Oscillation frequencies of plant stems with apical loads

The frequency of free oscillations of plant stems with apical loads, as found in some cereals, is different depending on whether the stems are oriented vertically or horizontally. Neglecting the stem's own weight the differential equations describing the oscillation can be solved for both cases, although in the vertical orientation only for a limited set of conditions including constant bending stiffness along the stem. Comparison with experimental data shows that the difference between the oscillation frequencies in vertical and horizontal orientations can be attributed to the fact that in the vertical orientation the top load due to gravity induces a bending moment varying with the oscillation, while in the horizontal case this bending moment is nearly constant.     

Damped oscillations of the giant reed Arundo donax (Poaceae)

The slender upright culms of the giant reed (Arundo donax L.) are often exposed to dynamic wind loads causing significant swaying. The giant reed has slightly tapered hollow stems (4-6 m high) with flat leaves and an extensive underground rhizomatous system with solid branches bearing adventitious roots. Quantitative analyses of videorecordings prove that A. donax responds to dynamic deflections of the stem with damped harmonic bending oscillations. The logarithmic decrement can be used to calculate the relative damping, as a measure of the plant's capacity to dissipate vibrational energy. Plants with leaves have a significantly higher damping compared to plants without leaves. A comparison of the relative damping of plants with and without leaves shows that this finding is only partly due to aerodynamic resistance of the leaves. Structural damping also contributes considerably to the overall damping of the foliate A. donax stem. By stepwise removal of the underground plant organs the influence of rhizome, roots, and soil on the vibrational behavior was determined. The data indicate that underground plant organs as well as leaf sheaths covering the nodes have no significant influence on damping.     

Oscillations of plants' stems and their damping: theory and experimentation

Free oscillations of upright plants' stems, or in technical terms slender tapered rods with one end free, can be modelled by considering the equilibrium between bending moments and moments resulting from inertia. For stems with apical loads and negligible mass of the stem and for stems with finite mass but without top loading, analytical solutions of the differential equations with appropriate boundary conditions are available for a finite number of cases. For other cases approximations leading to an upper and a lower estimate of the frequency of oscillation omega can be derived. For the limiting case of omega = 0, the differential equations are identical with Greenhill's equations for the stability against Euler buckling of slender poles. To illustrate, the oscillation frequencies of 25 spruce trees (Picea sitchensis (Bong.) Carr.) were compared with those calculated on the basis of their morphology, their density and their static elasticity modulus. For Arundo donax L. and Cyperus alternifolius L. the observed oscillation frequency was used in turn to calculate the dynamic elasticity modulus, which was compared with that determined in three-point bending. Oscillation damping was observed for A. donax and C. alternifolius for plants' stems with and without leaves or inflorescence. In C. alternifolius the difference can be attributed to the aerodynamic resistance of the leaves, whereas in A. donax structural damping in addition plays a major role.     

<Emphasis Type="Italic">Arabidopsis thaliana</Emphasis> as a model for gelatinous fiber formation

Trees and herbaceous plants continuously monitor their position to maintain vertical stem growth and regulate branch orientation. When orientation is altered from the vertical, they form a special type of wood called reaction wood that differs chemically and structurally from normal wood and forces reorientation of the organ or whole plant. The reaction wood of dicotyledons is called tension wood and is characterized by nonlignified gelatinous fibers. The altered chemical and mechanical properties of tension wood reduce wood quality and represent a major problem for the timber and pulping industries. Repeated clipping of the emerging inflorescence stems of Arabidopsis thaliana augments wood formation in organs, including those inflorescence stems that are allowed to develop later. Gravistimulation of such inflorescence stems induces tension wood formation, allowing the use of A. thaliana for a molecular and genetic analysis of the mechanisms of tension wood formation.     

