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Anatomy and Morphology |
2Department of Biophysics and Cell Biology, Silesian University, Jagiellonska 28, Katowice 40-032 Poland;and 3Nees-Institut f. Biodiversität der Pflanzen der Universität Bonn, Meckenheimer Allee 170, 53115 Bonn, Germany
Received for publication April 30, 2004. Accepted for publication December 6, 2004.
ABSTRACT
Petioles (up to 4 m tall) of huge solitary leaves of mature plants of Amorphophallus titanum and A. gigas resemble tree trunks supporting an umbrella-like crown. In a mechanical sense, the petiole is a shell, composed of compact parenchyma with embedded collenchyma strands. The core of the shell is filled with aerenchyma. Mechanical stability of the petiole strongly depends upon the turgor pressure in the parenchyma of the shell and the core. The petiole collapses upon senescence when the turgor pressure decreases as a result of increasing osmolality of the solution permeating cell walls. The present study supports the postulate that aerenchyma serves a mechanical function. The petiole can be easily broken by animals during a collision. This risk is proposed to be lowered by the mimicry of the color pattern of the petiole's surface, which resembles a stiff tree trunk covered with lichen thalli (in both species) and with bark in the case of A. gigas. The cellular basis of these color patterns is described.
Key Words: aerenchyma • Amorphophallus • buckling • color pattern • mimicry • petiole • stability • turgor
Older plants of Amorphophallus, such as A. titanum or A. gigas considered in this paper, produce huge solitary leaves, each with petioles a few meters long (Fig. 1). The petioles support huge tripinnate, palmate lamina, so that a leaf resembles a tree trunk bearing an umbrella-like crown. The leaf is borne on a huge tuberous rhizome. The petiole is a vertical, tapered cylinder that ends with a three-partite rachis. Each segment of the rachis forms an angle of about 135° with the petiole and of 120° with the adjacent segment. An individual leaf functions for 12–18 months. Leaf senescence begins structurally with the breakage of the base of one part of the rachis. This breakage disturbs the distribution of gravity force moment around the petiole axis, but the petiole still stays upright. Then the two remaining parts of the rachis break, and symmetric distribution of the gravity force is restored. However, a few days later, the petiole buckles at its base and falls down. This collapse of the petiole occurs (at least in the greenhouse) under the force of the leaf's own mass, axially directed, presumably eccentric, without the participation of any other force. During the period that the leaf functions, a new tuber is formed with new leaf primordia, the highest of which will grow into a new green leaf, while the remaining ones will form cataphylls that protect the main leaf before it enters its phase of intercalary growth. The roots form adjacent to the leaf-bearing portion of the tuber (Camp, 1937
; Kohlenbach, 1998
). Each successive tuber and green leaf are larger, and finally the plant develops a characteristic giant inflorescence without a green leaf. Because the plants live on sandy, humic soils primarily in open, young, secondary tropical forest, often near riverbanks, the tuber is relatively weakly anchored.
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The petiole is susceptible to damage by large animals when they collide with it. A running animal, however, is likely to avoid such a collision solely because the petiole diameter is large; the animal may associate it with something stiff. Moreover, the petiole is "colored," which makes it easier to recognize against the green background of the forest. However, the characteristic feature of its color pattern is its resemblance to neighboring trees, especially those bearing lichen thalli (Barthlott, 1992
), and may be an unusual type of mimicry in which large, delicate petioles mimic rigid trunks covered with bark and/or lichens. A collision with such a trunk would be catastrophic for the animal but not for the tree. Species of Amorphophallus differ in their quality of this mimicry; for instance, A. gigas, has patterns that appear to be nearly three-dimensional and one has not only the illusion of lichen thalli but also of traces of water streaming between the "thalli."
The aim of our study is to describe: (1) the anatomical basis of the mechanical stability of the petiole, (2) the mechanics underlying petiole collapse, and (3) the cellular basis of the color pattern.
MATERIALS AND METHODS
Plant material
Two leaves of Amorphophallus titanum Becc. (referred to as A. tit. I and A. tit. II) and one leaf of A. gigas Teijsm & Binn (A. brooksii Alder.), which grew in a glasshouse of the Botanical Garden of Bonn University, were studied. Because older plants of Amorphophallus are rare, the leaves were accessible for research only when they showed signs of senescence.
Light microscopy
Tissue blocks were fixed in FAA (formalin 2%, acetic acid 5%, ethanol 40%). For hand sectioning, the blocks were rinsed briefly in tap water. Blocks for microtome sectioning were dehydrated in an ethanol series (30, 50, 70, 95, 100%), embedded in Steedman wax prepared by mixing polyethylene-glycol 400 diesterase and 1-hexadecanol (9 : 1) (Aldrich, Sheboygan, Wisconsin, USA), and sectioned into semithin sections. Staining procedures followed those in O'Brien and McCully (1981)
. Phloroglucinol-HCl and anilinsulphate tests were used to detect lignin, I-KI for starch, FeCl3 solution for tannins, and aniline blue for callose using fluorescence microscopy. Tissue was cleared in lactic acid (60%).
To macerate tissue, strips of collenchyma were put in a mixture of acetic acid and 30% peroxide (1 : 1) in a water bath at 100°C for 2–6 h until the cells were easily separated. The strips were then rinsed twice with tap water and shaken in a small amount of water. The suspension was centrifuged, some glycerine added, and the suspension placed drop by drop on glass slides. The suspension prepared in this manner contained straight cells so that their lengths could be measured. To test whether cells in hand sections living, they were immersed in the vital stain 0.05% aqueous neutral red solution for 1 h.
