Figure 3

Mathematical model of planar polarity. The first term controls a cell’s polarisation, which in physical terms would relate to the underlying asymmetry in the proximal (P) and distal (D) proteins, whose strength is determined by B^asym and has a stable asymmetric state of magnitude m _asym . The schematic beneath illustrates a possible simplistic feedback pathway. The second term enforces uniformly orientated polarisation with its resistance to distortion determined by K^align , and ultimately the inter-cellular interactions between P and D proteins. The schematic beneath illustrates the necessary cell-cell interactions. The third term linearly couples the cell’s polarisation m to an increasing cue G^cue, with the response and mediation to that cue by C^mediator. The schematic beneath illustrates an increasing global cue’s differential action on a cell. The equation has been written in terms of a polarity vector (term 2 and 3) or its magnitude (term 1).