The Impact of Tissue Morphology,Cross-Section and Turgor Pressure on the Mechanical Properties of the Leaf Petiole in Plants

This paper describes a study of petiole structural morphology in which tissue materials, cross-sectional geometry, layer-architecture and hydrostatic condition are variables that affect the overall structural properties of the organ. Philodendron melinonii is selected as a model species for characterizing the mechanical properties of the petiole. The shape of the petiole is modeled through the polar parameterization of the Lame's curves, i.e. Gielis formulation. A multiscale model of bending stiffness is proposed to capture the impact of changing the constituent tissues and the cross-sectional geometry. Stiffness and density of different tissues are used to plot the domain bounded by the limiting curve of the respective tissue material. Shape parameters and the respective tissue properties are used to generate structural efficiency maps displaying property domains within which fall all possible combinations of tissues that are shaped into a certain geometry during growth. The turgor pressure is also taken into account to show how the domain of the effective material properties changes with water content. Finite element analysis besides experimental data is used to validate the theoretical results. The maps may offer a source of inspiration for biomimetic design, as they help to gain insight into the efficiency of biological beams described by different tissues properties, geometry and turgidity.     

Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.     

Development and Growth Form of the Neotropical Liana <Emphasis Type="Italic">Croton nuntians</Emphasis>: The Effect of Light and Mode of Attachment on the Biomechanics of the Stem

The neotropical liana Croton nuntians (Euphorbiaceae) can occur in a variety of different growth habits. Juvenile freestanding plants are mechanically stable without support and resemble morphologically young trees or shrubs, whereas adult plants are climbers. Ontogenetic variation of bending and torsion properties of different growth phases are analyzed by measurements of flexural stiffness, structural bending modulus, torsional stiffness and structural torsional modulus. Mechanical and anatomical data show two fundamentally different patterns for juvenile freestanding and adult climbing plants. In freestanding plants, mechanical properties and the contribution of cortex, wood, and pith to the stem cross-section vary only little during ontogeny as is typical for semi-self-supporting plants. In contrast, climbing plants become significantly more flexible during ontogeny, as is characteristic for lianas. This is accompanied by a transition to the formation of a less dense wood type with large diameter vessels and an increasing contribution of flexible tissues (less dense wood and cortex) to the cross-sectional area and the axial second moment of area of the stems. Depending on the environmental conditions, freestanding plants can differ considerably in their appearance due to differences in branching system or stem taper. Therefore the influence of light quantity, measured as percentage of canopy opening, on the mechanical properties and the stem anatomy was tested. Freestanding plants grown with strong shade are significantly more stiff in bending compared with plants grown with a moderate light environment.     

A parameter optimization method to determine ski stiffness properties from ski deformation data

The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.     

Unexpectedly high susceptibility of micropropagated rhubarb (Rheum rhaponticum L.) to spot disease caused by Ramularia rhei

Rapid, large-scale micropropagation of a Rheum rhaponticum (rhubarb) breeding line, selected for the absence of autumn dormancy, produces changes typical of somaclonal variation. Among these is enhanced susceptibility to foliar infection by the spot disease pathogen Ramularia rhei, with consequential increased spore production on infected leaves. This provides an increased level of inoculum in the late season, leading to commercially unacceptable petiole spotting as spores are washed from the lamina on to the petiole surface. Infection of conventionally propagated plants does not exceed market acceptability. Consequently, to maintain the commercial value of this rhubarb selection micropropagation must be avoided, at least until an acceptably modified protocol is available.     

Towards a molecular description of intermediate filament structure and assembly

Intermediate filaments (IFs) represent one of the prominent cytoskeletal elements of metazoan cells. Their constituent proteins are coded by a multigene family, whose members are expressed in complex patterns that are controlled by developmental programs of differentiation. Hence, IF proteins found in epidermis differ significantly from those in muscle or neuronal tissues. Due to their fibrous nature, which stems from a fairly conserved central alpha-helical coiled-coil rod domain, IF proteins have long resisted crystallization and thus determination of their atomic structure. Since they represent the primary structural elements that determine the shape of the nucleus and the cell more generally, a major challenge is to arrive at a more rational understanding of how their nanomechanical properties effect the stability and plasticity of cells and tissues. Here, we review recent structural results of the coiled-coil dimer, assembly intermediates and growing filaments that have been obtained by a hybrid methods approach involving a rigorous combination of X-ray crystallography, small angle X-ray scattering, cryo-electron tomography, computational analysis and molecular modeling.     