Scanning electron microscopy
Tissue blocks were fixed in 2.5% glutaraldehyde in 50 mM phosphate buffer (pH 7.2) for 2 h in room temperature. Pressure was lowered initially to infiltrate the air spaces with solution. The blocks were then washed in the buffer, and the solution within the air spaces was removed with the aid of filter paper. Tissue blocks were then frozen in liquid nitrogen, critical-point dried, mounted on metal stubs, and sputter-coated with gold. A Cambridge Steroscan 200 was used for the observations.
Mass, volume and density measurements
Each leaf lamina was cut off at the base of the rachis and weighed. The petiole was cut into segments 30 cm long (mostly) in the case of A. tit. I and A. gigas, and 37 cm in the case of A. tit. II. The segments were weighed, and their volume was determined as the volume of water displaced by a submerged segment. To prevent the parenchyma chambers at the cross-sectional faces from filling with water, these faces were covered by foil stuck to the segment edge with a thin layer of margarine. The calculated ratio of mass to volume gave the mean density of the segment. To estimate the local density of individual tissues, small tissue blocks were excised, and their mass and volume were determined. In the case of aerenchyma, pushing a block of this tissue (wrapped with foil) under water deformed the block. To minimize deformation, the block was fastened by a thin wire net to the bottom of a measuring cylinder. A known amount of water,enough to submerge the net, was poured into the cylinder. The difference between the volume of water containing the block and the volume of water added gave the block volume.
Determination of the diameter (radius)
The diameter was estimated at specific distances on the petiole using either cross-section photographs or contour drawings. Because the cross-section is only approximately circular (Fig. 2), the mean radius (Fig. 3) was calculated from the area of the cross-section assuming that it is circular.
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Measurement of tensile tissue stress in the shell tissue
A bar, 180 mm long and 8 mm wide, was applied longitudinally to the petiole surface, (A. tit. II at height 1.5 m) and the shell tissue was cut along the bar edges by means of a blade oriented perpendicular to the petiole surface (strictly followed in the case of transverse cuts at the bar ends) so that the cuts reached the aerenchyma. Then a strip of shell tissue, 180 long, 8 mm wide, and approx. 5 mm thick could be removed from the petiole. The strip, with the epidermis downward, was put on a flat surface between two glass plates, 2 mm thick. The tissue that protruded above the glass plates (outer part of the core) was removed by running a sharp knife over the surface of the glass plate. The whole procedure lasted no longer than 1 min. Immediately after obtaining the 2 mm thick strip of the shell tissue containing collenchyma, the strip was overlaid on the bar so that one end coincided with one of the bar ends. The displacement of the other strip end (
l) with respect to the bar edge was measured under a dissecting microscope. This displacement was due to the removal of the tensile longitudinal tissue stress (
t) that acted in the shell in situ. Because l/l = t/E, if the elastic modulus (E) is known, t can be estimated (roughly, because E is measured in uniaxial extension, while the shell in situ is in multiaxial stress state).
Tensiometric measurements
Modulus of elasticity (tissue composite modulus, Etc, Niklas, 1989
, 1992
) was determined with the aid of a tensiometer, as previously described (Hejnowicz and Sievers, 1995
). The Etc was determined in the longitudinal direction for thin strips of the shell tissue that contained mainly a collenchyma strand. The strips were peeled from the shell using a dissecting microscope. Immediately after peeling, the upper end of the strip was attached firmly in a light plastic clamp with a hook at the other end to attach it to the movable arm of the tensiometer. The lower end of the strip was clamped in the tensiometric chamber that could be filled with water (Hejnowicz and Sievers, 1996
). The transverse area of the strip was determined for hand sections. Etc was estimated from the slope of the line characterizing stress against strain.
To compare the radial strain for aerenchyma before and after perfusion of the cavities with water, rectangular blocks 10 x 10 x 25 mm (the longest in radial direction) were cut from the petiole of A. tit. II. One face of the block was the natural surface of the shell. A compressive force was applied to this surface similar to that described for the isolated inner tissue of sunflower hypocotyl (Hejnowicz and Sievers, 1995
; Fig. 2B), and the decrease in radial dimension was determined.
Polarizing microscopy
Specimens were observed with Zeiss polarizing microscope. The polarizer-analyzer cross was oriented diagonally with respect to the sides of the photographs,
Statistics
Only means of various mechanical properties (± standard error) were calculated.
RESULTS
Size, mass and density
The petioles attained record dimensions (Table 1). However, the mass of each was suprisingly low because the petiole is a thin cylindrical shells composed of a dense tissue surrounding an aerenchymatous core.
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Density as a function of the longitudinal position (Fig. 4) is similar in the petioles studied, despite differences in their dimensions. The density first slightly decreases with height and then slightly increases in the upper portion of a petiole. A rapid increase of the density occurs in the proximity to the lamina where the petiole branches into three-partite rachis. This increase probably insures against tearing moments exerted by the lamina parts. However, we did not study the "rachis node" any further in this study. The density varies in a radial direction. The most dense tissue occurs at the periphery forming a shell, while the density of the remaining part (aerenchymatic core) is below the mean value.
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The density of the shell is 920 ± 20 kg/m3 in A. gigas (determined for four samples) and 930 ± 40 kg/m3 in A. tit. I (also four samples). Within the core, the density rapidly decreases within the 5–25% of the radius (moving away from the surface) because the intercellular spaces that fill with air accordingly rapidly increase in diameter. This outer layer of the core (20% of the radius, beneath the shell) has a mean density of 350 ± 110 kg/m3 (for four samples of A. tit. I) The mean density of the core in the remaining (central) part of the petiole is 120 ± 35 kg/m3 (for four samples of A. tit. I).
