic modes of the work of a controlled convective loop are numerically studied. It was found that the excessive feedback gain can cause non-stationary convection modes in the system. Methods for weakening the delay effect are discussed.

Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A+B→S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

Spatial Effects of Delay-Induced Stochastic Oscillations in a Multi-scale Cellular System

The combined spatial effect of time delay and intrinsic noise on gene regulation is studied numerically. It is based on the multi-scale chemo-mechanical model of the epithelium. The protein fluctuations in each cell are described by a single-gene auto-repressor model with constant delay. It is found that time delay, noise and spatial signaling can result in the protein pattern formation even when deterministic description exhibits no patterns.

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.

Modeling Spatio-Temporal Dynamics of Taiga Boreal Forest

The simple three variable evolutionary model of boreal forest of Perm region has been proposed. The model is built as a complex system, where each population is represented by individual trees competing for solar light. Other factors taking into account are growth rate, seed dispersal and mortality. The parameter values used in the model were calibrated from the information available for Perm forests. This work has a fundamental aspect because a formation of dynamical macroscopic patterns in ecological systems attracts great interest of researchers. In addition, the proposed model can have many applications for more effective forest management.