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Physiology and Biochemistry |
Group MECA, UMR 547 Physiologie Intégrée de l'Arbre Fruitier et Forestier, Institut National de la Recherche Agronomique -Université Blaise Pascal, 234 Avenue du Brézet, F-63100 Clermont-Ferrand, France
Received for publication March 14, 2006. Accepted for publication July 28, 2006.
ABSTRACT
Self-supporting plant stems are slender, erect structures that remain standing while growing in highly variable mechanical environments. Such ability is not merely related to an adapted mechanical design in terms of material-specific stiffness and stem tapering. As many terrestrial standing animals do, plant stems regulate posture through active and coordinated control of motor systems and acclimate their skeletal growth to prevailing loads. This analogy probably results from mechanical challenges on standing organisms in an aerial environment with low buoyancy and high turbulence. But the continuous growth of plants submits them to a greater challenge. In response to these challenges, land plants implemented mixed skeletal and motor functions in the same anatomical elements. There are two types of kinematic design: (1) plants with localized active movement (arthrophytes) and (2) plants with continuously distributed active movements (contortionists). The control of these active supporting systems involves gravi- and mechanoperception, but little is known about their coordination at the whole plant level. This more active view of the control of plant growth and form has been insufficiently considered in the modeling of plant architecture. Progress in our understanding of plant posture and mechanical acclimation will require new biomechanical models of plant architectural development.
Key Words: architecture • biomechanics • equilibration • grasses • gravitropism • mechanosensing • modeling • trees
Plants are mostly fixed organisms that rely on light interception and photosynthesis for their energy supply. Most of them (i.e., land plants) have developed quite large architectures to display their photosynthetic leaves in well-lit zones. Plants may also be very long-lived, growing throughout life. Trees, for example, can live and grow for centuries, relying for their mechanical support on the "same" trunk. Furthermore, such performance is generally achieved in a mechanically challenging environment. Their stems have to withstand self-weight (see Peltola, 2006
). If they live in communities, they also have to grow tall to reach sufficient light, with the risk of becoming mechanically unstable (Fournier et al., 2005
). Last but not least, they experience wind drag, which usually increases with height and leaf area and is also highly variable in space and time (James et al., 2006
; Py et al., 2006
). Indeed a lot of ecological concern has been raised by gales devastating temperate forests (and crops), especially as models of global climate change forecast that the frequency of gales may increase, although the increase in mean wind speed may be modest in many areas (e.g., Quine and Gardiner, 2002
). Study has thus been devoted to the mechanical hazards that can occur during important ecological (and economical) events and as mechanical constraints on the evolution of plant morphology. However, the fact that most plants stand upright for their lifetime has received less attention. And understanding the processes underlying this ability and their acclimating to their mechanical environment is an important complement to damage studies and is likely to give new insights into the mechanical constraints on plant stem morphology.
When compared to engineering artefacts, plant stems are incredibly slender structures. This "graceful mechanical design" has long puzzled botanists and mechanical engineers. Since the end of 19th century, researchers have analyzed different plant forms in terms of mechanical performance and safety (see reviews in Niklas, 1992
; Nachtigal, 1994
). These analyses have demonstrated that mechanical performance relies on a specific skeletal design involving (1) a pericellular skeleton made of high-performance composite materials (the cell wall), (2) high-performance cellular tissues such as hydrostatic tissues or wood, and (3) well-adapted stem tapering.
However, these analyses ignored two key points: (1) plants are endowed with motors that allow auto-stressing and active movements, even in big trees (Fournier at al., 1994
, Moulia, 2000
), and (2) plant growth is regulated by mechanical loading (Jaffe and Forbes, 1992
; Coutand and Moulia, 2000
; Telewski, 2006
, in this issue). Both processes are controlled through the mechanoperceptive senses of gravi- and strain-perception (Coutand and Moulia, 2000
; Braam, 2004
; Morita and Tasaka, 2004
).
The purpose of this paper is to focus on the relevance of these two active aspects of plant mechanical design to explain how plants can stand upright for so long, making use of the current knowledge in biomechanics of growth (including modeling) and in mechanoperception. To gain some insights into the processes involved, we will start by reviewing briefly how land animals (active muscular structures) stand upright in a static position. Focus will be put on terrestrial vertebrates and arthropods (i.e., large terrestrial animals) as their size ranges and their habitats overlap with that of land plants. We will then compare land plants with terrestrial vertebrates and arthropods (called terrestrial animals for simplicity). The purpose of such comparison is not to perform a general comparative biomechanical approach between plants and animals (see Vogel [2003]
for a broad and detailed perspective of the diversity of animal biomechanical designs as well as of some plant biomechanics). Such a comparison is helpful in reducing our preconceptions about plant habit, bearing in mind the risks of anthropomorphism or zoomorphism. We will show that land plants, just as many terrestrial animals, (1) adapt their skeletal growth to the load conditions and (2) regulate their posture through dynamic and active control of movements. Both processes are crucial for standing upright. The major motors involved in posture control in plants will be presented. The two major kinematic systems of active movements and expansion growth in land plants will be described in (1) plants with localized active movement or articulated plants ("arthrophytes") and (2) plants with continuously distributed active movements ("contortionists"). The consequences for a biomechanical model of plant architecture will be then considered, as well as the benefit of a truly interdisciplinary modeling approach based on mechanics and plant integrative biology.
A GLANCE AT HOW LARGE TERRESTRIAL ANIMALS CAN REMAIN IN THE STANDING POSITION: SKELETONS, MOVEMENTS, LOADS, AND POSTURE
Terrestrial animal skeletons: a system of articulated stiff elements that is mechanically unstable
The ability of animals to remain standing in an aerial environment can obviously be traced back first to their skeleton. The usual definition of a skeleton in most terrestrial animals is "a system of rigid and semi-rigid elements that build the supporting structure of living organisms and the system of articulations and levers that allows for relative movements of its constitutive segments" (Baudry and Veron, 1998
, pp. 1288–1289).
