Self-organization, complexity and chaos: the new biology for medicine.

In a spontaneously bursting neuronal network in vitro, chaos can be demonstrated by the presence of unstable fixed-point behaviour. Chaos control techniques can increase the periodicity of such neuronal population bursting behaviour. Periodic pacing is also effective in entraining such systems, although in a qualitatively different fashion. Using a strategy of anticontrol such systems can be made less periodic. These techniques may be applicable to in vivo epileptic foci.

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).