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Journal of Experimental Botany, Vol. 64, No. 15, pp. 4617–4633, 2013
doi:10.1093/jxb/ert320 10.1093/jxb/ert320
review paper
Plant biomechanics and mechanobiology are
convergent paths to flourishing interdisciplinary
research
Bruno Moulia1,2,*
1 INRA (Institut National de la Recherche Agronomique), UMR0547 PIAF (Unité Mixte de Recherche PIAF Physique et Physiologie
Intégratives de l’Arbre Fruitier et Forestier), F-63100 Clermont-Ferrand, France
2 Clermont Université, Université Blaise Pascal, UMR0547 PIAF, BP 10448, F-63000 Clermont-Ferrand, France
* To whom correspondence should be addressed. E-mail: [email protected]
Received 6 June 2013; Revised 21 August 2013; Accepted 23 August 2013
Key words: Ecology, drag, growth, mechanotransduction, modelling, sap, stiffness, strength, stress, system biology.
Introduction
‘One sole point of view is always false.’
Paul Valéry (1871–1945)
Over recent decades, there has been a real renaissance of interest in how inner and outer mechanical forces influence biological systems at all scales from macromolecules up to functional
ecology. Many areas of animal and medical science are being
reshaped by considering biomechanical and mechanobiological aspects, like stiffness-driven differentiation of stem cells,
embryo development, tumour invasion, bone and cartilage
adaptation, cardiac and arterial remodelling, brain neurobiology, touch and haptics, motion control, and proprioception (e.g. Discher et al., 2005; Stoltz et al., 2005, Boccafoschi
et al., 2013; Bukoreshtliev et al., 2013). The same is true and
no less impressive in plant sciences where researchers continue
to be fascinated by the features that plants have evolved in
order to grow and sense, withstand, acclimate, and adapt to
the mechanical challenges they face. But what are the major
frontiers in plant biomechanics and mechanobiology, the hotspots where physical and biological disciplines cross over? Is
this really a new field or can we trace it back in time, and if
so, how far? And what exactly do the seemingly mirror-image
names biomechanics and mechanobiology mean?
What is plant biomechanics?
Mechanics is an inseparable feature of the abiotic interactions
of plants with gravity, wind, soil, aquatic currents, and waves,
and the biotic interactions with other plants, animals, and
microorganisms through contact, impact, adhesion, penetration, catching, or propagule transport. Internally, mechanics
is central to water transport, the ‘power of growth’, and cell–
cell interactions.
Plant biomechanics can be defined simply as the study of
the structures and functions of biological systems from the
phylum Plantae by making use of concepts and methods from
mechanics* (e.g. Hatze, 1974; Niklas, 1992; Boudaoud, 2010;
Jordan and Dumais, 2010; Ennos, 2011; Wojtaszek, 2011;
other essential mechanics terms that will be used repeatedly
in this review and throughout the special issue are defined in
Box 1 and marked with an asterisk in the text, and are illustrated with examples from plants).
As biological systems are often multiphasic, fluid*, solid*,
and soft matter* mechanics may all be implicated, either
separately or in combination. Overall, all areas of mechanics are involved somehow: kinematics*, statics*, dynamics*,
mechanism analysis*, structural analysis*, rheology*, fracture mechanics*, strength of materials*, hydraulics*, tribology*, mechanical metrology*, and phenomenological and/
or integrative modelling*. To yield meaningful and insightful knowledge, however, the mechanical principles need to be
combined with the relevant concepts and methods from the
biological subdiscipline concerned, whether it is genomics,
biochemistry, electrophysiology, ecophysiology, ecology, or
paleobotany.
© The Author 2013. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved.