Two major types of skeletal design can be found in large terrestrial animals: endoskeleton as in vertebrates and exoskeletons as in arthropods (de Ricle and François, 1995
; Fig. 1). Incidentally the materials constituting skeletons can be very variable. Bones in vertebrates are composites of collagen fibers and hydroxyapatite crystals organized in complex tissues, whereas shell material (cuticle) in arthropods is largely made of chitin fibers and proteins (see Vincent [1990]
for more details on structural biomaterials). But they are all stiff materials. Moreover, whatever the material and structural design, the stiff skeleton in animals is a system of well-defined stiff elements, i.e., a separated structure.
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; de Ricle and François, 1995
). We will consider the consequences of this aspect later.
Skeletons are not complete at birth; they change shape and grow. They also have to adapt to the changing size of the body and even more to possible differences in loading conditions during life (Fung, 1990
; Frost, 2003
). This is achieved in several ways, as we will discuss.
Finally it should be noted that several skeletal designs differing from that of large terrestrial animals can be found within the animal kingdom (de Ricle and François, 1995
; Vogel, 2003
). For instance, not all animals have a rigid articulated skeleton. A lot of soft invertebrates such as cnidarians have a hydrostatic skeleton. Flexural and torsional rigidity is produced by the pressurization of internal fluids in elements surrounded by stiff but thin membranes that cannot resist flexion and torsion on their own (Vincent, 1990
; de Ricle and François, 1995
). This hydrostatic skeleton can be stiffened by nonarticulated elements as in cephalopods (e.g., cuttlefish).
The involvement of the muscular system in support
The control of the degrees of freedom at the articulations involves muscles. In large terrestrial animals, most articulations are operated by a pair of antagonistic muscles. Thus their complete "supporting system" involves both the skeleton and the muscular system (de Ricle and François, 1995
; Fig. 2). It is thus a complex system with two very different components: the skeleton that provides "passive" articulated rigidity and the muscular system that provides active control.
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, for example). We will focus here on three basic issues that are useful for the comparison with plants.
First, muscles are "soft" but active tissues. More precisely, their apparent rigidity results from active processes of work production as well as from the intrinsic rigidity of their constitutive materials. This is the reason muscles are characterized by their tone, i.e., a state of slight active tension—an active auto-stressing—that is stimulated continuously through specialized nerves. Were this tone not present, the support system of terrestrial animals would collapse (Gribenski, 1995
). Muscular motor processes involved in standing upright and in motility are thus similar. The second characteristic is that muscles are fairly fast motors (although there are large differences between muscle types and between species). The third is that muscular tissues in terrestrial animals are organized into a clear system: a well-defined and organized architecture of muscles that bears clear topological relationship with the skeleton system through tendons in vertebrates or apodemes in arthropods (i.e., chitinous rods that serve as sites for muscle attachment) (Fig. 2). Note incidentally that soft invertebrates with hydrostatic skeletons also display a postural control involving muscles (de Ricle and François, 1995
), although they can be distributed or scattered (Vogel, 2003
).
The involvement of mechanoperceptive systems: posture control
A muscular system is not sufficient to keep a skeleton in the standing position. There is a need for a coordinated mechanoperceptive control of the degree of active auto-stressing of all the muscles acting about the different articulations. Moreover, mechanical perturbations such as transitory tilting should be damped so that the standing position remains stable. This has been called the equilibration process of postural control (Gribenski, 1995
). Our knowledge of equilibrium and postural control in vertebrates has been increased by spatial research and the analysis of animal and human behavior at low gravity. It involves several sensing pathways. The muscular tone is controlled by local mechanosensing in muscles and tendons, whereas bodily orientation depends mainly on graviperception. This graviperception involves specialized cells (statocytes) or organs (statocysts). The design of graviperceptive apparatus is fairly generic in animals. It involves sedimentation of small, rounded bodies (calcarious otoliths in humans, sand in shrimps) and mechanoperception of sedimentation orientation. Moreover, studies in humans demonstrated that correct gravitropic orientation and posture control also involve perception of pressure in the soles of the feet and phototropic perception through vision, as well as acceleration detection (Gribenski, 1995
).
Besides perception, the general coordination of the muscular system to match the upright position (or any set angle) involves computations by the nervous system. For example, the muscular control of the spinal column in humans involves two types of nervous computation. One is a local reflex loop involving the spine. It regulates tone in flexor–extensor muscles. It is not dependent on the general orientation of the body but on the state of strain in the muscles on both sides (Gribenski, 1995
). It thus could be called an autotropic regulation. The second one involves a complex computation in the central nervous system, in particular in the cerebellum, which controls orientation. As a whole then, equilibrium and postural control through muscles and the perceptive system can be viewed as an active corrective process preventing the amplification of perturbations and hence instabilities. It involves a general gravitropic control and a local "autotropic" component of tone regulation.
Active kinematics of movements and posture control
The supporting and motile system involving articulated skeleton and active muscle systems can be characterized by its active degrees of freedom, i.e., by the way articulations can be actuated (or blocked) by sets of flexor–extensor antagonist muscles (Fung, 1990
). The study of these active degrees of freedom and their coordination is called kinematics of active movement. It is a very active research area of animal mechanics and includes the study of large movements in locomotion and analysis of the small movements or auto-stressing involved in postural control.
Kinematics is dependent on the spatial distribution of the active degrees of freedom. The higher the number of articulations per unit length, the spatially smoother the possible contortions. Some arthropods display obvious segmental movements, whereas other animals have higher spatial resolution for active degrees of freedom, such as in the spinal column of vertebrates. But in general the kinematics of postural control involves coordinated and complex antagonistic movements to recover from static tilting or dynamic forces (Gribenski, 1995
).