The fresh mass of the shell makes up approximately 35% of the whole fresh mass of the petiole. Four strips of shell tissue with a total surface of 120 cm2 and known mass and two blocks of the central aerenchyma from A. gigas, were dried at 50°C. The (air) dry mass was 12% ± 3.8% of the fresh mass for the shell tissue, and 5 and 7% for the two aerenchyma blocks. The density of dry mass in the shell and the "central" aerenchyma was approximately 110 and 7 kg/ m3, respectively. The dry mass of the entire core is a bit more than half of the dry mass of the whole petiole, meaning that the investment in the core is quite high.
Anatomical structure
Except for the epidermis, the anatomy is nearly the same in both species. A shell of compact tissue surrounds an aerenchymatous core (Fig. 5). The shell is composed of a single-layered epidermis, thin parenchymatous cortex, and a relatively thick layer containing strands of collenchyma embedded in compact parenchyma. Each collenchyma strand is accompanied by a vascular bundle, so the parenchyma can be regarded as interfascicular. The core contains honeycomb aerenchyma composed of thin longitudinal diaphragms separating large, elongated air chambers. Some diaphragms are connected longitudinally by parenchymatous strands each containing single vascular bundle.
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). However, the wax does not seem to contribute to the appearance of the petiole surface. In A. titanum, the surface of the epidermis is rather smooth, i.e., the cells are not papillate and have no obvious cuticular sculpture. However, cuticular furrows, oriented mostly transversely, occur on the subsidiary cells (Fig. 7). These furrows are important because they indicate that A. titanum possesses the genetical potential to develop cuticular sculpture, but does not make use of it on the petiole surface, in contrast to A. gigas (Figs. 8–13).
Amorphophallus gigas has two levels of surface unevenness: (1) epidermal cells tend to be papillate, and (2) furrows occur on all epidermal cells except guard cells (Fig. 10). The papillae are of variable size and may have mamillary tips (Figs. 8, 11). In the case of larger papillae, the whole external wall protrudes into a conical or even cylindrical outgrowth (Fig. 11), which may surpass 150 µm in length (at the diameter of approx. 70 µm). Within the color patches imitating lichen thalli, all cells are markedly papillate, while those on the background of the patches have only rather small papillae or some are not papillate at all (Figs. 8, 10). In the lower portion of the petiole, which imitates the bark of a trunk, papillae occur on all cells but their height is very variable. The papillae contribute to the three-dimensional apppearance of the surface.
The cuticular furrows in A. gigas are arranged mostly in longitudinal stripes (Fig. 8), but in the vicinity of stomata, transverse stripes occur as well (Figs. 9, 10). The longitudinal stripes of furrows are especially apparent in those areas of the epidermis where papillae are small, but are also found in the areas with pronounced papillae. Most likely this arrangement of furrows causes the impression of three-dimensionality. Looking at the surface of the epidermis in SEM (Fig. 12), the furrows appear to be due to local accumulation of some material (like cutin). However, as seen in cell wall fractures, they are due to folding of the external layer of the wall within the cuticle layer as if the area of this layer was too large in comparison with that of the rest of the wall (Fig. 13).
Stomata on the petioles are relatively large. Their surface density is low: 12 ± 3 and 13 ± 4 per square cm for A. tit. I and A. gigas, respectively.
The epidermal cells are colorless except for some cells in A. titanum (single or in small groups) that are red, from a red pigment in the cell sap. In A. gigas, we did not observe pigments in the epidermis, even though the surface was much more colorful than that in A. titanum.
Cortex
The mean thickness of the parenchymatous cortex (between epidermis and outer collenchyma strands) in A. titanum is approx. 250 µm and is 5–7 cells thick, independent of its position along the petiole. In A. gigas, this tissue is more variable in thickness but in general is rather thinner. The cortex is mostly chlorenchymatous, though some parts of it may be devoid of chloroplasts and participate in the formation of the white patches in the color patterns.
The arrangement of cells in longitudinal rows is more apparent in the cortex than in the epidermis. Between the cortical cells are numerous small intercellular spaces filled with air, which are, however, not easily observed in anatomical sections. The intercellular spaces confer the matt appearance to the surface, which becomes glassy after water infiltration. Where the cells are devoid of chloroplasts, the intercellular spaces cause a more or less white coloring, depending on the number of cell layers.
In A. gigas, many cortical cells contain a red pigment. This red pigment was not observed in cortical cells of A. titanum. However, in the subepidermis of this species, solitary or grouped cells occur, which become brown after fixation (Figs. 14–16), probably from chemical changes in tannins during and after fixation. These cells are difficult to distinguish in fresh material; in A. titanum, the surface that appears to be uniformly green has a cryptic color pattern. The density of tannin-containing cells and the mean size of their groups is only slightly lower in white (nonchlorophyllous) patches of the color pattern on the petiole surface than in the green background (Fig. 16). In A. gigas, the tannin-containing cells were not observed.
The layer containing collenchyma strands
This layer is the main (volumetric) component of the shell. As already mentioned, each strand has a vascular bundle located centripetally (Fig. 17). The vascular tissue of the bundle is separated from the strand by two layers of parenchyma cells. The layer contacting the phloem is composed of relatively short cells that contain sedimenting amyloplasts (i.e., located in the part of the cell that represented the cell bottom before fixation). It is the statenchyma (perception site of gravity stimulus) of an incomplete starch sheath type (Fig. 18).