For permissions, please email: [email protected]
4618 | Moulia
Box 1. A primer in mechanics with examples from plant biomechanics and
mechanobiology
Cellular materials: materials in which the load-bearing material is arranged in walls around voids, the unit element being
called a cell, from the Latin word cellula, meaning a small box. Note that this definition differs from the biological definition
of a cell. Cellular solids are described according to the geometric structure of the cells, i.e. their shape, size, and distribution. The wall of the cell can be made of solids*, soft matter*, or even fluids* as in fluid foams. Cellular materials are widespread in nature and include meristematic tissues, parenchyma, wood, and cork in plants, and tissues such as trabecular
bone in animals. Natural cellular materials are often found to be mechanically very efficient. For instance, the honeycomblike microstructure of wood gives it exceptional resistance to bending and buckling. A particular type of cellular solid is
one in which a living protoplast is sitting inside the ‘material cell’, providing internal turgor pressure to the wall and making
the cellular solid act as a hydrostat.
Continuum mechanics: the branch of mechanics that models materials as continuous media rather than as discrete sets
of objects. Continuum mechanics involves kinematics*, statics*, and dynamics* and is the basis of both fluid* and solid*
mechanics*. Continuum mechanics can be used to study materials with internal structure such as cellular solids* or granular
media such as soils, as long as the scale of the study is larger that the typical size of internal constituents, and an equivalent
rheology* and effective properties can be defined (see for example, Baskin and Jensen, 2013; Jin et al., 2013, this issue).
Deformation: see Strain*.
Dynamics: generally speaking, the branch of mechanics that deals with the causes of motion and the attendant action
of forces and torques. In this sense, dynamics complements kinematics*. Dynamics is also used in a more specific way to
analyse the effects of loads on a mechanical system displaying acceleration and thus inertial forces (here complementing
both kinematics* and statics*). In plants, dynamical analysis sensu stricto has been applied to wind- or flow-induced vibrations in terms of resistance or failure, to mechanosensing, and to fast motions.
Fluid: matter that continuously and endlessly deforms and flows under shear stress*. Fluids have no zero-stress shape
(i.e. at rest) and will take on the same form as their container (although with distinct kinetics, depending on their rheology).
Examples of classical fluids are gases (e.g. air) and liquids (e.g. water). Liquids are dense and cohesive (having attractive
interactions between molecules) and display surface tension, unlike gases. Materials that have attributes of both solids and
liquids, like gels, suspensions, and polymers, are called complex fluids and come under the remit of soft matter mechanics*.
Fluid mechanics: the branch of physics that studies how fluids* flow under the influence of forces. It can be divided into
fluid statics* and fluid dynamics*. Fluid mechanics is not only used in plant biomechanics to understand the interaction of
plants with wind or other currents and the flow of internal saps, but also to understand the process of growth itself. The
general framework used to model the behaviour of fluids comprises the Navier–Stokes equations.
Fracture mechanics: the branch of mechanics that studies the propagation of cracks and bubbles in materials. Of specific concern is the influence of microscopic defects and crack ‘growth’ that lead to possible instabilities and subsequent
catastrophic ruptures. Fracture mechanics has been applied to plant tissues and organs such as wood, leaf, and fruit tissues, in relation to wind-break function, or the effect of herbivory. It is also a central aspect in studying the biomechanics
of invasive growth and root growth in soils.
Growth: the term ‘growth’ is polysemic, and may lead to confusion when used in an interdisciplinary context. In plants,
growth involves the deformation (strain*) of existing polymeric cell walls, so measuring the intensity and spatial distribution
of growth may require kinematical methods. Stressing of the cell wall to balance internal turgor pressure provides the power
for growth. This internal pressure itself results from the reaction of the cell wall (as well as that of neighbouring cells) to the
entrance of water driven by osmotic differences in cell contents. However, at the same time, some new wall material is synthesized and added to the inner side of the existing cell wall or into a new cell wall if the cell undergoes cell division while
expanding. Finally, the rheology* of growing cell walls is usually anisotropic and can be regulated very rapidly in response to
different cues, including mechanical ones. All these characteristics make the calculation of stress* distribution in plant biomechanics very different from standard strength of material* calculations as soon as growth needs to be taken into account.
