Compartmental Hybrid State Production-Diffusion Systems with Application to Prestalk-Prespore Pattern Regulation in Cellular Slime Molds

Since the works of Rashevsky(1940) and Turing(1952), the modelings of cell differentiation have been more or less identified with those of pattern formation of some chemical substances (morphogens). Their main concern is to account for the scheme of cell differentiation starting from a set of seemingly identical cells. The “diffusive instability” plays an essential role there for breaking the initial uniform state and producing some heterogeneous one. Thus the ultimate patterns obtained in a reaction-diffusion system are supposed to be responsible for the emerging cell state differences.(See, for example, the books by Nicolis and Prigogine(1 977), Murray(1977), and Meinhardt(1982).)