Leaf unfolding and lamina biomechanics in Syngonium podophyllum and Pilea peperomioides

In nature, leaves and their laminae vary in shape, appearance and unfolding behaviour. We investigated peltate leaves of two model species with peltate leaves and highly different morphology (Syngonium podophyllum and Pilea peperomioides) and two distinct unfolding patterns via time-lapse recordings: we observed successive unfolding of leaf halves in S. podophyllum and simultaneous unfolding in P. peperomioides. Furthermore, we gathered relevant morphological and biomechanical data in juvenile (unfolding) and adult (fully unfolded) leaves of both species by measuring the thickness and the tensile modulus of both lamina and veins as a measure of their stiffness. In S. podophyllum, lamina and veins stiffen after unfolding, which may facilitate unfolding in the less stiff juvenile lamina. Secondary venation highly contributes to stiffness in the adult lamina of S. podophyllum, while the lamina itself withstands tensile loads best in direction parallel to secondary veins. In contrast, the leaf of P. peperomioides has a higher lamina thickness and small, non-prominent venation and is equally stiff in every region and direction, although, as is the case in S. podophyllum, thickness and stiffness increase during ontogeny of leaves from juvenile to adult. It could be shown that (changes in) lamina thickness and stiffness can be well correlated with the unfolding processes of both model plants, so that we conclude that functional lamina morphology in juvenile and adult leaf stages and the ontogenetic transition while unfolding is highly dependent on biomechanical characteristics, though other factors are also taken into consideration and discussed.


Introduction
The morphology and size of plant leaves is highly variable, ranging from tiny leaves in some cacti or conifers [1,2] to very large floating leaves that can support the weight of a small child [3].Leaf shapes can vary from elliptic to oblong or compound, toothed and with or without lobation [4].This wide variation in leaf shape and size in adult leaves is reflected in ontogeny, when the leaf grows from a small bud to its final shape.This period of leaf growth is often accompanied by leaf opening at later stages of development [5,6].Leaves reach their final shape prior to unfolding [5] and different unfolding patterns have evolved in many species: there are leaves that unfold by creasing and folding, such as many leaves of trees [5,7] or grasses [8,9], and leaves that unfold by unrolling their lamina, such as waterlilies [6,10] or Araceae leaves [11].When open, the flat and wide lamina is susceptible to environmental influences.Leaves are exposed to static loads, such as their own weight and-e.g. in some conifers-snow or ice, and dynamic loads, usually wind or rain [12][13][14][15][16][17].To withstand these loads, the comparatively stiff leaf veins reinforce the less stiff laminae [18,19].The laminae, in turn, often consist of parenchymatous ground tissue, which occupies the highest volume fraction in leaves and represents the photosynthetically active leaf part [19,20].The lamina has been shown to be the least mechanically resistant tissue whereas the midrib reinforces the leaf the most.Moreover, the tensile modulus of the entire leaf positively correlates with the proportion of biomass of major veins to parenchymatous tissue [21].
Previous studies only investigated biomechanics of adult leaves without considering the unfolding process.We therefore aim to characterise leaf unfolding as such, and to examine mechanical properties that potentially influence the unfolding process in leaves.For this purpose, we chose the plant species Syngonium podophyllum (Araceae) and Pilea peperomioides (Urticaceae).These two species share a peltate leaf configuration but are adapted to different environmental conditions.S. podophyllum is native to tropical Central and South America and matures from self-supporting to hemi-epiphytic [22] whereas P. peperomioides grows subalpine to alpine in wet and shaded environments both in forests and on cliffs [23,24].We focus on these two species because of (1) their unfolding behaviour and (2) their appearance and morphology.On the one hand, their peltate leaves unfold their lamina during ontogeny (in contrast to other peltate species such as Tropaeolum majus (Tropaeolaceae) that grow leaves open with the lamina expanding in size only [25]) and they show disparate interspecific unfolding patterns, which we will investigate in more detail.On the other hand, they differ considerably in appearance and morphology: the leaves of S. podophyllum form a thin, basally lobed lamina with pinnate venation, whereas those of P. peperomioides form a succulent roundish lamina with inconspicuous palmate venation [16] (figures 1 and 2).These distinct peltate leaf characteristics may influence leaf unfolding and lamina biomechanics differently, as temperature and humidity of the growing sites may be responsible for intraspecific differences.
We aim for describing the leaf unfolding process and lamina biomechanics, and use the two species studied to compare if and how different leaf characteristics (and their ontogenetic changes), namely shape, thickness and Young's moduli in various directions and apical, central and basal parts of the lamina, and veins affect the unfolding process.
Leaf thickness might be crucial for duration of unfolding.We hypothesise that a thin lamina, as in S. podophyllum, will unfold faster than a thick lamina, as in P. peperomioides.Due to its more irregular leaf shape, S. podophyllum may exhibit intralaminar differences in stiffness whereas P. peperomioides, with its rather uniform leaf shape, may display more homogenous stiffnesses across its lamina.
In order to discuss the above assumptions, we will answer the following questions: • Is there a significant influence of leaf region (apical, central, basal) on (1) the thickness of the lamina and/or (2) the veins of S. podophyllum and/or P. peperomioides in a juvenile (unfolding) and in an adult (fully unfolded) phase?• Is there a significant change of thickness of (1) the lamina and/or (2) the veins from a juvenile (unfolding) to adult (fully unfolded) phase in S. podophyllum and/or P. peperomioides?
• Is there an influence of direction (as described in the material and methods section) and/or leaf region (apical, central, basal) on the Youngs' modulus of (1) the lamina and/or (2) the veins S. podophyllum and/or P. peperomioides in a juvenile (unfolding) to and in an adult (fully unfolded) phase?• Is there a significant change of Young`s modulus of (1) the lamina and/or (2) the veins from a juvenile (unfolding) to adult (fully unfolded) phase in S. podophyllum and/or P. peperomioides?