Flexural and torsional stiffness in multi-jointed biological beams

Flexibility, the ability to deform in response to loads, is a common property of biological beams. This paper investigates the mechanical behavior of multi-jointed beams, which are characterized by a linear series of morphologically similar joints. Flexural stiffness and torsional stiffness were measured in two structurally distinct beams, crinoid arms (Echinodermata, Comatulida) and crustacean antennae (Arthropoda, Decapoda). Morphological data from these beams were used to determine the relative contributions of beam diameter and joint density (number of joints per millimeter of beam length) to the flexural and torsional stiffness of these two structures. As predicted by beam theory, beam diameter influenced stiffness in both crinoid arms and crustacean antennae. In crinoid arms, increases in joint density were associated with decreases in stiffness, but joint density had no significant influence on stiffness in crustacean antennae. In both crinoid arms and crustacean antennae, the magnitudes of flexural and torsional stiffness, as well as the ratio of these two variables, were similar to previously reported values for non-jointed biological beams. These results suggest that the structural design of a biological beam is not a limiting factor determining its mechanical properties.     

Twisting and bending of biological beams: distribution of biological beams in a stiffness mechanospace

Most biological beams bend and twist relatively easily compared to human-made structures. This paper investigates flexibility in 57 diverse biological beams in an effort to identify common patterns in the relationship between flexural stiffness and torsional stiffness. The patterns are investigated by mapping both ideal and biological beams into a mechanospace defined by flexural and torsional stiffness. The distribution of biological beams is not random, but is generally limited to particular regions of the mechanospace. Biological beams that are stiff in bending are stiff in torsion, while those that bend easily also twist easily. Unoccupied regions of the mechanospace represent rare combinations of mechanical properties, without proving that they are impossible. The mechanical properties of biological beams closely resemble theoretical expectations for ideal beams. Both distributions are potentially being driven by the interdependence of the material and structural properties determining stiffness. The mechanospace can be used as a broadly comparative tool to highlight systems that fall outside the general pattern observed in this study. These outlying beams may be of particular interest to both biologists and engineers due to either material or structural innovations.     

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     

Reorientation of daffodil(Narcissus: Amaryllidaceae) flowers inwind: drag reduction andtorsional flexibility

Daffodil flowers extend laterally from the long axes of their stems; as a result, wind on a flower exerts torsional as well as flexural stress on the stem. Stems respond by twisting, and thus flowers reorient to face downwind in moderate winds, in the process reducing their drag by ～30%. This repositioning is facilitated by the stems' relatively low torsional stiffness. Daffodil stems have a ratio of flexural to torsional stiffness of 13.27 ± 0.96 (SD), compared with 8.33 ± 3.20 (SD) for tulip stems, which bear flowers as symmetrical extensions of their long axes, and compared with 1.5 for isotropic, incompressible, circular cylinders.     

The Honeybee's Protrusible Glossa is a Compliant Mechanism

Many biological structures can perform highly-dexterous actions by using dynamic surfaces.To deal with the contradictive demands of high feeding efficiency and low energy expenditure during nectar feeding,the glossal surface of a honeybee undergoes shape changes,in which glossal hairs erect together with segment elongation in a drinking cycle.In this paper,we extracted a transmission link embedded in the glossa from postmortem examination and found that the compliance of the intersegmental membranes provides more possibilities for this highly kinematic synchronicity.According to the morphing phenomena of honeybee's glossa,we proposed a compliant mechanism model to predict the deformation behavior of honeybee considering elastic properties of the glossal intersegmental membranes.The increase of membrane stiffness may improve the capacity of elastic potential energy transfer,but will still result in the increase of mass.An index is introduced to evaluate the contradiction for optimizing structural parameters.This work may arouse new prospects for conceptual design of micro-mechanical systems equipped with bio-inspired compliant mechanisms.     

Structural compliance: A new metric for protein flexibility

Proteins are the active players in performing essential molecular activities throughout biology, and their dynamics has been broadly demonstrated to relate to their mechanisms. The intrinsic fluctuations have often been used to represent their dynamics and then compared to the experimental B-factors. However, proteins do not move in a vacuum and their motions are modulated by solvent that can impose forces on the structure. In this paper, we introduce a new structural concept, which has been called the structural compliance, for the evaluation of the global and local deformability of the protein structure in response to intramolecular and solvent forces. Based on the application of pairwise pulling forces to a protein elastic network, this structural quantity has been computed and sometimes is even found to yield an improved correlation with the experimental B-factors, meaning that it may serve as a better metric for protein flexibility. The inverse of structural compliance, namely the structural stiffness, has also been defined, which shows a clear anticorrelation with the experimental data. Although the present applications are made to proteins, this approach can also be applied to other biomolecular structures such as RNA. This present study considers only elastic network models, but the approach could be applied further to conventional atomic molecular dynamics. Compliance is found to have a slightly better agreement with the experimental B-factors, perhaps reflecting its bias toward the effects of local perturbations, in contrast to mean square fluctuations. The code for calculating protein compliance and stiffness is freely accessible at https://jerniganlab.github.io/Software/PACKMAN/Tutorials/compliance .     