Skeletal and muscular growth and adaptation (acclimation) to loading regimens
The young animal experiences a phase of growth in which both mass and size increase. Thus the supporting system has to grow while being submitted to increasing static and dynamic loads (due, for example, to increasing lever arms in the skeleton [Frost, 2003
]). Moreover, the skeleton and the muscular system have to grow in a coordinated way. Both aspects—coordinated growth and adaptation to changing loading conditions—involve mechanosensitive pathways (Fung, 1990
).
We will here illustrate only the growth of the long bones in vertebrates (Fung, 1990
; Camus, 1995
). The osteogenesis of long bones involves a first step of cell proliferation, followed by ossification of cartilaginous tissues. This process is responsible for the bulk of osteogenesis. It then remains active near the end of the bones (near the epiphyseal plates), allowing longitudinal growth. A second type of growth involves the development of a specialized peripheral osteogenic tissue called the periosteum. It allows lateral thickening through the apposition of successive layers of bone material. Growth in girth can be asymmetric, leading to eccentric cross sections. Although terminologies in zoology and botany are opposed, this is basically analogous with primary and secondary growth of plant stems. However, in contrast with stiff plant tissues, bones also experience massive remodeling through osteoclastic–osteoblastic activity at the inner and outer surfaces of bones (trabecula, Haversian canals, periosteal and endoosteal surfaces) modifying not only cross-sectional size but also the bulk density of the inner bone tissue (Fung, 1990
; Frost, 2003
).
An important feature of bone growth and remodeling is that both processes are under mechanoperceptive control (Fung, 1990
; Ehrlich and Lanyon, 2002
). The living cells of bone tissue (osteocytes, osteoblasts and osteoclasts) have mechanoperceptive sensors. Recent research shows this control involves sensing strain and strain rate, probably primarily by osteocytes (Turner, 1988
; Ehrlich and Lanyon, 2002
). Such mechanoperceptive control is also likely to be involved in the coordination of bone growth with muscle growth in vertebrates (Fung, 1990
).
However, the exoskeleton of arthropods cannot coordinate its growth with the inner body, as vertebrates do. The exoskeleton is replaced periodically, depending on the growth and nutritional status. In a series of hormonally controlled processes, the old skeleton is largely resorbed, then is split open and the new, soft skeleton expands and stiffens, allowing more volume for growth (Gaumont, 1995
). In this case, there is thus a transitory loss of function of the stiff skeleton. Growth of a stiff supporting system without temporary loss of stiffness, as described previously for vertebrates' long bones, is thus likely to be a noteworthy evolutionary achievement in animals (Vogel, 2003
).
The mechanoperceptive control of bone growth and remodeling in vertebrates is also important, allowing the supporting system to adapt itself to loading conditions, even after growth has stopped (Fung, 1990
; Ehrlich and Lanyon, 2002
; Frost, 2003
). Indeed terrestrial vertebrates are submitted to highly variable loading conditions, due to self-weight and external loads such as fluid drag, as well as dynamic loads linked to locomotion or other activities. Such a biomechanical control of bone growth and remodeling is believed to be crucial in preventing fracture hazards in the skeleton (Fung, 1990
; Ehrlich and Lanyon, 2002
). By the same token, the corresponding mechanoperceptive changes in structure and physiology (tone) of muscles (e.g., stronger musculature due to exercise) may help prevent the skeleton from being overloaded. Because bone fracture may reduce the animal's ability to stand upright, this long-term mechanical acclimation of bones (and muscles) to the loading conditions is a key feature for maintaining a lifelong capability to stand upright.
WHAT ABOUT PLANTS? SKELETONS, MOVEMENTS, LOADS, AND POSTURE IN PLANT ORGANISMS
We have seen that standing in terrestrial animals is an active process involving (1) a dual supporting system with stiff articulated components (skeleton) and active motors (muscles), (2) fast postural control of the supporting system (skeleton + muscular system) based on gravitropic and strain mechanoperception, and (3) long-term mechanical acclimation of this dual support system to prevailing loading conditions driven through strain and strain rate mechanoperception, at least in the long bones of vertebrates. What about plants?
The diffuse but mechanically stable skeleton of plants
It is often stated in textbooks that plants have a stiff pericellular exoskeleton, called the cell wall (e.g., de Ricle and François, 1995
). This cell wall is an extracellular matrix of hemicelluloses, pectins, and eventually lignins, stiffened by cellulose microfibrils acting as stiff tensile fibers in composite materials. However, referring to the cell wall as a plant skeleton is somewhat misleading. Indeed bones also have a strong and stiff extracellular matrix (Vincent, 1990
), but this matrix is not called the animal skeleton. The word "skeleton" designates the whole support system of the body (de Ricle and François, 1995
). By the same token, the plant skeleton has hierarchies of organization. Two types of supporting tissues are usually described: hydrostatic tissues and sclerified tissues (Niklas, 1992
). In hydrostatic tissues the flexural and torsional rigidities of cells and tissues are obtained through active pressurization of the living cells by turgor pressure (Niklas, 1992
). Sclerified tissues are made mostly of dead cell fibers with much stiffer cell walls (e.g., sclerenchyma and wood fibers; Niklas, 1992
). The stems are made of several tissues with different stiffnesses. And the mechanical consequences of cross-sectional anatomy has been a subject of attention since the pioneering work of Schwendener (e.g., see Nachtigal, 1994
, for an historical perspective; see also Niklas, 1992
; Moulia and Fournier, 1997
). Finally, in a branched architecture such as a tree, it can be considered that the whole architecture of the wooden core of the tree is its skeleton.
Small herbs are mostly hydrostatic. Trees rely mostly on sclerified tissues for the support of their trunk and big branches. Intermediate situations also exist, e.g., grass stems or midribs (e.g., Niklas, 1992
; Moulia and Fournier, 1997
), in which design involves a stiff sclerenchymous hypodermic exoskeleton and internal spongy parenchymous tissues (both necessary for bending stiffness). But despite this clear supracellular organization of supporting tissues, the plant skeleton involves most of the cells of the plant aerial architecture. It can be called a diffuse skeleton that cannot be viewed as a discrete system. In many plants, particularly trees, it is intricately associated with the vascular system.
Plant stems are usually not considered to be articulated. Segments such as internodes can be recognized, at least in young stems, but nodes are usually fairly stiff and are not articulations. This type of skeletal design could be called a continuous skeleton. This design hold for most trees and herbaceous dicots with the exception of some composite leaves in Leguminosae displaying pulvinous articulations. Grasses, however, display a segmental stem design with swollen junctions, called (false) pulvini that provide localized degrees of freedom for active movements (Dayanandan et al., 1976
). These false pulvini are hydrostatic zones with a thin cell wall that retain the capacity for differential expansion, whereas the stem segments undergo significant endodermic sclerification and are no longer growing. This bears some analogy with what is observed in arthropod joints, where the exoskeleton at some joint between stiffened segments is thin, defining flexible areas that form movable joints. There are thus two different types of skeletal design at the whole plant level: spatially continuous and articulated (Fig. 3). Continuous skeletons can be identified in the woody skeleton of trees or in the continuous mixed sclerified-hydrostatic skeleton of herbaceous dicots as well as in purely hydrostatic plants. Articulated skeletons, usually sclerified-hydrostatic, can be found in grasses and in some other groups such as Equisetaceae (B. Moulia, unpublished data).
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Growth as a double mechanical constraint
However such view of plant mechanical design is not sufficient (Fig. 4). Indeterminate growth in length and mass will increase weights and lever arms and thus the bending moments to which a plant is submitted (Fournier et al., 2005
). By the same token, the probability that all branches display perfect axial symmetry about the trunk is close to zero, so that even an erect trunk will experience increasing bending moment. Increasing self-weight can even trigger elastic instabilities or buckling in vertical stems (Niklas, 1992
; Fournier et al., 2005
). Thus most trees adapt their cross-section size to their global size through cambial growth in girth (Niklas, 1992
). However, growth in girth, by molding new cell layers around a bent plant axis will tend to retain any established curvature (Fournier et al., 2005
). In fact this retention can be generalized to primary growth because of the continuous apposition of cell wall material on the inner side of all cell walls. Growth can thus be seen as a double mechanical challenge. If no motor mechanisms correct this trend, both branches and the main stem would sag increasingly with time (e.g., Schaeffer, 1991
).
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; Moulia, 2000
). Although the power of movement in plants has been emphasized since long ago (Darwin and Darwin, 1880
), most attention has been paid to (1) tropic and nastic movements during primary growth (e.g., Salisbury and Ross, 1992
; Iino, 2006
) and (2) rapid nastic movements (e.g., Forterre et al., 2005
; see Stockheim and Mahadevan, 2005
, for a review).
If we define a motor as a means of converting (chemical) free energy into work, two basic motor processes have been described in plants. The most classically described motors are the hydraulic motor cells in primary tissues (Fig. 5A1). An hydraulic motor transforms a gradient of osmotic potential into pressure-driven expansion (and work). Depending on cell wall rheology, the extension can be reversible (elastic cell wall) as in leguminous pulvini cells or irreversible (visco-plastic) as in growing cells (see Geitmann, 2006
, and Schopfer, 2006
, in this issue). When there are cross-sectional heterogeneities and/or eccentricity in (1) osmotic pressure or in (2) cell wall mechanics and/or in the wall-to-lumen ratio, internal bending moments are produced, leading to active curving (Fig. 5A2). If the cell wall is elastic and the cross section has bilateral symmetry, this can produce pure active bending, i.e., rotational active degrees of freedom. This is found in pulvini of legume leaves and is analogous to an articulation actuated by flexor–extensor muscles. When the cell wall undergoes irreversible stretching, it produces a combination of irreversible longitudinal extension and bending (usually known as differential primary growth), providing the plant with active translational–rotational degrees of freedom. This is found in any young stem during primary growth as well as in the false pulvini of mature grass stems. Although reversible bending and differential growth are usually considered separately in textbooks and are physiologically different, they share the same basic hydraulic motor process.
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; Fournier et al., 1994
; Fig. 5B). During the late stages of cell wall differentiation, in situ polymerization of lignins in the matrix and/or increasing crystallinity of the cellulose microfibrils induce a longitudinal shrinkage or swelling of the newly formed cells. This chemomechanical effect has been called maturation strains. Whether the cell wall contracts or elongates during maturation depends on its ultrastructure, in particular, microfibrillar orientation in the cell wall. As new layers of cells are laid down at the stem periphery, they tend to load the inner tissues. For example, if the maturation strain is shrinkage, the incoming layer of wood cells will tend to compress the tissues to which it adheres (Fig. 5B1). Because these tissues are stiff, compression of the core will be very limited and the new layer will be placed into a state of longitudinal extension (compared to the length it would have if isolated). This motor is thus incremental, linked to secondary growth. As for hydraulic motors, if there are cross-sectional heterogeneities and/or eccentricity (Fig. 5B2), internal bending moments are produced, leading to active curving (Fournier et al., 1994
). Indeed trees are known to produce sectors of specialized wood called "reaction wood," with extreme microfibril angles in response to leaning (Sinnott, 1952
; Wilson and Archer, 1979
; Fournier et al., 1994
). In most angiosperms, reaction wood is characterized by a very intense contraction of the cell wall during final maturation. The cells thus tend to put themselves into tension, pulling down the inner tissues, and have thus been called "tension wood." The involvement of reaction wood in producing movements in trees has been completely demonstrated using kinematic studies (e.g., Coutand et al., 2003a
). Motor systems in plants thus have three basic characteristics. First, their motor systems are not separate from the skeleton. Hydrostatic skeletal cells can be hydraulic motors. Sclerified wood cells are involved in both the sclerified skeleton and in the maturation strain incremental motor. In both cases, motor activity induces the deformation of the existing cell wall network. Therefore the cell-wall mechanical properties relevant for skeletal function are also relevant for motor function (though of course motor aspects involve additional properties such as osmotic regulation or maturation strains). There is nothing like the two-component support system found in large terrestrial animals with a stiff, passive skeleton and soft, but active motors. Moreover, motor processes in stems are closely related to growth itself. Plants have thus "invented" a very specific "two-in-one" design for their support system in which the skeleton and the motor system are combined: stiff but active.
