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A 3D study of the relationship between leaf vein structure and mechanical function
Acta Biomaterialia 88 (2019) 111–119
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Full length article
A 3D study of the relationship between leaf vein structure and mechanical function Maria Pierantoni a, Vlad Brumfeld b, Lia Addadi a, Steve Weiner a,⇑ a b
Department of Structural Biology, Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel Department of Chemical Research Support, Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel
a r t i c l e
i n f o
Article history: Received 15 August 2018 Received in revised form 3 February 2019 Accepted 15 February 2019 Available online 16 February 2019 Keywords: Biomechanics microCT Calcium oxalate crystals Lignified fibers Biological composite material
a b s t r a c t We investigate the structures and mechanical properties of leaf midribs of Ficus microcarpa and Prunus dulcis, which deposit calcium oxalate crystals, and of Olea europaea midribs which contain no mineral deposits, but do contain lignified fibers. The midrib mechanical performance contributes to the leaf’s ability to maintain a flat conformation for light harvesting and to efficiently reconfigure to reduce wind drag. We use a novel approach involving 3D visualization of the vein structure during mechanical load. This involves the use of customized mechanical loading devices that fit inside a microCT chamber. We show that the elastic, compression and torsional moduli of the midribs of leaves from the 3 species examined vary significantly. We also observed different modes of fracture and buckling of the leaves during compression. We assess the contributions of the calcium oxalate crystals to the mechanical and fracture properties. In F. microcarpa midrib linear arrays of calcium oxalate crystals contribute to resisting the bending, in contrast to P. dulcis leaves, where the calcium oxalate crystals do not resist bending. In both F. microcarpa and P. dulcis isolated calcium oxalate crystals enable high torsional compliance. The integrated microCT – mechanical testing approach could be used to investigate the structure-mechanics relationships in other complex biological samples. Statement of significance Leaves need to maintain a flat conformation for light harvesting, but they also need to efficiently reconfigure to reduce wind drag. The leaf central vein (midrib) is a key structural component for leaf mechanicss. 3D visualization of the vein structure under mechanical loads showed that veins can be stiffened by reinforcement units composed of calcium oxalates crystals and lignin. The stiffening units can influence the bending and fracture properties of the midribs, and can contribute to determine if buckling will occur during folding. Mineral stiffening elements could be a widespread strategy to reinforce leaf veins and other biological structures. This structural-mechanical approach could be used to study other complex biological samples. Ó 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction In leaves mechanical resistance to bending is necessary for maintaining a flat conformation, which in turn is essential for light harvesting. Torsional compliance reduces drag, and is also important, as leaves have to withstand strong winds and to reconfigure efficiently [1–3]. Key components contributing to these mechanical properties are the leaf veins and especially the midrib. For maize ⇑ Corresponding author at: Weizmann Institute of Science, Department of Structural Biology, Herzl Street, Rehovot 7610001 Israel. E-mail addresses: [email protected] (M. Pierantoni), [email protected] (V. Brumfeld), [email protected] (L. Addadi), steve. [email protected] (S. Weiner). https://doi.org/10.1016/j.actbio.2019.02.023 1742-7061/Ó 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
leaves it was shown that the midrib greatly stiffens the leaf, especially in locations where bending moments are high [4]. The elastic modulus of the leaf blade (lamina) is primarily related to the mass ratio of major veins to the rest of the lamina [4]. Consequently an increase in the fraction of veins increases the mechanical strength of the entire leaf [4]. A recent study of leaves from 21 different species showed that mechanical resistance differed among the leaf component tissues, and that the tissue with the highest resistance is always the midrib [5]. Furthermore, the largest differences in mechanical resistance between the 21 species were associated to the midrib, and not to the leaf lamina [5]. Despite all these observations, leaf mechanical responses are usually studied only as a function of lamina thickness, tissue density and toughness per unit
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tissue density. To our knowledge, the midrib mechanics were never studied in relation to its different components [6]. Many leaves also contain minerals. In a previous study we investigated mineral deposits in leaves from 10 different Ficus species [7]. We showed that the veins are always associated with calcium oxalate crystals, and that this is the only common mineral deposition trait between all the studied Ficus species [7]. Calcium oxalate crystals have been documented along the veins of many other genera of higher plant leaves, from trees to herbaceous plants [8–11]. Calcium oxalates crystals are isolated stiff components organized along the vein fibers. This mode of mineral organization is not unique to leaves. Many organisms have, embedded in their tissues, reinforcing small particles of stiff material [12]. The reinforcing effect of such stiff particles was documented for the spicules of sponges and cnidarians [12,13], for the ossicles of starfish [14], for the sclerites of corals, and for the lignified material in the stem of sedge [15]. Koehl suggested that stress can be transferred from the tissue to the stiff particles, which will bear part of the force applied to the whole material [12]. The stiff particles restrict the movements of the soft tissue around them, and consequently they help to prevent rearrangement of the whole structure under stress. When the whole structure is deformed, the rigid particles do not change shape, but may change relative positions. The soft tissue between the particles can deform, but because of the rigid particles, the deformation of the whole material will be smaller than the deformation of the soft tissue alone. Thus the distribution and orientation of the particles within the soft tissue can affect the way in which the whole structure responds to mechanical stress [12]. Calcium oxalate crystals along leaf veins could have an important, but as yet undocumented function in reinforcing the veins. Plant structures, in general, are hierarchically organized so that the microstructural features greatly contribute to their macroscopic properties [16,17]. In order to rationalize how different components, including minerals, contribute to the mechanical performance of the midribs, we use a novel approach involving 3D visualization of the vein structure under controlled loads. We perform tension tests, compression-bending tests and torsion tests on the midribs using custom made setups, which were designed to function inside the chamber of an X-ray microtomography scanner (microCT). This enables the study of midrib mechanical behavior at micrometer resolution, in relation to structural changes. Here we investigate the midribs of Ficus microcarpa, Prunus dulcis (common name almond) and Olea europaea (common name olive), which all have blade and midribs of approximately the same size, but with different midrib structures. F. microcarpa and P. dulcis midrib cells also deposit calcium oxalate crystals. The midribs of O. europaea do not contain calcium oxalate crystals, but contain lignified fibers in the xylem [18]. Ficus microcarpa, Prunus dulcis and Olea europaea have ellipsoidal leaves. Ellipsoidal leaves are particularly interesting for the study of midrib mechanics, because in these leaves the midribs have to support laminae in which the leaf mass center (index of distribution of leaf mass along the leaf length) is located closer to the leaf tips than to the petioles [19]. Consequently, in these leaves petioles contribute only partially to the support of the leaf mass, which needs to be borne by the midrib and by the other veins. We study how differences in midrib structure and composition in each of the three species relate to their mechanical properties.