Effect of methyl jasmonate on gummosis in petioles of culinary rhubarb (<Emphasis Type="Italic">Rheum rhabarbarum</Emphasis> L.) and the determination of sugar composition of the gum

This study aimed to know the key chemical compound influencing gummosis in petioles of intact growing culinary rhubarb (Rheum rhabarbarum L.) with special emphasis on its sugar composition. The application of methyl jasmonate (JA-Me, 0.5 and 1% in lanolin, w/w) in the middle of intact petiole of growing rhubarb substantially induced gummosis in the entire petioles, below and above the treatment, within several days. JA-Me at 0.5% in lanolin greatly stimulated ethylene production in intact petiole of growing rhubarb, on the 3rd day after JA-Me treatment, ethylene level being increased five times or more. However, an ethylene-releasing compound, ethephon (2-chloroethylphosphonic acid, 1 and 2% in lanolin, w/w) alone had no effect on gummosis. Analysis of gum polysaccharides by a gel permeation chromatography with a Tosho TSK-gel G5000PW gel permeation column revealed that almost all of rhubarb gum polysaccharides were eluted near the void in this gel chromatography system, suggesting that molecular mass of rhubarb gum polysaccharides are more than 500 kDa, while precise mass has not been decided in this study. Analysis of gum sugar composition after hydrolysis revealed that rhubarb gums is rich in galactose (ca. 30%), arabinose (ca. 20%), and galacturonic acid (15–20%), although other sugars also existed in small quantities. These results suggest that the key chemical compound of gummosis in petioles of rhubarb is jasmonates rather than ethylene, and gum polysaccharides consist of not only pectic arabinogalactans but also homogalacturonans.     

Study of thermal effects of ultrasound stimulation on fracture healing

Low intensity ultrasound stimulation has been used as a strategy to promote fracture healing. This study investigated the mechanism of ultrasound stimulation in enhancing fracture healing. Forty-five adult New Zealand White rabbits were divided into control, microwave treated, and ultrasound stimulation groups. After anesthesia, transverse osteotomy was created at midportion of the fibula bone. Intravital staining followed by fluorescence microscopic examination of new bone formation in the osteotomy site and biomechanical tests on torsional stiffness of the osteotomy site were performed. The difference between each examination was evaluated and analyzed. After ultrasound stimulation, new bone formation in the osteotomy site of the stimulated limb was 23.1-35.8% faster than that of the sham treated limb; the torsional stiffness of the stimulated limb was 44.4-80.0% higher than that of the sham treated limb. In the group of microwave hyperthermia treatment, the new bone formation was higher than that of the sham treated limb, but the difference was not statistically significant. The difference in torsional stiffness between the microwave hyperthermia treated limbs and the sham treated limb was not quite statistically significant. We demonstrated that low intensity ultrasound stimulation could increase the new bone formation and torsional stiffness. These effects probably are not mediated via hyperthermia.     

A new model to simulate the elastic properties of mineralized collagen fibril

Bone, because of its hierarchical composite structure, exhibits an excellent combination of stiffness and toughness, which is due substantially to the structural order and deformation at the smaller length scales. Here, we focus on the mineralized collagen fibril, consisting of hydroxyapatite plates with nanometric dimensions aligned within a protein matrix, and emphasize the relationship between the structure and elastic properties of a mineralized collagen fibril. We create two- and three-dimensional representative volume elements to represent the structure of the fibril and evaluate the importance of the parameters defining its structure and properties of the constituent mineral and collagen phase. Elastic stiffnesses are calculated by the finite element method and compared with experimental data obtained by synchrotron X-ray diffraction. The computational results match the experimental data well, and provide insight into the role of the phases and morphology on the elastic deformation characteristics. Also, the effects of water, imperfections in the mineral phase and mineral content outside the mineralized collagen fibril upon its elastic properties are discussed.     

