Spatio-temporal patterns generated by Salmonella typhimurium

We present experimental results on the bacterium Salmonella typhimurium which show that cells of chemotactic strains aggregate in response to gradients of amino acids, attractants that they themselves excrete. Depending on the conditions under which cells are cultured, they form periodic arrays of continuous or perforated rings, which arise sequentially within a spreading bacterial lawn. Based on these experiments, we develop a biologically realistic cell-chemotaxis model to describe the self-organization of bacteria. Numerical and analytical investigations of the model mechanism show how the two types of observed geometric patterns can be generated by the interaction of the cells with chemoattractant they produce

Population Dynamics and Non-Hermitian Localization

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.Comment: 19 pages, 11 figure

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Dynamics of formation of symmetrical patterns by chemotactic bacteria

MOTILE cells of Escherichia coli aggregate to form stable patterns of remarkable regularity when grown from a single point on certain substrates. Central to this self-organization is chemotaxis, the motion of bacteria along gradients of a chemical attractant that the cells themselves excrete. Here we show how these complex patterns develop. The long-range spatial order arises from interactions between two multicellular aggregate structures: a 'swarm ring' that expands radially, and focal aggregates that have lower mobility. Patterning occurs through alternating domination by these two sources of excreted attractant (which we identify here as aspartate). The pattern geometries vary in a systematic way, depending on how long an aggregate remains active; this depends, in turn, on the initial concentration of substrate (here, succinate)

Social behavior of bacteria: from physics to complex organization

87.10.-e General theory and mathematical aspects, 87.18.-h Multicellular phenomena, 87.18.Fx Multicellular phenomena, biofilms, 87.18.Gh Cell-cell communication; collective behavior of motile cells,

A user’s guide to PDE models for chemotaxis

Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399–415, 1970; 30:225– 234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display “auto-aggregation”, has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller–Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work