On the role of probability amplitudes in cell aggregation: an approach study towards morphogenesis

We present a mathematical model inspired on field theory formalism that allowed us to treat biological systems composed of many interacting cells. Cells interact through diffusive substances and/or by contact (adhesion, tissue induction, etc.). Probability densities (that describe the spatial distribution of the cells in the system) are obtained from the model by a proposed Lagrangian density related to the dynamics of the system. The model is implemented in order to analyze cell aggregation and their dependence on the model parameters and boundary conditions, respectively. Three different classes of solutions are found and discussed.