VARIATION IN ANATOMICAL AND MATERIAL PROPERTIES EXPLAINS DIFFERENCES IN HYDRODYNAMIC PERFORMANCES OF FOLIOSE RED MACROALGAE (RHODOPHYTA)1

Over the last two decades, many studies on functional morphology have suggested that material properties of seaweed tissues may influence their fitness. Because hydrodynamic forces are likely the largest source of mortality for seaweeds in high wave energy environments, tissues with material properties that behave favorably in these environments are likely to be selected for. However, it is very difficult to disentangle the effects of materials properties on seaweed performance because size, shape, and habitat also influence mechanical and hydrodynamic performance. In this study, anatomical and material properties of 16 species of foliose red macroalgae were determined, and their effects on hydrodynamic performance were measured in laboratory experiments holding size and shape constant. We determined that increased blade thickness (primarily caused by the addition of medullary tissue) results in higher flexural stiffness (EI), which inhibits the seaweed’s ability to reconfigure in flowing water and thereby increases drag. However, this increase is concurrent with an increase in the force required to break tissue, possibly offsetting any risk of failure. Additionally, while increased nonpigmented medullary cells may pose a higher metabolic cost to the seaweed, decreased reconfiguration causes thicker tissues to expose more photosynthetic surface area incident to ambient light in flowing water, potentially ameliorating the metabolic cost of producing these cells. Material properties can result in differential performance of morphologically similar species. Future studies on ecomechanics of seaweeds in wave‐swept coastal habitats should consider the interaction of multiple trade‐offs.     

The Growth Form of Croton pullei (Euphorbiaceae) - Functional Morphology and Biomechanics of a Neotropical Liana

Abstract: Croton pullei (Euphorbiaceae) is a woody climber of the lowland rainforest in French Guyana and Surinam. During ontogeny, a shift from a juvenile free-standing growth phase to an older supported growth phase is observed. The following biomechanical parameters were studied: structural Young's modulus, structural torsional modulus, flexural stiffness and bend to twist ratios. Changes in anatomical development were also analysed for different stages of development of C. pullei which differ significantly in their mechanical properties. Free-standing plants show a nearly constant structural Young's modulus and structural torsional modulus during ontogeny, with flexural stiffness increasing proportionally with the axial second moment of area. These patterns are typical for “semi-self-supporting plants". In contrast, supported plants show a significant decrease in structural Young's modulus in older stem parts, as well as a decrease in structural torsional modulus. Due to the decrease in structural Young's modulus, flexural stiffness does not increase proportionally with the axial second moment of area. These patterns are typical for non-self-supporting lianas. In all supported plants, a sudden transition occurs from early dense wood to a wood type with a much higher proportion of large diameter vessels. In contrast, only the dense wood type is present in all tested free-standing plants. The data are compared with results from other climbing species of the same study area and discussed with reference to observed features characterizing the growth form and life history of C. pullei.     

Comparison of two systems for tibial external fixation in rabbits

BACKGROUND AND PURPOSE: Use of rabbits in orthopedic investigations is common. In this study, focus is on factors that influence bone healing and on distraction osteogenesis. Biomechanical characteristics of two external fixator systems (Orthofix device and Hoffmann device) for long bones were tested. METHODS: Twelve freshly dissected tibiae were obtained from six skeletally mature New Zealand White rabbits, and four-point bending stiffness in two planes (90 and 180 degrees to the fixator pins) and torsional stiffness and strength of the bone-fixator complex were evaluated by use of a material testing machine. RESULTS: In four-point bending, Orthofix device had higher stiffness and strength, compared with Hoffmann device. When the load was applied 180 degrees to the pins, both devices had higher stiffness, compared with that at 90 degrees. In torsional testing, Orthofix device had significantly higher stiffness and strength. CONCLUSIONS: Significant differences in structural properties between the two systems were evident. Loading direction and gap conditions were important factors in determining properties of the systems. Therefore, type of external fixation system and fixation technique should be considered when designing experiments, using the rabbit long bone model.     

Fluctuation analysis of Caulobacter crescentus adhesion

The aquatic bacterium Caulobacter crescentus divides asymmetrically to a flagellated swarmer cell and a cell with a stalk. At the end of the stalk is an adhesive organelle known as the holdfast, which the stalked cell uses to attach to a solid surface. Often there are two or more cells with their stalks attached to the same holdfast. By analyzing the fluctuations in the stalk angle for a pair of cells attached to a single holdfast, we determine the elastic stiffness of the holdfast. We model the holdfast as three torsional springs in series and find that the effective torsional spring constant for the holdfast is of the order of (10(-17)-10(-18)) Nm, with unequal spring constants. The asymmetry suggests the sequence in which the cells attach to each other, and in some cases suggests that strong crosslinks form between the stalks as they make a shared holdfast.     

Effect of tensile force on the mechanical behavior of actin filaments

Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately -2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament.