Patterns on Plants
Plyllotaxis, namely the arrangement of phylla (leaves, florets, etc) has intrigued natural scientists for over four hundred years. Current theories and models of the formation of phyllotactic patterns at the plant apical meristem focus on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. Each of the mechanisms alone can give rise to an instability that leads to patterned states. However, it is known that the two mechanisms interact with each other instead of acting independently. We (Alan C Newell, Patrick Shipman and I) develop a model that incorporates the coupling of biochemistry and mechanics. I will discuss the parameter choices under which the two mechanisms may cooperate in determining the pattern, or under which one or the other mechanism may dominate. Analysis of these equations shows that the coupling of the two mechanisms acts like a positive-feed-back system and relaxes the condition for primordium initiation. Also, on real plants, the pattern doesn't form all at once. Rather, the primordia are formed sequentially over time and gradually add to the existing pattern. Therefore, between the stable patterned state and the unstable non-patterned state, there exists a front that propagates with some finite velocity into the non-patterned state. I will discuss how this idea of front propagation coincides with a well-accepted conceptual model for phyllotaxis proposed over a hundred years ago by Hofmeister and Snow&Snow.