Parenchyma between the strands (interfascicular parenchyma) is composed of short, compactly arranged, thin-walled cells. In cross-sections, only a few small intercellular air spaces are found in the interfascicular parenchyma. However, they must make aproximately 10% of the total volume of the parenchyma because the density of the shell is only 940 kg/m3 (after removal of the cortex and without the inner part of the shell, where big intercellular spaces occur). The collenchyma strands and probably also the vascular bundles are completely devoid of intercellular spaces, and their density is somewhat higher than 1000 kg/m3.
The diameter of collenchyma strands is variable in both species; it ranges between 180 and 1000 µm with the tangential dimension generally larger in the lower portion of the petiole, and radial dimension larger in the upper portion. In a thicker shell, the cross-sectional dimensions of strands first slightly increase with increasing distance from the surface, but then they rapidly decrease, so that the vascuar bundles in the outer part of the core are not accompanied by collenchyma. Neighboring strands can join together or a strand can split. Joining and splitting occur mainly in a tangential plane, but sometimes also in the radial plane so that the strands form a continuous system in the shell.
Structure of the collenchyma strands
Each strand consists of fusiform cells, which are relatively long, but small in cross-section. Their walls in fresh or fixed, hydrated material are nonuniformly thickened, similar to the angular collenchyma. However, this nonuniformity in thickness is hardly visible in dehydrated material (i.e., in SEM), likewise in the cross-sections of specimens embedded in Steedman wax and viewed in ethanol to dissolve the wax (Fig. 19). However, after the addition of water or glycerin solution (40%), the local thickenings become pronounced (Figs. 20–22). The cell walls in the cross-sections of the dehydrated material examined in ethanol are cracked (Fig. 19). These cracks then disappear when the sections are hydrated (Fig. 20). Surely, the walls of these cells shrank transversely and reversibly upon dehydration, then cracked.
In contrast to typical collenchyma, the strands could be macerated into straight cells. The mean length of these cells is 1.65 ± 0.42 mm in A. gigas and 1.46 ± 0.38 mm in A. titanum. Maximal and minimal lengths are 3 and 0.6 mm, respectively. The relatively small length (in comparison with the petiole length attained through intercallary elongation) indicates that the mother cells of the collenchyma frequently divided transversely or pseudotransversely during the elongation. The fusiform shape (Fig. 23) in turn indicates that intensive intrusive growth of the cells must have taken place during their differentiation, which is typical of fibers rather than of collenchyma. The cell walls in the strands remain unlignified until the end of petiole life, and the cells also remain alive as shown by the neutral red accumulation.
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Aerenchymatous core
On the inner border of the shell, easily recognizable schizogenous intercellular spaces appear, which gradually change centripetally into chambers typical of the aerenchyma. Thus without doubt, the chambers are schizogenous. They are axially elongated and mostly hexagonal in cross-sections. Their mean diameter increases centripetally until they plateau at approx. 1.5 mm in A. titanum. In A. gigas, the maximum diameter is slightly higher than in A. titanum, but the mean cell density of the aerenchyma is not lower. However, we became aware of this fact only when the material was already fixed and turgorless, which precluded inspection of this feature.
The chambers are highly elongated. Their length varies from 4 mm to more than 12 mm. The ends of small groups of chambers look like cells in a honeycomb, i.e., the longitudinal diaphragms above and below a transverse diaphragm are not superimposed (Fig. 25). However, the opposite ends of the chambers in such a group are on rather different levels.
Neighboring chambers are separated longitudinally by diaphragms one cell thick. The thickness measured in SEM is approx. 60 µm, but the exact thickness at full turgor is not known. The width of a diaphragm embraces from four to more than a dozen cells. The cells are slightly elongated, thin-walled, and arranged in longitudinal rows without any intercellular spaces (Fig. 26). The surface outline of the cells is mostly hexagonal, which means that most of the cells are octahedrons. Their arrangement indicates that after formation of "primordial" diaphragms, when longitudinal divisions must have occurred, there was a considerable, mainly longitudinal, growth accompanied by transverse divisions.
Surrounding the chamber is a single cell wall ("surface wall") of the diaphragm cells, which is less than 1 µm thick, as measured in fractured materials in the SEM. The surface wall is not wettable. In the surface wall, both on its outer and inner face, fibrils form nets, in a predominantly oblique direction with respect to the petiole axis (Fig. 26). The main layer of the surface wall contains cellulose mainly microfibrils arranged transversely as can be judged from the investigation with polarized light.
On the inner surface of the (double) walls within the diaphragms (longitudinal and transverse), fibrils are arranged mainly in the plane of the diaphragm. However, the main arrangment of the microfibrils (beyond the fibrils) is normal to this plane as indicated by the fissures visible in polarized light (Fig. 27, arrow).
Tranverse diaphragms are more than one cell thick and are two or three cells across in the thinnest area. Small intercellular spaces are also seen (Fig. 28). Some transverse (oblique) diaphragms are much thicker, and each contains one transverse (oblique) vascular bundle.
