Morphology and anatomy of the foliage leaf of Pilea peperomioides (a). The thin-sections of the transition zone are stained with acridine orange (c) and those of the petiole are stained with toluidine blue (b). The scale bar of the leaf morphology equals 2 cm and those of the anatomical sections equal 1 mm.

Morphology and anatomy of the foliage leaf of Pilea peperomioides (a). The thin-sections of the transition zone are stained with acridine orange (c) and those of the petiole are stained with toluidine blue (b). The scale bar of the leaf morphology equals 2 cm and those of the anatomical sections equal 1 mm.

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Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans...

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... petiole is slightly offset adaxially. The leaves have a rotate venation, with the veins radiating from the entry point of the transition zone into the lamina (Figure 6a). ...
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... petiole of P. peperomioides is a circular truncated cone that tapers hyperbolically (Table 3). The geometrical change from a circular (Figure 6b) to an elliptical cross-section indicates the beginning of the petiole-lamina transition zone (Figure 6c). This change from the petiole into the lamina is also reflected in the change from a linear increase to an exponential increase of A, I, and J (Figure 1f). ...
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... petiole of P. peperomioides is a circular truncated cone that tapers hyperbolically (Table 3). The geometrical change from a circular (Figure 6b) to an elliptical cross-section indicates the beginning of the petiole-lamina transition zone (Figure 6c). This change from the petiole into the lamina is also reflected in the change from a linear increase to an exponential increase of A, I, and J (Figure 1f). ...
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... change from the petiole into the lamina is also reflected in the change from a linear increase to an exponential increase of A, I, and J (Figure 1f). The exponential increase of the crosssectional area can also be seen in the transverse thin-sections, particularly in the lobes forming in the middle transition zone (Figure 6c). Because of the 3D nature of the lamina, a hole occurs in the middle of the thin-section in the apical transition zone (Figure 6c). ...
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... exponential increase of the crosssectional area can also be seen in the transverse thin-sections, particularly in the lobes forming in the middle transition zone (Figure 6c). Because of the 3D nature of the lamina, a hole occurs in the middle of the thin-section in the apical transition zone (Figure 6c). The I/J ratio of the transition zone is not significantly smaller than that of the petiole (W = 48, p = 0.190) (Table 3). ...
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... the petiole, the vascular bundles are present as six strands in the center and, in the acropetal direction, converge closer together and partly merge with each other (Figure 6b, the bundles appear in dark violet). At the entry to the basal transition zone, the thinsections (Figure 6c, the bundles appear in orange) and the µCT data (Figure 2l) show that the vascular bundles form a single U-profiled strand that is thicker on the abaxial side than on the adaxial side and that splits acropetally into eight separate vascular strands that radiate in all directions into the lamina (Figure 2d,h). ...
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... the petiole, the vascular bundles are present as six strands in the center and, in the acropetal direction, converge closer together and partly merge with each other (Figure 6b, the bundles appear in dark violet). At the entry to the basal transition zone, the thinsections (Figure 6c, the bundles appear in orange) and the µCT data (Figure 2l) show that the vascular bundles form a single U-profiled strand that is thicker on the abaxial side than on the adaxial side and that splits acropetally into eight separate vascular strands that radiate in all directions into the lamina (Figure 2d,h). Since the petiole is slightly inclined to the abaxial side, the abaxial strands enter the lamina with less curvature than the strands on the adaxial side (Figure 2d). ...

Citations

... While anatomical and biomechanical properties of leaves are generally well studied, not many research efforts have been devoted to investigate the peltate leaf shape. Peltate leaves are defined by the petiole inserting on the abaxial side of the lamina resulting in a 3-dimensional spatial arrangement (Troll, 1932;Langer et al., 2021b;Wunnenberg et al., 2021). The peltate leaf shape is not very common in the plant kingdom. ...
... In comparison, leaves with a 2D configuration need to be resistant in bending in one direction while still being flexible in torsion (Langer et al., 2021a). The transition zone is characterized by a significant change in geometry from petiole to lamina, plays a crucial role in the dissipation of mechanical loads and is optimized to cope with different loads in comparison to the petiole (Sacher et al., 2019;Langer et al., 2021b;Langer et al., 2022). ...
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Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work.
... The following procedures (histochemical tests) are a starting point to identify the potential compounds and their exact location. The limited number of studies (Andrić et al. 2016, Langer et al. 2021 is one of the key reasons for choosing these three species of Asparagaceae. ...