Species cultivation
The plant species were cultivated in the Freiburg Botanic Garden.S. podophyllum individuals were kept at an average temperature of 25

Characterisation of leaf geometry
For S. podophyllum, both juvenile and adult leaves were examined.Leaves were defined as 'juvenile' , if one leaf half was unfolded, on which the tests were carried out.Leaves were defined as 'adult' when unfolding was complete and the two leaf halves were open.For P. peperomioides, only adult leaves could be analysed as in earlier stages-during the entire unfolding process-the two leaf halves are folded, i.e. rolled up, preventing sample preparation for and clamping in the micro-tensile testing machine.
Likewise, leaves of P. peperomioides were defined as 'adult' when unfolding was complete and the two leaf halves were open.Three different regions of the lamina (apical, central and basal) and three different sample orientations (see below for detailed description) were tested and analysed in both species.In S. podophyllum, both the parenchymatous tissue and secondary venation (SV) were investigated for the respective lamina regions to investigate reinforcement of the lamina.In P. peperomioides, parenchymatous tissue only was investigated for the respective lamina regions since the secondary veins were small and not much pronounced in the lamina.
In the case of parenchymatous tissues, the three sample orientations were: parallel (PA) and perpendicular (PE) to secondary venation as well as parallel to the unfolding direction of the lamina (PU) (figure 3).
Concerning leaf region, the basal region was defined as the region from the petiole-lamina transition point to the basal leaf margin.The central region was defined as the region from the petiole-lamina transition point towards half the distance to the apical leaf end.The apical region was defined as the region from the apical leaf tip towards half the distance between the apical tip and the petiole-lamina transition point (figure 3).

Time-lapse recording
For time-lapse recordings, the plant species were transferred into a phytochamber (0.7 × 0.7 × 1.2 m) custom-built by the technical department (Faculty of Biology II/III, University of Freiburg) and kept at the same environmental conditions as for general species cultivation.
Single frames of unfolding leaves were taken with a digital camera (Panasonic Lumix DMC-FZ1000, Panasonic Corporation, Kadoma, Japan) at 20 min intervals for S. podophyllum and 30 min intervals for P. peperomioides.As a built-in function of the camera, single frames were spliced together at 25 fps for timelapse videos.
This methodology allowed for detailed observation of unfolding patterns in S. podophyllum and P. peperomioides (figure 4).