The second characteristic is that controlled cross-sectional asymmetries (e.g., heterogeneous cell wall properties, eccentricity) provide the plant with a mechanism of local active bending that is at least analogous to the flexor–extensor antagonist couple in the animal muscular system (Fig. 5A2, B2). But because of the two-in-one skeletal-motor design, no clear skeletal articulation can be seen from anatomical inspection. For example, in grass stems, joints with a more hydrostatic skeletal design can be observed but their motor function cannot be inferred directly (given our current knowledge). It becomes apparent only when studying responses to mechanical disturbance such as tilting (Dayanandan et al., 1976
). Because no soft, active tissue separated from the skeleton is involved in the motor activity, no supplementary energetic cost is involved for keeping a new stable configuration once it has been achieved (besides the maintenance of the skeletal stiffness).
The third characteristic is just a physical consequence of the two-in-one design: plant motors are very slow (Stockeim and Mahadevan, 2005). Rapid movements in plants require very specialized secondary devices, accumulating elastic strain energy and triggering its sudden discharge (e.g., Forterre et al., 2005
). Such devices have been limited to very specialized functions in which speed may provide fitness, such as in trapping insects (Forterre et al., 2005
) or escaping from grazing animals. It can be argued that, due to the branched habit of plants, rapid movement for reorientation would bring huge costs and would not be very efficient for posture regulation in large, branched architectures.
Whatever the speculation about fitness, the facts that the motor system is (1) not separated from the skeleton and (2) very slow are probably the two other reasons that motor aspects involved in maintaining the standing position have been somewhat disregarded (apart from the stability of erect configurations).
Kinematics of movements and posture control in plants
In many textbooks, the relevance of motors to the control of plant spatial display is implicitly limited to the onset of growth directionality through primary gravitopism. Secondary maturational motors or zones of differential growth outside the primary growth zone, such as in grasses, are often treated as a small marginal item in even the best plant physiology books. However, as can be shown experimentally (e.g. Fournier et al., 1994
; Dayanandan et al., 1976
), gravitropic reorientation is necessary to any plant stem to keep or restore the standing position and can be viewed as a postural control.
We have seen previously that there are basically two types of skeletal design in plants: continuous and articulated. In both, the whole supporting system can make many coordinated movements through active degrees of freedom (Figs. 6 and 7).
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; Ledent, 1978
; Drouet and Moulia, 1997
). The motor design in grasses can be described as articulated-telescopic (Fig. 6A). At the nodes (false pulvini, as stated earlier) and at the limit between the blade lamina and the sheath (Ledent, 1978
) are zones that retain competence for differential primary growth, even when surrounding segments are fully differentiated. They thus behave as a hydraulic motor zone with a translational–rotational degree of freedom (e.g., Dayanandan et al., 1976
; Kaufman, 1992
; Fig. 7A). Given that (1) the global organization of articulated plants is clearly metameric, (2) that their skeletal organization involves sclerified peripheral tissues (e.g. Moulia and Fournier, 1997
), and (3) that their growth in girth needs breakage of enclosing sheaths, we could coin for them the name "arthrophytes," by analogy with arthropods. (Note, however, that the name arthrophytes does not refer here to a plant taxon but to a functional design to perform the active function of standing upright.) When tilted, grass stems will straighten gravitropically through the activation of their inter-metameric pulvini (Fig. 7A). Moreover the hinge between the lamina and the sheath may be activated to control laminar positioning (Ledent, 1978
). Gravitropic straightening thus involves a coordinated activation of several motor articulations. Note also that such gravitropic responses can also be triggered for small deviations from the vertical (B. Moulia, unpublished data).
The kinematical analysis of the gravitropic response in plants with a continuous skeleton has been conducted for a seedling coleoptile (Me
kauskas et al., 1999a
), tree trunks (Fournier et al., 1994
; C. Coutand et al., unpublished data), and mushroom stipe (Mekauskas et al., 1999b
). Similar spatiotemporal patterns with two distinct phases were revealed (Fig. 7B). Initially, an acropetal curving occurs all along the stem, followed by a phase of basipetal decurving. Moreover the decurving process starts well before the organ passes the vertical and is thus not a tropic gravitropic orientation but an auto-tropic reaction (Mekauskas et al., 1999a
; Coutand et al., 2003a
; Iino, 2006
). Similar continuous design skeletons are thus correlated with similar and complex kinematics of posture control, despite huge differences in size, skeletal material, and the motors involved (hydrostatic skeleton and hydraulic motors in the mushroom stem and coleoptile, woody skeleton and maturation strain incremental motors in tree saplings). We could coin the name "contortionist" (or contortionophyte) to describe this type of active kinematic system. Such combined and coordinated gravitropic and anticipated autotropic behavior in erect plants as well as in erect fungal organs bares strong functional resemblance to postural control of upright animals (e.g., global gravitropic and local tonal control of spinal posture in humans).
Note that in branched architecture, particularly in trees, active movements are also observed in branches (e.g., Sinnott, 1952
; Almeras and Gril, 2002
). In particular, plagiotropic branches are maintained in their tilted position by active control (Firn et al., 1999
). They can also move actively relative to their bearing axis, such as in negative epinastic movements. It is very likely that the posture of the whole plant is actively controlled, beside the main stem. This probably contributes to the stable habits of plant species. How such a general coordination of branch and trunk movements within the whole architecture could be achieved remains largely unknown and is very puzzling.
