Bakh Institute of Biochemistry, Moscow, and Institute of Cytology and Genetics SB RAS, Novosibirsk, Russia
A morphodynamic model for phyllotaxis based upon an axiomatic approach is presented. We show that the helical forms of alternate phyllotaxis can be derived from the assumption of the rudiment's growth and movement on the cylindrical embryo surface in the absence of a longitudinal displacement. This leads to the repeating transition of tetragonal packaging of the rudiments into hexagonal packaging and vice versa. Under these conditions, sequences of rudiments produce either left-handed or right-handed helices, the number of which at the circumference of the cylinder corresponds to adjacent numbers of the Fibonacci series. Cross-opposite phyllotaxis forms are defined as superior with respect to the alternate ones, and verticillate phyllotaxis forms as superior with respect to the cross-opposite ones. Different phyllotaxis forms can be interpreted as a result of stretching of crystalline structures of the embryo formed by dense packing of rudiments. The superior phyllotaxis forms can be considered as the additive summation of lower forms. Morphodynamic mechanisms underlying the formation of multiple forms of helical phyllotaxis are discussed.
morphogenesis, phyllotaxis, helical form, polymorphism, Fibonacci series