Biomechanical testing
The laminae of S. podophyllum and P. peperomioides leaves were biomechanically tested in tensile experiments.A custom-built micro-tensile testing machine (technical department, Faculty of Biology II/III, University of Freiburg) with a 2.5 N load cell (Model 31, Honeywell, Columbus, USA) was used and samples were tested at 0.1 mm s −1 tension speed.The end criterion of measurement was the rupture of the sample.
To prepare the samples for tensile experiments, they were cut to the following dimensions: 10 × 18 mm for parenchyma and 1 × 18 mm for vein samples.The cut samples were clamped into 3D-printed PLA-holders whose customised configuration allowed a free sample length of 10 × 12 mm and 1 × 12 mm respectively.
Force and displacement were recorded from the tensile experiments and tensile modulus was calculated.The standard formula for calculating the tensile modulus was used for both parenchyma tissue and vein samples [26], as it was not possible to determine the ratio of vascular bundle to parenchyma in the latter: with E: tensile modulus, σ: stress, and ε: strain.The mean thickness for both parenchymatous tissue and secondary veins was measured via a digital calliper for each lamina region in order to calculate the crosssectional area A, which was relevant to determine stress σ (σ = F/A) (figures 5 and 6).[27].While processing data, the following R packages were used: tidyr (dataset rearrangement) [28] and ggplot2 (plot generation) [29].
For statistical analyses, data were tested for parametric distribution using the Shapiro-Wilk normality test.Due to non-parametric distribution, Kruskal-Wallis rank sum test and pairwise Wilcoxon rank sum test were used as post-hoc tests.The statistical significance threshold was set at p < 0.05.Significant differences (p < 0.05) were indicated by lower-case letters.Groups that differ significantly have no letter in common whereas groups that do not differ significantly share at least one letter.

Data description
For clarity in the description of results on leaf thickness and its Young`s modulus, we first describe intraspecific data in regional and directional orientation for the juvenile and the adult phase in S. podophyllum and P. peperomioides This is followed by the description of ontogenetic changes between the juvenile and the adult phase of S. podophyllum and P. peperomioides and then by interspecific (non-)differences between the two species.Our descriptions are based on the pooled data in figures 5 and 6, which are simplified versions of the detailed figures S1 and S2 in the supplement.

Leaf unfolding process
The unfolding process of S. podophyllum and P. peperomioides differ in two main aspects: (1) the unfolding pattern and (2) the unfolding duration.S. podophyllum leaf halves unfold successively whereas P. peperomioides leaf halves unfold simultaneously (figure 4 and videos in supplement).S. podophyllum leaves grow with one leaf half wrapped around the other one, only allowing successive unfolding, which takes about 7 d (videos 1 and 2 in supplement).During the unfolding process, the leaf undergoes a 'posture' in which one half is open while the other one is still folded.This stage was defined as 'juvenile leaf stage' for the biomechanical analyses.Nonetheless, this is one of several intermediate stages that occur during leaf development.S. podophyllum leaves initially emerge from a leaf sheath and transition smoothly from juvenile to adult, as leaf unfolding and development represent a continuous process (videos 1 and 2 in supplement).for the juvenile and the adult lamina of S. podophyllum, the adult lamina of P. peperomioides and the juvenile veins of S. podophyllum due to non-significant differences in leaf thickness in these leaf regions.A detailed analysis of the respective regions is provided in the supplemental material (figure S1).AP-apical leaf region, CE-central leaf region, BA-basal leaf region.Lower case letters indicate statistical significance: groups that differ significantly have no letter in common.
After the leaf halves are fully unfolded along the midrib, the basal parts of the lamina unfold parallel to the basal venation (see late stages of videos 1 and 2).
P. peperomioides develops leaf halves that are folded side by side towards the mid rib, thus enabling simultaneous unfolding which is completed in about 30 d. New leaves develop and grow from inside the dense cluster of helically arranged leaves at the stem apex, causing older leaves to enclose the next younger leaf prior to unfolding.Upon opening, the leaf halves unfold simultaneously and outgrow the next inner leaf by elongation of the petiole (video 3 in supplement).In general, the leaf spatial orientation realigns in both investigated species from vertical in young stages to horizontal in fully developed stages.

Leaf thickness
No significant differences exist for the regional measurements (apical, central, basal) in the juvenile phase in both species and for the adult phase in P. peperomioides.In contrast, there is a high regional dependence of the veins in adult phases of S. podophyllum (figure 4).The central and basal secondary veins in S. podophyllum are significantly thicker compared to the apical secondary veins and the parenchymatous leaf lamina which does not change significantly in S. podophyllum during the developmental process (see figure S1 for detailed information).No significant differences were found between the regional measurements in all juvenile specimens and in all adult specimens of P. peperomioides (figure 4).However, the lamina significantly thickens from juvenile to adult.Moreover, P. peperomioides shows a significantly thicker lamina in both ontogenetic stages compared to the lamina of S. podophyllum, and is, in the adult phase, also significantly thicker than the adult central and basal secondary veins in S. podophyllum (figure 5).

Tensile experiments on the lamina
In the biomechanical analyses, the tensile moduli of S. podophyllum and P. peperomioides show notable differences (cf figure 6).For both ontogenetic stages, the lamina of S. podophyllum is not equally stiff in all directions.There are significant differences in directional stiffness in the juvenile as well as the adult lamina.Orientations parallel (PA) to the secondary venation show highest and orientations perpendicular (PE) to secondary venation show lowest tensile moduli, whereas orientations parallel to the direction of unfolding (PU) show intermediate values.Tertiary and other smaller veins run toward the leaf margin (figure 2(B)) and probably contribute to the directional leaf stiffness (parallel to secondary venation).
When comparing the two ontogenetic stages, the lamina of adult leaves is significantly stiffer than the lamina of juvenile leaves in S. podophyllum (high statistical significance p < 0.001) with median values of the Young's modulus for adult leaves approximately 1.6-2 times higher than the values for juvenile leaves.
As for the veins of S. podophyllum, stiffness is region dependant for both juvenile and adult leaves.

Logarithmic representation of tensile modulus of
Syngonium podophyllum and Pilea peperomioides.Concerning the laminae of both species, the results are pooled per leaf stage and region due to high homogeneity.A detailed analysis of the respective stages and regions is provided in the supplemental material (figure S2).JUV-juvenile leaf, PA-tensile load parallel to secondary venation, PE-tensile load perpendicular to secondary venation, PU-tensile load parallel to unfolding direction.Lower case letters indicate statistical significance: groups that differ significantly have no letter in common.
In juvenile leaves, basal veins are significantly stiffer than central veins, which in turn are stiffer than apical veins.In adult leaves, basal and central veins are significantly stiffer than apical veins.When comparing the venation of the two ontogenetic stages, the stiffness of juvenile basal and adult apical veins is similar.During development from juvenile to adult, a regional increase in stiffness takes place in the secondary venation.In the juvenile stage, apical veins display significantly lower stiffness than the parenchymatous tissue, while the central and basal veins are significantly stiffer.In the adult stage, apical venation shows a similar tensile modulus than the lamina in direction parallel to it, while central and basal veins are significantly stiffer than all values for the mainly parenchymatous lamina.We provide a detailed analysis of the regional conditions in the supplemental material (figure S2).
In contrast to S. podophyllum, the leaves of P. peperomioides show palmate venation with several major veins emerging from the petiole (figure 2), and its lamina is equally stiff in region and direction (figure 6).No significant differences were observed (figure S2).When comparing both species, the adult lamina of S. podophyllum is significantly stiffer than the adult lamina of P. peperomioides.In turn, the lamina of adult P. peperomioides displays significantly higher stiffness than the juvenile lamina of S. podophyllum.

Discussion
The tensile experiments on the leaf lamina of S. podophyllum and P. peperomioides have revealed high differences within and between species and these mechanical dissimilarities (which we discuss in the section 'Tensile experiments on the lamina') are at the base of understanding leaf unfolding in these two model plants.Other factors which might influence the unfolding patterns of S. podophyllum and P. peperomioides are discussed in a broader context in the following section 'Unfolding processes in peltate leaves' .