... Contrary to the 2-dimensional architecture of leaves with a marginally attached petiole, peltate leaves are defined by a 3-dimensional spatial arrangement [20]. In particular the transition zone from petiole to peltate lamina shows a significant change in geometry [11,20]. ...
... Contrary to the 2-dimensional architecture of leaves with a marginally attached petiole, peltate leaves are defined by a 3-dimensional spatial arrangement [20]. In particular the transition zone from petiole to peltate lamina shows a significant change in geometry [11,20]. To secure the connection between petiole and lamina, the transition zone needs to provide mechanical stability while transporting water and nutrients through petiole and lamina. ...
... The important role of the transition zone of peltate leaves in handling mechanical stress and load dissipation has already been demonstrated [21] and showed significant differences in mechanical properties of petiole and petiole-lamina transition zone indicating that petiole and transition zone are optimized to cope with different mechanical loads [22]. Additionally, in several studies different types of fiber organization in the transition zone were revealed [20,21]. A following anatomical study focusing on the fiber orientation in the transition zone from petiole to lamina in a variety of peltate plant species identified seven types of strengthening structures [11]. ...
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Plants are exposed to various external stresses influencing physiology, anatomy, and morphology. Shape, geometry, and size of shoots and leaves are particularly affected. Among the latter, peltate leaves are not very common and so far, only few studies focused on their properties. In this case study, four Begonia species with different leaf shapes and petiole attachment points were analyzed regarding their leaf morphology, anatomy, and biomechanical properties. One to two plants per species were examined. In all four species, the petiole showed differently sized vascular bundles arranged in a peripheral ring and subepidermal collenchyma. These anatomical characteristics, low leaf dry mass, and low amount of lignified tissue in the petiole point toward turgor pressure as crucial for leaf stability. The petiole-lamina transition zone shows a different organization in leaves with a more central (peltate) and lateral petiole insertion. While in non-peltate leaves simple fiber branching is present, peltate leaves show a more complex reticulate fiber arrangement. Tensile and bending tests revealed similar structural Young’s moduli in all species for intercostal areas and venation, but differences in the petiole. The analysis of the leaves highlights the properties of petiole and the petiole-lamina transition zone that are needed to resist external stresses.
... It is worth remarking that here we have neglected the fact that petioles are not homogeneous and isotropic structures. This is the reason why their bending and tensile modulus derived by biomechanical tests can differ, sometimes largely [See, e.g., Langer et al. (2021a;2021b)]. An advantage of our approach, based on NMSA, is that it allows us to model possible nonhomogeneities that cannot be ignored. ...
... It would be also interesting to include the petiole transition zones (at stem and lamina) with geometric and mechanical properties differing from the petiole in the model to better describe the behavior provided that the data on the structure are available, either from the literature or obtained by mechanical characterization. Recent studies showed that the damage-resistant petiole-lamina transition zone is indeed an overlooked but essential part of the foliage leaves, as for example, the twist-to-bend ratio (flexural rigidity divided by the torsional rigidity) varies along the structure (Sacher et al., 2019;Langer et al., 2021b). ...
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High-tech sensors, energy harvesters, and robots are increasingly being developed for operation on plant leaves. This introduces an extra load which the leaf must withstand, often under further dynamic forces like wind. Here, we took the example of mechanical energy harvesters that consist of flat artificial “leaves” fixed on the petioles of N. oleander, converting wind energy into electricity. We developed a combined experimental and computational approach to describe the static and dynamic mechanics of the natural and artificial leaves individually and join them together in the typical energy harvesting configuration. The model, in which the leaves are torsional springs with flexible petioles and rigid lamina deforming under the effect of gravity and wind, enables us to design the artificial device in terms of weight, flexibility, and dimensions based on the mechanical properties of the plant leaf. Moreover, it predicts the dynamic motions of the leaf–artificial leaf combination, causing the mechanical-to-electrical energy conversion at a given wind speed. The computational results were validated in dynamic experiments measuring the electrical output of the plant-hybrid energy harvester. Our approach enables us to design the artificial structure for damage-safe operation on leaves (avoiding overloading caused by the interaction between leaves and/or by the wind) and suggests how to improve the combined leaf oscillations affecting the energy harvesting performance. We furthermore discuss how the mathematical model could be extended in future works. In summary, this is a first approach to improve the adaptation of artificial devices to plants, advance their performance, and to counteract damage by mathematical modelling in the device design phase.