Finally in both arthrophytes and contortionist plants, growth zones retaining growth and motor competence (false pulvini or cambium) remain in all mature stems, endowing them with analogues of the antagonist muscle system involved in animal posture control.
Moreover, besides occurring in many, if not all, plant species, these movements occur all the time, and as we can see when observing the shapes of stems after wind throw or buckling without breakage. This active postural control is the main reason cereals or maize mostly lodge at the end of the growing season, when the stem is drying and their motor pulvini die. Wind throw earlier in the growing season is repaired within a few days, as long as stem or roots are not broken. For example a lodged sorghum field displayed a complete recovery over 3 days (B. Moulia, personal observation). Fournier et al. (2005)
have observed in a sapling community of more than 25 species in the tropical rainforest that active gravitropic reaction curvatures were greater than passive bending under self-weight in c. 90% of the cases, despite the fact that the ground was flat and prevailing winds were negligible. Postural control is thus generalized.
The involvement of mechanoperceptive systems in posture control in plants
As with animals, the motor system in plants is not sufficient to retain them upright. A coordinated control of the active auto-stressing for all motors is required. There is some consensus that plant graviperception involves specialized cells or apparatus named statocytes. The mechanism could be based on the sedimentation of small rounded bodies (mostly amyloplasts) and the mechanoperception of the orientation of this sedimentation. Groups of statocytes can be found in the endoderm surrounding vascular tissues in dicot stems (Taiz and Zeiger, 1998
; Morita and Tasaka, 2004
) as well as in grass false pulvini (Dayanandan et al., 1976
). Whether amyloplasts are needed for graviperception is controversial. Indeed it seems that amyloplasts are not required per se. The sedimentation of other large intracellular bodies or the weight of the protoplasm itself would lead to a much weaker but still significant graviperception (see review in Taiz and Zeiger, 1998
; Morita and Tasaka, 2004
). However amyloplasts greatly amplify signal sensitivity (Morita and Tasaka, 2004
) and were shown to be required for gravitropic responses in false pulvini of grasses (Kaufman, 1992
). Whatever the sedimenting bodies involved, the analogy with statocysts in animals is obvious and indeed was instrumental in the discovery of statocytes in plants. As in animals, the global stem orientation in plants involves a gravi-mechano perceptive system involving statocytes, measuring inclination in respect to gravity through mechanoperception. However, recent analyses of the kinematics of stem straightening have clearly shown that sensing inclination is not enough (Mekauskas, 1999a
, b; Coutand et al., 2003a
; Iino, 2006
; C. Coutand, et al., unpublished data). Indeed the autotropic corrective movement cannot be explained solely on this basis. Setting a minimal model for the gravi- and auto-tropic kinematics of a mushroom stipe, Mekauskas et al. (1999b)
showed that a local control loop based on local curvature mechanosensing was also required, as also suggested by Wilson and Archer (1979)
for formation of reaction wood in trees. This bears some functional analogy with the local loop of tonus control in the antagonist muscles of vertebrates.
Besides perception, the system integrating postural control over the whole plant remains largely unknown (a plant has no nervous central system), although interesting issues are emerging (see Trewavas, 2003
; Stahlberg, 2006
). Auxin distribution in a plant (one "phytohormone" or growth factor that controls expansion rates and cell wall architecture) receives experimental support for gravitropic curving in primary growth zone (Taiz and Zeiger, 1998
; Morita and Tasaka, 2004
), but not for the autotropic counter-curving (Iino, 2006
). Moreover our quantitative understanding of the spatiotemporal patterning of this control is limited to kinematic modeling of a single axis (Mekauskas et al., 1999b). This model has been nicely tested for some of its physiological hypotheses. But it remains phenomenological in essence and awaits more mechanistic analyses for both biomechanical and molecular processes involved. Moreover, the way the "computations" necessary for posture control of a complex branched architecture is achieved remains to be studied.
Mechanoperceptive acclimation of the plant skeleton growth in height and girth
Stem growth in plants is under the mechanoperceptive control of mechanical loading, a phenomenon called thigmomorphogenesis (thigmo is the Greek for touch) (Jaffe and Forbes, 1992
). Because recent reviews are available on plant thigmomorphogenesis (e.g., Braam et al., 2004; Fournier et al., 2005
; and Telewski, 2006
, in this issue), we will concentrate here on the comparison with the mechanical control on the animal supporting system. Mechanical stimulation of a plant induces a reduction of primary elongation of the stem and stimulates secondary growth in girth (in species displaying secondary thickening), as well as changes in wood density and mechanical properties. The dimensioning of plant stem (size and taper) is thus under permanent mechanoperceptive control and acclimates to the plant's mechanical state. Wood rays and rings may follow principal stress trajectories (Mattheck and Bethge, 1998
) reminiscent of Wolf and Roux' "law" for trabecular organization in bones (Fung, 1990
). But this last analogy remains to be tested experimentally.
