The plant hormone auxin plays a central role in growth and morphogenesis. In the shoot apical meristem, the auxin flow is polarized through its interplay with PIN proteins through local positive feedback rules. Concentration based mathematical models of the auxin flow permit to explain some aspects of phyllotaxis, where auxin accumulation points in tissue act as auxin sinks and correspond to primordia. Simulations show that these models can reproduce geometrically regular patterns like spirals in sunflowers or Fibonacci numbers. We then consider a concurrent model which is based on the so-called canalization hypothesis, and show that it can explain the self-organization of plant vascular systems through local positive feedback rules that might lead to near optimal transport networks.
|Prof. Christian Mazza, Département de mathématiques, Unifr
|Département de physique