Biomechanical Responses of Chamaedorea and Spathiphyllum Petioles to Tissue Dehydration

Data are presented for the mechanical responses to dehydrationof petioles from two monocotyledons (Chamaedorea erumpens andSpathiphyllum Clevelandii). These data were used to test thehypothesis that the mechanical properties (elastic modulus Eand flexural stiffness EI) of petioles from C. erumpens arealtered significantly less by dehydration than those of petiolesfrom Spathiphyllum. Dehydration, resulting from either dryingat room temperature or from submergence in various concentrationsof mannitol solutions, produced significant increases in E anddecreases in EI (due to geometric distortions) in both youngand mature Spathiphyllum petioles. Similar trends were observedfor young petioles of C. erumpens, but significantly less sofor mature petioles of this species. Regardless of petiolarage, E increased allometrically as a linear function of tissuedensity, which in turn correlated with the volume fraction oflignified tissues in petioles; however, the proportional increaseof E as a function of tissue density was significantly greaterfor C. erumpens petioles than for Spathiphyllum. Anatomicalanalyses of petiolar transections indicated that Chamaedoreapetioles had larger volume fractions of lignified tissues thanthose of Spathiphyllum and that these tissues were located tomaximize stiffness. These data (and previously reported allometricrelationships between EI and petiolar length) shed light onthe difficulties in evaluating the ‘costs’ of committingtissues to mechanical support. Petioles, biomechanics, leaf anatomy, monocotyledons     

Petiole mechanics,light interception by Lamina,and “Economy in Design”

Summary Computer simulations were used to assess the influence of palmate leaf morphology, decussate phyllotaxy, and the elastic moduli of petioles on the capacity of turgid and wilted twigs ofAesculus hippocastanum to intercept direct solar radiation. Leaf size, morphology, orientation, and the Young's and shear moduli (E and G) of petioles were measured and related to leaf position on 8 twigs whose cut ends were placed in water (turgid twigs) and 8 twigs dried for 8 h at room temperature (wilted twigs). Petioles mechanically behaved as elastic cantilevered beams; the loads required to shear petioles at their base from twigs were correlated with the cross-sectional areas of phyllopodia but not with petiole length or tissue volume. Empirically determined morphometric and biomechanical data were used to construct average turgid and wilted twigs. The diurnal capacity to intercept direct sunlight for each was simulated for vertically oriented twigs for 15 h of daylight, 40° N latitude. The daily integrated irradiance (DII) of the wilted twig was roughly 3% less than that of the otherwise comparable twig bearing turgid leaves. Simulations indicated that the orientation of turgid leaves did not maximize DII. More decumbent (wilted) petioles increased DII by as much as 4%. Reduction in the girth, E, or G of petioles, or an increase in petiole length or the surface area of laminae (with attending increase in laminae weight), increased petiolar deflections and DII. Thus, the mechanical design of petioles ofA. hippocastanum was found not to be economical in terms of investing biomass for maximum light interception.     

Morphological adaptations byGlehnia littoralis to the biomass and heights of peripheral herbaceous plants in coastal sand dunes

To clarify the effects of peripheral herbal plants onGlehnia littoralis growth in coastal sand dunes, the morphology of their aboveground portions was surveyed in five communities:Carex kobomugi, Calystegia soldanella, Ischaemum anthephoroides, Oenothera biennis, andElymus mollis. Correlation coefficients (CC) were generally significant at the 1% level between community properties [total aboveground biomass (B) and height (H) of dominant species per unit area] and those ofG. littoralis [leaf number (Nl), petiole angle (Anp), petiole length (Lp), petiole weight (Wp), Lp/Wp, Lp/weight of leaf blade (Wb), Wp/total weight (Wt), specific leaf area (SLA), stem length (Ls), and Ls/weight of stem (Ws)J The exceptions were among four pairings: B and NI, B and Wt, H and Nl, and H and Wt. Of the two community properties, biomass had the greatest association with leaf properties while H was most closely related to those of the stems. Petiole angle increased along with leaf order, from 0° to 42° for the C.kobomugi community, from 5° to 55° forCalystegia soldanella, from 49° to 74° forI. anthephoroides, from 54° to 80° forO. biennis, and from 75° to 85° forE. mollis. In all communities, the properties of Wp, SLA, and Wb increased up to the third or fourth leaf, but then decreased; the exception was for Lp/Wp, which was the reverse. Leaf order of the largest one moved from first position to third as either B or H increased in a community.     