REPRODUCTIVE BIOLOGY OF ASCLEPIAS EXALTATA

An analysis of the relationships between plant size and survivorship and reproductive success was carried out by sampling four populations of the herbaceous perennial milkweed Asclepias exaltata in Virginia from 1980 to 1982. The annual survivorship rate (about 65%) is the lowest measured for any species of Asclepias. Survivorship was strongly size-dependent but showed no clear relationship with previous history of fruit production. Non-flowering plants were significantly smaller than flowering plants and showed very strong (r > 0.87) correlations between root dry weight and stem or leaf dry weight. Flowering plants were similar to nonflowering plants in root: shoot ratio (approximately 1:1) but differed in that root dry weight was not strongly correlated with stem or leaf dry weight. Components of inflorescence size were strongly correlated within a given level of comparison (e.g., stems per plant with flowers per plant) but less strongly correlated between levels (e.g., stems per plant with flowers per stem). Number of fruits per plant and percentage fruit-set were positively correlated with every component of inflorescence size. Although overall fruit-set was low (about 2%), fruits that were initiated had a high probability of surviving to maturity. There was no evidence of an early period of high fruit abortion: a relatively constant proportion of fruits aborted between each age class.     

Oscillation frequencies of tapered plant stems

Free oscillations of upright plant stems, or in technical terms, slender tapered rods with one end free, can be described by considering the equilibrium between bending moments in the form of a differential equation with appropriate boundary conditions. For stems with apical loads, where the mass of the stem is negligible, Mathematica 4.0 returns solutions for tapering modes α = 0, 0.5, and 1. For other values of α, including cases where the modulus of elasticity varies over the length of the stem, approximations leading to an upper and a lower estimate of the frequency of oscillation can be derived. For the limiting case of ω = 0, the differential equation is identical with Greenhill's equation for the stability against Euler buckling of a top-loaded slender pole. For stems without top loads, Mathematica 4.0 returns solutions only for two limiting cases, zero gravity (realized approximately for oscillations in a horizontal orientation of the stem) and for ω = 0 (Greenhill's equation). Approximations can be derived for all other cases. As an example, the oscillation of an Arundo donax plant stem is described.     

Biomechanical investigations of Limnopithecus with special reference to the influence exerted by body weight on bone thickness

Some of the most significant traits of the fossil Limnopithecus parallel those of modern gibbons and large cebids. Several hypotheses have been proposed in the attempt to explain this convergence: taxonomic relationship, moderate body mass (in contrast to the great apes), and similar locomotor habits, or, more precisely, adaptations to brachiation or semibrachiation. A biomechanical analysis of the Limnopithecus remains did not, however, yield satisfying results. Changes in stress patterns caused by variations of body weight have been investigated theoretically, therefore, under the assumptions of constant body posture and constant arrangement of musculature. Compressive forces and bending moments on limb bones are linear functions of body weight. The resistance of a bone to compression usually increases with the square of the diameter. The resistance to bending (more critical than compression) increases with the third power of the bone diameter, rates of increase greater than that of body weight to limb diameter. Thus, the heavier animal may possess relatively more slender limb bones. This surprising result is supported by some empirical data taken from the literature.     

Estimating the flexural rigidity of Arabidopsis inflorescence stems: Free-vibration test vs. three-point bending test

The mechanical strength of a plant stem (a load-bearing organ) helps the plant resist drooping, buckling and fracturing. We previously proposed a method for quickly evaluating the stiffness of an inflorescence stem in the model plant Arabidopsis thaliana based on measuring its natural frequency in a free-vibration test. However, the relationship between the stiffness and flexural rigidity of inflorescence stems was unclear. Here, we compared our previously described free-vibration test with the three-point bending test, the most popular method for calculating the flexural rigidity of A. thaliana stems, and examined the extent to which the results were correlated. Finally, to expand the application range, we present an example of a modified free-vibration test. Our results provide a reference for improving estimates of the flexural rigidity of A. thaliana inflorescence stems.     

