The epidermis of aerial plant organs is thought to be limiting for growth, because it acts as a continuous load-bearing layer, resisting tension. Leaf epidermis contains jigsaw puzzle piece-shaped pavement cells whose shape has been proposed to be a result of subcellular variations in expansion rate that induce local buckling events. Paradoxically, such local compressive buckling should not occur given the tensile stresses across the epidermis. Using computational modeling, we show that the simplest scenario to explain pavement cell shapes within an epidermis under tension must involve mechanical wall heterogeneities across and along the anticlinal pavement cell walls between adjacent cells. Combining genetics, atomic force microscopy, and immunolabeling, we demonstrate that contiguous cell walls indeed exhibit hybrid mechanochemical properties. Such biochemical wall heterogeneities precede wall bending. Altogether, this provides a possible mechanism for the generation of complex plant cell shapes.

Phyllotactic patterns, as indicated by the number of helices in opposed parastichy pairs, were determined in elongated shoots. Twelve patterns were found, including very rare patterns such as tetrajugy and secondary bijugy. Typically, the same pattern was repeated each year along a particular axis. Changes in pattern occurred between annual growth increments, more rarely within one increment. Pattern changes were not random, rather they occurred in a manner that minimized the change in the number of helices in the opposed parastichy pairs. A reversal in the direction of the ontogenetic helix often accompanied a pattern change.

Impermanent initials and thus the shift of the axis in the stochastic meristems are postulated to be responsible for ontogenetic phyllotactic diversity in plants. In the gynoecium of Magnolia acuminata the main Fibonacci pattern develops in much less than 50% of individual generative shoots. There is also an extremely wide spectrum of other patterns, among them even the rarest I, 3, 8, 11 ... pattern is present. Regarded sometimes as "impossible", the pattern has been documented in SEM for the first time. Beside the presence of various patterns, frequent ontogenetic transformations of phyllotaxis have been found in Magnolia. These are indicated by dislocations in the periodic distribution of carpel primordia. In other magnolias, exemplified by M. soulangeana, the Fibonacci pattern prevails, but not as much as in coniferous vegetative shoots, where, as demonstrated earlier, it reaches 95%. Other pattern numbers are also different. This suggests the involvement of the genetic factor and may be attributed to the higher frequency of discontinuous phyllotactic transformations in some species. The stochastic character of the meristem is perhaps more pronounced in some plants, which leads in turn to more frequent transitions and greater pattern diversity

Abstract. Phyllotactic pattern results from genetic control of lateral primordia size (physiological or physical) relative to the size of organogenic lateral surface of shoot apical meristem (SAM). In order to understand the diversity of patterns and ontogenetic transitions of phyllotaxis we have developed a geometric model allowing changes of the above proportion in a computer simulation of SAM's growth. The results of serial simulations confirmed that many phyllotactic patterns (including most esoteric ones) and ontogenetic transitions known from real plant model cases can be easily obtained in silico. Properties of virtual patterns often deviated from those of ideal mathematical lattices but closely resembled those of the natural ones. This proved the assumptions of the model, such as initiation in the first available space or ontogenetic changes in primordia size, to be quite realistic. Confrontation of simulation results with some sequences of real phyllotactic patterns (case study Verbena) questions the autonomy of SAM in its organogenic activity and suggests the involvement of unknown signal positioning primordia in a non-random manner in the first available space.

The ratio of primordium size to the meristem size (P/M ratio) is regarded by some geometrical models of phyllotaxis as the parameter, which determines the quality of spiral and whorled patterns of lateral organ arrangement. This assumption was tested on floral meristems in four genets representing four Magnolia taxa: M. × salicifolia, M. stellata, M. denudata and M. acuminata. In successive zones of Magnolia flower, lateral organs are initiated in specific phyllotactic patterns and at specific values of the meristem and primordia sizes. The elements of perianth, usually positioned in three trimerous whorls, are initiated as large primordia on relatively small meristem. The switch in the identity of primordia, from tepals to stamens is accompanied by an abrupt increase in the size of the meristem and decrease in the primordia size. Small values of P/M ratio and frequent occurrence of qualitative transformations of phyllotaxis contribute to the exceptionally rich spectrum of spiral patterns in androecium zone. New spiral patterns emerge when bigger primordia of carpels are initiated on the meristem, which at the same time starts diminishing in size either abruptly (M. × salicifolia, M. stellata, M. acuminata) or slowly (M. denudata). Spiral patterns identified in gynoecia have lower numbers of parastichies than the patterns of androecia and occur in frequencies specific for the genet. Although noted ranges of the meristem and primordia sizes, justify the occurrence of phyllotactic patterns observed in successive zones of Magnolia flower, they do not explain genet-specific frequencies of the patterns observed in gynoecium zone. The lack of straightforward relationship between frequency of the patterns and P/M ratio in gynoecium suggests that more complex geometrical factors or factors of non-geometrical nature are engaged in determination of Magnolia floral phyllotaxis