EFFECTS OF TISSUE VOLUME AND LOCATION ON THE MECHANICAL CONSEQUENCES OF DEHYDRATION OF PETIOLES

Data are presented on the mechanical consequences of dehydration for the petioles of two monocots and two dicots differing in leaf morphology (pinnate leaves ofChamaedorea erumpens and simple leaves of Spathiphyllum ‘clevelandii‘; pinnate leaves of Acer negundo and simple leaves of A. saccharum). The flexural stiffness EI of petioles decreased over a broad range of tissue water potential (– 10 < ψ_w <– 50 bars). Within the same range of ψ, the second moment of area I and the elastic modulus E were observed to decrease and increase, respectively. However, the mechanical alterations of Chamaedorea and A. negundo petioles were significantly less than those observed for Spathiphyllum and A. saccharum petioles. The increase in E of Spathiphyllum and A. saccharum petioles attending dehydration was linearly correlated with an increase in the relative volume fraction of tissues with lignified, thick cell walls (“support tissues”). The decrease in I of Spathiphyllum and A. saccharum petioles was linearly correlated with a decrease in the relative volume fraction of tissues with nonlignified, thin cell walls (“ground tissues”). Similar trends were observed for the petioles of C. erumpens and A. negundo but were found not to be statistically significant. Anatomical differences in the relative volume fraction and spatial locations of support tissues in the petioles of these four taxa appear to account for the differences observed in the mechanical consequences of petiole dehydration.     

Twist-to-Bend Ratios and Cross-Sectional Shapes of Petioles and Stems

Two structural properties, resistance to twisting (torsionalrigidity or torsional stiffness, GJ) and resistance to bending(flexural rigidity or flexural stiffness, El), were measuredon a variety of herbaceous stems and petioles. Specimens withnon-circular cross-sections had higher values of the ratio ofEl to GJ that is, such specimens were relatively more flexiblein twisting than in bending. But both kinds had higher ratiosthan those that characterize simple, isotropic materials, andthus both structural and material factors contribute to achievinga high twist-to-bend ratio. The composite property expressedas the dimensionless variable EI/GJ appears to be a functionallyrelevant parameter in many biological situations. Key words: Stems, petioles, flexural rigidity, torsional rigidity, biomechanics     

Theoretical analysis of twist/bend ratio and mechanical moduli of bacterial flagellar hook and filament

Certain motile bacteria employ rotating flagella for propulsion. The relative flexibility of two key components of the flagellum, filament and hook, is partially responsible for the mechanistic workings of this motor. A new computational method, the quantized elastic deformational model, was employed in this article to calculate the dimensionless twist/bend ratio (EI/GJ) of the filament and hook, providing a quantitative means to compare their relative stiffness. Both ratios were much <1.0, an average of 0.0440 for the filament and 0.0512 for the hook, indicating that within each structure bending is favored over twisting. These two ratios, along with previous experimental measurements, allowed us to propose a theoretical Young's modulus (E) between 10(6) and 10(7) dyn/cm(2) for the hook. This value is orders of magnitude smaller than experimentally determined Young's moduli of the filament, hence in agreement with empirical evidence linking compliance in the flagellum mainly to the hook.     

