Cellular Automata with Dynamic Structure to Simulate the Growth of Biological Tissues

摘要

A concept of cellular automaton with dynamic structure of the cellular space (DCA) is proposed. The DCA extends the capabilities of classical cellular automata (CA) and allows using a cellular automata approach to the problems of simulating biological tissue growth. A DCA differs from a classical CA in that its cells are not located on a regular lattice, and the intercellular connections are explicitly described by a neighborhood matrix. In addition, insertion and partition operators are introduced in the DCA. These operators allow one to dynamically change the cell space structure. Based on this extension, a DCA-model of growth of a shoot apical meristem of Arabidopsis Thaliana is constructed, being a parallel composition of two DCA: an asynchronous two-dimensional DCA simulating self-regulation of biological cells and a synchronous one-dimensional DCA simulating the growth and division of biological cells. The results of computer simulation have shown that the behavior of the DCA-model is the same as that of an existing model based on a composition of differential equations and L-system (Lindenmayer system) methods. The DCA-model allows one to simulate the growth of individual biological cells and to visualize the dynamics of substances in these cells (decay, synthesis, and diffusion).