Multiarmed Spirals in Excitable Media

Numerical studies of the properties of multiarmed spirals show that they can form spontaneously in low excitability media. The maximum number of arms in a multiarmed spiral is proportional to the ratio of the single spiral period to the refractoriness of the medium. Multiarmed spirals are formed due to attraction of single spirals if these spirals rotate in the same direction and their tips are less than one wavelength apart, i.e., a spiral broken not far from its tip can evolve into a 2-armed spiral. We propose this mechanism to be responsible for the formation of multiarmed spirals in mounds of the slime mold Dictyostelium discoideum

Modelling Chemotactic Motion of Cells in Biological Tissues

Developmental processes in biology are underlined by proliferation, differentiation and migration of cells. The latter two are interlinked since cellular differentiation is governed by the dynamics of morphogens which, in turn, is affected by the movement of cells. Mutual effects of morphogenetic and cell movement patterns are enhanced when the movement is due to chemotactic response of cells to the morphogens. In this study we introduce a mathematical model to analyse how this interplay can result in a steady movement of cells in a tissue and associated formation of travelling waves in a concentration field of morphogen. Using the model we have identified four chemotactic scenarios for migration of single cell or homogeneous group of cells in a tissue. Such a migration can take place if moving cells are (1) repelled by a chemical produced by themselves or (2) attracted by a chemical produced by the surrounding cells in a tissue. Furthermore, the group of cells can also move if cells in surrounding tissue are (3) repelled by a chemical produced by moving cells or (4) attracted by a chemical produced by surrounding cells themselves. The proposed mechanisms can underlie migration of cells during embryonic development as well as spread of metastatic cells

Formation of morphogenetic patterns in cellular automata

One of the most important problems in contemporary science, and especially in biology, is to reveal mechanisms of pattern formation. On the level of biological tissues, patterns form due to interactions between cells. These interactions can be long-range if mediated by diffusive molecules or short-range when associated with cell-to-cell contact sites. Mathematical studies of long-range interactions in-volve models based on differential equations while short-range interactions are modelled using discrete type models. In this paper, we use cellular automata (CA) technique to study formation of patterns due to short-range interactions. Namely, we use von Neumann cellular automata represented by a finite set of lattices whose states evolve according to transition rules. Lattices can be considered as representing biological cells (which, in the simplest case, can only be in one of the two different states) while the transition rules define changes in their states due to the cell-to-cell contact interactions. In this model, we identify rules result-ing in the formation of stationary periodic patterns. In our analysis, we distin-guish rules which do not destroy preset patterns and those which cause pattern formation from random initial conditions. Also, we check whether the forming patterns are resistant to noise and analyze the time frame for their formation. Transition rules which allow formation of stationary periodic patterns are then discussed in terms of pattern formation in biology

Temperature expressions and ergodicity of the Nosé-Hoover deterministic schemes

Thermostats are dynamic equations used to model thermodynamic variables in molecular dynamics. The applicability of thermostats is based on the ergodic hypothesis. The most commonly used thermostats are designed according to the Nos\'e-Hoover scheme, although it is known that it often violates ergodicity. Here, following a method from our recent study \citep{SamoletovVasiev2017}, we have extended the classic Nos\'e-Hoover scheme with an additional temperature control tool. However, as with the NH scheme, a single thermostat variable is used. In the present study we analyze the statistical properties of the modified equations of motion with an emphasis on ergodicity. Simultaneous thermostatting of all phase variables with minimal extra computational costs is an advantage of the specific theoretical scheme presented here

A Combined Experimental and Mathematical Study of The Evolution of Microbial Community Composed of Interacting Staphylococcus Strains

The emergence of the phenomenon known as ABR (anti-bacterial resistance), is the result of the gradual decrease in the efficacy of antibiotics and the increase in the cost of producing new antibiotics. Hence, alternative solutions to prevent the spread of the pathogenic species are required. Here we present a combined experimental and mathematical study of the evolution of microbial communities. The aim was to investigate the role of skin bacteria invasion and competition in limiting pathogenic species growth and colonisation, and to determine and reveal factors and conditions that alter and influence the dynamics of interactions between species. The focus in this study was Staphylococcus aureus as it is considered a major human pathogen that shows colonisation traits distinct from the more abundant skin antimicrobial-secreting residents, S. epidermidis and S. hominis. The method adopted when conducting this study was based on two approaches: experimental and mathematical. The novelty and significance of this study lies in the fact that, unlike that found in a previous studies the manipulation of spatial structures, the level of toxicity, and initial frequencies did not prevent the emergence of resistance in the evolved S. aureus populations. The evolved S. aureus populations were able to dominate their opponents regardless of the environmental conditions. However, it was found that the level of toxicity and environmental regulations made it harder for evolved S. aureus populations to recover.Comment: 45 pages, 25 figure

