Mathematical modeling of cell junctional rearrangements. (A) Schematic illustrations of cellular rearrangements and changes in the distribution of β-catenin in WT (left) or αN-catenin KO (right) mice during development. (B) Mathematical modeling of cell junctional rearrangements. (left) Polygonal cellular patterns are shown for the case in which heterophilic interactions between O polygons (O) and S polygons (S) are as strong as homophilic interactions between S polygons (S-S = O-S > O-O, adhesiveness strengths a_ss = a_os = 1.0, a_oo = 0.533. Steps 0–2,300). The O-O edge was then replaced with a new contact formed between S polygons (asterisks). The horizontal edges were elongated after step 2,300 (a_os = 0.89). (right) Intercalation did not occur between O and S polygons when heterophilic interactions between O and S polygons are weaker than homophilic interactions between S polygons (i.e., S-S > O-S > O-O, a_ss = 1.0, a_os = 0.833, a_oo = 0.533). Bold lines, O-S boundary; narrow lines, S-S boundary; double lines, O-O boundary. See Materials and methods for details.