How plants grow up

A plant's lateral structures, such as leaves,branches and flowers, literally hinge on the shoot axis,making its integrity and growth fundamental to plant form.In all plants, subapical proliferation within the shoot tip displaces cells downward to extrude the cylindrical stem.Following the transition to flowering, many plants show extensive axial elongation associated with increased subapical proliferation and expansion. However, the cereal grasses also elongate their stems, called culms, due to activity within detached intercalary meristems which displaces cells upward, elevating the grain-bearing inflorescence. Variation in culm length within species is especially relevant to cereal crops, as demonstrated by the high-yielding semi-dwarfed cereals of the Green Revolution. Although previously understudied, recent renewed interest the regulation of subapical and intercalary growth suggests that control of cell division planes,boundary formation and temporal dynamics of differentiation, are likely critical mechanisms coordinating axial growth and development in plants.     

Spatio-temporal kinematic analysis of shoot gravitropism in Arabidopsis thaliana

Plant shoots can bend upward against gravity, a behavior known as shoot gravitropism. The conventional quantification of shoot bending has been restricted to measurements of shoot tip angle, which cannot fully describe the spatio-temporal bending process. Recently, however, advanced imaging analyses have been developed to quantify in detail the spatio-temporal changes in inclination angle and curvature of the shoot. We used one such method (KymoRod) to analyze the gravitropism of the Arabidopsis thaliana inflorescence stem, and successfully extracted characteristics that capture when and where bending occurs. Furthermore, we implemented an elastic spring theoretical model and successfully determined best fitted parameters that may explain typical bending behaviors of the inflorescence stem. Overall, we propose a data-model combined framework to quantitatively investigate shoot gravitropism in plants.     

播种季节和种植方式对多年生苦荞主要农艺性状的影响

该研究选取六个多年生苦荞新品系,对春季、秋季直播与秋季再生其主要农艺性状进行调查。结果表明:(1)不同播种季节对多年生苦荞新品系主花序的花粉可育率、总结实率、有效结实率、植株株高、主茎粗、主茎分枝数、主茎节数、籽粒百粒重、单株粒数、单株产量的影响均达到显著或极显著水平;秋播主花序花粉可育率、总结实率、有效结实率、植株主茎分枝数、籽粒百粒重、单株粒数、单株产量均极显著高于春播;植株株高、主茎粗、主茎节数均极显著低于春播;主花序花朵大小、籽粒种子长宽比无显著差异。(2)不同种植方式对主花序花粉可育率、有效结实率、植株主茎节数及籽粒百粒重的影响达到显著或极显著水平;秋季再生主花序花粉可育率、籽粒单株粒数显著高于秋季直播;主花序有效结实率、植株主茎粗、主茎节数、籽粒百粒重显著低于秋季直播;主花序花朵大小、总结实率、植株株高、主茎分枝数、籽粒种子长宽比、单株产量无显著差异;相关分析表明,各生长季节下主花序有效结实率及单株粒数与单株产量的相关系数均最高。(3)所有参试品系中,1612-241秋季直播的单株产量显著高于其他品系; 1612-16、1612-33秋季再生单株产量较正季优势显著。该研究结果有助于筛选出适宜一季播种两季收获的优良品系,为今后多年生苦荞的选择育种提供线索基础。     

Responses of Hollow, Septate Stems to Vibrations: Biomechanical Evidence that Nodes Can Act Mechanically as Spring-like Joints

