Differentiation and replication of spots in a reaction-diffusion system with many chemicals

E-ISSN： 1286-4854|56|1|145-151

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.56, Iss.1, 2010-03, pp. : 145-151

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Abstract

The replication and differentiation of spots in reaction-diffusion equations are studied by extending theGray-Scott model with self-replicating spots to includemany degrees of freedom needed to model systems with many chemicals. By examining many possible reaction networks,the behavior of this model is categorized into three types:replication of homogeneous fixed spots,replication of oscillatory spots, and differentiation from "multipotent spots" .These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and, as a result, an inhomogeneous pattern of spots is formed.This differentiation process of spots is analyzed in terms ofthe loss of chemical diversity and decrease of the local Kolmogorov-Sinai entropy.The relevance of the results to developmental cell biology andstem cells is also discussed.