A mathematical framework for the statistical interpretation of biological growth models.

Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary differential equations.

Modelling ethnogenesis.

One of the fundamental problems of contemporary history is to understand the processes governing the rise and fall of polities. The universality of boom-and-bust dynamics associated with the life-cycle of polities tempts to treat the problem mathematically and thus brings it to the framework of cliodynamics. Here we introduce a mathematical model of evolving polity under assumption that its evolution is associated with interactions of certain groups of people, forming the polity and differing by their psycho-ethic characteristics.

Toxin-mediated competition in weakly motile bacteria.

Many bacterial species produce toxins that inhibit their competitors. We model this phenomenon by extending classic two-species Lotka-Volterra competition in one spatial dimension to incorporate toxin production by one species. Considering solutions comprising two adjacent single-species colonies, we show how the toxin inhibits the susceptible species near the interface between the two colonies.

Scaling of Morphogenetic Patterns.

Mathematical studies of morphogenetic pattern formation are commonly performed by using reaction-diffusion equations that describe the dynamics of morphogen concentration. Various features of the modeled patterns, including their ability to scale, are analyzed to justify constructed models and to understand the processes responsible for these features in nature. In this chapter, we introduce a method for evaluation of scaling for patterns arising in mathematical models and demonstrate its use by applying it to a set of different models.

Dynamic principle for ensemble control tools.

Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure.

On the heterogeneity of human populations as reflected by mortality dynamics.

The heterogeneity of populations is used to explain the variability of mortality rates across the lifespan and their deviations from an exponential growth at young and very old ages. A mathematical model that combines the heterogeneity with the assumption that the mortality of each constituent subpopulation increases exponentially with age, has been shown to successfully reproduce the entire mortality pattern across the lifespan and its evolution over time. In this work we aim to show that the heterogeneity is not only a convenient consideration for fitting mortality data but is indeed the actual structure of the population as reflected by the mortality dynamics over age and time.

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.

Scaling of morphogenetic patterns in reaction-diffusion systems.

Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling.

Time-evolution of age-dependent mortality patterns in mathematical model of heterogeneous human population.

The widely-known Gompertz law of mortality states the exponential increase of mortality with age in human populations. Such an exponential increase is observed at the adulthood span, roughly after the reproductive period, while mortality data at young and extremely old ages deviate from it. The heterogeneity of human populations, i.

A mathematical model of mortality dynamics across the lifespan combining heterogeneity and stochastic effects.

The mortality patterns in human populations reflect biological, social and medical factors affecting our lives, and mathematical modelling is an important tool for the analysis of these patterns. It is known that the mortality rate in all human populations increases with age after sexual maturity. This increase is predominantly exponential and satisfies the Gompertz equation.

Mathematical modelling in developmental biology.

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before.

Coordination of cell differentiation and migration in mathematical models of caudal embryonic axis extension.

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally.

Modeling gastrulation in the chick embryo: formation of the primitive streak.

The body plan of all higher organisms develops during gastrulation. Gastrulation results from the integration of cell proliferation, differentiation and migration of thousands of cells. In the chick embryo gastrulation starts with the formation of the primitive streak, the site of invagination of mesoderm and endoderm cells, from cells overlaying Koller's Sickle.

An individual based model of rippling movement in a myxobacteria population.

Migrating cells of Myxococcus xanthus (MX) in the early stages of starvation-induced development exhibit elaborate patterns of propagating waves. These so-called rippling patterns are formed by two sets of waves travelling in opposite directions. It has been experimentally shown that formation of these waves is mediated by cell-cell contact signalling (C-signalling).

Modelling of Dictyostelium discoideum slug migration.

The development of most multicellular organisms involves differential movement of cells resulting in the formation of tissues. The principles governing these movements are poorly understood. One exception is the formation of the slug in the social amoebae Dictyostelium discoideum.

Becoming Multicellular by Aggregation; The Morphogenesis of the Social Amoebae Dicyostelium discoideum.

The organisation and form of most organisms is generated during theirembryonic development and involves precise spatial and temporal controlof cell division, cell death, cell differentiation and cell movement.Differential cell movement is a particularly important mechanism in thegeneration of form. Arguably the best understood mechanism of directedmovement is chemotaxis.

The control of chemotactic cell movement during Dictyostelium morphogenesis.

Differential cell movement is an important mechanism in the development and morphogenesis of many organisms. In many cases there are indications that chemotaxis is a key mechanism controlling differential cell movement. This can be particularly well studied in the starvation-induced multicellular development of the social amoeba Dictyostelium discoideum.

A model for dictyostelium slug movement.

Dictyostelium slug movement results from the coordinated movement of its 10(5)constituent cells. We have shown experimentally that cells in the tip of the slug show a rotational cell movement while the cells in the back of the slug move periodically forward (Siegert & Weijer, 1992). We have put forward the hypothesis that cell movement in slugs is controlled by chemotaxis to scroll waves generated in the tip which convert to twisted scroll or planar waves in the back of the slug (Bretschneider et al.

Modeling chemotactic cell sorting during Dictyostelium discoideum mound formation.

Coordinated cell movement is a major mechanism of the multicellular development of most organisms. The multicellular morphogenesis of the slime mould Dictyostelium discoideum, from single cells into a multicellular fruiting body, results from differential chemotactic cell movement. During aggregation cells differentiate into prestalk and prespore cells that will form the stalk and spores in the fruiting body.

Propagating waves control Dictyostelium discoideum morphogenesis.

The morphogenesis of Dictyostelium results from the coordinated movement of starving cells to form a multicellular aggregate (mound) which transforms into a motile slug and finally a fruiting body. Cells differentiate in the mound and sort out to form an organised pattern in the slug and fruiting body. During aggregation, cell movement is controlled by propagating waves of the chemo-attractant cAMP.

A Model for Cell Movement During Dictyostelium Mound Formation.

Dictyostelium development is based on cell-cell communication by propagating cAMP signals and cell movement in response to these signals. In this paper we present a model describing wave propagation and cell movement during the early stages of Dictyostelium development, i.e.

[Refractory properties of cardiac tissue at fast sodium current decrease. Comparison of atrium and ventricle].

Investigation of the membrane potential of Neurospora crassa mycelial cells was carried out by standard microelectrode technique. The resting potential is equal to--156 +/- 11 mV (negative inside the cell). The light of the spectrum blue-violet zone causes transient hyperpolarization of the cell membrane reaching --38 +/- 5 mV after 25 minutes of illumination.