A hysteresis model for bacterial growth patterns

Abstract

Growth patterns in bacterial cultures have been observed and studied by several scientists. In 1978, Hoppensteadt, Jäger, Roth and Schmid observed ring structures in cultures of histidine auxotrophic salmonella typhimurium. Similar to the classical experiment for Liesegang phenomena in chemical precipitation, concentrical growth rings are formed in response to a diffusing front of histidine spreading from the center of a Petri dish to its boundary. In many examples for growth patterns in cell populations the cells are mobile; the systems can be modelled by reaction diffusion equations showing diffusive instabilities (see e.g. the papers [1], [9], [11] in this volume). However, in this case it is impossible to observe mobility of the population: the bacteria are fixed on an agar gel containing all chemicals necessary for growth except the missing amino acid. Therefore, the spatial interaction is caused only by the diffusion of the nutrients and the buffer neutralized by acids produced as by-products of the cell growth. It has been impossible to find a mathematical model explaining the ring structures without assuming a growth inhibiting change of the pH-value. This assumption was justified experimentally. There are strains of salmonella needing other amino acids for growth, e.g. proline or histidine and proline. The experiments in case of two missing substances and two diffusion centers show lens shaped growth structures which can be explained by the same mechanisms.