Mathematical Analysis of Branching Morphogenesis

We investigated the minimal condition for symmetry breaking in morphogenesis of cellular population using cellular automata based on reaction-diffusion dynamics. We started to understand the morphogenic process and provide the mathematical formulations of the fields aassociated with cellular activity, environmental struture and dynamics, and mutual influence of the environment in cells activity ans self-organisation. Then we model morphogenesis in cellular clusters, starting from a single seed cell, in the context of some environment, considering a variety of cellular and environmental processes, and the interaction between the two types of processes in the cellular dynamics. In particular, we looked for the possibility of the emergence of branching structures due to mechanical interactions. The model used two types of cells an external gradient. The results showed that the external gradient influenced movement of cell type-I, also revealed that clusters formed by cells type-II worked as barrier to movement of cells type-I.