... Figure 2 illustrates various transverse sections of plant axes with differing cross-sectional geometries and tissue patterns. Based on stained thin sections from previous studies [1,21,[23][24][25], corresponding schematic drawings were created depicting the cross-sectional geometry of the plant axes and the distribution of the tissues involved. These plant examples were selected because their geometric, mechanical and structural properties were available for discussion of the results of the simulations of this study (electronic supplementary material, S1 and table S1.1). ...
Article
During the evolution of land plants many body plans have been developed. Differences in the cross-sectional geometry and tissue pattern of plant axes influence their flexural rigidity, torsional rigidity and the ratio of both of these rigidities, the so-called twist-to-bend ratio. For comparison, we have designed artificial cross-sections with various cross-sectional geometries and patterns of vascular bundles, collenchyma or sclerenchyma strands, but fixed percentages for these tissues. Our mathematical model allows the calculation of the twist-to-bend ratio by taking both cross-sectional geometry and tissue pattern into account. Each artificial cross-section was placed into a rigidity chart to provide information about its twist-to-bend ratio. In these charts, artificial cross-sections with the same geometry did not form clusters, whereas those with similar tissue patterns formed clusters characterized by vascular bundles, collenchyma or sclerenchyma arranged as one central strand, as a peripheral closed ring or as distributed individual strands. Generally, flexural rigidity increased the more the bundles or fibre strands were placed at the periphery. Torsional rigidity decreased the more the bundles or strands were separated and the less that they were arranged along a peripheral ring. The calculated twist-to-bend ratios ranged between 0.85 (ellipse with central vascular bundles) and 196 (triangle with individual peripheral sclerenchyma strands).
... In addition, they can occur at interfaces of biological composites (STUDART et al., 2014) and, as in the case of bamboo (WEGST et al., 2015) and coconut (GRAUPNER et al., 2017;SCHMIER et al., 2020a;SCHMIER et al., 2020b), encompass various hierarchical levels to increase the rigidity and strength of the material. Gradients at the levels of geometry, shape, size, and tissue arrangement are also found between the petiole and lamina of foliage leaves, providing a damage-resistant transition zone (LANGER et al., 2021). A further concept enabling plants to avoid damage is to respond to changing environmental conditions. ...
... Die Querschnitte wurden mit Acridinorange gefärbt. Maßstab 1 mm (verändert nach Artikel C (Langer et al., 2021b)). ...
... Um den Einfluss der Größe zu verstehen, wurden verschiedene Größenvariablen untersucht: (Langer et al., 2021b) (Yin, 1938;Foster und Arnott, 1960;Sacher et al., 2019) (Artikel C). Eine ...
... In der seitlichen Ansicht ist die abaxiale Seite nach rechts orientiert und die adaxiale Seite nach links. Maßstab 1 mm (verändert nach Artikel C (Langer et al., 2021b) (King und Loucks, 1978;Niklas, 1990Niklas, , 1992 ...
... In literature, the biomechanical role of the petiole is well described, especially in terms of its support for the lamina and yielding under wind loads. However, little is known about the biomechanical behaviour of the short transition zone between the rod-shaped or U-profiled petiole and the (nearly) planar lamina (Langer et al., 2021b). As described above, petiole, transition zone, and lamina of foliage leaves respond to wind or to touch by passing animals by simultaneously bending downwind and twisting away. ...
... As far as the general geometry of petioles is concerned, we mainly find circular, elliptical, and adaxially grooved cross-sections (Vogel, 1992;Ennos et al., 2000;Pasini and Mirjalili, 2006;Langer et al., 2021b). With the exception of a perfectly circular cross-section, the torsion constant K is usually smaller than J. ...
... point, area, zone, joint, juncture) or quality of connection (e.g. transition, union, attachment, junction, border) (Langer et al., 2021b). However, the biomechanical behaviour of the petiole-lamina transition zone has not yet been studied in detail. ...
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Plants are exposed to various environmental stresses. To mechano-stimulation, such as wind and touch, leaves immediately respond by bending and twisting or acclimate over a longer time period by thigmomorphogenetic changes of mechanical and geometrical properties. We selected the peltate leaves of Pilea peperomioides for a comparative analysis of mechano-induced effects on morphology, anatomy and biomechanics of petiole and transition zone. The plants were cultivated for six weeks in a phytochamber divided into four treatment groups: control (no stimulus), touch stimulus (brushing every 30 s), wind stimulus (constant air flow of 4.6 ms -1), and a combination of touch and wind stimuli. Comparing the treatment groups, neither the petiole nor the transition zone show significant thigmomorphogenetic acclimations. However, comparing the petiole and the transition zone, the elastic modulus (E), the torsional modulus (G), the E/G ratio and the axial rigidity (EA) differed significantly, whereas no significant difference was found for the torsional rigidity (GK). The twist-to-bend ratios (EI/GK) of all petioles ranged between 4.33 and 5.99, and of all transition zones between 0.67 and 0.78. Based on the twist-to-bend ratios, we hypothesise that bending loads are accommodated by the petiole, while torsional loads are shared between the transition zone and petiole.
... This is crucial as leaves and their petioles show a wide variety of morphological and anatomical characteristics. One aspect is the spatial configuration of the lamina and petiole, described by Langer et al. (2021) as three-dimensional (3D) for peltate leaves and two-dimensional (2D) for leaves in which the petiole is attached to the lamina base. Moreover, marked differences are found between the cross-sectional geometries of petioles, which can be circular, elliptical or U-profiled (Vogel, 1992;Ennos et al., 2000;Pasini and Mirjalili, 2006). ...
... (hereafter H. alternata), and Pilea peperomioides Diels (hereafter P. peperomioides) were cultivated in the greenhouse of the Botanic Garden (University of Freiburg, Germany). These four species were selected based on the same criteria as those described by Langer et al. (2021): (1) two species of each body plan (monocotyledonous and dicotyledonous) having a foliage leaf with either a 2D or 3D spatial configuration of petiole and lamina, (3) herbaceous, (4) perennial, and (5) easy to cultivate to provide sufficient material for experimentation. One random leaf of each of the 25 plants studied per species was investigated (Figure 1). ...
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From a mechanical viewpoint, petioles of foliage leaves are subject to contradictory mechanical requirements. High flexural rigidity guarantees support of the lamina and low torsional rigidity ensures streamlining of the leaves in wind. This mechanical trade-off between flexural and torsional rigidity is described by the twist-to-bend ratio. The safety factor describes the maximum load capacity. We selected four herbaceous species with different body plans (monocotyledonous, dicotyledonous) and spatial configurations of petiole and lamina (2-dimensional, 3-dimensional) and carried out morphological-anatomical studies, two-point bending tests and torsional tests on the petioles to analyze the influence of geometry, size and shape on their twist-to-bend ratio and safety factor. The monocotyledons studied had significantly higher twist-to-bend ratios (23.7 and 39.2) than the dicotyledons (11.5 and 13.3). High twist-to-bend ratios can be geometry-based, which is true for the U-profile of Hosta x tardiana with a ratio of axial second moment of area to torsion constant of over 1.0. High twist-to-bend ratios can also be material-based, as found for the petioles of Caladium bicolor with a ratio of bending elastic modulus and torsional modulus of 64. The safety factors range between 1.7 and 2.9, meaning that each petiole can support about double to triple the leaf’s weight.
... The tensile, bending and torsional loads that occur in nature, e.g., because of selfweight, external influences such as wind or snowfall [18] or contact with passing mammals [35], can be counteracted by morphological adaptations such as an increase in crosssections, the axial second moment of area or the torsion constant of the loaded structure [36]. In this context, the external appearance of a plant body can be described and defined by its geometry (e.g., circular, elliptical), its size (e.g., cross-sectional area, axial second moment of area, torsion constant) and its shape (the ratios and gradients between these variables) [37,38]. ...
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The Opuntioideae include iconic cacti whose lateral branch–branch junctions are intriguing objects from a mechanical viewpoint. We have compared Opuntia ficus-indica, which has stable branch connections, with Cylindropuntia bigelovii, whose side branches abscise under slight mechanical stress. To determine the underlying structures and mechanical characteristics of these stable versus shedding cacti junctions, we conducted magnetic resonance imaging, morphometric and anatomical analyses of the branches and tensile tests of individual tissues. The comparison revealed differences in geometry, shape and material properties as follows: (i) a more pronounced tapering of the cross-sectional area towards the junctions supports the abscission of young branches of C. bigelovii. (ii) Older branches of O. ficus-indica form, initially around the branch–branch junctions, collar-shaped periderm tissue. This secondary coverage mechanically stiffens the dermal tissue, giving a threefold increase in strength and a tenfold increase in the elastic modulus compared with the epidermis. (iii) An approximately 200-fold higher elastic modulus of the vascular bundles of O. ficus-indica is a prerequisite for the stable junction of its young branches. Our results provide, for both biological and engineered materials systems, important insights into the geometric characteristics and mechanical properties of branching joints that are either stable or easily detachable.