GRAVITY-INDUCED EFFECTS ON MATERIAL PROPERTIES AND SIZE OF LEAVES ON HORIZONTAL SHOOTS OF ACER SACCHARUM (ACERACEAE)

The influence of gravity on the size and mechanical properties of mature leaves on horizontal shoots and etiolated seedlings of Acer saccharum Marsh. (Aceraceae) was examined. Leaves were grouped into three categories regarding their location on shoots (dorsal or “top” T, lateral or “left/right” L/R, and ventral or “bottom” B). Young's modulus E, petiole length L, lamina surface area A and weight P, and the cross-sectional areas of different tissues within petioles were measured for each leaf and were found to be correlated with leaf location (T, L/R, and B): T leaves were smaller and had lower E than their B counterparts; the size and material properties of L/R leaves were intermediate between those of T and B leaves. In general, A, P, and E decreased from the base to the tip of shoots. In addition to anisophylly, the influence of gravity induced petiole bending and torsion and resulted in the horizontal planation of laminae. This was observed for field-grown mature plants and etiolated seedlings. Petiole bending and torsion were interpreted as gravimorphogenetic phenomena. Anatomically, L, E, and petiole deflection angle Fv measured from the vertical were highly correlated with the combined cross-sectional areas of phloem fibers and xylem in petioles of B leaves and when data from all leaves were pooled. It is tentatively advanced that the correlation of E with the transverse areas of phloem fibers and xylem is evidence that either the pattern or the extent of lignification of petiole tissues is influenced by petiole position with respect to gravity.     

Differences in mechanical and structural properties of surface and aerial petioles of the aquatic plant Nymphaea odorata subsp. tuberosa (Nymphaeaceae)

Lily pads (Nymphaea odorata) exhibit heterophylly where a single plant may have leaves that are submerged, floating, or above (aerial) the surface of the water. Lily pads are placed in a unique situation because each leaf form is exposed to a distinctly different set of mechanical demands. While surface petioles may be loaded in tension under conditions of wind or waves, aerial petioles are loaded in compression because they must support the weight of the lamina. Using standard techniques, we compared the mechanical and morphological properties of both surface and aerial leaf petioles. Structural stiffness (EI) and the second moment of area (I) were higher in aerial petioles, although we detected no differences in other mechanical values (elastic modulus [E], extension ratio, and breaking strength). Morphologically, aerial petioles had a thicker rind, with increased collenchyma tissue and sclereid cell frequency. Aerial petioles also had a larger cross-sectional area and were more elliptical. Thus, subtle changes in the distribution of materials, rather than differences in their makeup, differentiate petiole forms. We suggest that the growth of aerial petioles may be an adaptive response to shading, allowing aerial leaves to rise above a crowded water surface.     

FLEXURAL STIFFNESS ALLOMETRIES OF ANGIOSPERM AND FERN PETIOLES AND RACHISES: EVIDENCE FOR BIOMECHANICAL CONVERGENCE

Evidence for convergence in biomechanical and anatomical features of leaves (elastic modulus E, second moment of area I, taper of petioles, the longitudinal distribution of petiolar and laminar weight, and volumes of tissues) is presented based on a survey of 22 species (distributed among dicots, monocots, and ferns). In general, regardless of taxonomic affinity, petioles were found to be mechanically constructed in one of two ways: Type I petioles—as cantilevered, end-loaded beams with relatively uniform flexural stiffness (EI) (simple and palmate leaves); and Type II petioles—as tapered cantilevered beams whose static loadings (biomass) and EI increase basipetally (pinnate leaves). In general, collenchyma and sclerenchyma were found to be peripherally located in transections through Type I and II petioles, respectively. Statistical analyses within each species and among species with either type of petiole indicated that EI ≈ k₁Lp^2.98 and EI ≈ k₂Lp^2.05 for Type I and II petioles, respectively, where k₁ and k₂ are dimensional constants and Lp is petiolar length. The data are interpreted to indicate that Type I and II petioles mechanically operate to deal with static loadings in two distinct ways, such that Type II petioles function in an analogous manner to branches supporting separate leaves (leaflets). The convergence in mechanical “designs” among taxonomically distinct lineages (angiosperms and ferns) is interpreted as evidence for selection on mechanical attributes of load supporting structures (petioles).     

