Spatial patterns formed by chemotactic bacteria Escherichia coli

In certain experimental conditions, bacteria form complex spatial-temporal patterns. A striking example of such kind was reported by Budrene and Berg (1991), who observed a wide variety of different colony structures ranging from arrays of spots to radially oriented stripes or arrangements of more complex elongated spots, formed by Escherichia coli. We discuss the relevant mechanisms of intercellular regulation in bacterial colony which may cause pattern formation, and formulate the corresponding mathematical model. In numerical experiments a variety of patterns, observed in real systems, is reproduced. The dynamics of their formation is investigated.     

Mathematical modelling of intercellular regulation causing the formation of spatial structures in bacterial colonies

Bacterial colonies may grow forming stable spatial, particularly circular, structures. For instance, motile bacteria Proteus vulgaris or Escherichia coli grown on agar under certain conditions may form concentric rings with the centre in the inoculation point (Rüss-Münzer, 1935, Bact. Parasit Kde (Abt 1) 7, 214; Budriené, 1985, Dokl. Acad. Nauk SSR, 283, 470). A similar picture can be observed in a different situation, i.e. when a lawn of non-motile Salmonella typhimurium bacteria is cultivated on a solid agar with the locally introduced substrate (Hoppensteadt & J?ger, 1980, Lecture Notes in Biomath. 38, 68). This paper describes a mechanism of bacterial interactions through a hypothetical mediator released by the organisms. A mathematical model has been built. Its analysis has shown that the selected laws of secretion and reception of the mediator can adequately account for the formation of circular structures in the case of both motile and non-motile bacteria.     

Light-triggered pH banding profile in Chara cells revealed with a scanning pH microprobe and its relation to self-organization phenomena

When exposed to light, Characean cells develop a pattern of alternating alkaline and acid bands along the cell length. The bands were identified with a tip-sensitive antimony pH microelectrode positioned near one end of Chara internode at a distance of 50-100 microm from the cell wall. The stage with Chara cell was moved along its longitudinal axis at a computer-controlled speed (100 or 200 microm s(-1)) relative to the pH probe over a distance of 50 mm. Under sufficient uniform illumination of the cell (from 100 to 2.5 Wm(-2)), the homogeneous pH distribution becomes unstable and a banding pattern is formed, the spatial scale of which decreases with the light intensity. If the cell is locally illuminated, bands are formed only in the region of illumination. It is shown that the inhibition of cyclosis by cytochalasin B leads to the disappearance of the banding pattern. The addition of ammonium (weak base) inhibited the banding pattern, whereas acetate (weak acid) alleviated the inhibitory effect of ammonium and restored the pH banding. A model explaining the observed phenomena is formulated in terms of proton concentration outside and bicarbonate concentration inside the cell. It contains two diffusion equations for the corresponding ions with nonlinear boundary conditions determined by ion transport processes across the cell membrane. The model qualitatively explains most of the experimental observations. It describes the dependence of the pattern characteristics on the light intensity and reveals the role of cyclosis in this phenomenon.     

A mathematical model of the mechanism of vertebrate somitic segmentation.

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that the metameric arrangement first appears before somite formation at the stage of transition of mesodermal cells into a polarized state. The model is based on the assumption that besides the mechanism of contact cell polarization there exists a mechanism of polarization suppression due to excretion of some chemical substance by polarized cells. Periodicity appears as a result of interaction of a kinematic wave of somitogenic cell determination with the cell cycles of mesodermal cells.     

Nonlinear dynamics of the distributed biochemical systems functioning in the dissipative structure formation mode

Nonlinear dynamical biomolecular systems can evidently be considered as prototypes of information processing devices at molecular level capable to solve problems of high computational complexity. Keeping in mind this goal the dynamics of biochemical system based on enzymatic oxidation of uric acid was considered. The system was studied in the version of distributed biomolecular structure having predetermined geometry of enzyme distribution on a porous planar medium. Being in the regime of stepwise dissipative structure formation this system demonstrated complicated modes of behaviour.