2. Materials and methods 2.1. Plant material Ficus microcarpa, Prunus dulcis and Olea europaea leaves were collected and analyzed fresh from mature trees growing outdoors
in Rehovot, Israel. All the leaves were collected from about 1.5 m to maximum 2.5 m from the ground. For the mechanical tests midribs of diameter 1 mm and length 30 mm were dissected using a razor blade and tested. 2.1.1. Phase contrast enhanced microCT MicroCT scans were acquired using a Micro XCT-400 (Zeiss Xray Microscopy, California, USA) as in Pierantoni at al. [7]. Triangular sections of leaves (base1 cm, length 2 cm) were cut and placed in a sealed plastic pipette tip. The tips were partially filled with water to prevent dehydration of the samples. Only the part of the leaf not immersed in water was imaged. The scans were performed keeping the source and the detector at the optimal distances for phase contrast propagation (50 mm and 75 to 90 mm to the sample respectively). Phase contrast improves the quality of images, by increasing contrast sensitivity especially around edges [20]. This enables detection of the soft tissue anatomy of minute structures. The tomographic images were obtained from 1500 projections (acquired over180°) at 30 kV and 450 mA. The final voxel size was 0.95–1.05 mm (depending on the source and detector positions). The microCT volumes were reconstructed using a back projection filtered algorithm (Zeiss). 2.1.2. Image processing and analysis 3D image processing and analysis of the reconstructed microCT volumes were carried out using the Avizo software. The mineral volume fraction was obtained by contrast thresholding the minerals (the most absorbing bodies in the veins). The midrib volume was calculated considering xylem, phloem and ground tissue together. The reproducibility of the data was estimated by analyzing the same volume within a specimen 3 times. A variance of 0.03% was obtained. 2.2. Confocal microscopy Cross-sections of a few hundred micrometers were cut from fresh F. microcarpa and P. dulcis midribs using a razor blade in the direction of the vein main axes. The cell walls of the exposed tissue were stained with a solution composed of 0.05 ml of Calcofluor White Stain (Calcofluor White M2R 1 g/l, Evans blue 0.5 g/l, 18,909 Sigma Aldrich) and 0.05 ml of 10% potassium hydroxide. The sections were placed between coverslips and imaged with a confocal FW1000 laser scanning microscope, Olympus IX81. The excitation laser wavelength is k = 402 nm for both the chlorophyll and the PDMPO dye. The emission was obtained with a 420–520 nm band-pass filter. The volumes were acquired with 60 oil objective lens magnification, with z steps of 1 lm. 2.3. Micro-mechanical devices The system used for the tensile tests and the compressionbending tests was attached to the standard rotating stage of the microCT. It consists of an open cylindrical sample testing chamber (85 mm in height and 50 mm in diameter) stabilized by two metallic posts of 5 mm in diameter (Fig. S1A). The system includes two anvils, one of which (the upper) is mobile and the second is fixed to the base of the chamber. An axial-motion DC motor moves the upper anvil into the testing chamber in sub-micron steps. The anvil position is controlled by a position servocontroller (C-863 Mercury, Physik Instrumente, GmbH, Germany). The anvil is attached to a load cell (C31, Honeywell, USA) of range between 0 and 120 N and sensitivity of 0.4 N. The force is measured with a GM signal conditioner-indicator (Sensotec, Honeywell, USA), which is connected to the load cell. Both the anvils terminate with a groove (15 mm 10 mm 5 mm) in which the sample is inserted and is held by a clamp (Fig. S1 B). The two clamps are positioned out of
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the microCT detector field of view. As the setup is inside the microCT chamber, it was possible to visualize minerals and vein tissue during the force measurement. Note that since the two posts limit the field of view when microCT volumes are acquired (the field of view is not 180° but 140°), the contrast is preserved but the resolution is reduced. The system used for the torsion tests consists of an upper stable anvil (Fig. S1C a) connected to a torque sensor (TD50TD70 ± 50 Nm, accuracy class: 0,1%; 0.5 mV/V/FS, LARIT Measurements). The torque sensor (Fig. S1C b) is attached to a metallic pivot of adjustable length (Fig. S1C c) which in turn is screwed to a magnet (Fig. S1C d) fixed to the ceiling of the microCT chamber. The lower anvil is connected to the microCT stage, which is used to rotate at 0.15 deg/s the anvil and the sample fixed to it by fixed angles. The upper and lower anvils are the same used for the tensile tests and the compression-bending tests (Fig. S1B). Since there is no physical connection between the upper part of the setup and the lower part, the two sides have to be carefully aligned. The alignment is performed using a pendulum connected to the upper anvil. The lower anvil is moved by microsteps using the microCT stage motor until the pendulum tip touches the center of the lower anvil and the two parts are perfectly aligned. 2.4. Mechanical tests For the tension tests midrib sections of diameter of 1 mm and length of 30 mm were inserted between two posts at a distance of 15 mm. Double sided carbon tape was applied in the grooves of the anvils so that they were in contact with the sample. This prevents the midribs from drifting during the test. The lower anvil is stable while the upper anvil can move up at controlled speed of 20 mm/s until the leaf portion breaks. The tests were conducted within approximately 2 min during which time the samples do not dry significantly. For compression-bending tests leaf portions of 3 cm 1 cm 1 mm or extracted midribs (30 mm 1 mm 1 mm) were cut and inserted into the grooves of the two anvils at a distance of 15 mm. The lower anvil is stable while the upper anvil moves down at a controlled speed of 20 mm/s for a total displacement of 7 mm. The force was recorded every 100 ms and a force-displacement curve was obtained. For leaf portions, we verified that the recorded force was due only to the midrib by conducting the same tests, but placing the leaf perpendicular to the midrib, and again on a leaf portion without the midrib. In both control cases the force required to bend the leaf portion was below the detection limit. For the torsion tests, midribs (diameter 1 mm) were cut from the leaf and 30 mm long sections were inserted between two posts which are at a distance of 15 mm from each other. The midrib was torqued from 0° to 90° and back to 0° at an angular velocity of 0.15 deg/s. The moment of torsion was recorded every 50 ms and the curve moment of torsion vs. angle of twist was generated. Since the obtained curves are noisy, they were smoothed by exponential smoothing (0.95 damping). The behavior of the midribs during the mechanical tests was monitored by acquiring microCT 2D projection images every 3.5 s without rotating the sample. The projection images were used to produce a video showing the midrib macroscopic conformational changes during the tests. 2.5. Statistical analysis Elastic moduli (n) were obtained from the force-displacement curves by applying Eq. (1):
n¼
DF 4L Dx pr2
ð1Þ
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where DDxF is the initial slope of the curve, L is the distance between the posts and r is the midrib radius. The calculation was repeated for 15 different samples in the case of F. microcarpa and O. europaea and for 19 different samples in the case of P. dulcis. The average value of n and the standard error were obtained for each species. Compression moduli (nc) were obtained by applying Eq. (1) to the initial slope of the force-displacement curves. The calculation was repeated for 17 different samples in the case of F. microcarpa and for 15 different samples in the case of P. dulcis and O. europaea. The average value of nc and the standard error were obtained for each species. From the torque vs. angle of twist curves the torsion modulus (ɣ) was obtained applying Eq. (2),
c¼
DT 1 Dh r
ð2Þ
where DDTh is the initial slope of the curve and r is the midrib radius. The calculation was repeated for 17 different samples in the case of F. microcarpa, for 18 different samples in the case of P. dulcis and for 15 different samples for O. europaea. The average value of ɣ and the standard error were obtained for each species. 3. Results 3.1. 3D anatomy of midribs We use phase contrast enhanced microCT in order to visualize minerals and soft tissue structures in F. microcarpa, P. dulcis and O. europaea leaf midribs (Fig. 1). In F. microcarpa midribs the xylem and phloem cross sections form a complete circle of about 400 mm diameter (Fig. 1 A). In P. dulcis midrib xylem and phloem the cross sections have a U-shape and have a maximum diameter of about 500 mm (Fig. 1 B). In O. europaea the xylem also forms a U-shape that has a maximum diameter of about 250 mm and all around the xylem the phloem forms a circle of about 500 mm (Fig. 1 C). In F. microcarpa and P. dulcis xylem tissue forms the vascular bundles. In O. europaea xylem the fibers are associated with some lignin [18] (arrows in Fig. 1 C, and F). The content of lignin increases during the maturation of the leaf (Fig. S2). The mean length of the units forming the continuous fibers is 217 mm ± 12 mm (n = 30). In mature leaves the fibers run continuously along the whole xylem. In the phloem of both F. microcarpa and P. dulcis calcium oxalate crystals are deposited (highly contrasting bodies in Fig. 1 A, D and Fig. 1 B, E). Calcium oxalate crystals are organized in parallel lines along the vein major axes. In O. europaea phloem no calcium oxalates are deposited. All three species have ground tissue extensions on the lower side of the phloem, and above the phloem in the case of P. dulcis and O. europaea (Fig. 1 A–C). The ground tissue cells are arranged to form a honeycomb structure (Fig. S3). All the midribs protrude from the leaf blade in the direction of the lower leaf side (the leaf mesophyll is rendered in green in Fig. 1). 3.2. 3D organization of calcium oxalate crystals Calcium oxalates are deposited in F. microcarpa and P. dulcis phloem along well defined lines. The vein soft tissue components seem to determine this deposition pattern. The phloem consists of sieve tubes and companion cells. Sieve tubes are elongated cells which have groups of pores at their extremities and companion cells are smaller cells surrounding the sieve tubes (Fig. S4). We use confocal microscopy to identify which cells contain calcium oxalate crystals and whether the crystals are located inside cells or between cells. Transverse sections of the midribs were cut,
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Fig. 1. The anatomy of the midribs. MicroCT volumes of: (A and D) F. microcarpa midrib, (B and E) P. dulcis midrib, (C and F) O. europaea midrib. (A–C) Perspective views perpendicular to the main vein axes of the midribs. In all the volumes the upper surface of the leaves is pointing upwards. The types of soft tissue components forming the vein are indicated. Calcium oxalate crystals are the highly contrasting bodies, and lignified fibers are marked by the arrow. (D–F) Transverse oblique view of the midribs showing calcium oxalate crystals and lignified fiber distribution along the vein main axes. The contrast was adjusted to show minerals and lignified fibers in their anatomical locations. The leaf mesophyll was artificially colored in green. Note that the cross sectional area of the xylem of O. europaea is much smaller than the xylem sections of F. microcarpa and P. dulcis. Scale bars: 200 lm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and the exposed cell walls were stained with Calcofluor White and examined in fluorescence by confocal microscopy (Fig. S4 A and D). The calcium oxalates were located by transmitted light (Fig. S4 B and E). Based on the cell morphologies it is possible to distinguish between different cell types. The 3D superimposition of fluorescence and transmission images shows that in F. microcarpa and P. dulcis phloem calcium oxalate crystals are deposited inside companion cells and that the cells are almost completely occupied by the calcium oxalate crystals (Fig. S4 C and F). This can account for their linear arrangement. In the F. microcarpa midrib cross section (yellow arrow in Fig. 2 A) calcium oxalate crystals are very densely organized around the sieve tube perimeters (Fig. 2 B). In P. dulcis midrib cross section (yellow arrow in Fig. 3 D) calcium oxalate crystals are located mostly on the sides of the sieve tubes (Fig. 2 E), resulting in a less compact organization than in the case of F. microcarpa. In F. microcarpa, along the main axis of the vein (blue arrow in Fig. 2 A), calcium oxalate crystals are organized in straight lines that run along the whole vein (Fig. 2 C). In P. dulcis calcium oxalate crystals form spirals that twist clockwise and anticlockwise on the sides of the sieve tubes (Fig. 2 E and F). The volume fraction of the midrib occupied by calcium oxalate crystals is 0.5% and 0.2% for F. microcarpa and P. dulcis, respectively. O. europaea does not deposit crystals. 3.3. Mechanical tests We designed custom made mechanical setups which fit inside the microCT, to perform mechanical tests and study the structural changes of the midrib components during the tests (Fig. 3). One system (Fig. 3 A) was designed to measure leaf midribs in tension or by bending due to compression. Midribs or leaf portions were secured between the two anvils and then pulled or bent under defined loads at controlled speeds (Fig. 3 C and D). A second set up (Fig. 3 B) was designed to torque the samples placed between the anvils (Fig. 3 E) at desired angular velocity (for more information see Materials and Methods).