Scaling of Petiole Dimensions with Respect to Leaf Size for a Tropical Tree, Scaphium macropodum (Sterculiaceae), in Borneo

Scaphium macropodum (Miq.) Beumee ex Heyne (Sterculiaceae) in a tropical rain forest in West Kalimantan (Indonesia) was analyzed from the viewpoint of statics. The petiole diameter must increase with increasing leaf size to retain enough mechanical stability and a sufficient amount of conductive vessels. The petiole's cross-sectional area at its base was found to be proportional to the leaf blade's dry mass, which indicates that Shinozaki's pipe model is applicable to leaves with different sizes. Although larger leaves produce greater bending moments on the petiole's cross-section as a result of their greater weights, the bending stresses at the petiole's base caused by the leaf's weight were constant at ca. 76,900 g cm⁻² regardless of leaf size. Thicker petioles increase the leaf's mechanical stability, but require sizable energy investments for their construction. It is hypothesized that the constant value for petiolar stress indicates an optimal balance between energy economy and the mechanical stability of S. macropodum leaves. To keep bending stress constant, the leaf blade's center of gravity shifts to a more proximal position and the cross-sectional area of the petiole increases. Received 8 December 1997/ Accepted in revised form 1 December 1998     

The Mechanical Roles of Clasping Leaf Sheaths: Evidence fromArundinaria tecta(Poaceae) Shoots Subjected to Bending and Twisting Forces

Representative shoot segments of the grass speciesArundinariatéctaconsisting of one intact internode and its subtendingnode and clasping leaf sheath were tested to determine the mechanicalinfluence of the leaf sheath on the ability of stems to resistbending and twisting forces. These segments were also used tomeasure shoot morphometry and composite tissue Young's and shearmoduli (EandG,respectively) to simulate the global deformationpatterns attending bending and twisting by means of finite elementanalyses. On average, leaf sheaths contributed 33% of the overallbending stiffness and 43% of the overall torsional stiffnessof stem segments. Comparisons betweenEandGof isolated internodesand leaf sheaths indicated that sheaths were composed of stiffertissues measured either in bending or twisting. Thus, leaf sheathscould act as an external cylindrical brace composed of stiffermaterials than those of the internodes they enveloped. The magnitudesof internodalEandGwere correlated with internodal shape suchthat the ability of internodes to resist twisting relative tothe ability to resist bending forces decreased as internodesbecame more slender or developed thinner walls (both of whichoccur in an acropetal direction from the base to the tip ofshoots). Finite element simulations predicted that, in bending,the leaf sheath laterally braces internodal walls as they tendto ovalize in cross section and push against its inner surfacewhich ovalizes to a lesser extent in the plane normal to thecurvature of shoot flexure. In twisting, the successive ovalizedtransections of internodal walls assumed a helical pattern alongthe length of shoot segments. This helical deformation patternwas attended by an inner lateral contraction of internodal wallsthat was less developed in the leaf sheath that thus provideddecreasing mechanical support to the internode as the lateralcontraction of internodal walls amplified. The twisting of internodesand sheaths was also predicted to concentrate tensile and shearstrains in the nodal diaphragm. Here stress intensities sufficientto produce tissue shear failure were concentrated at two opposingpoints on the surface of the diaphragm. Finite element analysesthus identified a potential weak point in the mechanical constructionof hollow, septate shoots that are, nevertheless, more thanadequately stiff to support their own weight, yet sufficientlyflexible to twist without irreparable damage in normal winds.Copyright1998 Annals of Botany Company Plant stems; nodes; internodes; leaf sheaths; elastic moduli; wind lodging; biomechanics.     