Unfolding processes in peltate leaves
Leaves are the main organ of photosynthesis in plants and individual leaves should shade each other as little as possible to be most efficient.Self-shading can be reduced by increasing the distance of the leaves from the stem and by their inclination angle relative to incident light [30,31].P. peperomioides has relatively long petioles relative to leaf surface and both S. podophyllum and P. peperomioides spatially rearrange their leaves during development (timelapse videos in supplement), probably to counteract self-shading of (adult) leaves.While P. peperomioides unfolds its leaves simultaneously, a distinct trait of S. podophyllum leaves during development is the successive unfolding of the two leaf halves, which could be shown to happen in three main phases: (1) the unfolding along the midrib of one leaf half, followed by ( 2) the unfolding of the other leaf half and then (3) the simultaneous unfolding of basal parts of the lamina.Alocasia macrorrhiza and Schismatoglottis calyptrata, two species belonging to the Araceae family, also grow their leaf halves wrapped around one another [11,32].This configuration forces successive leaf unfolding also in this species although Sims and colleagues [11] did not specify the process of leaf unfolding in their developmental analyses study.Other Araceae species show the same leaf disposition (personal observation in the Freiburg Botanic Garden), indicating an evolutionary trait in this family.
Euryale ferox, an aquatic plant bearing peltate leaves, unfolds its leaf halves simultaneously but, unlike P. peperomioides, the unfolding process is extremely fast, being completed in one day after initiation of unfolding [3].The same unfolding pattern can be found in the giant waterlily Victoria amazonica [6].These three species (E.ferox, P. peperomioides and V. amazonica) share a peltate orbicular leaf shape.If an orbicular leaf shape, however, causes or eases leaf growth with leaf halves folded side by side-thus allowing simultaneous unfoldinghas yet to be determined.There is evidence that waterlilies with lobed leaf bases-thus non-orbicular leaves-also perform simultaneous unfolding (work in progress).As aquatic plants develop floating leaves, the stiffness of leaves is probably secondary because the aerenchyma, a tissue ensuring floating by big intercellular spaces typically present in aquatic plants, provides mechanical stability by buoyancy and ensures ventilation [10,16,33].
Leaves of trees and grasses also show simultaneous unfolding [5,[7][8][9] but these species can hardly be compared to the leaves analysed in this study because of their distinct morphology (non-peltate leaves) and because the unfolding takes place via creases.
As for the duration of the unfolding process, S. podophyllum leaves are faster than P. peperomioides (approximately one vs.three weeks).Leaf morphology might be relevant for unfolding duration with thinner leaves of S. podophyllum unfolding faster than thick succulent leaves of P. peperomioides.We hypothesise that the unfolding of a thick lamina is slower as the forces that have to be generated during unfolding are dominated by the (higher) bending stiffness of such a lamina.Bending stiffness is not only dependent of the Young's modulus but also by the axial second moment of area, which is markedly higher in a thick lamina.E. ferox unfolds its lamina within one day and has a relatively thin lamina (ca.200 µm) [3], thus being similar in thickness as S. podophyllum leaves (figure 5).
Other than leaf morphology and thickness, leaf unfolding duration can be influenced by the amount of precipitation, temperature, light, altitude, nutrients etc [34][35][36][37][38][39][40].For example, leaf unfolding from the bud stage in broad leaved trees might set in earlier at higher temperatures and/or precipitation [34][35][36].In the same way, a lack of nutrients can delay unfolding [39,40].The leaves of A. macrorrhiza (Araceae) show adaptations to different light conditions by growing thicker leaves under high-light (as leaves of many broad leaved trees do, e.g.[41]), thus being photosynthetically more active.Moreover, when being transferred from low-to high-light conditions, developing leaves increase in thickness, other than adult, fully mature leaves that are not anymore able to adapt [11].To minimise these external effects on unfolding duration for S. podophyllum and P. peperomioides, the plants were grown under standardised conditions (see 'Species cultivation' in material and methods).