Mostly three longitudinal diaphragms meet at a longitudinal edge (Figs. 29, 30). Some diaphragms join the longitudinal parenchymatous strands, each of which contain a vascular bundle (Figs. 29, 30). Within the central core, such a strand abuts six chambers (as if replacing a chamber, Fig. 29). The strands are thicker at the core periphery than in the remaining part of the core (Figs. 5, 29, 30). The number of these strands per unit of cross-sectional area decreases only slightly with distance from the shell, attaining a maximum in the central region. In the parenchyma surrounding the vascular bundle, characteristic laticifers occur (Figs. 31, 32). They have small side extensions at the vertices of neighboring parenchymatous cells. Their latex probably discourages biting of the petiole by animals. On the phloem side of the vascular bundle is a layer of relatively short parenchymatous cells of statenchyma type (starch sheath), similar to that in the bundles within the shell.
Vascular bundles
As mentioned before, single vascular bundles occur within the shell on the adaxial side of each collenchyma strand (Fig. 17) and in each longitudinal parenchymatous strand in the core (Figs. 29, 30). The shell and core bundles do not differ qualitatively; however, there is a variation of cross-sectional dimensions of the bundles. The range of this variation is wider in the shell. An apparent tendency is that the bundles in the outer part of the shell, especially in the lower portion of the petiole, are smaller. The core bundles are not accompanied by any collenchyma or sclerenchyma like tissue, but are surrounded only by thin-walled large parenchyma cells. In fact, no sclerenchyma occurs in the petiole at all.
Vascular bundles are collateral. They are unique because of the scarcity of lignin, occurring only in bar-type thickenings of tracheary elements (Fig. 33), which occur in an astonishingly small number (mostly two or three on the cross-section through a bundle). In each bundle on the side opposite to the phloem is a characteristic canal (Figs. 17, 30–33) with a nonlignified wall, similar in general appearance to a small aerenchyma chamber cavity. This structure is so unusual that our study of it will be presented in a separate paper. The canal turns out to be a wide, extremely long (>40 mm) metaxylem tracheary element with a nonnlignified lateral wall.
The phloem area of the bundle is not significant from our point of view. Nevertheless, we briefly describe it. The phoem contains a few (in cross-section) sieve tubes, with a smaller diameter than in those of the parenchymatous cells outside the bundle. The sieve plates are simple (Fig. 34) and are slightly obliquely oriented with respect to the sieve tube axis. The length of the sieve tube members is 240 ± 48 µm (N =18), although some phloem parenchyma cells are over 2 mm in length and their mean length could not be measured. The length of the identified sieve tube members is surprisingly small in comparison with the length of tracheary elements and with the immense elongation of the petiole. This fact means that the elongation of sieve tube mother cells was accompanied by numerous transverse divisions, a feature that must be taken into account when considering the mechanism of translocation along the sieve tubes.
Color patterns on the petiole surface
The pattern is based on (1) the number and location of chloroplastless cells the cortex, (2) differences in light reflection on air/cell wall interfaces of intercellular spaces, (3) the presence of a red (or/and brown) pigment in subepidermal cells, and (4) the presence of epidermal papillae and cuticular furrows, both of which cause complex optical effects.
In A. gigas, the pattern changes along the petiole. The bottom portion of the petiole looks like a tree trunk with fine cracked bark in grey, brownish, and green tones (Fig. 35), while in the remaining areas, it looks like a young tree stem with whitish lichens (Fig. 36).
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In the middle and upper portions of the A. gigas petiole, the pattern resembles the surface of a tree stem with apparent lichen thalli. The lichen-type patches are due to achlorophyllous cortical layers. In the lightest parts (that occur at the "thallus" border, not inside it), chloroplasts are missing in three or four layers of the cortex cells. In these parts, the red pigment does not occur; however, in the neighboring background, the pigment may be present in the chlorophyllous subepidermis. In this way, the border has contrast (Figs. 39, 40). The red pigment also occurs in dark spots in the central part of the "thallus," which makes the "thallus" seem older in the center and younger (growing) at the periphery. There are no indications of cell lineage in the formation of the "thallus."
In A. titanum, the bark-type color pattern is not present, but the lichen-type pattern is present throughout the petiole. Its whitish elements do not imitate the lichen thalli as well as those in A. gigas. Only the chloroplasts and light reflectance in the intercellular spaces are involved. Nor did we did observe the red pigment in the subepidermis, only in some of the epidermal cells.
Osmolality of cell sap
Osmolality was measured on for the petiole of A. tit. II when the lamina first had signs of senescence (3 d before the petiole collapse) and immediately after the collapse. The sap was squeezed from the shell after removal of the cortex, and from the core aerenchyma. The results are shown in Table 2. The data are scanty; nevertheless, they indicate that the direct reason of the collapse was not a decrease in cell sap osmolality.
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Deformation and turgor pressure in aerenchyma
Measurements were made on aerenchyma blocks cut off from the petiole of A. tit. II: (1) 3 d before the petiole collapsed and (2) after the collapse. Before the collapse, pressing the aerenchyma blocks in a radial direction caused a linear deformation that was reversible within a narrow range (up to 2.3 x 103 Pa), so that the apparent modulus of elasticity could be estimated. However, after the collapse, there was no range of linear and reversible deformation. Measurements for the two blocks cut before collapse are interesting inasmuch as there was a large increase in the modulus when the block was infiltrated with distilled water (Table 3). The modulus nearly doubled after the infiltration.
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DISCUSSION
Mechanics of the petiole
The petioles studied in this paper turn out to be the largest cylindrical structure that relies entirely on turgor pressure for mechanical support. Such a strategy in Amorphophallus is possible because water is not a limiting factor in its habitat and the leaves are relatively lightweight in spite of their size. Other huge petioles, like those of banana leaves have lignified, longitudinal strengthening elements, yet turgid longitudinal parenchymatous partitions and transverse stellate parenchyma plates add to mechanical functioning of these petioles (Ennos et al., 2000
).