The role of light and growth regulators in the opening of the dentaria petiolar hook

The phenomenon of the etiolated hook is not restricted to the hypocotyl of the dicotyledenous plant (e.g., Phaseolus) but appears to serve a similar, adaptive function in the petioles of certain rhizomatous plants. The commonly employed regulants of hypocotyl hook opening were tested for their effect on the petiolar hook of Dentaria diphylla. The hook was found to require both light (red light promoted, far red inhibited) and the intact leaf for opening. The leaf requirement was fully replaced by gibberellic acid (0.04% in lanolin) but only in light; cobalt chloride (0.1-1.0 mm) promoted a partial opening in dark with or without leaf; and coumarin (1 mm), indoleacetic acid (1-4% in lanolin), and ethylene 10 microliter per liter all inhibited opening of hooks with or without lamina. The absolute requirement for light and leaf tissue and the replacement of proximal tissue by GA₃ alone represent marked differences in the physiology of hypocotyl and petiolar hooks. These differences are believed to indicate the necessity for concomitant leaf maturation in petiolar hook opening.     

FLEXURAL RIGIDITY OF CHIVE AND ITS RESPONSE TO WATER POTENTIAL

The biomechanical relationship between the ability of a plant organ to resist bending and the extent to which tissues are hydrated is illustrated for the cylindrical leaves of chive (Allium schoenoprasnum var. schoenoprasnum L.). The flexural rigidity (EI), which measures the ability to resist bending, is maximum when leaves are fully turgid and decreases monotonically as a function of water potential (r² = 0.99). Dehydration results in a reduction in the elastic modulus (E) of leaves. Reductions in E are correlated with geometric distortion in the transverse geometry of leaves which influences their second moment of inertia (I). The traditional theory of elastic stability (developed on the basis of the mechanical behavior of nonbiological systems) is shown to be inadequate to distinguish the behavior of E as plant organs geometrically distort during dehydration. This inadequacy results from the violation of a principal assumption made by the theory (= uniform cross-sectional geometry). A derivation is presented that accommodates the localized geometric distortions in cylindrical plant organs and permits a valid estimate of reductions in E as tissues dehydrate. Based on this derivation, the Young's modulus of chive leaves just before mechanical failure due to buckling is shown to be less than 50% of that calculated for fully turgid leaves.     

Translocation pathways in the petioles and stem between source and sink leaves of Populus deltoides Bartr. ex Marsh.

Microautoradiography was used to follow the translocation pathways of ¹⁴C-labeled photosynthate from mature source leaves, through the stem, to immature sink leaves three nodes above. Translocation occurred in specific bundles of the midveins and petioles of both the source and sink leaves and in the interjacent internodes. When each of six major veins in the lamina of an exporting leaf was independently spot-fed ¹⁴CO₂, label was exported through specific bundles in the petiole associated with that vein. When the whole lamina of a mature source leaf was fed ¹⁴CO₂, export occurred through all bundles of the lamina, but acropetal export in the stem was confined to bundles serving certain immature sink leaves. Cross-transfer occurred within the stem via phloem bridges. Leaves approaching maturity translocated photosynthate bidirectionally in adjacent subsidiary bundles of the petiole. That is, petiolar bundles serving the lamina apex were exporting unlabeled photosynthate while those serving the lamina base were simultaneously importing labeled photosynthate. The petioles and midveins of maturing leaves were strong sinks for photosynthate, which was diverted from the export front to differentiating structural tissues. The data support the idea of bidirectional transport in adjacent bundles of the petiole and possibly in adjacent sieve tubes within an individual bundle.Abbreviations C central leaf trace - L left leaf trace - LPI leaf plastochron index - R right leaf trace     

