Morphogenesis and chemical dissipative structures: A computer Simulated Case Study

Abstract

A basis for the chemical prepattem concept of morphogenesis in multi-cellular organisms is examined in terms of a computer simulated case study of a compartmentalized, reaction-diffusion system. The simulation provides a non-linear extension of Turing's linear analysis of similar systems. Using a chemical reaction type posed by Prigogine, it is shown how spatially non-homogeneous and stable, steady-state concentration distributions result when the system is maintained under conditions far from thermodynamic equilibrium. Interpreting these stable, non-homogeneous, steady states as chemical prepatterns for the spatial structuring of growth and/or differentiation, time structuring can also be obtained in the form of a sequence of prepatterns generated by the rule that a prepattem is converted into its successor when the growth it is directing results in conditions which render it unstable. The physical simplicity of such a scheme for obtaining spatial and temporal structuring suggests it as a primitive ordering method in the morphogenesis of multicellular organisms. Examples are also given of how complicated spatial prepatterns can be viewed as the piecing together of independent, simple prepatterns.