A statistical interpretation of the logistic equation

The logistic equation is one of the established paradigms in modelling population growth. Here we propose a statistical interpretation of the logistic equation. This interpretation is based on modelling the population-environment relationship, the mathematical theory of which we discuss in detail. By applying this theory, we obtain stochastic evolutionary equations, for which the logistic equation is a limiting case. The prospect of modifying logistic population growth is discussed.Comment: 12 pages, 4 figure

3D self-folding tissue engineering scaffold origami

In the field of tissue engineering complex 3D architecture has become increasingly relevant in the pursuit of precisely engineered control over living tissue. It is needed to recreate the heterogeneous and complex arrangements of cells seen in nature, and to be able to influence their proliferation, differentiation and fate. A method for the 3D structuring of cells is therefore desired and is something standard lithographic methods cannot provide - the precision engineered 3D cellular niche. This work transfers traditional 2D lithographic techniques used in MEMS (E-beam lithography, photolithography, soft lithography and nanoimprint lithography) to the construction of 3D as well as complex hierarchical structures compatible with cell culture. To address this, hydrogel bilayers act as biocompatible, flexible and environmentally responsive hinges to fold the 2D structure into a 3D conformation. To achieve this, a rapid method of producing nanopatterns with the potential for large area patterning was developed. These were fluorinated ethylene propylene (FEP) and polydimethylsiloxane (PDMS) replica stamps with 2D and 2.5D hierarchical patterns. They were capable of bending and conforming to uneven and curved surfaces. These were used in a novel combinational lithography approach to construct complex hierarchical structures by photolithography through photomasks with nanopatterned transparent FEP inlays to create unfolded 3D cellular niches by a 2D method. Several different hydrogels were synthesised and patterned by photolithography to be used as bilayer hinges. Actuation mechanisms included thermoresponsive N-isopropylacrylamide (NIPAAm), and anionic acrylic acid (AA) monomers. Successful bilayers were formed using acrylate based photochemistry with poly(ethylene glycol) dimethacrylate (PEGDMA) and pH responsive polyacrylic acid (PAA) in a novel sacrificial layer functionalisation method. These structures would bend and roll due to differential swelling in neutral pH and when acting as a hinge would result in self-folding of photolithographically defined 2D structures into 3D containers. To test the compatibility of this method of manufacture with cell culture hESCs were trialled on the container materials, and showed excellent adhesion on the SU8 structures. More ambitiously to see if they could in the future be used for the directed differentiation of stem-cells, hESCs were cultured on nanopatterned injection moulded polymer substrates with varying nanofeature type. It was found that hESEs had improved adhesion on vitronectin coated nanotopographies even at extremely low vitronectin concentrations, and showed an increased 3D colony structure leading to the enhanced expression of certain lineage markers. It was found that hESC attachment could be mediated by feature height and substrate elasticity. This work has demonstrated as a proof-of-principle, a rapid and simple method of producing nanopatterned 3D self-folding containers, compatible with cell culture which could in the future serve as 3D self-folding nanopatterned cellular niches for tissue engineering

Stochastic thermostats and temperature expressions

Abstract Molecular dynamics (MD) is in the core of fundamental research for a range of disciplines in natural sciences and is known for its applications in the design of new functional materials and the drug discovery. MD simulations are performed under certain thermodynamic conditions, typically at fixed temperature and pressure. The thermodynamic variables in the MD are modeled using equations that are called thermostats. Many different thermostats have been proposed. Recently (Samoletov A and Vasiev B 2017 J. Chem. Phys. 147 204106), we have shown that a range of thermostats can be derived in the framework of a unified approach based on the fundamental principles of statistical physics, so that the relevant dynamic schemes are based on the concept of temperature expression (in short, ϑ-expression). However, only a few specific ϑ-expressions have been used so far and reported in the literature. In this paper, we are using a wider set of ϑ-expressions and their mathematical properties that allow us to modify the known and offer new thermostats with improved computational efficiency and ergodicity. We focus on the Nosé-Hoover-Langevin stochastic scheme and extend it with additional temperature control tools. Simultaneous thermostatting of all phase space variables with minimal additional computational costs is an advantage of the modified dynamics.</jats:p