Cells-gene interactions simulation on a coupled map lattice

A discontinuous mapping, developed to model gene expression inside cells and cellular interactions on a lattice, is described. Gene dynamics (considered here only as genetic trans regulations) are formulated in a way similar to the Boolean-neural network (BN) approach through a step function, and gene products are supposed to diffuse on a regular discrete lattice of cells, giving rise to nearest neighbour--cellular automata (CA) type--interactions. The time evolution of the model is discrete and synchronous. Despite its simple form the system shows a variegate pattern of behaviour, and certain regions in parameter space show a rich series of bifurcations and multistability already in the case of networks with two genes. The patterns of distribution of the products on the lattice are similar to the ring dynamics observed in CA following Wolfram's formulation and two-dimensional (torus) dynamics described in the Greenberg-Hasting model for excitable media.