When analyzing mechanoperception biomechanically, Coutand and Moulia (2000)
demonstrated that strain, not stress, is the perceived variable at the tissue level and produced log dose-response curves for growth inhibition. Such strain-adaptive response is very similar to what was found in bones (Turner, 1988
; Ehrlich and Lanyon, 2002
). Such similarity even led Goldsmith (1994)
to propose plant thigmomorphogenetic control as a model for bone mechanical adaptation. It might be questioned whether the land plant could be as sensitive as terrestrial animals to mechanical stimulations. This is a difficult matter as strain sensing is dependent (1) on amplifying mechanisms such as lever arms or signal summation over many cells (Coutand and Moulia, 2000
) and (2) the loading history through the process of strain accommodation (Schriefer et al., 2005
). Moreover, genetic variation is likely, and because very few quantitative analyses have been conducted, our data are limited to a few species. However, we can compare minimal threshold values for responses—what is called the minimal effective strains (MES; Frost, 2003
)—in plants (Coutand and Moulia, 2000
) and in bones (Frost, 2003
). The MES threshold for primary growth inhibition in tomato stem was c. 15 microstrains (recalculated from Coutand and Moulia, 2000
), whereas the MES for human bone remodeling ranges between 50 and 100 microstrains (Frost, 2003
). Mechanical sensitivity in plant stems is thus probably at least similar to that in vertebrates' bones. Even though the bases of such similarity remain largely unknown, its functional significance is clear. As in terrestrial animals (Frost, 2003
), long-term safety against changes in loading conditions is very likely to act as a mechanical constraint on the long-term ability of a plant to keep standing and thus on viability. Moreover, plants are submitted to an even greater challenge due to their continuous growth. Therefore, mechanisms of mechanical acclimation to their habitual external loading environment have been selected. Note finally that because of the two-in-one design joining the skeleton and the motor system, the size of the motor system also will be acclimated through thigmomorphogenesis. For example, an increase of secondary growth rate in girth allows a more efficient motor for gravitropic straightening, because the efficiency of the incremental shrinkage/swelling motor directly depends on radial growth rate (Fournier et al., 1994
).
Consequences for biomechanical modeling of plant architecture
Any model of plant architecture includes at least some geometric representation of the plant stem and branch system and of their spatial display. In most cases, interest is on a more dynamical understanding of architectural development and growth. Plant functional structural models (FSMs) thus tend to incorporate biophysical and biological processes, including dynamic representations of architectural development (Godin and Sinoquet, 2005
). Although mechanical aspects are often acknowledged, few models incorporate biomechanical modeling of plant spatial display. Even so, there are many mechanical models of the static and dynamic behavior of plants under external loads (see reviews in James et al., 2006
; Peltola, 2006
, in this issue). However, using them directly to analyze successive plant stem forms or overall architecture is not mechanically correct (Moulia and Fournier-Djimbi, 1997
) because, as emphasized earlier, (1) growth involves changes in the amount of load-bearing material as well as changes in weight and (2) active motors are also present. Thus we cannot assume that structures are completely built before being loaded by their self-weight and that no internal work source exists (Fournier et al., 1994
). Care should thus be taken when using standard formula from textbooks in mechanical engineering (e.g., strength of material and standard beam theory). For example, in maize, Moulia et al. (1994)
could demonstrate that only 30% of the posture of the maize leaves was due to passive bending under self-weight, whereas the rest required active motors. Whether or not a standard mechanical model based on passive mechanical behavior at constant mass can be used to model plant mechanics is thus dependent on the relative kinetics of loading vs. biologically driven changes in mass and rheology vs. active motor pre-stressing (see Fournier et al. [1994,
2005
] for a more detailed discussion of this topic). Care should be taken when using mechanical engineering models for modeling plant architecture. For example, plant FSMs usually incorporate some allometric relations between basal diameter and height and/or a tapering relation for diameter changes along trunk or branches. In some cases, these allometries are based on models assuming optimal mechanical design (e.g., Ford and Ford, 1990
; see review in Moulia and Fournier-Djimbi, 1997
). However, most of these optimal mechanical models were derived many years ago using assumptions that have since been questioned (see Moulia and Fournier-Djimbi, 1997
; Niklas and Spatz, 2004
, for more details). Moreover, when self-weight is involved as a static load, such models can no longer be assumed correct, given our current mechanical understanding (Moulia and Fournier-Djimbi, 1997
). A few models are available that simulate the mechanical effects of maturation incremental motors and reaction wood on the straightening of a single stem (Fournier et al., 1994
; Almeras and Gril, 2002
; Fourcaud and Lac, 2003
; Coutand et al., 2003b
). And some efforts have been made to translate them into formalisms used for current FSMs (Jirasek et al., 2000
; Fourcaud et al., 2003
). Only one dealt with a branched architecture (Fourcaud et al., 2003
). However, a proper modeling of the mechanoperceptive control of plant motor activities is still lacking (Moulia, 2003
). Mekauskas et al. (1999b)
introduced a model for stem straightening through hydraulic motors that involves some interesting considerations about gravi- and mechanoperception, but it does not incorporate the biomechanics of motor effects. Last but not least, although the focus in this paper is on the gravitropic-autotropic orientation, important interactions with the light environment have also to be considered (Iino, 2006
). We are thus not able to model posture control in plants yet.
Concerning the long-term strain-adaptive response of stem growth, even fewer models have been proposed. The only attempt was by Mattheck and co-workers (e.g. Mattheck and Bethge, 1998
). They proposed a dynamic model of stress equalization through secondary growth in girth. Mattheck and coworkers also described a wide range of shapes that could be qualitatively explained with a constant stress hypothesis (Mattheck, 1991
). However, the loads and the resulting stress fields were not modeled accurately so that their approach remains mainly qualitative. Therefore, no direct quantitative testing of the model predictions has ever been made. Moreover, subsequent studies verifying the constant stress hypothesis using fairly detailed modeling of the wind loads involved (West et al., 1989
; Niklas and Spatz, 2000
) have dismissed this hypothesis for wind loads on trees (although a consensus has not been reached yet, see Mattheck, 2000
). Finally, because of motor activity and auto-stressing, internal stresses are far from constant over cross sections in plants (Moulia and Fournier-Djimbi, 1997
).
It is unlikely that much progress could be made on the analysis of posture control and/or long-term acclimation to the mechanical environment without proper mechanical modeling. Indeed both are spatiotemporal responses involving clear mechanical aspects as well as the propagation of biological signals. Biomechanical models combined with experiments are very valuable tools to disentangle physical and biological aspects of such phenomena. But this would require extending the current biomechanical models as well as the current plant FSM to take into account (1) the mechanical consequences of growth, (2) active motors, and (3) mechanical perception and internal biological signaling (Moulia, 2003
). A real and strong coupling between biological and mechanical processes is needed, and working on common formalisms (e.g., Jirasek et al., 2000
; Fourcaud et al., 2003
) is likely to be more productive than interfacing independent, existing models for plant mechanics on one hand and pure biology on the other.