Tensile experiments on the lamina
An ontogeny-dependent increase in stiffness could be measured for both parenchymatous and secondary vein tissue in S. podophyllum (figure 6), indicating maturation within the developmental and unfolding process.We suppose that a low lamina stiffness is essential for the development of wrapped up young leaves and also for the unfolding process, so that the lamina only has to overcome low internal forces while opening.As in grasses, turgor pressure is probably responsible for leaf unfolding in S. podophyllum.Decreasing turgor pressure causes folding of the two leaf halves in grasses via bulliform cells, whereas increasing turgor pressure causes unfolding [9,42].High turgor pressure, in turn, can provoke high tissue stiffness [43,44] and parenchyma stiffness can increase up to 70% due to increasing turgor [45].A low stiffness in juvenile leaves of S. podophyllum might therefore be turgor-related and essential for enabling the unfolding movement.After unfolding and exposure of the flattened lamina, the leaf has to become resistant towards external mechanical stress factors.A strengthened lamina is more robust towards abiotic and biotic damage and thus increases the leaf life span [46].The adult lamina becomes stiffest in direction parallel to secondary veins (PA), which could be an indication of external stresses acting along that direction in adult leaves.Lowest stiffness was found in direction perpendicular to secondary veins, probably indicating less intense intra-laminar stresses horizontally across the leaf in S. podophyllum.
In contrast to S. podophyllum, adult leaves of P. peperomioides show neither region-dependent nor directional changes in stiffness (figure S2).We assume that (1) the relatively thick lamina together with (2) the orbicular shape, and (3) the (not very pronounced) palmate venation are responsible for a uniform stiffness across the entire lamina.The veins are in plane with the lamina and hardly pronounced.This structure together with the over all directions and leaf regions constant tensile moduli (figure S2) allow to hypothesise that the venation probably contributes to leaf reinforcement more or less constantly over the entire lamina.Furthermore, the location of the centre of mass of the lamina with respect to the attachment point to the petiole (i.e. the leaf base in non-peltate leaves) plays an important role in leaf stability.When the centre of mass is close to the attachment point, the leaf requires less intra-lamina support by the venation [47].
On the other hand, the venation seems to be crucial for the overall and locally variable stiffness in the strongly lobed leaves of S. podophyllum.The highest stiffness was found in basal veins, which, at the same time, are significantly thicker than the apical venation, implicating a higher bending stiffness in this region.These basal venation parts are, as described, unfolding in approximately 45 • to the midrib, parallel to their secondary veins (so that the unfolding is limited to the mainly parenchymatous, less stiff part of the lamina) after the rest of leaf is already unfolded.We assume that this is a necessary step, as these adult high stiffness veins cannot be 'unrolled' along their axis by the forces that can be generated during the unfolding of the leaf halves.The higher stiffness is likely the result of the lobed shape of the lamina as the basal lobes are very pronounced (long) and therefore subjected to higher bending loads than the unlobed central and apical part parts of the lamina.High stiffness of the lamina due to stabilising effects of the venation has been proven also for other leaf species [3,18,48].In an empirical study for peltate leaves of V. amazonica and in simulations for other peltate floating leaves, it was shown that a nonuniform vein network increases resistance to deformation [3].An irregular vasculature thus increases structural efficiency of leaves [3] and the analogous vein arrangement found in S. podophyllum leaves therefore may also contribute to an effective within-lamina load distribution.
Pinnate-veined leaves, as in S. podophyllum, are characterised by one central midrib from which second-order veins branch off.Secondary veins become more frequent (number of veins per area) in the apical leaf region, probably compensating the decrease in vein thickness.In palmate-veined leaves, as in P. peperomioides, several major veins emerge directly from the petiole into the lamina (figure 2(D)) [4].Compared to palmate-veined leaves, pinnateveined leaves show a higher vein density and minor (tertiary) veins contribute to lamina biomass in a higher extent [47].Minor veins are located in the parenchymatous tissue and, due to their larger (biomass) proportion, they have a higher influence on lamina stabilisation in pinnate-veined leaves than in palmate-veined leaves.Accordingly, leaves of S. podophyllum are significantly stiffer in direction parallel to secondary venation compared to P. peperomioides.
Data for a comparison of the mechanical properties of the two species measured in the present study and other peltate leaves is very scarce.Compared to adult leaves of S. podophyllum and P. peperomioides, tensile stiffness is explicitly lower in T. majus leaves (3.00 ± 0.62 N mm −2 ) and in a similar range in case of Colocasia fallax (8.06 ± 2.61 N mm −2 ) [18].T. majus has an orbicular lamina shape and palmate venation, similarly to P. peperomioides, and also originally grows at higher altitudes while being native to the Andes [49].However, it grows a flat 'unfolded' leaf that only expands while developing [25].The markedly lower stiffness in T. majus may result from the thin lamina together with low stiffness of minor venation.C. fallax has pinnate venation but, in contrast to S. podophyllum, shows a lobed basal end in which the incision does not extend to the petiole-lamina transition zone [18].However, lamina characteristics of C. fallax and S. podophyllum might be comparable (e.g.regarding tissue distribution and occurrence) and thus influence its stiffness in a similar way.Both species grow under tropical to subtropical conditions [22], which probably favours the development of leaf laminae with similar properties.