Fig. 4 A–C show representative force-displacement curves (F-Dd) obtained during tensile tests of F. microcarpa, P. dulcis and O. europaea midribs. The first part of all the curves is linear and reflects the elastic behavior of the materials. The slopes of the curves obtained for P. dulcis (Fig. 4 B) and F. microcarpa (Fig. 4 A) are similar, indicating that their midribs have similar stiffness. The slope of the O. europaea midribs are higher (Fig. 4 C), and hence the stiffness is higher than the values measured for F. microcarpa and P. dulcis. Fracture patterns following failure show that the O. europaea leaf fractured uniformly, while leaves of F. microcarpa and P. dulcis exhibited ragged fracture patterns indicating that tissues within the leaf have structures that resist fracture to different extents. The elastic modulus (n) was obtained from the forcedisplacement curves by applying Eq. (1) (the stress vs. strain curves are shown in Fig. S5 A–C). The results obtained for the midribs of the three species are reported in Table S1. F. microcarpa and P. dulcis have the same elastic moduli (same stiffness), whereas the average elastic modulus of O. europaea is 5 times higher (Fig. 5 A). It is important to notice that since leaf veins are composite materials, each modulus should be considered as an ‘‘effective modulus” resulting from the contribution of all structural components. During the compression-bending tests, force-displacement (F-Dd) curves were recorded for F. microcarpa, P. dulcis and O. europaea (Fig. 4 D–F). The curves show that the maximum tangential compression force is comparable for F. microcarpa and O. europaea, while it is more than three times lower for P. dulcis (Fig. 4 D–F). For F. microcarpa, P. dulcis and O. europaea midribs the maximum force is reached at 0.2 mm, 0.3 mm and 0.4 mm, respectively (Inserts in Fig. 4 D–F), and then the force is released. The behavior of the midrib during the test was monitored by acquiring microCT projection images (Fig. S6 and Video S1). Before the force is released the midrib is compressed. After a displacement of 0.2 mm, 0.3 mm and 0.4 mm in F. microcarpa, P. dulcis and O. europaea, respectively, the leaf starts bending. When the midribs bend, the force is released transversally and this can explain the recorded decrease
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Fig. 2. The organization of the calcium oxalate crystals. MicroCT volume renderings showing calcium oxalates organization in (A–C) F. microcarpa midrib and (D–F) P. dulcis midrib. (A and D) Perspective volumes display the orientations of B and E (yellow arrow) and of C and F (blue arrow), relative to the midribs. (B and E) Front view showing calcium oxalate organization around sieve tubes. Circles mark the possible location of some sieve tube perimeters deduced form the calcium oxalate organization. (C and F) Different organizations of minerals along the sieve tubes along the midrib main axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Custom-made setups to perform mechanical tests inside the microCT. (A) System designed to perform compression-bending tests and tensile tests under controlled loads. (B) System designed to perform torsion tests using the microCT stage rotation. The main components of the setups are indicated. (C) F. microcarpa midrib during a tension test, (D) F. microcarpa midrib during a compression-bending test, (E) F. microcarpa midrib during a torsion test. Scale bars: (A–B) 50 mm, (C–D) 2.5 mm.
in the tangential force after less than 0.5 mm displacement, while the displacement is continuing. After approximately one additional mm the slope of the curves decreases. This could be due to the failure of the midrib structure. The compression modulus (nc) was obtained by applying Eq. (1) to the initial slope of the force-displacement curves (before the midribs bend) and for the same part of the curves the stress vs. strain curves are shown in Fig. S5 D–F. The results obtained for each leaf are shown in Table S2. In general, F. microcarpa midribs are stiff during compression and hard to bend (they have the highest average compression modulus of the three species, Fig. 5B). P.
dulcis midribs are characterized by the lowest average compressive modulus of the tree species and O. europaea shows intermediate values (Fig. 5B). For each species we tested 30 leaves to determine which leaf side will be on the concave side and which on the convex side. 97% of F. microcarpa leaves bend so that the lower abaxial side of the leaf, from where the midrib protrudes, is on the concave side. In this case fracture of the vein always occurs during the compression test. 80% of P. dulcis leaves bend so that the lower abaxial leaf side, together with the vein protrusion, is on the convex side (if we consider the vein structure the arms of the U-shape cross section
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Fig. 4. Representative force (F) – displacement (Dd) curves and torque (T) – angle of twist (a) curves obtained during mechanical load of midribs. The colors indicate 4 different replications of the measurements. (A–C) Curves obtained during tensile tests for (A) F. microcarpa, (B) P. dulcis and (C) O. europaea midribs. (D–F) Curves obtained during compression-bending tests for (D) F. microcarpa, (E) P. dulcis and (F) O. europaea midribs. Inserts: magnification of the linear part of the curves. (G–I) Curves obtained during torsion tests for (G) F. microcarpa, (H) P. dulcis and (I) O. europaea midribs. The torque-angle of twist curves were smoothed by exponential smoothing (0.95 damping).
Fig. 5. Bar plots summarizing the mechanical properties obtained for F. microcarpa, P. dulcis and O. europaea midribs. (A) elastic moduli n (obtained from the curves generated during the tension tests), (B) compression moduli nc (obtained from the linear initial slope of curves generated during the compression/bending tests), (C) torsion moduli ɣ (obtained from the curves generated during the torsion tests), and (D) the ratio between average compression moduli and average torsion moduli nc/ɣ which defines the relative resistance to bending versus twisting. Note that the scale varies widely between different bar plots. The number of measurements used to calculate the average is shown under the bar.
will be on the concave side during the bending). Irrespective of the side toward which the leaf bends, the P. dulcis midribs never fracture. O. europaea leaves bend 53% of the time keeping the vein protrusion on the convex side and 47% of the time on the concave side. During bending none of the O. europaea midribs fracture. During the torsion tests the midribs are first turned 90°and then allowed to relax to the initial position. The maximum torque is reached for an angle of 90° and it is comparable for the three species (Fig. 4 H–J). From the torque vs. angle of twist curves the torsion modulus (ɣ) was obtained applying Eq. (2). The results obtained are shown in Table S3. The average torsion modulus is the highest for O. europaea and the lowest for P. dulcis (Fig. 5C). The relative resistance of the midribs to bending versus twisting is expressed as the ratio of the average compressive rigidity to average torsional rigidity. The index is dimensionless because it is the ratio of two parameters, both expressed in MPa [17]. This ratio is significantly higher for F. microcarpa and the same for P. dulcis and O. europaea (Fig. 5 D). F. microcarpa midribs efficiently resist bending, while still preserving torsional compliance.
F. microcarpa midribs are almost 25 times easier to twist than to bend. P. dulcis and O. europaea are both 5 times easier to twist than to bend.
3.4. Microstructural changes under mechanical load We can relate aspects of the mechanical behavior to structural changes by microCT imaging the midribs during the mechanical tests (Figs. 6–8). During tension tests of F. microcarpa, P. dulcis and O. europaea midribs there are no visible differences in fiber and mineral organization until the fracture occurs. In F. microcarpa and in P. dulcis the fracture patterns are tortuous and especially in the xylem (square brackets in Fig. 6 A and B) the fracture deviates along the linear structures, most possibly along fiber bundles (Fig. 6 A and B). In O. europaea the fracture of the central fibers (square brackets in Fig. 6 C) is sharp while in the soft tissue around the fibers the fracture is more discontinuous (Fig. 6 C). In F. microcarpa, P. dulcis and O. europaea the epidermis collapses after the fracture (arrows in Fig. 6).
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Fig. 6. MicroCT volume side views of midribs after tensile fracture. (A) F. microcarpa, (B) P. dulcis and (C) O. europaea. The arrows indicate the collapsed epidermis. The fracture is discontinuous in F. microcarpa and P. dulcis, whereas in O. europaea the fracture of the central fibers is sharp. Scale bar: 100 lm.
Fig. 7. MicroCT images of the midribs before and during bending. (A–D) F. microcarpa midrib, (E–H) P. dulcis midrib and (I–L) O. europaea midrib. (A, E, I) Volume rendering showing calcium oxalate crystals and lignified fibers before loading. Please note that O. europaea midribs do not contain calcium oxalates. (B, F, J) MicroCT projection image of the external midrib during bending. F. microcarpa midrib fractures while P. dulcis and O. europaea midribs buckle (arrows). (C, G, K) Volume rendering showing calcium oxalate crystals and fibers during loading. The arrows in (C) show where calcium oxalates form continuous linear units. (D, H, L) High magnification image of calcium oxalates and fibers during the loading. Scale bars: (A–C, E-G, I–K) 100 lm, (D, H, L) 20 lm.
During the bending of F. microcarpa buckling never occurs, but the midrib fails by fracture (Fig. 7 B). During compression and bending the linear arrays of minerals do not bend (Fig. 7 C and D). We infer from their linearity during bending that these continuous mineralized units resist the mechanical stress in bending. During compression and bending of the P. dulcis midrib, fracture never occurs, but the structure undergoes intensive buckling (Fig. 7 F). Calcium oxalate crystals never come into contact during
Fig. 8. MicroCT images of the midribs before and during torsion. (A, B) F. microcarpa, (C–D) P. dulcis and (E–F) O. europaea midribs. (A, C, E) Midribs before torsion, (B, D, E) under a 90° torsion. In F. microcarpa and P. dulcis mineral relative positions are not affected and calcium oxalate crystals do not come in contact during the torsion (arrowheads). In O. europaea midribs slight buckling of the fibers is occurring (arrows in F). Scale bars: 100 lm.
bending and comply with the soft tissue (Fig. 7 G and H). During compression and bending the O. europaea midrib also does not fracture, but undergoes slight buckling (Fig. 7 J). The buckling mostly involves the soft tissue around the fibers, but the fibers bend without buckling (Fig. 7 K and L).
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In F. microcarpa, the mineral relative positions are not significantly affected by torsion and calcium oxalate crystals do not come into contact with each other remaining organized in straight lines (Fig. 8 A and B arrowheads). In P. dulcis the torsion of the midribs causes an increase in the twist of the calcium oxalate crystal chains (Fig. 8 C and D arrowheads). In torsion O. europaea fiber organization is slightly affected and weak buckling occurs (arrows in Fig. 8 F). 4. Discussion The 3D study of the anatomy of F. microcarpa, P. dulcis and O. europaea leaf midribs reveals that they are composite, highly anisotropic materials with a complex structure. F. microcarpa and P. dulcis midribs contain calcium oxalate crystals which function as isolated stiff components. In O. europaea midribs no minerals are present, but stiff fibers run continuously along the whole main vein. Histochemical studies of Olea midribs show that the fibers are lignified [18]. It is conceivable, although not demonstrated, that this lignin may be contributing to the observed mechanical properties. Structure-mechanical function relations documented in this study for each leaf provide some key insights. We will discuss the relation between structure and mechanical properties for each leaf on the base of the following general considerations: The elastic modulus obtained in tension tests is a mechanical property that measures a material stiffness and it can be compared between different samples. When a beam is reinforced by isolated stiff particles the stress can be partially redistributed from the matrix to particles increasing the resistance of the whole material [12]. The distribution and orientation of the particles can affect the way in which the whole structure responds to mechanical stresses [12]. When the reinforcing isolated units are arranged near the periphery of the beam, the beam can have high flexural rigidity comparable to a beam reinforced by a continuous ring. However, since the reinforcing units are isolated, the beam preserves higher torsional compliance [2]. Stiff units close to the center of the beam reduce the buckling [21]. The compressive rigidity/torsional rigidity ratios are known to be significantly higher for beams of non-circular cross-section than for beams with circular cross-sections [22]. A U-shaped cross-section increases the torsional compliance compared to a circular cross-section [22]. Furthermore, a U-shape can help resist downward bending during loading. This is due to the fact that the arms of the U will tend to move inwards, increasing the second moment of area [3]. Cellular materials are characterized by a low density structure, which can facilitate buckling during compression. Buckling of the structure can cause the compression modulus to be lower than the tension modulus. The midrib tissue density may easily differ in different leaf species [23]. It was shown that leaves with long petioles have lower drag in strong wind with respect to leaves with short petioles [24]. The petiole length can change in adaptive response to the wind speed gradient which increases with the height (i.e. in the higher part of the canopy leaves have longer petioles) [25]. It may well be that also leaf midribs are adapted in different ways to resist mechanical challenges. 4.1. Olea europaea O. europaea midribs have an elastic modulus that is about 5 times higher than the moduli of F. microcarpa and P. dulcis, which
are similar one to the other. This implies that in tension O. europaea midribs are 5 time stiffer than F. microcarpa and P. dulcis midribs. The elastic moduli of the midribs of 21 plant species native to Southern California range from 0.5 to 41 MPa [5]. The elastic moduli measured for F. microcarpa and P. dulcis fall in the interval of elastic modulus values measured for the midribs of the 21 plant species. However, the elastic modulus measured for O. europaea midribs (100 MPa) is more than double the highest modulus measured for the Southern California species (41 MPa). Other studies show that there is a direct correlation between tensile strength and lignin content in the leaf cross section [26–28]. It will be interesting to determine whether the extremely high tensile strength and smooth fracture of O. europaea midrib, relative to F. microcarpa and P. dulcis is, at least in part, due to the presence of the compact xylem fibers which are lignified. During compression-bending O. europaea midrib only buckles slightly and during the bending, fracture of the midrib never occurs. This indicates that the structure of the center of the midrib reduces the buckling but still allows sufficient flexibility for the beam not to fracture. O. europaea midribs have a U-shaped crosssection, however, the continuous fibers contribute to the strengthening of the midrib also during the torsion. 4.2. Ficus microcarpa During the compression-bending tests F. microcarpa midribs do not buckle, but fail by fracture. This behavior can, in part, be attributed to the presence of stiff units composed of linear arrays of calcium oxalate crystals. These crystal arrays remain linear during bending (Fig. 7 C and D). These stiff mineral-fiber units oppose the bending. The stiff units may also contribute to preventing the buckling. The F. microcarpa fracture pathway is tortuous and clearly follows the linear arrays and their associated fibers. However, when the leaf is not bent, calcium oxalate crystals are separate units. Thus the crystal arrays do not affect significantly the torsional compliance of the midrib. We showed that the stiff mineral arrays remain linear during the midrib bending. The structural properties responsible for this stiffness, could also conceivably contribute to the response of the midrib to compression. This could could be one of the reasons why F. microcarpa midribs have a high ratio of compression to twisting resistance even though they have a circular (and not U-shaped) cross section. Another reason for the higher compression to twisting resistance of F. microcarpa midrib in comparison to the other two species may be related to slightly higher density of the cellular structure of F. microcarpa relative to P. dulcis and O. europaea. 4.3. Prunus dulcis During compression-bending, P. dulcis midribs undergo strong buckling, but never fracture. The results obtained for P. dulcis midribs show that the presence of minerals in the midrib is not sufficient in itself to guarantee high resistance to bending. In P. dulcis calcium oxalates are spiraling up on the sides of the sieve tubes. This organization could be one of the reasons why calcium oxalate arrays do not form stiff units during bending, but comply with the soft tissue facilitating the buckling. Furthermore a low density of the cellular structure of this species could also lead to an easier buckling of the vein structure. During torsion of P. dulcis midribs, high compliance is achieved due to their U-shaped cross section and to the fact that the isolated calcium oxalate crystals do not resist the torsion but twist even further. A documented advantageous function of lignin and minerals is to protect the veins against insects [29–34], but almost nothing is known about the contribution of minerals or lignified fibers to the vein mechanics. Minerals and lignin could have a double function:
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confer strength on the leaf midrib while protecting it from insects. Depositing stiffening elements, such as calcium oxalates crystals or lignified fibers, could be a very widespread strategy to reinforce veins of plant leaves. An interesting aspect that could be further investigated is whether some mechanical properties of the midribs change in adaptation to the height in the canopy, as documented for petioles [24]. Studying microstructural changes occurring under load can help to understand how organisms adapt to mechanical stress [35,36]. The approach that we propose could be used to study the mechanics in relation to structure of other complex biological samples. 5. Conclusions We show here that carrying out mechanical tests of leaves inside a microCT enables not only the measurement of various mechanical properties, but also provides insights into the structures responsible for some of these mechanical properties. The mechanical properties of the midribs can be clearly influenced by the nature and structural organization of the reinforcement units: minerals and lignin. We demonstrate that in Ficus microcarpa linear arrays of calcium oxalate crystals resist bending, whereas in Prunus dulcis these crystals are spaced such that they do not resist bending. Acknowledgments We thank Dr. Vladimir Kiss for the help with the confocal measurements, Dr. Adam van Casteren and Dr. Junning Chen for useful discussions. We thank Shaked Addadi for providing almond (Prunus dulcis) leaves from her tree. L.A. is the recipient of the Dorothy and Patrick Gorman Professorial Chair of Biological Ultrastructure. Disclosure None Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.actbio.2019.02.023. References [1] A. Ennos, Compliance in plants, WIT Trans. State-of-the-art Sci. Eng. 20 (2005). [2] A. Ennos, Wind as an ecological factor, Trends Ecol. Evol. 12 (1997) 108–111. [3] A. Ennos, H.C. Spatz, T. Speck, The functional morphology of the petioles of the banana, Musa textilis, J. Exp. Bot. 51 (2000) 2085–2093. [4] B. Moulia, M. Fournier, D. Guitard, Mechanics and form of the maize leaf: in vivo qualification of flexural behaviour, J. Mat. Sci. 29 (1994) 2359–2366. [5] R. Méndez Alonzo, F.W. Ewers, L. Sack, Ecological variation in leaf biomechanics and its scaling with tissue structure across three Mediterranean-climate plant communities, Funct. Ecol. 27 (2013) 544–554. [6] Y. Onoda, M. Westoby, P.B. Adler, A.M. Choong, F.J. Clissold, J.H. Cornelissen, S. Díaz, N.J. Dominy, A. Elgart, L. Enrico, Global patterns of leaf mechanical properties, Ecol. Lett. 14 (2011) 301–312. [7] M. Pierantoni, R. Tenne, B. Rephael, V. Brumfeld, A. van Casteren, K. Kupczik, D. Oron, L. Addadi, S. Weiner, Mineral deposits in Ficus leaves: morphologies and locations in relation to function, Plant Physiol. (2017). 01516.2017.
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Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Full length article
A 3D study of the relationship between leaf vein structure and mechanical function Maria Pierantoni a, Vlad Brumfeld b, Lia Addadi a, Steve Weiner a,⇑ a b
Department of Structural Biology, Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel Department of Chemical Research Support, Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel
a r t i c l e
i n f o
Article history: Received 15 August 2018 Received in revised form 3 February 2019 Accepted 15 February 2019 Available online 16 February 2019 Keywords: Biomechanics microCT Calcium oxalate crystals Lignified fibers Biological composite material
a b s t r a c t We investigate the structures and mechanical properties of leaf midribs of Ficus microcarpa and Prunus dulcis, which deposit calcium oxalate crystals, and of Olea europaea midribs which contain no mineral deposits, but do contain lignified fibers. The midrib mechanical performance contributes to the leaf’s ability to maintain a flat conformation for light harvesting and to efficiently reconfigure to reduce wind drag. We use a novel approach involving 3D visualization of the vein structure during mechanical load. This involves the use of customized mechanical loading devices that fit inside a microCT chamber. We show that the elastic, compression and torsional moduli of the midribs of leaves from the 3 species examined vary significantly. We also observed different modes of fracture and buckling of the leaves during compression. We assess the contributions of the calcium oxalate crystals to the mechanical and fracture properties. In F. microcarpa midrib linear arrays of calcium oxalate crystals contribute to resisting the bending, in contrast to P. dulcis leaves, where the calcium oxalate crystals do not resist bending. In both F. microcarpa and P. dulcis isolated calcium oxalate crystals enable high torsional compliance. The integrated microCT – mechanical testing approach could be used to investigate the structure-mechanics relationships in other complex biological samples. Statement of significance Leaves need to maintain a flat conformation for light harvesting, but they also need to efficiently reconfigure to reduce wind drag. The leaf central vein (midrib) is a key structural component for leaf mechanicss. 3D visualization of the vein structure under mechanical loads showed that veins can be stiffened by reinforcement units composed of calcium oxalates crystals and lignin. The stiffening units can influence the bending and fracture properties of the midribs, and can contribute to determine if buckling will occur during folding. Mineral stiffening elements could be a widespread strategy to reinforce leaf veins and other biological structures. This structural-mechanical approach could be used to study other complex biological samples. Ó 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction In leaves mechanical resistance to bending is necessary for maintaining a flat conformation, which in turn is essential for light harvesting. Torsional compliance reduces drag, and is also important, as leaves have to withstand strong winds and to reconfigure efficiently [1–3]. Key components contributing to these mechanical properties are the leaf veins and especially the midrib. For maize ⇑ Corresponding author at: Weizmann Institute of Science, Department of Structural Biology, Herzl Street, Rehovot 7610001 Israel. E-mail addresses: [email protected] (M. Pierantoni), [email protected] (V. Brumfeld), [email protected] (L. Addadi), steve. [email protected] (S. Weiner). https://doi.org/10.1016/j.actbio.2019.02.023 1742-7061/Ó 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
leaves it was shown that the midrib greatly stiffens the leaf, especially in locations where bending moments are high [4]. The elastic modulus of the leaf blade (lamina) is primarily related to the mass ratio of major veins to the rest of the lamina [4]. Consequently an increase in the fraction of veins increases the mechanical strength of the entire leaf [4]. A recent study of leaves from 21 different species showed that mechanical resistance differed among the leaf component tissues, and that the tissue with the highest resistance is always the midrib [5]. Furthermore, the largest differences in mechanical resistance between the 21 species were associated to the midrib, and not to the leaf lamina [5]. Despite all these observations, leaf mechanical responses are usually studied only as a function of lamina thickness, tissue density and toughness per unit
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tissue density. To our knowledge, the midrib mechanics were never studied in relation to its different components [6]. Many leaves also contain minerals. In a previous study we investigated mineral deposits in leaves from 10 different Ficus species [7]. We showed that the veins are always associated with calcium oxalate crystals, and that this is the only common mineral deposition trait between all the studied Ficus species [7]. Calcium oxalate crystals have been documented along the veins of many other genera of higher plant leaves, from trees to herbaceous plants [8–11]. Calcium oxalates crystals are isolated stiff components organized along the vein fibers. This mode of mineral organization is not unique to leaves. Many organisms have, embedded in their tissues, reinforcing small particles of stiff material [12]. The reinforcing effect of such stiff particles was documented for the spicules of sponges and cnidarians [12,13], for the ossicles of starfish [14], for the sclerites of corals, and for the lignified material in the stem of sedge [15]. Koehl suggested that stress can be transferred from the tissue to the stiff particles, which will bear part of the force applied to the whole material [12]. The stiff particles restrict the movements of the soft tissue around them, and consequently they help to prevent rearrangement of the whole structure under stress. When the whole structure is deformed, the rigid particles do not change shape, but may change relative positions. The soft tissue between the particles can deform, but because of the rigid particles, the deformation of the whole material will be smaller than the deformation of the soft tissue alone. Thus the distribution and orientation of the particles within the soft tissue can affect the way in which the whole structure responds to mechanical stress [12]. Calcium oxalate crystals along leaf veins could have an important, but as yet undocumented function in reinforcing the veins. Plant structures, in general, are hierarchically organized so that the microstructural features greatly contribute to their macroscopic properties [16,17]. In order to rationalize how different components, including minerals, contribute to the mechanical performance of the midribs, we use a novel approach involving 3D visualization of the vein structure under controlled loads. We perform tension tests, compression-bending tests and torsion tests on the midribs using custom made setups, which were designed to function inside the chamber of an X-ray microtomography scanner (microCT). This enables the study of midrib mechanical behavior at micrometer resolution, in relation to structural changes. Here we investigate the midribs of Ficus microcarpa, Prunus dulcis (common name almond) and Olea europaea (common name olive), which all have blade and midribs of approximately the same size, but with different midrib structures. F. microcarpa and P. dulcis midrib cells also deposit calcium oxalate crystals. The midribs of O. europaea do not contain calcium oxalate crystals, but contain lignified fibers in the xylem [18]. Ficus microcarpa, Prunus dulcis and Olea europaea have ellipsoidal leaves. Ellipsoidal leaves are particularly interesting for the study of midrib mechanics, because in these leaves the midribs have to support laminae in which the leaf mass center (index of distribution of leaf mass along the leaf length) is located closer to the leaf tips than to the petioles [19]. Consequently, in these leaves petioles contribute only partially to the support of the leaf mass, which needs to be borne by the midrib and by the other veins. We study how differences in midrib structure and composition in each of the three species relate to their mechanical properties.
2. Materials and methods 2.1. Plant material Ficus microcarpa, Prunus dulcis and Olea europaea leaves were collected and analyzed fresh from mature trees growing outdoors
in Rehovot, Israel. All the leaves were collected from about 1.5 m to maximum 2.5 m from the ground. For the mechanical tests midribs of diameter 1 mm and length 30 mm were dissected using a razor blade and tested. 2.1.1. Phase contrast enhanced microCT MicroCT scans were acquired using a Micro XCT-400 (Zeiss Xray Microscopy, California, USA) as in Pierantoni at al. [7]. Triangular sections of leaves (base1 cm, length 2 cm) were cut and placed in a sealed plastic pipette tip. The tips were partially filled with water to prevent dehydration of the samples. Only the part of the leaf not immersed in water was imaged. The scans were performed keeping the source and the detector at the optimal distances for phase contrast propagation (50 mm and 75 to 90 mm to the sample respectively). Phase contrast improves the quality of images, by increasing contrast sensitivity especially around edges [20]. This enables detection of the soft tissue anatomy of minute structures. The tomographic images were obtained from 1500 projections (acquired over180°) at 30 kV and 450 mA. The final voxel size was 0.95–1.05 mm (depending on the source and detector positions). The microCT volumes were reconstructed using a back projection filtered algorithm (Zeiss). 2.1.2. Image processing and analysis 3D image processing and analysis of the reconstructed microCT volumes were carried out using the Avizo software. The mineral volume fraction was obtained by contrast thresholding the minerals (the most absorbing bodies in the veins). The midrib volume was calculated considering xylem, phloem and ground tissue together. The reproducibility of the data was estimated by analyzing the same volume within a specimen 3 times. A variance of 0.03% was obtained. 2.2. Confocal microscopy Cross-sections of a few hundred micrometers were cut from fresh F. microcarpa and P. dulcis midribs using a razor blade in the direction of the vein main axes. The cell walls of the exposed tissue were stained with a solution composed of 0.05 ml of Calcofluor White Stain (Calcofluor White M2R 1 g/l, Evans blue 0.5 g/l, 18,909 Sigma Aldrich) and 0.05 ml of 10% potassium hydroxide. The sections were placed between coverslips and imaged with a confocal FW1000 laser scanning microscope, Olympus IX81. The excitation laser wavelength is k = 402 nm for both the chlorophyll and the PDMPO dye. The emission was obtained with a 420–520 nm band-pass filter. The volumes were acquired with 60 oil objective lens magnification, with z steps of 1 lm. 2.3. Micro-mechanical devices The system used for the tensile tests and the compressionbending tests was attached to the standard rotating stage of the microCT. It consists of an open cylindrical sample testing chamber (85 mm in height and 50 mm in diameter) stabilized by two metallic posts of 5 mm in diameter (Fig. S1A). The system includes two anvils, one of which (the upper) is mobile and the second is fixed to the base of the chamber. An axial-motion DC motor moves the upper anvil into the testing chamber in sub-micron steps. The anvil position is controlled by a position servocontroller (C-863 Mercury, Physik Instrumente, GmbH, Germany). The anvil is attached to a load cell (C31, Honeywell, USA) of range between 0 and 120 N and sensitivity of 0.4 N. The force is measured with a GM signal conditioner-indicator (Sensotec, Honeywell, USA), which is connected to the load cell. Both the anvils terminate with a groove (15 mm 10 mm 5 mm) in which the sample is inserted and is held by a clamp (Fig. S1 B). The two clamps are positioned out of
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the microCT detector field of view. As the setup is inside the microCT chamber, it was possible to visualize minerals and vein tissue during the force measurement. Note that since the two posts limit the field of view when microCT volumes are acquired (the field of view is not 180° but 140°), the contrast is preserved but the resolution is reduced. The system used for the torsion tests consists of an upper stable anvil (Fig. S1C a) connected to a torque sensor (TD50TD70 ± 50 Nm, accuracy class: 0,1%; 0.5 mV/V/FS, LARIT Measurements). The torque sensor (Fig. S1C b) is attached to a metallic pivot of adjustable length (Fig. S1C c) which in turn is screwed to a magnet (Fig. S1C d) fixed to the ceiling of the microCT chamber. The lower anvil is connected to the microCT stage, which is used to rotate at 0.15 deg/s the anvil and the sample fixed to it by fixed angles. The upper and lower anvils are the same used for the tensile tests and the compression-bending tests (Fig. S1B). Since there is no physical connection between the upper part of the setup and the lower part, the two sides have to be carefully aligned. The alignment is performed using a pendulum connected to the upper anvil. The lower anvil is moved by microsteps using the microCT stage motor until the pendulum tip touches the center of the lower anvil and the two parts are perfectly aligned. 2.4. Mechanical tests For the tension tests midrib sections of diameter of 1 mm and length of 30 mm were inserted between two posts at a distance of 15 mm. Double sided carbon tape was applied in the grooves of the anvils so that they were in contact with the sample. This prevents the midribs from drifting during the test. The lower anvil is stable while the upper anvil can move up at controlled speed of 20 mm/s until the leaf portion breaks. The tests were conducted within approximately 2 min during which time the samples do not dry significantly. For compression-bending tests leaf portions of 3 cm 1 cm 1 mm or extracted midribs (30 mm 1 mm 1 mm) were cut and inserted into the grooves of the two anvils at a distance of 15 mm. The lower anvil is stable while the upper anvil moves down at a controlled speed of 20 mm/s for a total displacement of 7 mm. The force was recorded every 100 ms and a force-displacement curve was obtained. For leaf portions, we verified that the recorded force was due only to the midrib by conducting the same tests, but placing the leaf perpendicular to the midrib, and again on a leaf portion without the midrib. In both control cases the force required to bend the leaf portion was below the detection limit. For the torsion tests, midribs (diameter 1 mm) were cut from the leaf and 30 mm long sections were inserted between two posts which are at a distance of 15 mm from each other. The midrib was torqued from 0° to 90° and back to 0° at an angular velocity of 0.15 deg/s. The moment of torsion was recorded every 50 ms and the curve moment of torsion vs. angle of twist was generated. Since the obtained curves are noisy, they were smoothed by exponential smoothing (0.95 damping). The behavior of the midribs during the mechanical tests was monitored by acquiring microCT 2D projection images every 3.5 s without rotating the sample. The projection images were used to produce a video showing the midrib macroscopic conformational changes during the tests. 2.5. Statistical analysis Elastic moduli (n) were obtained from the force-displacement curves by applying Eq. (1):
n¼
DF 4L Dx pr2
ð1Þ
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where DDxF is the initial slope of the curve, L is the distance between the posts and r is the midrib radius. The calculation was repeated for 15 different samples in the case of F. microcarpa and O. europaea and for 19 different samples in the case of P. dulcis. The average value of n and the standard error were obtained for each species. Compression moduli (nc) were obtained by applying Eq. (1) to the initial slope of the force-displacement curves. The calculation was repeated for 17 different samples in the case of F. microcarpa and for 15 different samples in the case of P. dulcis and O. europaea. The average value of nc and the standard error were obtained for each species. From the torque vs. angle of twist curves the torsion modulus (ɣ) was obtained applying Eq. (2),
c¼
DT 1 Dh r
ð2Þ
where DDTh is the initial slope of the curve and r is the midrib radius. The calculation was repeated for 17 different samples in the case of F. microcarpa, for 18 different samples in the case of P. dulcis and for 15 different samples for O. europaea. The average value of ɣ and the standard error were obtained for each species. 3. Results 3.1. 3D anatomy of midribs We use phase contrast enhanced microCT in order to visualize minerals and soft tissue structures in F. microcarpa, P. dulcis and O. europaea leaf midribs (Fig. 1). In F. microcarpa midribs the xylem and phloem cross sections form a complete circle of about 400 mm diameter (Fig. 1 A). In P. dulcis midrib xylem and phloem the cross sections have a U-shape and have a maximum diameter of about 500 mm (Fig. 1 B). In O. europaea the xylem also forms a U-shape that has a maximum diameter of about 250 mm and all around the xylem the phloem forms a circle of about 500 mm (Fig. 1 C). In F. microcarpa and P. dulcis xylem tissue forms the vascular bundles. In O. europaea xylem the fibers are associated with some lignin [18] (arrows in Fig. 1 C, and F). The content of lignin increases during the maturation of the leaf (Fig. S2). The mean length of the units forming the continuous fibers is 217 mm ± 12 mm (n = 30). In mature leaves the fibers run continuously along the whole xylem. In the phloem of both F. microcarpa and P. dulcis calcium oxalate crystals are deposited (highly contrasting bodies in Fig. 1 A, D and Fig. 1 B, E). Calcium oxalate crystals are organized in parallel lines along the vein major axes. In O. europaea phloem no calcium oxalates are deposited. All three species have ground tissue extensions on the lower side of the phloem, and above the phloem in the case of P. dulcis and O. europaea (Fig. 1 A–C). The ground tissue cells are arranged to form a honeycomb structure (Fig. S3). All the midribs protrude from the leaf blade in the direction of the lower leaf side (the leaf mesophyll is rendered in green in Fig. 1). 3.2. 3D organization of calcium oxalate crystals Calcium oxalates are deposited in F. microcarpa and P. dulcis phloem along well defined lines. The vein soft tissue components seem to determine this deposition pattern. The phloem consists of sieve tubes and companion cells. Sieve tubes are elongated cells which have groups of pores at their extremities and companion cells are smaller cells surrounding the sieve tubes (Fig. S4). We use confocal microscopy to identify which cells contain calcium oxalate crystals and whether the crystals are located inside cells or between cells. Transverse sections of the midribs were cut,
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Fig. 1. The anatomy of the midribs. MicroCT volumes of: (A and D) F. microcarpa midrib, (B and E) P. dulcis midrib, (C and F) O. europaea midrib. (A–C) Perspective views perpendicular to the main vein axes of the midribs. In all the volumes the upper surface of the leaves is pointing upwards. The types of soft tissue components forming the vein are indicated. Calcium oxalate crystals are the highly contrasting bodies, and lignified fibers are marked by the arrow. (D–F) Transverse oblique view of the midribs showing calcium oxalate crystals and lignified fiber distribution along the vein main axes. The contrast was adjusted to show minerals and lignified fibers in their anatomical locations. The leaf mesophyll was artificially colored in green. Note that the cross sectional area of the xylem of O. europaea is much smaller than the xylem sections of F. microcarpa and P. dulcis. Scale bars: 200 lm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and the exposed cell walls were stained with Calcofluor White and examined in fluorescence by confocal microscopy (Fig. S4 A and D). The calcium oxalates were located by transmitted light (Fig. S4 B and E). Based on the cell morphologies it is possible to distinguish between different cell types. The 3D superimposition of fluorescence and transmission images shows that in F. microcarpa and P. dulcis phloem calcium oxalate crystals are deposited inside companion cells and that the cells are almost completely occupied by the calcium oxalate crystals (Fig. S4 C and F). This can account for their linear arrangement. In the F. microcarpa midrib cross section (yellow arrow in Fig. 2 A) calcium oxalate crystals are very densely organized around the sieve tube perimeters (Fig. 2 B). In P. dulcis midrib cross section (yellow arrow in Fig. 3 D) calcium oxalate crystals are located mostly on the sides of the sieve tubes (Fig. 2 E), resulting in a less compact organization than in the case of F. microcarpa. In F. microcarpa, along the main axis of the vein (blue arrow in Fig. 2 A), calcium oxalate crystals are organized in straight lines that run along the whole vein (Fig. 2 C). In P. dulcis calcium oxalate crystals form spirals that twist clockwise and anticlockwise on the sides of the sieve tubes (Fig. 2 E and F). The volume fraction of the midrib occupied by calcium oxalate crystals is 0.5% and 0.2% for F. microcarpa and P. dulcis, respectively. O. europaea does not deposit crystals. 3.3. Mechanical tests We designed custom made mechanical setups which fit inside the microCT, to perform mechanical tests and study the structural changes of the midrib components during the tests (Fig. 3). One system (Fig. 3 A) was designed to measure leaf midribs in tension or by bending due to compression. Midribs or leaf portions were secured between the two anvils and then pulled or bent under defined loads at controlled speeds (Fig. 3 C and D). A second set up (Fig. 3 B) was designed to torque the samples placed between the anvils (Fig. 3 E) at desired angular velocity (for more information see Materials and Methods).
Fig. 4 A–C show representative force-displacement curves (F-Dd) obtained during tensile tests of F. microcarpa, P. dulcis and O. europaea midribs. The first part of all the curves is linear and reflects the elastic behavior of the materials. The slopes of the curves obtained for P. dulcis (Fig. 4 B) and F. microcarpa (Fig. 4 A) are similar, indicating that their midribs have similar stiffness. The slope of the O. europaea midribs are higher (Fig. 4 C), and hence the stiffness is higher than the values measured for F. microcarpa and P. dulcis. Fracture patterns following failure show that the O. europaea leaf fractured uniformly, while leaves of F. microcarpa and P. dulcis exhibited ragged fracture patterns indicating that tissues within the leaf have structures that resist fracture to different extents. The elastic modulus (n) was obtained from the forcedisplacement curves by applying Eq. (1) (the stress vs. strain curves are shown in Fig. S5 A–C). The results obtained for the midribs of the three species are reported in Table S1. F. microcarpa and P. dulcis have the same elastic moduli (same stiffness), whereas the average elastic modulus of O. europaea is 5 times higher (Fig. 5 A). It is important to notice that since leaf veins are composite materials, each modulus should be considered as an ‘‘effective modulus” resulting from the contribution of all structural components. During the compression-bending tests, force-displacement (F-Dd) curves were recorded for F. microcarpa, P. dulcis and O. europaea (Fig. 4 D–F). The curves show that the maximum tangential compression force is comparable for F. microcarpa and O. europaea, while it is more than three times lower for P. dulcis (Fig. 4 D–F). For F. microcarpa, P. dulcis and O. europaea midribs the maximum force is reached at 0.2 mm, 0.3 mm and 0.4 mm, respectively (Inserts in Fig. 4 D–F), and then the force is released. The behavior of the midrib during the test was monitored by acquiring microCT projection images (Fig. S6 and Video S1). Before the force is released the midrib is compressed. After a displacement of 0.2 mm, 0.3 mm and 0.4 mm in F. microcarpa, P. dulcis and O. europaea, respectively, the leaf starts bending. When the midribs bend, the force is released transversally and this can explain the recorded decrease
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Fig. 2. The organization of the calcium oxalate crystals. MicroCT volume renderings showing calcium oxalates organization in (A–C) F. microcarpa midrib and (D–F) P. dulcis midrib. (A and D) Perspective volumes display the orientations of B and E (yellow arrow) and of C and F (blue arrow), relative to the midribs. (B and E) Front view showing calcium oxalate organization around sieve tubes. Circles mark the possible location of some sieve tube perimeters deduced form the calcium oxalate organization. (C and F) Different organizations of minerals along the sieve tubes along the midrib main axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Custom-made setups to perform mechanical tests inside the microCT. (A) System designed to perform compression-bending tests and tensile tests under controlled loads. (B) System designed to perform torsion tests using the microCT stage rotation. The main components of the setups are indicated. (C) F. microcarpa midrib during a tension test, (D) F. microcarpa midrib during a compression-bending test, (E) F. microcarpa midrib during a torsion test. Scale bars: (A–B) 50 mm, (C–D) 2.5 mm.
in the tangential force after less than 0.5 mm displacement, while the displacement is continuing. After approximately one additional mm the slope of the curves decreases. This could be due to the failure of the midrib structure. The compression modulus (nc) was obtained by applying Eq. (1) to the initial slope of the force-displacement curves (before the midribs bend) and for the same part of the curves the stress vs. strain curves are shown in Fig. S5 D–F. The results obtained for each leaf are shown in Table S2. In general, F. microcarpa midribs are stiff during compression and hard to bend (they have the highest average compression modulus of the three species, Fig. 5B). P.
dulcis midribs are characterized by the lowest average compressive modulus of the tree species and O. europaea shows intermediate values (Fig. 5B). For each species we tested 30 leaves to determine which leaf side will be on the concave side and which on the convex side. 97% of F. microcarpa leaves bend so that the lower abaxial side of the leaf, from where the midrib protrudes, is on the concave side. In this case fracture of the vein always occurs during the compression test. 80% of P. dulcis leaves bend so that the lower abaxial leaf side, together with the vein protrusion, is on the convex side (if we consider the vein structure the arms of the U-shape cross section
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Fig. 4. Representative force (F) – displacement (Dd) curves and torque (T) – angle of twist (a) curves obtained during mechanical load of midribs. The colors indicate 4 different replications of the measurements. (A–C) Curves obtained during tensile tests for (A) F. microcarpa, (B) P. dulcis and (C) O. europaea midribs. (D–F) Curves obtained during compression-bending tests for (D) F. microcarpa, (E) P. dulcis and (F) O. europaea midribs. Inserts: magnification of the linear part of the curves. (G–I) Curves obtained during torsion tests for (G) F. microcarpa, (H) P. dulcis and (I) O. europaea midribs. The torque-angle of twist curves were smoothed by exponential smoothing (0.95 damping).
Fig. 5. Bar plots summarizing the mechanical properties obtained for F. microcarpa, P. dulcis and O. europaea midribs. (A) elastic moduli n (obtained from the curves generated during the tension tests), (B) compression moduli nc (obtained from the linear initial slope of curves generated during the compression/bending tests), (C) torsion moduli ɣ (obtained from the curves generated during the torsion tests), and (D) the ratio between average compression moduli and average torsion moduli nc/ɣ which defines the relative resistance to bending versus twisting. Note that the scale varies widely between different bar plots. The number of measurements used to calculate the average is shown under the bar.
will be on the concave side during the bending). Irrespective of the side toward which the leaf bends, the P. dulcis midribs never fracture. O. europaea leaves bend 53% of the time keeping the vein protrusion on the convex side and 47% of the time on the concave side. During bending none of the O. europaea midribs fracture. During the torsion tests the midribs are first turned 90°and then allowed to relax to the initial position. The maximum torque is reached for an angle of 90° and it is comparable for the three species (Fig. 4 H–J). From the torque vs. angle of twist curves the torsion modulus (ɣ) was obtained applying Eq. (2). The results obtained are shown in Table S3. The average torsion modulus is the highest for O. europaea and the lowest for P. dulcis (Fig. 5C). The relative resistance of the midribs to bending versus twisting is expressed as the ratio of the average compressive rigidity to average torsional rigidity. The index is dimensionless because it is the ratio of two parameters, both expressed in MPa [17]. This ratio is significantly higher for F. microcarpa and the same for P. dulcis and O. europaea (Fig. 5 D). F. microcarpa midribs efficiently resist bending, while still preserving torsional compliance.
F. microcarpa midribs are almost 25 times easier to twist than to bend. P. dulcis and O. europaea are both 5 times easier to twist than to bend.
3.4. Microstructural changes under mechanical load We can relate aspects of the mechanical behavior to structural changes by microCT imaging the midribs during the mechanical tests (Figs. 6–8). During tension tests of F. microcarpa, P. dulcis and O. europaea midribs there are no visible differences in fiber and mineral organization until the fracture occurs. In F. microcarpa and in P. dulcis the fracture patterns are tortuous and especially in the xylem (square brackets in Fig. 6 A and B) the fracture deviates along the linear structures, most possibly along fiber bundles (Fig. 6 A and B). In O. europaea the fracture of the central fibers (square brackets in Fig. 6 C) is sharp while in the soft tissue around the fibers the fracture is more discontinuous (Fig. 6 C). In F. microcarpa, P. dulcis and O. europaea the epidermis collapses after the fracture (arrows in Fig. 6).
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Fig. 6. MicroCT volume side views of midribs after tensile fracture. (A) F. microcarpa, (B) P. dulcis and (C) O. europaea. The arrows indicate the collapsed epidermis. The fracture is discontinuous in F. microcarpa and P. dulcis, whereas in O. europaea the fracture of the central fibers is sharp. Scale bar: 100 lm.
Fig. 7. MicroCT images of the midribs before and during bending. (A–D) F. microcarpa midrib, (E–H) P. dulcis midrib and (I–L) O. europaea midrib. (A, E, I) Volume rendering showing calcium oxalate crystals and lignified fibers before loading. Please note that O. europaea midribs do not contain calcium oxalates. (B, F, J) MicroCT projection image of the external midrib during bending. F. microcarpa midrib fractures while P. dulcis and O. europaea midribs buckle (arrows). (C, G, K) Volume rendering showing calcium oxalate crystals and fibers during loading. The arrows in (C) show where calcium oxalates form continuous linear units. (D, H, L) High magnification image of calcium oxalates and fibers during the loading. Scale bars: (A–C, E-G, I–K) 100 lm, (D, H, L) 20 lm.
During the bending of F. microcarpa buckling never occurs, but the midrib fails by fracture (Fig. 7 B). During compression and bending the linear arrays of minerals do not bend (Fig. 7 C and D). We infer from their linearity during bending that these continuous mineralized units resist the mechanical stress in bending. During compression and bending of the P. dulcis midrib, fracture never occurs, but the structure undergoes intensive buckling (Fig. 7 F). Calcium oxalate crystals never come into contact during
Fig. 8. MicroCT images of the midribs before and during torsion. (A, B) F. microcarpa, (C–D) P. dulcis and (E–F) O. europaea midribs. (A, C, E) Midribs before torsion, (B, D, E) under a 90° torsion. In F. microcarpa and P. dulcis mineral relative positions are not affected and calcium oxalate crystals do not come in contact during the torsion (arrowheads). In O. europaea midribs slight buckling of the fibers is occurring (arrows in F). Scale bars: 100 lm.
bending and comply with the soft tissue (Fig. 7 G and H). During compression and bending the O. europaea midrib also does not fracture, but undergoes slight buckling (Fig. 7 J). The buckling mostly involves the soft tissue around the fibers, but the fibers bend without buckling (Fig. 7 K and L).
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In F. microcarpa, the mineral relative positions are not significantly affected by torsion and calcium oxalate crystals do not come into contact with each other remaining organized in straight lines (Fig. 8 A and B arrowheads). In P. dulcis the torsion of the midribs causes an increase in the twist of the calcium oxalate crystal chains (Fig. 8 C and D arrowheads). In torsion O. europaea fiber organization is slightly affected and weak buckling occurs (arrows in Fig. 8 F). 4. Discussion The 3D study of the anatomy of F. microcarpa, P. dulcis and O. europaea leaf midribs reveals that they are composite, highly anisotropic materials with a complex structure. F. microcarpa and P. dulcis midribs contain calcium oxalate crystals which function as isolated stiff components. In O. europaea midribs no minerals are present, but stiff fibers run continuously along the whole main vein. Histochemical studies of Olea midribs show that the fibers are lignified [18]. It is conceivable, although not demonstrated, that this lignin may be contributing to the observed mechanical properties. Structure-mechanical function relations documented in this study for each leaf provide some key insights. We will discuss the relation between structure and mechanical properties for each leaf on the base of the following general considerations: The elastic modulus obtained in tension tests is a mechanical property that measures a material stiffness and it can be compared between different samples. When a beam is reinforced by isolated stiff particles the stress can be partially redistributed from the matrix to particles increasing the resistance of the whole material [12]. The distribution and orientation of the particles can affect the way in which the whole structure responds to mechanical stresses [12]. When the reinforcing isolated units are arranged near the periphery of the beam, the beam can have high flexural rigidity comparable to a beam reinforced by a continuous ring. However, since the reinforcing units are isolated, the beam preserves higher torsional compliance [2]. Stiff units close to the center of the beam reduce the buckling [21]. The compressive rigidity/torsional rigidity ratios are known to be significantly higher for beams of non-circular cross-section than for beams with circular cross-sections [22]. A U-shaped cross-section increases the torsional compliance compared to a circular cross-section [22]. Furthermore, a U-shape can help resist downward bending during loading. This is due to the fact that the arms of the U will tend to move inwards, increasing the second moment of area [3]. Cellular materials are characterized by a low density structure, which can facilitate buckling during compression. Buckling of the structure can cause the compression modulus to be lower than the tension modulus. The midrib tissue density may easily differ in different leaf species [23]. It was shown that leaves with long petioles have lower drag in strong wind with respect to leaves with short petioles [24]. The petiole length can change in adaptive response to the wind speed gradient which increases with the height (i.e. in the higher part of the canopy leaves have longer petioles) [25]. It may well be that also leaf midribs are adapted in different ways to resist mechanical challenges. 4.1. Olea europaea O. europaea midribs have an elastic modulus that is about 5 times higher than the moduli of F. microcarpa and P. dulcis, which
are similar one to the other. This implies that in tension O. europaea midribs are 5 time stiffer than F. microcarpa and P. dulcis midribs. The elastic moduli of the midribs of 21 plant species native to Southern California range from 0.5 to 41 MPa [5]. The elastic moduli measured for F. microcarpa and P. dulcis fall in the interval of elastic modulus values measured for the midribs of the 21 plant species. However, the elastic modulus measured for O. europaea midribs (100 MPa) is more than double the highest modulus measured for the Southern California species (41 MPa). Other studies show that there is a direct correlation between tensile strength and lignin content in the leaf cross section [26–28]. It will be interesting to determine whether the extremely high tensile strength and smooth fracture of O. europaea midrib, relative to F. microcarpa and P. dulcis is, at least in part, due to the presence of the compact xylem fibers which are lignified. During compression-bending O. europaea midrib only buckles slightly and during the bending, fracture of the midrib never occurs. This indicates that the structure of the center of the midrib reduces the buckling but still allows sufficient flexibility for the beam not to fracture. O. europaea midribs have a U-shaped crosssection, however, the continuous fibers contribute to the strengthening of the midrib also during the torsion. 4.2. Ficus microcarpa During the compression-bending tests F. microcarpa midribs do not buckle, but fail by fracture. This behavior can, in part, be attributed to the presence of stiff units composed of linear arrays of calcium oxalate crystals. These crystal arrays remain linear during bending (Fig. 7 C and D). These stiff mineral-fiber units oppose the bending. The stiff units may also contribute to preventing the buckling. The F. microcarpa fracture pathway is tortuous and clearly follows the linear arrays and their associated fibers. However, when the leaf is not bent, calcium oxalate crystals are separate units. Thus the crystal arrays do not affect significantly the torsional compliance of the midrib. We showed that the stiff mineral arrays remain linear during the midrib bending. The structural properties responsible for this stiffness, could also conceivably contribute to the response of the midrib to compression. This could could be one of the reasons why F. microcarpa midribs have a high ratio of compression to twisting resistance even though they have a circular (and not U-shaped) cross section. Another reason for the higher compression to twisting resistance of F. microcarpa midrib in comparison to the other two species may be related to slightly higher density of the cellular structure of F. microcarpa relative to P. dulcis and O. europaea. 4.3. Prunus dulcis During compression-bending, P. dulcis midribs undergo strong buckling, but never fracture. The results obtained for P. dulcis midribs show that the presence of minerals in the midrib is not sufficient in itself to guarantee high resistance to bending. In P. dulcis calcium oxalates are spiraling up on the sides of the sieve tubes. This organization could be one of the reasons why calcium oxalate arrays do not form stiff units during bending, but comply with the soft tissue facilitating the buckling. Furthermore a low density of the cellular structure of this species could also lead to an easier buckling of the vein structure. During torsion of P. dulcis midribs, high compliance is achieved due to their U-shaped cross section and to the fact that the isolated calcium oxalate crystals do not resist the torsion but twist even further. A documented advantageous function of lignin and minerals is to protect the veins against insects [29–34], but almost nothing is known about the contribution of minerals or lignified fibers to the vein mechanics. Minerals and lignin could have a double function:
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confer strength on the leaf midrib while protecting it from insects. Depositing stiffening elements, such as calcium oxalates crystals or lignified fibers, could be a very widespread strategy to reinforce veins of plant leaves. An interesting aspect that could be further investigated is whether some mechanical properties of the midribs change in adaptation to the height in the canopy, as documented for petioles [24]. Studying microstructural changes occurring under load can help to understand how organisms adapt to mechanical stress [35,36]. The approach that we propose could be used to study the mechanics in relation to structure of other complex biological samples. 5. Conclusions We show here that carrying out mechanical tests of leaves inside a microCT enables not only the measurement of various mechanical properties, but also provides insights into the structures responsible for some of these mechanical properties. The mechanical properties of the midribs can be clearly influenced by the nature and structural organization of the reinforcement units: minerals and lignin. We demonstrate that in Ficus microcarpa linear arrays of calcium oxalate crystals resist bending, whereas in Prunus dulcis these crystals are spaced such that they do not resist bending. Acknowledgments We thank Dr. Vladimir Kiss for the help with the confocal measurements, Dr. Adam van Casteren and Dr. Junning Chen for useful discussions. We thank Shaked Addadi for providing almond (Prunus dulcis) leaves from her tree. L.A. is the recipient of the Dorothy and Patrick Gorman Professorial Chair of Biological Ultrastructure. Disclosure None Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.actbio.2019.02.023. References [1] A. Ennos, Compliance in plants, WIT Trans. State-of-the-art Sci. Eng. 20 (2005). [2] A. Ennos, Wind as an ecological factor, Trends Ecol. Evol. 12 (1997) 108–111. [3] A. Ennos, H.C. Spatz, T. Speck, The functional morphology of the petioles of the banana, Musa textilis, J. Exp. Bot. 51 (2000) 2085–2093. [4] B. Moulia, M. Fournier, D. Guitard, Mechanics and form of the maize leaf: in vivo qualification of flexural behaviour, J. Mat. Sci. 29 (1994) 2359–2366. [5] R. Méndez Alonzo, F.W. Ewers, L. Sack, Ecological variation in leaf biomechanics and its scaling with tissue structure across three Mediterranean-climate plant communities, Funct. Ecol. 27 (2013) 544–554. [6] Y. Onoda, M. Westoby, P.B. Adler, A.M. Choong, F.J. Clissold, J.H. Cornelissen, S. Díaz, N.J. Dominy, A. Elgart, L. Enrico, Global patterns of leaf mechanical properties, Ecol. Lett. 14 (2011) 301–312. [7] M. Pierantoni, R. Tenne, B. Rephael, V. Brumfeld, A. van Casteren, K. Kupczik, D. Oron, L. Addadi, S. Weiner, Mineral deposits in Ficus leaves: morphologies and locations in relation to function, Plant Physiol. (2017). 01516.2017.
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