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Phys. Rev. E 60, 4604–4609 (1999)

Avalanche of bifurcations and hysteresis in a model of cellular differentiation

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Gábor Fáth*
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, England

Zbigniew Domański
Institute of Theoretical Physics, University of Lausanne, CH-1015 Lausanne, Switzerland
Institute of Mathematics and Computer Sciences, Technical University of Czȩstochowa, Da̧browskiego 69, PL-42200 Czȩstochowa, Poland

Received 6 May 1999; published in the issue dated October 1999

See accompanying Physics Focus

Cellular differentiation in a developing organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emanating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received and either cells change type up to a given distance or, under other conditions, the differentiation process propagates throughout the whole domain. When the signal diminishes, hysteresis is observed.

© 1999 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.60.4604
DOI:
10.1103/PhysRevE.60.4604
PACS:
87.16.Ac, 87.17.Ee, 87.18.Hf

*Permanent address: Research Institute for Solid State Physics, P.O. Box 49, H-1525 Budapest, Hungary.

 
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