Co-evolving cellular automata for morphogenesis
Achilles A. Beros, Monique Chyba, Kari Noe · Discrete and Continuous Dynamical Systems - B · 2019
Morphogenesis, the shaping of an organism, is a complex biological process accomplished through an well organized interplay between growth, differentiation and cell movement.It is still today one of the major outstanding problems in the biological sciences. Pattern formation has been well-addressed in the literature with the development of many mathematical models including the famous reaction-diffusion ones. We here take a different approach, introducing a controlled cellular automaton in order to model the signal molecules, known as growth factors, that convey information from one cell to another during an organism's development and help maintain the viability of the adult. This control represents extracellular structures that have been associated with the regulation of stem cell proliferation and are called fractones. In this paper we introduce two co-evolving automata, one describing the perturbed diffusion of growth factors and one accounting for the rules of basic cellular functions (proliferation, differentiation, migration and apoptosis). Fractones are introduced as an external input to control the shaping of multi-cellular organisms; we analyze their influence on the emerging shape. We illustrate our theory with 2 and 3 dimensional simulations. This work presents the foundation upon which to develop cellular automata as a tool to simulate the morphodynamics in embryonic development.