The hypothesis is proposed that nodes of hollow plant stemsact as spring-like joints by storing strain energy when stemsare bent and releasing this energy to elastically restore theoriginal postures of stems when bending forces are removed.This hypothesis was tested by subjecting stem segments consistingof four nodes and three intervening hollow internodes to axialcompressive loads and by determining the natural frequenciesof vibration of their nodes. Compression tests were used todetermine the critical load required to produce elasticallyrecoverable deformations for each of a total of 115 stem segmentsof the grassArundinaria técta(Walt.) Muhl. Each segmentwas observed to flex at or very near its nodes while internodesappeared to act as rigid bars. The natural (fundamental) frequenciesof vibrations of the nodes of these stem segments were subsequentlydetermined and equalled those predicted by engineering theoryassuming that nodes behave as spring-like joints. The data fromresonance frequency tests were then used to calculate the springconstants of stem segments (i.e. the force required to producea unit deflection in stems). These constants were found to agreewith those predicted by theory provided that nodes acted mechanicallyas spring-like joints. The transverse septa of the nodes of20 randomly selected stem segments were perforated with a needleand the spring constants of the impaired nodes were remeasuredand compared with those of the same stems before surgical manipulation.On average, nodal spring constants were reduced by 35%. Thisreduction agreed with the prediction that the perforation ofsepta would significantly reduce the ability of nodes to storestrain energy. Collectively, these results are interpreted tosupport the hypothesis that septate nodes can store and releasestrain energy. The hypothesis is discussed further in lightof the behaviour of a physical model which shows that nodal‘diaphragms’ can substantially stiffen a hollowcylindrical structure, although they are neither essential forthe storage of strain energy nor the subsequent elastic restorationof the model's shape once bending loads are removed. Plant stems; nodes; internodes; strain energy; elastic buckling; Brazier buckling; biomechanics     

Changes in Florets’ Vertical Direction within Inflorescence Affects Pollinator Behavior,and Fitness in <i>Trifolium repens</i>

Ecological interactions between flowers and pollinators greatly affect the reproductive success. To facilitate these interactions, many flowers are known to display their attractive qualities, such as scent emission, flower rewards and floral vertical direction, in a rhythmic fashion. However, less is known about how plants regulate the relationship between these flower traits to adapt to pollinator visiting behavior and increase reproduction success. Here we investigated the adaptive significance of the flower bending from erect to downward in Trifolium repens. We observed the flowering dynamic characteristics (changes of vertical direction of florets, flowering number, pollen grain numbers, pollen viability and stigma receptivity over time after blossom) and the factors affecting the rate of flower bending in T. repens. Then we altered the vertical direction of florets in inflorescence of different types (upright and downward), and compared the pollinator behaviors and female reproductive success. Our results showed that florets opened sequentially in inflorescence, and then bend downwards slowly after flowering. The bending speed of florets was mainly influenced by pollination, and bending angle increased with the prolongation of flowering time, while the pollen germination rate, stigma receptivity and nectar secretion has a rhythm of “low-high-low” during the whole period with the time going. The visiting frequency of all the four species of pollinators on upward flowers was significantly higher than that of downward flowers, and they especially prefer to visit flowers with a bending angle of 30°–60°, when the flowers was exactly of the highest flower rewards (nectar secretion and number of pollen grains), stigma receptivity and pollen germination rate. The seed set ratio and fruit set ratio of upward flowers were significantly higher than downward flowers, but significantly lower than unmanipulated flowers. Our results indicated that the T. repens could increase female and male fitness by accurate pollination. The most suitable flower angle saves pollinators’ visiting energy and enables them to obtain the highest nectar rewards. This coordination between plants and pollinators maximizes the interests of them, which is a crucial factor in initiating specialized plant-pollinator relationships.     

An auxin-responsive 1-aminocyclopropane-1-carboxylate synthase is responsible for differential ethylene production in gravistimulated<Emphasis Type="Italic"> Antirrhinum majus</Emphasis> L. flower stems