PETIOLE DEVELOPMENT AND XYLEM DIFFERENTIATION IN XANTHIUM REPRESENTED BY THE PLASTOCHRON INDEX

Petiole development and formation of xylem vessels have been investigated in Xanthium leaves from early ontogeny to maturity. Kinetics of growth was presented in terms of absolute and relative elemental rates of elongation. The process of vascularization was assessed by the number of differentiated xylem vessels. The leaf plastochron index (LPI) developed by Erickson and Michelini (1957) was used for designating the various stages of development. An exponential increase in petiole length was observed between the LPIs –3 and +4 indicating a constant relative rate of 0.20 or 20% increase per day. After cessation of lamina elongation at LPI 8, petiole elongation continued for an additional 5 day period, to LPI 9.5. Relative elemental rate analysis revealed that the basipetal pattern of elongation was maintained throughout the leaf development. At a specific plastochron age, the only growth was due to the petiole elongation. Leaves which ceased elongating had not completed their internal development, since the process of xylem formation continued for several plastochrons, or about 8 days. The highest rate of xylem formation was ten vessels per day at LPI 5. On the average, about five xylem vessels differentiated per day in the middle portion of a Xanthium petiole. Mature petioles contained an average of 218 xylem vessels. About 12 canals of schizogenous origin preceeded the development of the vascular tissue.     

Differences between Acer saccharum Leaves from Open and Wind-Protected Sites

Size-correlated variations of sugar maple (Acer saccharum L.)leaf anatomy and mechanical properties were determined for twosaplings (from open and wind protected sites) to examine theeffects of chronic wind-induced mechanical disturbance on leafsize, rigidity and flexibility. Based on a total sample of 78leaves, comparisons indicated that the mean size of the opensite leaves (n =37) was smaller in every measured respect comparedwith that of the closed site leaves (n =41). Open site leaveshad, on average, smaller lamina surface area, shorter and narrowerpetioles with a smaller volume fraction of lignified tissuesthan those from the closed site. Biomechanical comparisons alsoindicated that the petioles of open site leaves were significantlyless rigid and more flexible than the petioles of closed siteleaves. Despite differences in mean leaf size and petiolar rigidityand flexibility, allometric comparisons indicated the size-dependentvariations in leaf properties were continuous across the twosites. Also, the allocation of leaf biomass with respect tostem biomass along the lengths of the two saplings was statisticallyidentical and indistinguishable from an isometric relationship.However, the smaller diametered branches of the open site saplingbore smaller and fewer leaves with less stiff and rigid petiolesthan those of the closed site sapling. The differences betweenopen and closed site leaves are interpreted to be functionallyadaptive and to indicate that chronic mechanical disturbanceof developingAcer saccharum leaves prefigures mature leaf sizeand petiole properties that have the capacity to reduce winddrag. Results from petioles are contrasted with those of mechanicallydisturbed stems. Leaves; Acer saccharum ; biomechanics; wind-drag; allometry     

Carbohydrate translocation in sugar beet petioles in relation to petiolar respiration and adenosine 5'-triphosphate

Earlier studies have shown that the retarding effect of low petiolar temperatures on sucrose transport through sugar beet (Beta vulgaris L.) petioles is markedly time-dependent. Although the initial effect of chilling the petiole to near 0 C is severely inhibitory, translocation rates soon recover (usually within about 2 hours) to values at or near the control rate. In the present studies, selected metabolic parameters were measured simultaneously with translocation. No stoichiometric relationships among petiolar sucrose transport, petiolar respiration (CO₂ production), and calculated petiolar ATP turnover rates were evident. It appears that the major sources of energy input energizing carbohydrate transport in sieve tubes function mainly at either loading or unloading sites and not at the level of individual sieve-tube elements.     

