Proliferation and competition in discrete biological systems |
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Authors: | Louzoun Yoram Solomon Sorin Atlan Henri Cohen Irun R |
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Institution: | (1) Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel;(2) Racah Institute for Physics, Hebrew University, Jerusalem, Israel;(3) Human Biology Research Centre, Hadassah Hebrew University Hospital, Jerusalem, Israel;(4) Department of Immunology, The Weizmann Institute of Science, Rehvot, Israel |
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Abstract: | 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. |
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