The regulation of gravistimulation-induced ethylene production and its role in gravitropic bending was studied in Antirrhinum majus L. cut flower stems. Gravistimulation increased ethylene production in both lower and upper halves of the stems with much higher levels observed in the lower half. Expression patterns of three different 1-aminocyclopropane-1-carboxylate (ACC) synthase (ACS) genes, an ACC oxidase (ACO) and an ethylene receptor (ETR/ERS homolog) gene were studied in the bending zone of gravistimulated stems and in excised stem sections following treatment with different chemicals. One of the ACS genes (Am-ACS3) was abundantly expressed in the bending zone cortex at the lower side of the stems within 2 h of gravistimulation. Am-ACS3 was not expressed in vertical stems or in other parts of (gravistimulated) stems, leaves or flowers. Am-ACS3 was strongly induced by indole-3-acetic acid (IAA) but not responsive to ethylene. The Am-ACS3 expression pattern strongly suggests that Am-ACS3 is responsible for the observed differential ethylene production in gravistimulated stems; its responsiveness to IAA suggests that Am-ACS3 expression reflects changes in auxin signalling. Am-ACS1 also showed increased expression in gravistimulated and IAA-treated stems although to a much lesser extent than Am-ACS3. In contrast to Am-ACS3, Am-ACS1 was also expressed in non-bending regions of vertical and gravistimulated stems and in leaves, and Am-ACS1 expression was not confined to the lower side cortex but evenly distributed over the diameter of the stem. Am-ACO and Am-ETR/ERS expression was increased in both the lower and upper halves of gravistimulated stems. Expression of both Am-ACO and Am-ETR/ERS was responsive to ethylene, suggesting regulation by IAA-dependent differential ethylene production. Am-ACO expression and in vivo ACO activity, in addition, were induced by IAA, independent of the IAA-induced ethylene. IAA-induced growth of vertical stem sections and bending of gravistimulated flowering stems were little affected by ethylene or 1-methylcyclopropene treatments, indicating that the differential ethylene production plays no pivotal role in the kinetics of gravitropic bending.     

The effect of accelerated sand accretion on growth,carbohydrate reserves,and ethylene production in Ammophila breviligulata (Poaceae)

In a 3-yr field study Ammophila breviligulata responded positively to sand accretion by maintaining plant height above a rising sand surface. Vertical growth for treated plants was approximately 80 cm over 3 yr. Bunch size did not differ between treated and control plants in the first or second year. But by Year 3, bunch circumference, number of stems per bunch, and plant height above the sand surface were significantly greater in plants receiving accelerated sand accretion. During the first year, treated plants flowered significantly less than controls. The greater vertical growth necessary for the treated plants may have depleted the energy reserves of a young rhizome system otherwise used for inflorescence production. The percent of the total nonstructural carbohydrates in rhizomes in the form of sugar was greater in plants in the accelerated sand accretion treatment, perhaps sustaining the necessary rapid vertical growth. To determine whether ethylene plays a role in stimulating stem elongation, endogenous ethylene accumulation was measured in plants in the field and seedlings in the greenhouse exposed to sand accretion. Treated plants responded by accumulating higher levels of ethylene in their stems, after 10 and/or 30 d, than did control plants. However, plants treated with exogenous ethylene exhibited growth and elongation inhibition.     

Biomechanics of the columnar cactus Pachycereus pringlei

We report the longitudinal variations in stiffness and bulk density of tissue samples drawn from along the length of two Pachycereus pringlei plants measuring 3.69 and 5.9 m in height to determine how different tissues contribute to the mechanical stability of these massive vertical organs. Each of the two stems was cut into segments of uniform length and subsequently dissected to obtain and mechanically test portions of xylem strands, stem ribs, and a limited number of pith and cortex samples. In each case, morphometric measurements were taken to determine the geometric contribution each tissue likely made to the ability of whole stems to resist bending forces. The stiffness of each xylem strand increased basipetally toward the base of each plant where stiffness sharply decreased, reaching a magnitude comparable to that of strands 1 m beneath the stem apex. The xylem was anisotropic in behavior, i.e., its stiffness measured in the radial and in the tangential directions differed significantly. Despite the abrupt decrease in xylem strand stiffness at the stem base, the contribution made by this tissue to resist bending forces increased exponentially from the tip to the base of each plant due to the accumulation of wood. A basipetal increase in the stiffness of the pith (and, to limited extent, that of the cortex) was also observed. In contrast, the stiffness of stem rib tissues varied little as a function of stem length. These tissues were stiffer than the xylem in the corresponding portions of the stem along the upper two-fifths of the length of either plant. Tissue stiffness and bulk density were not significantly correlated within or across tissue types. However, a weak inverse relationship was observed for these properties in the case of the xylem and stem rib tissues. We present a simple formula that predicts when stem ribs rather than the xylem strands serve as the principal stiffening agents in stems. This formula successfully predicted the observed aspect ratio of the stem ribs (the average quotient of the radial and tangential dimensions of rib transections), and thus provided circumstantial evidence that the ribs are important for mechanical stability for the distal and younger regions of the stems examined.     

