We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by re presenting individually the elementary interactions between its microscopic components (antibodies, antigen s, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging ove r individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations show even for very simple elementary reactions the spontaneous emergence of localized compl ex structures. In turn the effective dynamics of these structures affects the average behavior of the system in a very dec isive way: systems which would according to the differential equations approximation die, display in realit y a very lively behavior. Our conclusions are supported both by explicit microscopic simulations and by analytic calculations. As the optimal method we propose a mixture of microscopic simulation (MS) systems describing each reaction separately, and average methods describing the average behavior of the agents.
|Original language||American English|
|Journal||arXiv preprint nlin/0006043|
|State||Published - 2000|