PATTERN-FORMATION IN SHOOTS - A LIKELY ROLE FOR MINIMAL ENERGY CONFIGURATIONS OF THE TUNICA

When simple shoots and flowers are examined, a restricted set of patterns is found. Characterization involves three levels of scale: (1) The overall array is roughly radially symmetrical. (2) The elements within it are usually arranged in either straight radii or in spiral lines. (3) The element itself, e.g., a leaf or petal, has a plane of bilateral symmetry that lies on a radius of the overall array. Proposed morphogenetic mechanisms have centered on the second level, where the propagation of pattern is based on "feed forward," an influence of recently made primordia on the site of initiation of the next. This influence has been postulated to be chemical inhibition emanating from the center of each primordium. New primordia would arise in uninhibited regions and then produce inhibitor. An alternate candidate for this influence rests on the fact that the buckling of a constrained inanimate sheet can also propagate pattern. Bump formation on a sheet experiencing uniform upward pressure is influenced both by the boundary of the sheet and by humps already present on it. I propose that in meristems the tunica exhibits minimal energy buckling behavior, and the corpus supplies upward pressure. Simulations involving bumps can propagate patterns with straight or spiral configurations. This is feed-forward of pattern, at the second level. When bumps also develop adaxial creases tangential to the margin of the dome, these creases link the bilateral symmetry of the appendage with the overall radial symmetry (levels 1 and 3). By serving as an apparent new linear anchor for buckling of the dome, a new crease converts the influence of a leaf on the dome from modifying internal curvature to becoming an external boundary condition. Creases appear stiff and tend to form a ring. When such a ring is kept taut by internal pressure, it promotes radial symmetry, stabilizing the whole array. The biomechanical model ties together all three levels of scale. Cyclic buckling phenomena could explain why the number of patterns is restricted and why they take the form that they do.