Auxin, one of the plant hormones, forms characteristic distribution patterns in plant tissue. These patterns are classified into two types, "spot" patterns and "passage" patterns. These diversified patterns are considered to be responsible for positioning shoot apical meristems and formation of leaf veins, respectively. However, the mechanism producing these patterns remains unclear.

An auxin efflux carrier protein called PINFORMED (PIN) is also important for auxin pattern formation. In this study, we developed several different models for specific interactions between auxin and PIN. By analyzing these models with numerical simulation and mathematical analysis, we are studying the mechanism of auxin pattern formation and the diversity of the patterns. Mathematical analysis shows the possible mechanisms by which plants can realize pattern switch between passage and spot patterns in different organs by small modification.

Examples of numerical calculations

(a) Spot pattern and (b) Passage pattern