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.