Hydraulics: a set of simplified models of fluid dynamics specifically adapted to a set of engineering situations such as
pipe flow and river channels. Hydraulic models are relevant to many biological situations, e.g. sap conduction in xylem, but
care should be taken when using them in plant systems.
Instability: a situation where some output or internal state variable of a system varies greatly (through positive feedback) under small perturbations from the background mechanical noise. The system may thereby move from an unstable
equilibrium state to another state of (stable) equilibrium or undergo rupture. For instance, in fracture mechanics*, a crack
can propagate without bounds when its length reaches a critical value. Similarly, in a fluid that is under tension (e.g. xylem
Biomechanics and mechanobiology | 4619
Box 1. Continued
sap), small gaseous bubbles can grow suddenly and boundlessly as soon as they reach a critical size, creating cavitation
and embolism. On a different scale, in structural mechanics, a column under compression can become unstable when it
exceeds a critical length. Any deflection of that column increases the lever arm on it, and hence the torque, which in turn
increases deflection, and so on. This is called buckling or buckling instability. Both processes may be important to plant
mechanical integrity and life. Instability is also a central aspect of fast active motion in plants, where the sudden release of
accumulated elastic energy can be understood as an elastic instability.
Integrative modelling: this is modelling* that explicitly combines several mechanisms and usually deals with changes in
scale. This integration relies on the theory of mechanics, and is at the heart of structural mechanics*. Integrative modelling
is thus a tool to interpret experiments, estimate non-observable variables such as stress*, and identify the mechanisms
driving a given phenomenon or trait. It has also been used to integrate the model of mechanosensing from the cell scale
up to the organ scale.
Kinematics: the quantitative and phenomenological* study of the motion, deformation, and flow of bodies, without analysing their causes. Kinematics is a central tool in studying the movement of plants and the quantitative analysis of growth
and morphogenesis, allowing for a consistent spatiotemporal description of all the biophysical and biochemical processes
involved, e.g. water and nutrient influxes, gene regulation, and protein synthesis.
Mechanical metrology: the branch of mechanics dealing with theoretical and practical aspects of measurement. In
mechanics, it is important to distinguish between variables that can be measured directly (displacement, strain*, motion
velocity and acceleration, strain rate) and those that can only be calculated from combinations of observable variables
(derived variables such as force and stress*) through a model. A large part of metrology is devoted to establishing principles and accurate devices for indirect measurements (e.g. photoelasticimetric measurement of strains and stresses
through changes of light polarization within the strained object).
Mechanical modelling: the development of a set of mathematical equations to describe the behaviour of a mechanical system and to help understand its behaviour and determinism. This kind of modelling may be phenomenological* or integrative*.
Mechanics: the science that deals with movements (displacements and deformations) of bodies under the influence
of forces.
Mechanics of cellular solids: a developing branch of mechanics at the intersection between structural, continuum,
and soft matter mechanics that focuses on the mechanical behaviour of cellular materials*. Many plant tissues have been
described as cellular solids (e.g. parenchyma, sclerenchyma, wood), and quantitative links can be drawn between the
microscopic anatomical layout of these tissues and their macroscopic mechanical function at the whole-tissue scale. For
example, this approach has been used to analyse the strength* of wood and the mechanical stability of plants in wind, the
resistance of xylem conduits to collapse under the internal depression of the sap, and the behaviour of meristems.
Mechanism analysis: a mechanism is an assembly of bodies connected by joints that produces a force or motion
transmission. Mechanism analysis has been used to study animal locomotion but is also relevant in some types of plant
motion, such as fast motions.
Nastic movement: active plant movement triggered by environmental stimuli (e.g. touch, temperature, humidity, or
light irradiance) in which the direction of movement is not dependent on the direction of the stimulus. Some fast motions
in plants are nastic movements, such as the closing of the Venus flytrap leaf when it captures prey or the folding of the
mimosa leaf when it is disturbed. The mechanical energy for nastic motion can be provided by turgor pressure changes in
elastic cells or through growth*.
