Proliferation and competition in discrete biological systems.

We study the emergence of collective spatio-temporal objects in biological systems by representing individually the elementary interactions between their microscopic components. We use the immune system as a prototype for such interactions. The results of this detailed explicit analysis are compared with the traditional procedure of representing the collective dynamics in terms of densities that obey partial differential equations. The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures, from microscopic noise. In turn the effective dynamics of these structures affects the average behaviour of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behaviour. As the optimal modelling method we propose a mixture of microscopic simulation systems describing each reaction separately, and continuous methods describing the average behaviour of the agents.