SIGNIFICANCE OF PLANT–ANIMAL ANALOGIES AND SOME OPEN QUESTIONS
Comparative biomechanics
We have used a comparative and analogical approach to illustrate that plants can be standing for long time not only because they are stiff and their structural design somewhat genetically optimized, but also because they undergo active postural and equilibration control and long-term acclimation of their supporting structure. We think this is a general mechanical constraint on any standing and growing organism in a land environment with low buoyancy, high turbulence, and intermittency. Indeed we could find analogous systems of equilibration and acclimation of the supporting system in erect terrestrial animals, plants, and fungi. Moreover, this constraint is probably even stronger for plants submitted to (1) the double mechanical constraint of indeterminate growth and (2) the competition for light through growth in height and the development of large leaf area and thus of large wind drag. Delving into the ecological significance of such adaptive processes would be beyond the scope of this paper, but a recent review on this topic can be found in Fournier et al. (2005)
.
We might question whether this comparative approach over such a huge span of taxa and kingdoms is meaningful, useful, and not too skewed by zoomorphism. Comparison between animals and plants has a long but discontinuous history, from Duhamel du Monceau (1758)
, who pioneered both plant biomechanics and osteohistology (Camus, 1995
), to more recent analyses such as in Hallé (1999)
and Vogel (2003)
. It raises the important issue of the scientific value of such analogies, which is largely beyond the scope of this paper. Here we set up a few elements.
The term "analogy" has two meanings in science. In the first, analogy is a method by which insights of heuristic or pedagogical values may be gained by comparing a largely unknown system (e.g., the control of standing position in plants) to a more studied system (e.g., equilibration and mechanical adaptation processes in animals) on the basis of functional or structural similarities. It can be used to generate hypotheses and models or to illustrate differences (Hallé, 1999
). We feel that the comparison with terrestrial animals has pedagogical value in highlighting the active and sensitive mechanical behavior of plants. We also think it has been of heuristic value in helping us to escape from the paradigm of the "stiff (though optimal) pole." Indeed, it was instrumental in the identification of one major peculiarity of plant mechanical design, namely the two-in-one design of skeletal and motor systems. Whether this comparison will generate other insightful hypotheses remains to be assessed. Questions emerging from this comparison with animals are: (1) how can motor actions involved in posture control be coordinated without a central computing system and (2) are plant motors responsive to their "work-out," i.e., do they acclimate their structure and power to their loading environments? This may also be used to question animal biomechanics, e.g., do maturation strain analogues exist in animal skeletons? A more systematic comparative biomechanical analysis of bone, chitinous exoskeleton, and wood would be also interesting, because they display quite high analogies in their structure (Vincent, 1990
) and growth. However it should be recalled that we have just focused here on a comparison between land spermatophyta (mostly angiosperms and conifers) and large terrestrial animals (vertebrates and arthropods). The animal kingdom displays many other biomechanical designs than that of vertebrates and arthropods (Vogel, 2003
). And a comparative biomechanics of plants and animals in general is far beyond the scope of this paper. Finally, concerning possible anthropomorphic bias, it is noteworthy that all facts and models presented here for plant motors came from biomechanical and biological research, independently of any analogy with any animal. The analogy came only when considering the whole picture.
The second meaning of analogy is confined to comparative and evolutionary biology (e.g., Niklas, 1997
). It designates similarities between functions or structures, determined by similar environmental constraints selecting for similar functional phenotypes. Analogy contrasts with homology, which is determined by a common genetic background from a common ancestor and by conserved gene networks and embryological origin. From that perspective, because our central argument deals with mechanical constraints on any erect and growing living being, it is better to use a phyletic range including taxa that have diverged before land colonization (such as animals, plants, and fungi). However, possible partial homologies cannot be excluded: some parts of a mechanoperceptive signaling pathway might have been conserved (Braam, 2004
).
Biomechanics of posture control and long-term skeletal acclimation in plants: a new paradigm for the support function in plants?
Just as in animals, plant stems and their architecture are much more than a "cleverly optimized fixed pole or aerial antennas." Land plants implemented a solution of embedding skeletal and motor functions in the same anatomical elements, even though two types of kinematical designs (arthrophytes and contortionists) could be described. This biomechanical design makes it possible for land plants to grow without any loss of function in terms of rigidity, stability, and motor capacity, as only found in vertebrates. Therefore they can perform active postural and equilibrium control, and long-term mechanical acclimation of their supporting structure, through mechano-controlled growth and cell-wall differentiation processes. It is likely that to further our understanding of plant posture and mechanical acclimation will require integrative interdisciplinary approach of mechanics and biology and particularly a new generation of biomechanical models of plant architectural development. Moreover, more detailed phyletic studies in the context of land plant evolution should be conducted following the studies done for stiffness and stability design (Niklas, 1992
) and for the involvement of reaction wood (Mosbrugger, 1990
).
FOOTNOTES
1 The first author would like to dedicate this paper to Francis Hallé who recently retired. He was very influential in convincing us about the heuristic value of comparing plant and animal design and architecture. His book Eloge de la Plante (Hallé, 1999
) is a landmark in comparative biology. This work also stems from an invited lecture at a Jacques Monod Conference on the Physicochemical Ecology of Organisms, and the first author thanks the organizers J. Casas and G. Jeronimidis. The authors thank the two anonymous referees for stimulating a sharpening of the arguments and helping with the English and B. E. Hazen for providing helpful suggestions to revise the manuscript. 
2 Author for correspondence (moulia{at}clermont.inra.fr
)
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K. J. Niklas, H.-C. Spatz, and J. Vincent Plant biomechanics: an overview and prospectus Am. J. Botany, October 1, 2006; 93(10): 1369 - 1378. [Abstract] [Full Text] [PDF]
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