The Amorphophallus petioles are suprisingly light. Air occupies nearly 80% of their volume, even though they are not hollow cylinders like many stem internodes (Niklas, 1997
). Surely, the effectiveness of lifting the lamina to a proper height (the cost and rate of petiole formation) is optimized by such a low specific density of the turgor-dependent structure. The low cost and fast rate of petiole formation are important because the leaves are periodically replaced. Moreover, the replacement means that not only a new leaf must develop, but also that an old petiole has to be removed. There are no processes like abscission in the petiole; it buckles (collapses) at the end of its life under its own (and lamina) weight force that acts vertically (axisymmetrically).
Our data indicate that the tissue composite modulus of elasticity of the aerenchyma in the senescing leaf greatly increased when the aerenchyma was infiltrated with distilled water. Assuming that the increase was due to increasing turgor pressure in the aerenchyma cells, and that the turgor pressure was proportional to the difference in osmolality of the cell sap and the solution within the cell wall, we infer that the turgor pressure in aerenchyma with air-filled chambers was considerably lower than potentially possible (i.e., when there would be pure water externally to plasmalemma). We also infer that in the senescing petiole the osmolality of the solution permeating the cell walls increases (presumably due to a passive leakage of solutes), which leads to a decrease in turgor pressure, and ultimately to the buckling from the leaf's own weight. This turgor-based strategy can be thus considered as an adaptation to the leaf removal. Any strategy of autonomous stability, independent of turgor pressure, would be more expensive, slower, and would complicate the mechanism of leaf removal. Moreover, a stiffer petiole would increase the likelihood that the tuber would be mechanically dislodged.
Turgor pressure strongly influences the stiffness of thin-walled tissues (Falk et al., 1958
; Nilsson et al., 1958
; Burström et al., 1967
; Niklas, 1988
, 1989
; Niklas and O'Rourke, 1987
; Niklas and Paolillo, 1997
, 1998
). The pressure causes tensile stress in the thin walls, which are resistant to such a stress. All forces, even compressive and torsional, acting on a turgid cell only increase this tensile "pre-stress." Therefore, it is obvious that in the petiole case, turgor pressure would have an especially strong effect on the stiffness of the parenchyma. The pressure has, however, little effect on the stiffness of the thick-walled collenchyma (Niklas, 1992
; Spatz et al., 1998
): collenchyma can act as a supporting element independently of the turgor pressure in its cells.
In stems of Equisetum, there is a living, strengthening tissue that is interpreted as nonlignified sclerenchyma or "fully differentiated collenchyma" (Spatz et al., 1998
; Speck et al., 1998
), very similar to the collenchyma of the Amorphophallus petiole. The stems of E. hyemale do not buckle locally upon the reduction of turgor pressure, though their resistance against ovalization in bending (Brazier effect) decreases by about 20% (Speck et al., 1998
). In contrast, the stems of E. giganteum buckle locally after the loss of turgor (Spatz et al., 1998
). The collenchyma forms radial extensions, which are deeper in E. hyemale than in E. giganteum, and form in E. hyemale, together with the double ring of endodermis, a mechanically stable structure. Probably such a strenghening structure of tissue, that depends little on turgor for its stiffness, enables the stems of E. hyemale to withstand even extended periods of subfreezing temperatures with the concomittant loss of turgor pressure. The reaction to the reduction of turgor pressure in the collenchyma of the Amorphophallus petiole may in general be similar to that in E. giganteum. However, although stiffness of the collenchyma does not depend much upon turgor pressure in its own cells, this tissue can contribute significantly to the stiffness of the petiole under tensile tissue stress as a result of the turgor pressure in parenchyma. Namely, if an organ is composed of tissues with different mechanical parameters (wall thickness, lumen diameter, elastic moduli of the cell wall), tissue stresses (TSs, tensile and compressive) are an unavoidable effect of turgor in thin-walled cells (Hejnowicz and Sievers, 1996
; Hejnowicz, 1997
; Niklas and Paollilo, 1998
). In the petiole, the tendency toward elastic, longitudinal extension of thin-walled tissue as a result of turgor pressure is restricted by the strands of collenchyma. As a consequence, the collenchyma is subject to tensile TS and the thin-walled parenchyma is brought under compressive TS. TSs originating in this way may be called structural TSs (Hejnowicz, 1997
), in contrast to TSs that are due to differential growth of different layers or strands (Peters and Tomos, 1996
). This study shows that in the Amorphophallus petiole, there is tensile TS in the outer part of the shell and especially in the collenchyma strands. This TS is probably a structural type.
It can be easily demonstrated with young petioles of celery, which also contain collenchyma strands, that these strands are under high tensile TS. During cutting of such a strand, a characteristic sound can be heard, similar to that produced by cutting a stretched string. Whether such a sound occurs during cutting of the collenchyma strands in the petioles of Amorphophallus could not be answered univocally. Special acoustic instrumentation would be needed to recognize the sound unmistakably. The answer is likely to be easier in the case of nonsenescing petioles, which cannot be cut.
The TSs in a turgid organ are analogues of pre-stresses in enginnering constructions, with pre-stretched steel elements in the construction periphery, which are known to increase the stability of the construction. In the case of the petiole, the "pre-stretched" collenchyma strands presumably act as tension elements in tensegrity structures (Ingber, 2003
).
