Modeling, simulation and analysis of mechanochemical patterns in active tissues

Cell mechanics and cell-cell signaling are expected to play important roles in determining the tissue organization and patterning during morphogenesis. Modeling efforts have, thus far, treated these two processes separately. Experiments in recent years, however, suggest that both these processes could be tightly coupled. Hence, in the present thesis, we propose a vertex model to study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signaling molecules such as Delta and Notch. We then extend this vertex model framework to include a simple feedback mechanism between cell-cell adhesion and the expression of signaling molecules in cells to explore the origin and diverse manifestation of chemical and cell morphological patterns in the tissues.