Boundary propagation of planar cell polarity is robust against cell packing pattern

Planar cell polarity is an important property of epithelial tissue. The boundary propagation model was proposed as the mechanism of PCP induction, while it has been doubted whether it can induce PCP on wide tissue. Using simulation, a set of proteins can be shown to induce PCP, but it does not explain why and how the set can induce PCP. In this study, we made theoretical model and simulation model to explore when and how the boundary propagation induce PCP. We incorporated multipolar cell in our model. Intracellular interactions have been thought to amplify polarity of a cell, but we propose instead that they are to keep a cell-cell interface polarized, and bipolarity of cell is obtained as a result. We show that the boundary propagation can propagate polarity as long as average size of local cell group is constant and levels of PCP proteins are balanced in every cell. Therefore, this model provide an explanation for PCP induction on a tissue with multiple cell types.