14C fixation,metabolic labeling patterns,and translocation profiles during leaf development in Populus deltoides

The incorporation of photosynthetically fixed ¹⁴CO₂ and the distribution of ¹⁴C among the main chemical constituents of laminae and petioles were examined in cottonwood (Populus deltoides Bartr. ex Marsh.) leaves ranging in age from Leaf Plastochron Index (LPI) 3 (about one-quarter to one-third expanded) to LPI 30 (beginning of senescence). In addition, carbon flow among chemical fractions and translocation from leaves of LPI 7 and 14 were examined periodically up to 24 h after labeling. Specific activity of ¹⁴C (on dry-weight basis) increased in developing laminae to full leaf expansion, decreased in the mature leaves to LPI 16, then remained constant to LPI 30. In developing leaves (LPI 3-5), after 2 h, most of the ¹⁴C was found in protein, pigments, lipids, and other structural and metabolic components necessary for cell development; only 28% was in the sugar fraction of the lamina. In fully expanded leaves (LPI 6-8), after 2 h, the sugar fraction contained 50–60% and about 90% of fixed ¹⁴C in the lamina and the petiole, respectively. In a pulsechase kinetic series with recently mature leaves, 60% of the ¹⁴C was found in the sugar fraction after 15 min of ¹⁴CO₂ fixation. Over the 24-h translocation period, ¹⁴C decreased in sugars to 23% and increased in the combined residue fraction (protein, starch, and structural carbohydrates) to about 60% of the total activity left in the lamina. Within 24 h after labeling, the turnover of ¹⁴C-organic acids,-sugar, and-amino acids (either metabolzed or translocated from the leaf) was 30, 70 and 80%, respectively, of that initially incorporated into these fractions by a leaf at LPI 7 (turnover was 55% of ¹⁴C-organic acids, 80% of ¹⁴C-sugar, and 95% of ¹⁴C-amino acids at LPI 14). Anatomical maturity in cottonwood leaves is closely correlated with physiological maturity and with production of translocatable sugar.Abbreviations LPI leaf plastochron index - PI plastochron index Research Plant Physiologist and Chief Plant Physiologist, respectively     

Anatomy of the gas canal system of Nelumbo nucifera

Nelumbo nucifera (Gaertn.) grows by extending a creeping rhizome through anaerobic sediments. Nodes form at intervals along the rhizome, each producing a single leaf, and gas canals channel air from the leaves throughout the petioles and rhizomes. The gas flow pathway was mapped by casting the canals in growing shoots with silicone and by blowing air through complexes of rhizomes and petioles. Air from a leaf flows to a rhizome through one of two petiolar canal pairs, joining with the lowermost of three canal pairs in the rhizome through a chamber in the node. The lowermost canal pair links these nodal chambers along the length of a rhizome, allowing air from a node to flow both forward, toward a growing shoot, and backward, toward preceding leaves. These linked chambers also connect with the middle pair of canals on their proximal side, enabling flow to proceed backward along the rhizome to an adjacent node. A chamber in the next node then diverts the flow into the upper canal pair. This pair leads to a third node and chamber from which the air vents to the atmosphere through the second petiolar canal pair. Thus, pressurised air from one leaf must flow backward through two nodes before it returns to the atmosphere. Forward flow also ventilates a shoot's growing tip, with air from the lowermost canal pair entering a chamber in the developing node which, as described above, connects with the middle canal. This allows the air to reverse direction at the tip and enter the vent flow pathway.     

Twist-to-bend ratios of woody structures

Flexural rigidity (El), or resistance to bending loads, andtorsional rigidity (GJ), or resistance to twisting loads, weremeasured on a variety of woody structures-bamboo culms, threekinds of hardwood trunks, two softwood trunks, two vines, andpine roots. The ratios of these rigidities, EI/GJ, was highestand relatively constant for bamboo and hardwoods, slightly lowerfor softwoods, and lower still for vines and roots. All valueswere substantially above those for circular cylinders of ordinaryisotropic materials; since all specimens were nearly circularin cross-section, the high values reflect the elastic moduliof wood rather than geometric factors. While all material showedsubstantial creep under torsional loading, only the vine, Wisteria,crept appreciably under flexural loading as well. Key words: Wood, trees, flexural rigidity, torsional rigidity, biomechanics