The movement patterns of carpenter beesXylocopa micans and bumblebeesBombus pennsylvanicus onPontederia cordata inflorescences

The movement patterns of carpenter bees (Xylocopa micans) and bumblebees (Bombus pennsylvanicus) foraging for nectar on vertical inflorescences ofPontederia cordata were studied near Miami, Florida. The floral biology ofP. cordata is unique in several ways: (a) many short-lived flowers per inflorescence, (b) constant nectar production throughout the life span of each flower, and (c) abscence of vertical patterning of nectar and age of flowers. Inflorescences ranged between 3.5 and 15.8 cm long and had between 9 and 55 open flowers. Both carpenter bees and bumblebees arrived mostly on the bottom third of the inflorescence and left after visiting flowers on the top third of the inflorescence. The departure position from the inflorescence was higher up than observed in studies of other insect pollinators foraging on other speces of plants. This pattern of departure probably occurs in the absence of a vertical gradient of nectar or floral morphology.     

Gravitropism in Higher Plant Shoots : II. Dimensional and Pressure Changes during Stem Bending

Dimensional changes during gravitropic bending of cocklebur (Xanthium strumarium L.) dicot stems were measured using techniques of stereo photogrammetry. The differential growth is from an increased growth rate on the bottom of the stem and a stopping or contraction of the top.

Contraction of the top was especially evident upon release and immediate bending of horizontal stems that had been restrained between stiff wires for 36 hours. The energy for this could have been stored in both the top and bottom, since the bottom elongated, and the top contracted.

Forces developed during bending were measured by fastening a stem tip to the end of a bar with attached strain gauges and recording electrical output from the strain gauges. Restrained mature cocklebur stems continued to accumulate potential energy for bending for about 120 hours, after which the recorded force reached a maximum.

Pressures within castor bean (Ricinus communis L.) stems were also measured with 3.5-millimeter diameter pressure transducers. As expected, the pressure on the bottom of the restrained plants increased with time; pressures decreased in vertical controls, tops of restrained stems, and bottoms of free-bending stems. Pressures increased in tops of free-bending stems. When restrained plants were released, pressure on the bottom decreased and pressure on the top increased. Results suggest a possible role for cell contraction in the top of stems bending upward in response to gravity.

     

The influence of gravity and wind on land plant evolution

Aspects of the engineering theory treating the elastic stability of vertical stems and cantilevered leaves supporting their own weight and additional wind-induced forces (drag) are reviewed in light of biomechanical studies of living and fossil terrestrial plant species. The maximum height to which arborescent species can grow before their stems elastically buckle under their own weight is estimated by means of the Euler-Greenhill formula which states that the critical buckling height scales as the 1/3 power of plant tissue-stiffness normalized with respect to tissue bulk density and as the 2/3 power of stem diameter. Data drawn from living plants indicate that progressively taller plant species employ stiffer and lighter-weight plant tissues as the principal stiffening agent in their vertical stems. The elastic stability of plants subjected to high lateral wind-loadings is governed by the drag torque (the product of the drag force and the height above ground at which this force is applied), which cannot exceed the gravitational bending moment (the product of the weight of aerial organs and the lever arm measured at the base of the plant). Data from living plants indicate that the largest arborescent plant species rely on massive trunks and broad, horizontally expansive root crowns to resist drag torques. The drag on the canopies of these plants is also reduced by highly flexible stems and leaves composed of tissues that twist and bend more easily than tissues used to stiffen older, more proximal stems. A brief review of the fossil record suggests that modifications in stem, leaf, and root morphology and anatomy capable of simultaneously coping with self-weight and wind-induced drag forces evolved by Devonian times, suggesting that natural selection acting on the elastic stability of sporophytes occurred early in the history of terrestrial plants.