The petiole of Amorphophallus can be treated as a cylindrical shell with a soft, elastic core. In the petiole, the ratio of shell thickness to the radius is less than 0.08; therefore, it is in the range in which the centric weight of the leaf is critical for local buckling of the shell (Spatz et al., 1990
). It is known from biomechanics (Niklas, 1991
, 1992
) and from engineering that the core increases stiffness and especially increases the shell resistance against buckling. It may be effective in this respect even when the ratio of Young's modulus of the core to that of the shell is as low as 0.0001 (Karam and Gibson, 1995
). However, elastic stability of the cylindrical shell with a soft, elastic core depends upon so many parameters, even if pre-stresses are not considered, that modeling the stability of core–rind designs of cylindrical structures is difficult even in the case of engineering structures. In the case of the petiole, the task is additionally complicated by mechanical anisotropy of the tissues, the turgor pressure in cells, and the TSs. Initially, we planned to treat the petioles more strictly in biomechanical terms, however, we gave up knowing the complexity of the problem. Having some experience in attempts to elaborate the mechanical stability of a characteristic part of Amorphophallus inflorescence called the appendix (Hejnowicz, 1998
), we were aware that even if we had very detailed data on elastic moduli and Poisson coefficients, we would not be able to "consume" them without a proper model that accounts for turgor pressure and TSs.
The petiole sustains its own weight (force) and that of the lamina, which causes axial compression in the petiole. Its own weight may cause a bending moment when the gravity center is not on the petiole axis, i.e., when the petiole orientation is changed from vertical to inclined or when the lamina becomes assymmetric. The petiole must therefore be resistant to different instabilities caused by compression: (1) the Euler column buckling (in the primary mode), which is a sudden, large, lateral deflection of a vertical column caused by a small increase in an existing load (as in a vertical flower stalk visited by an insect that is heavy enough) or small decrease in stiffness (as in a tulip stalk when the temperature decreases); (2) local, axial compression buckling; and (3) local buckling under pure bending. The resistance of a cylindrical shell to Euler buckling increases with the shell diameter. However, the resistance to local buckling under bending decreases with the diameter (Niklas, 1992
). The petioles of Amorphophallus are rather resistant to Euler buckling, because there is no long-lasting lateral deflection of the petiole before it ultimately collapses.
Local buckling caused by axial compression may occur in vertically oriented petioles. In fact, the petiole is nearly perfectly vertical, a feature that should be considered in connection with the occurrence of the statenchyma (where the gravity stimulus is perceived). Surely, the statenchyma allows the petiole to maintain the vertical orientation during elongation. Whether it enables correctional bending of a mature petiole, when an external factor changes its initial vertical orientation, is an interesting problem for gravitational plant biology.
One possibility for the initiation of local buckling of a cylindrical shell is a characteristic sinusoidal wrinkling (with buckling wavelength) of the surface; this symptom occurs when the shell is still straight. This symptom would probably appear in a senescing petiole at the right time, if the deflection of the petiole were prevented by a holding device at the top of the petiole, so that it could not be deflected but could move longitudinally. In a free-standing petiole, both the local buckling under the axial gravity force and the arising bending moment are responsible for the collapse of the senescing petiole. In the initial phase of the buckling, a bending moment appears that increases significantly the compressive stress in the shell on the "concave" side, so that the critical compressive buckling stress is reached asymmetrically. The bending moment increases further, and the petiole falls on that side.
The diameter at the petiole base must be large enough to ensure the stability of the petiole (before senescence). Theoretical prediction of this diameter is not possible at present for the petioles. It is interesting that among the three studied petioles, the diameter of the petiole in A. gigas was the smallest, even though this petiole was the longest. However, the mass of the lamina of this leaf was the lowest. We compared the relationship between height and diameter of the petioles with those of 190 nonwoody species (mosses, pteridophytes, herbaceous dicotyledons, and palms) and 420 woody species (gymnosperms and dicotyledonous trees) studied by Niklas (1993)
. When the data points for the Amorphophallus petioles were marked on the log/log plot for the 610 species in the Niklas paper (Niklas, 1993
; Fig. 1), the Amorphophallus petioles were positioned as if the petioles were trunks of small dicotyledonous trees.
Color patterns on petiole surface
In the older literature, the pattern is described as creating a snake-like appearance— hence, common names such as snake plant and devil's tongue (Gandawijaja et al., 1983
). Probably a human, when in a rainforest, is especially afraid of snakes or other dangers, which can be generalized as devils. Thus, he sees what he fears, while a four-footed animal sees the pattern in another way. When running, it must avoid collisions with trees, so it should be afraid of tree trunks. According to the concept that the petiole mimics mechanical stability, a running animal perceives the relatively thick petiole with the color pattern as a trunk to be avoided.
It is worth mentioning that variable patterns of pigmentation on different organs such as leaves, spatha, and cataphylls are common in Araceae. This means that there is great potential within the genetic information in Amorphophallus plants to form color patterns. It is easy to imagine that if a pattern on a petiole has a functional significance, then there would be a selective evolution pressure on the pattern. Why then is there such a big difference in the "quality" of the patterns between A. titanum and A. gigas? This last species appears to be a champion with respect to the height of the leaves in older plants—more than 3.5 m (Ittenbach, 1998
)—probably the source for the name gigas. Nothing can be found in the literature about other dimensions of the leaves in A. gigas, but judging from the leaf we studied, the diameter is smaller and the length larger than in A. titanum, i.e., the leaves are more slender. This is reasonable because the mass of the lamina is lower in A. gigas (at least in the specimens we have studied). The significance of the color pattern could possibly increase with slenderness. The increasing height, which allows better competition for light, would sharpen the selective pressure on the pattern. Indeed, not only the pattern resembling the lichen thalli was improved, but also the pattern resembling a trunk covered with bark (not present in A. titanum) developed.