Conclusion and outlook
Two different unfolding patterns have been observed in the studied species with peltate leaves: simultaneous and successive unfolding of the two leaf halves (P.peperomioides and S. podophyllum respectively).It is, however, not yet clear whether an orbicular leaf shape (as in P. peperomioides) favours leaf growth in a way that simultaneous unfolding can occur.In thinner leaf species, like S. podophyllum, the secondary venation markedly strengthens the entire leaf.This allows for assuming that highest mechanical loads act on the adult lamina in direction parallel to secondary venation.High stresses probably occur in the basally lobed ends that possess the stiffest secondary veins.Overall leaf stiffness in S. podophyllum increases during leaf maturation.A low stiffness in young leaves may be a prerequisite for the development of wrapped up young leaves, and-probably even more important-facilitate unfolding by low internal forces that have to be overcome.
Based on morphological evidence and biomechanical data, we propose the following model for the successive unfolding pattern in S. podophyllum, which might ensure leaf stability in young leaves and during the entire unfolding process: While the outer leaf half is unfolding, the petiole together with the inner leaf half wrapped around it stabilises the petiole-leaf structure especially also in the petiole-lamina transition zone [50,51].
The petiole-leaf structure is strengthened by the unfolded leaf forming a hollow tube that acts as a compound beam structure that is stiffer than an isolated lamina which is prone to buckling.Such structures with a stiff backbone and a flexible lamina are being used as robust elements for façade shading systems as the Flectofin ® [52].The hollow tube in S. podophyllum can be speculated to also act additionally as a guiding structure that determines the direction of unfolding, analogous to a carpet that can only be unrolled parallel to the rotational axis of the roll.
In a next step, the inner leaf half can unfold while the already unfolded leaf half can mechanically support the developing leaf lamina.The unfolded leaf half forms a structure that helps counteract bending and buckling from base to tip of the leaf, so that the rotational axis of the inner leaf half remains undeformed and the unfolding is unhindered.
In a last step, while the apical and central part of the leaf are already unrolled and stabilised, the basal part of the mainly parenchymatous lamina leaf fully unrolls parallel to the highly stiff secondary veins, in order to support the lobed ends of the leaf.
In species with thicker leaf laminae, such as P. peperomioides, the lamina is equally stiff in region and direction.The thick lamina may allow for a uniform distribution of loads but might have a detrimental effect on the unfolding speed.Another important factor for leaf development and unfolding speed is growth, so that a relatively thick lamina as present in P. peperomioides requires more time to develop (and unfold) its 'bending zone' compared to the thinner lamina of S. podophyllum.Future studies could contribute to a better understanding of the form-structure-function relation during leaf unfolding by examining distinctly shaped leaves to assess the directional stiffness of the leaf lamina.

2. 5 .
Data processing and statistical analyses R (version 4.3.0)and RStudio (version 2023.03.1) were used for results evaluation and statistical testing

Figure 2 .
Figure 2. Adaxial and abaxial view of adult leaves of Syngonium podophyllum and Pilea peperomioides.Adaxial (A), (B) and abaxial view of S. podophyllum (C) as well as adaxial and abaxial view of P. peperomioides (D).(B) is a detail of (A).PV-primary vein, SV-secondary vein, TV-tertiary vein.

Figure 3 .
Figure 3. Schematic illustration of sample preparation for tensile experiments of Syngonium podophyllum and Pilea peperomioides.Analyses comprised juvenile (upper) and adult (middle) leaves of S. podophyllum and adult leaves of P. peperomioides (lower).PA-parallel to secondary venation, PE-perpendicular to secondary venation, PU-parallel to unfolding direction.SV-secondary venation.

Figure 5 .
Figure 5. Leaf thickness in Syngonium podophyllum and Pilea peperomioides for different leaf stages and tissues.Results are pooledfor the juvenile and the adult lamina of S. podophyllum, the adult lamina of P. peperomioides and the juvenile veins of S. podophyllum due to non-significant differences in leaf thickness in these leaf regions.A detailed analysis of the respective regions is provided in the supplemental material (figureS1).AP-apical leaf region, CE-central leaf region, BA-basal leaf region.Lower case letters indicate statistical significance: groups that differ significantly have no letter in common.

Figure 6 .
Figure 6.Logarithmic representation of tensile modulus of