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Biomechanical Model of the Xylem Vessels in Vascular Plants

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Biomechanical Model of the Xylem Vessels in Vascular Plants Annals of Botany 95: 1179–1186, 2005 doi:10.1093/aob/mci130, available online at www.aob.oupjournals.org Biomechanical Model of the Xylem Vessels in Vascular Plants GEBRAN N. KARAM* Lebanese American University, Byblos, PO Box 166864, Beirut, Lebanon Received: 17 January 2004 Returned for revision: 1 July 2004 Accepted: 14 February 2005 Published electronically: 31 March 2005 Background and Aims The xylem, or water transport system, in vascular plants adopts different morphologies that appear sequentially during growth phases. This paper proposes an explanation of these morphologies based on engineering design principles. Methods Using microscopic observations of the different growth stages, an engineering analysis of the xylem vessels as a closed cylinder under internal pressure is carried out adopting pressure vessel design concepts. Key Results The analysis suggests that the xylem vessel structural morphology follows the ‘constant strength’ design principle, i.e. all of the material within the wall of the xylem is loaded equally to its maximum allowable stress capacity, and the amount of material used is therefore systematically minimized. The analysis shows that the different structural designs of the xylem vessel walls (annular, helical, reticulate and pitted) all quantitatively follow the constant strength design principle. Conclusions The results are discussed with respect to growth and differentiation. It is concluded that the morphology of the xylem vessel through the different phases of growth seems to follow optimal engineering design principles. Key words: Xylem vessel, vascular plant, constant strength, structural design, xylem cell wall, biomechanics. INTRODUCTION xylem vessel cell walls as reported in the published liter- ature and as observed on some herbaceous and non-woody The xylem is the principal water conducting tissue in a vascular plants to provide a new functional explanation for vascular plant. It is divided between primary and secondary the different observed types of secondary wall thickening: xylem. Primary xylem consists of an early part, the proto- annular, helical, reticulate and pitted. xylem, which differentiates and matures among actively elongating plant organs, and a later part, the metaxylem, which initiates during the growth of the primary body of the plant but matures after elongation has ceased. Secondary BIOMECHANICS OF THE VESSEL xylem forms during secondary growth stages and initiates ELEMENTS after all elongation has been completed. Cell walls in the From an engineering point of view, the xylem is the water tracheary elements of the xylem have a variety of secondary distribution network that transmits water from the root wall thickenings. Different types appear in an ontogenetic collection system to the main consumers, the leaves, in sequence with annular thickening occurring first, followed the upper parts of the plant. Transpiration of the leaf meso- in order by helical, scalariform, reticulate and pitted thick- phyll cells causes a water potential difference between the ening. Occurrence of the secondary wall types depends on leaf and the xylem, resulting in water transport. During the the growth and maturity of the tracheary element and can- growing season the water is lifted up to the leaves by neg- not be assigned distinctly to any one type of xylem. Two ative pressures, less than atmospheric, created by transpira- types of tracheary elements can be distinguished: tracheids tion. Vessels, made of elongated hollow cells connected end and vessel elements. Tracheids appear mainly in woody to end (Zimmerman, 1983), are subjected to high internal plants and are connected laterally through multiple pits. negative pressures (Choat et al., 2003) that must be resisted Vessels appear in both woody and non-woody plants and by their walls to prevent cell collapse. Microscopic invest- are built of numerous vessel members joined at their ends. igation shows that primary vessel walls are reinforced by the They are typically found in vascular bundles inside different secondary wall, a lignified cell-wall thickening, deposited plant organs (Fig. 1). on the inside of the primary wall of the cell (Wooding and In this study, the biomechanics of vessel elements are Northcote, 1964; Bierhorst and Zamora, 1965; Ray, 1972; analysed from an engineering point of view. An engineering Neushul, 1974) (Fig. 2). Secondary wall first appears as an model is derived by assuming that the design of the wall annular thickening. Subsequently, the thickening becomes thickening follows a constant strength design principle, helical, followed by interconnected helices, coils or scalari- which, by loading all parts to their maximum allowable form thickening. The final structure, encountered in the last stress capacity, minimizes the amount of material used. The ontogenetic stage, has reticulate or net-like thickening, or quantitative and qualitative predictions of this engineering uniform thickening with staggered pits in pitted vessels model are compared with the structural designs of plant (Fig. 2) (Bierhorst and Zamora, 1965; Jensen and Salisbury, 1972; Ray, 1972; Neushul, 1974; Esau, 1977; Fahn, 1990). * For correspondence. E-mail [email protected] The type of secondary wall thickening is determined by the ª The Author 2005. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: [email protected] 1180 Karam — Biomechanical Model of Xylem Vessels R t p Cross-section Vascular bundle p Phloem Longitudinal view Functional metaxylem F IG. 3. Xylem vessel modelled as a pressurized tube (see text for detail). Crushed protoxylem an internal pressure, p, which can be either negative or F IG. 1. Micrograph of vascular bundle in a grass stem showing large open vessels (metaxylem), early formed collapsed vessels (protoxylem) positive; engineers call such a structure a ‘pressure vessel’ and phloem. (Fig. 3). The primary cell wall is a layer made of randomly orientated cellulose microfibrils in a relatively visco-elastic Early formed vessels Secondary wall (Protoxylem) matrix that allows extension and elongation (Bodig and Primary walls thickening Pit Jane, 1982; Niklas, 1992). Some re-orientation of the microfibrils is thought to take place under elongation stres- ses during growth. There is evidence that microfibrils get deposited mostly along the transverse or hoop direction before some get realigned along the fibre axis (Niklas, 1992) due to elongation stresses. For the purposes of the analysis the primary wall is considered to be homogeneous and isotropic with a maximum allowable stress of s* both axially and transversely. The secondary wall layer of xylem tracheids is known to consist of highly orientated cellulose microfibrils with a structure stabilized by lignin (Mark, 1967; Bodig and Jane, ABC D E 1982; Niklas, 1992; Reiterer et al., 1999). The secondary wall of tracheids contributes over 80 % of the cell wall F IG. 2. Types of vessel elements with different secondary wall thicknening thickness and provides mechanical support to the plant. patterns. (A) Annular; (B) annular/helical; (C) double helical opposite curl; The same structure of highly orientated cellulose microfib- (D) double helical same curl; and (E) pitted (after Ray, 1972; permission rils is usually assumed for the secondary wall layer of xylem requested from Holt, Reinhart and Winston Inc.). vessels in woody and non-woody plants, albeit the structural support function to the plant is not required. The cellulose dimension (diameter) of the vessel and the maturity and microfibrils in the secondary wall of vessels are expected to growth stage of the plant (ontogeny). The literature contains be more-or-less aligned along the direction of deposition many descriptions and discussions of the secondary wall (annular, helical, etc.) with varying amounts of lignin patterns without an exact analysis or explanatory model. deposited along the microfibrils. These factors result in The mechanical engineering design problem of the xylem differing strengths between the primary and secondary lay- vessel element is treated in the next section to provide a ers. In order to allow for this possible difference, a strength possible explanation for these observations. ratio, r, is introduced where the maximum allowable In addition to mechanically resisting the water pressure, stress of the secondary wall layer along the direction of the xylem also has to satisfy other design constraints such as its deposition would be rs*. The secondary wall layer, plant growth strains, hydraulic conductivity and connectiv- which is deposited along circular, spiral or net-like patterns, ity between adjacent cells. These will not be considered in acts as a unidirectional reinforcement and hence only its the derivation of the engineering model. axial properties are relevant to the analysis. The anisotropy of the secondary wall does not affect the model. It is worth- while noting that the strength ratio, r, could be derived from basic composite theory as r = E /E ; where E is the ENGINEERING MODEL sw pw sw modulus of elasticity of the secondary wall, and Epw is The vessel element is analysed as a closed-end cylinder, the modulus of elasticity of the primary wall, when both of uniform radius, R, and wall thickness, t, subjected to walls are subjected to the same strains. The use of this Karam — Biomechanical Model of Xylem Vessels 1181 strength ratio would account in the most general way for the Longitudinal direction difference in properties between the primary and secondary walls. When r = 1, the secondary and primary walls are assumed to have the same maximum allowable stress. s To minimize the total amount of material used, a fully stressed design is sought, i.e. all parts of the xylem are assumed to be equally stressed in all directions. The internal pressure causes hoop and longitudinal stresses, with the hoop stresses being twice the longitudinal. The forces per unit length in the hoop and longitudinal directions, Fh and Hoop direction F1, respectively, that the tube has to resist can be written as: Fh = pR ð1aÞ F1 = pR=2 ð1bÞ Note that a positive pressure (cell pressure greater than F IG.
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