In A. titanum petioles, a pattern of tannin-containing cells in the subepidermis is present, but it is not visible. It is interesting that in the subepidermis of ovaries of the same species, a purple pattern occurs, which is underlaid with a similar pattern of tannin-containing cells (Boecker et al., 1998
). A color pattern underlaid by the tannin pattern may have a selective value for the ovaries, but not for lowering the risk of collision with an animal.
The sculpture of the epidermis surface contributes to the three-dimensional appearance of the pattern in A. gigas. It is interesting that this possibility is not exploited in A. titanum though in this species both the cellular phenotypes "papillae" and "furrows" occur. The first is expressed on the ovary surface (Boecker et al., 1998
) but is not expressed in the petiole at all. The furrows occur on the petiole only near the stomata, but are present on the whole epidermis in the spathe (Neinhuis and Wolter, 1998
).
It is possible to write computer programs to simulate even the most sophisticated pigmentation patterns, such as on the shells of mollusk (Meinhardt, 1995
, 2000
). Such programs assume a few specific interactions between virtual chemical reactions involving local autocatalysis (positive feedback) of activator and long-range inhibition (Turing pattern). Depending on the parameters of the reactions and transport processes (mainly diffusion) of the reactants, very different, but more or less regular patterns can be generated. The patterns on the petiole surface should also be simulatable. Chemical reactions in petiole do appear to be necessary for the pattern formation. However, Turing patterns are local phenomena on such a spatial scale in which diffusion may play a role (i.e., <1 cm), while the color pattern characterizes the huge petiole as a whole. However, even a huge petiole is small at the primordial stage; perhaps a Turing pattern occurred at this stage and in some way determined the color pattern. It is interesting, however, that there are no indications for lineage basis in the color pattern.
Another way of looking at the pattern would be to start with an organ or a tissue as a population of cellular oscillators with a certain spectrum of frequencies and with initially chaotic phase differences between the cells, so that at first no waves could be recognized (a wave arises when there is a gradient of the phase). A feature of chaos is that it is very sensitive to initial conditions (i.e., conditions established at a given starting time). A small change in these conditions leads to large changes in the system (e.g., resulting in a pattern of oscillations in the system). If the pattern of oscillations present at a certain time affects cell determination, a pattern may result (the color on the petiole surface). Oscillations and waves may provide a map and a clock for pattern formation (Hejnowicz, 1975
). Such a mechanism of pattern formation is implicated from the study of domain patterns in tree cambia (Hejnowicz and Romberger, 1973
) where domains are local areas (sometimes very large) in the cambium, which differ in the configuration of chiral events like pseudotransverse (inclined) cell divisions. The domain patterns, which occur in the cambia, are so variable that some are similar to the color pattern on the petiole surface.
The color pattern on the petioles is interesting not only from the point of view of the mechanism of its formation (ontogenesis), but also from the view of the evolutionary development of the mechanism (phylogenesis). Chaotic phase variation and evolutionarily developed conditions for "phase filtration" are challenging.
Aerenchyma as supporting tissue
Aerenchyma is traditionally regarded as part of the aerating system of plant organs, functioning in the transport of oxygen and/or as a reservoir of oxygen. Indeed, aerenchyma is a feature specific to plants of wet habitats where this function may be expected. However, aerenchyma can also play a mechanical function. This is possible only when cells are in full turgor, which means that the strategy to use aerenchyma as a mechanical tissue can be effective only in plants, which always have enough water, those growing in wet habitats. Thus the argument that aerenchyma is characteristic for plants of wet habitats, does not differentiate between the hypotheses of aerating and mechanical functions. The petioles of Amorphophallus surely do not suffer from lack of oxygen, and the occurrence of aerenchyma cannot be explained as an adaptation to difficult aerating conditions. It is thus rather a mechanical adaptation. Williams and Barber (1961)
discussed very convincingly the functional significance of aerenchyma in plants and showed the difficulties that arise when aerenchyma is considered as a tissue transporting and storing air. They also suggested that the honeycomb aerenchyma is a unique tissue that fulfills a "mechanical-cum-metabolic" requirement, providing the greatest possible strength with the least possible amount of tissue. Amorphophallus petioles appear to be the best example supporting the postulate that the aerenchyma serves a mechanical function.
Honeycomb aerenchyma is the lightest supporting tissue as long as it is in full turgor. As a living tissue, it needs some metabolic energy to be in such a state; however, it is still "cheaper" than a thick-walled tissue independent of turgor because the petiole has a limited life span.
The importance of aerenchyma may be underestimated based on the notion that the distance that neighboring cells can hydrostatically reinforce one another is a function of the cell-to-cell contact area, which in aerenchyma is very small (Niklas, 1992
, p. 273). The aerenchyma in Amorphophallus petiole contradicts this notion. Aerenchyma by itself provides little stiffness to the organ, similar to air in a car tire, but in concert with the compact peripheral tissue may be very effective in contributing to stiffness, similar to engineering foam cores in cylindrical shells (Karam and Gibson, 1995
).
FOOTNOTES
The authors thank Mr. H.-J. Ensikat (Bonn), Mrs. Ewa Kolano, Mr. Jerzy Karczewski (Katowice) for technical assistance, Dr. Dorota Kwiatkowska (Wroclaw), Prof. Thomas Speck (Freiburg i.Br.) for their comments on the manuscript, and the anonymous reviewers for very helpful suggestions and criticism. 
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