A bilayer cellular Potts model of epithelial docking

Fusion of two epithelial cell sheets brought together in a bilayer configuration is a common step in animal morphogenesis, yet, in contrast to other epithelial fusion processes such as wound healing in a monolayer of cells, it has not been a strong focus of modeling efforts. Here we consider a preliminary stage of bilayer fusion, recently termed "docking." In multiple instances of docking that span apical and basal varieties, cells appear to have a tendency to remodel so as to co-localize their bilateral junctions (match their edges) across the bilayer. Motivated by this observation, we introduce a bilayer cellular Potts model that couples two standard 2D area- and perimeter-elasticity models via short-range, out-of-plane interactions between cell edges. The new coupling involves a single adjustable parameter that minimally models the combined effect of dynamic cytoskeletal protrusions, cadherins, and other potential edge-associated adhesion molecules. Our model predicts that bilayer edge matching is maximized when the two monolayers are in their fluid-like regimes (average cell shape index greater than 4.6 in our implementation), and when the bilayer coupling strength strikes a balance between in-plane and out-of-plane energy scales. At higher coupling strengths, the system tends to get stuck in metastable states with sub-optimal edge matching. Exploration of the mechanisms of edge matching reveals that pairs and quadruplets of coordinated T1 transitions play a particularly important role. We also find numerous examples of emergent features we term "domain walls" - branching or unbranching curves that cross no matched edges, but that separate regions of nearly complete matching. These domain walls can be both system spanning and long lived. Finally, we extend our model to crudely account for bending of the two sheets, and study the distributions of docking front speeds that result.