Mathematical Models of Plant Pattern Formation: Leaf Venation and Shoot Apical Meristem

Pattern formation in biological systems usually involves interaction and diffusion of molecular factors such as genes and proteins. In this presentation, we will introduce analysis of mathematical models of leaf venation and shoot apical meristem (SAM) as examples of plant pattern formation.<br> Leaf venation pattern shows distinct variation such as pinnate, branching, palmate and parallel patterns. Since feedback regulation between plant hormone auxin and its efflux carrier PIN1 is important for plant vascular formation, a mathematical model based on auxin-PIN1 dynamics was investigated. The model generates diverse leaf venation patterns and provides insight into pattern diversity among plants.<br> SAM keeps almost constant size despite active cell division. Arabidopsis clv mutant results in enlarged SAM and frequently shows fasciation and dichotomous branching of shoots. On the other hand, wus mutant shows reduced SAM activity but produces many ectopic shoots after prolonged incubation. Because WUS-CLV interaction is essential for the formation and maintenance of SAM, a model including WUS-CLV dynamics was constructed and analyzed to generate SAM patterning of wild type and mutants.