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

The replication and differentiation of spots in reaction-diffusion equation s are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemi cals. By examining many possible reaction networks, the behavior of this mo del is categorized into three types: replication of homogeneous fixed spots , replication of oscillatory spots, and differentiation from "multipotent s pots". These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and, as a result, an i nhomogeneous pattern of spots is formed. This differentiation process of sp ots is analyzed in terms of the loss of chemical diversity and decrease of the local Kolmogorov-Sinai entropy. The relevance of the results to develop mental cell biology and stem cells is also discussed.