Nutation: an active and autonomous helicoidal plant movement due to the successive bending of the organ in different
directions while elongating. Whether or not this is related to gravitropism* is a long-debated question. The amplitude of
nutation is much larger in twining plants and is usually referred to as circumnutation.
Phenomenological modelling: the development of models that relate parsimoniously empirical measures of phenomena in a way that is consistent with relevant theory (symmetry, topology, conservation laws) but not derived from it.
Examples of phenomenological modelling in mechanics are kinematic and rheological modelling.
Rheology: the quantitative and qualitative study of the deformation and flow of matter (from the aphorism ta panta rhei:
‘everything flows’ from the philosophy of Heraclitus). Rheological studies lead to the definition of phenomenological models called ‘constitutive laws’ that relate stresses* to strains* and strain rates and potentially to other physical variables (e.g.
temperature). The strength* of the material, i.e. the limit of the constitutive equations, is also studied. Numerous studies
of cell-wall, cell, and tissue rheology have been undertaken in plant biomechanics, in particular to understand the involvement of the cell wall in the control of expansion growth, morphogenesis, stiffness*, and strength* in plants.
4620 | Moulia
Box 1. Continued
Soft matter and disordered media: states of matter that do not have the precise order of crystalline solids and are
often intermediate between fluid* and solid* states. They include polymers, colloids, gels, vesicles, emulsions, foams,
films, surfactants, micelles, suspensions, liquid crystals, and granular materials. Therefore, many biological materials fall in
this category such as growing cell walls, cytoplasm, root and leaf exudates, cuticles, and soft tissues, as well as materials
in the plant’s environment like soil. In general, these states are characterized by mesoscopic structures (e.g. polymeric
chains, chains of contacts between grains and force arches in granular solids, bubbles, or drops) that strongly influence
their mechanical properties. (See also Fluid* and Solid*.)
Soft matter mechanics and rheology: mechanical and physical analysis of soft matter. Due to the existence of mesoscopic structures, soft matter displays mechanical properties that are intermediate between typical solids* and fluids*
(such as non-linear rheology*, flow thresholds, and internal relaxation time), which may lead to many instabilities*, symmetry breaking, and pattern formation. Soft matter mechanics has reinvigorated fluid and solid mechanics and is being
applied, for example, to plant growth and morphogenesis and to plant motion and tribology*.
Solid: one of the states of matter characterized by rigidity and resistance to change in volume and shape. A solid object
does not flow to take on the shape of its container or expand to fill its entire volume. Deformation of a solid requires work.
A solid may be compact or cellular*. (See also Fluid* and Soft matter and disordered media*).
Solid mechanics: the branch of continuum mechanics that studies the behaviour of solid materials, especially their
motion and deformation under the action of forces, temperature and humidity changes, phase changes, and other external
or internal agents. Solid mechanics allows the mechanistic integration between the scale of the material (e.g. elements of
a cell wall or a tissue) to that of the whole solid (respectively, a cell or an organ) using integrative mechanical modelling*.
Statics: branch of mechanics analysing the effects of loads on a mechanical system with no acceleration and thus no
inertial forces. These systems are said to be in static equilibrium. This analysis can usually be extended to quasi-static
systems in which the inertial forces are negligible relative to the static forces. (Compare with Dynamics*.)
Stiffness, Rigidity: the extent to which an object resists deformation without any damage (not to be confused with
strength*). The stiffer the object, the more force has to be applied for the same deformation. The stiffness or rigidity of a
material can be characterized as the amount of stress* per unit strain*. It may display isotropy* or anisotropy*. Some materials also increase their stiffness when strained, a process called strain stiffening, as is found to occur in some meristematic
cells. Stiffness can also be characterized at the level of a structure (e.g. a beam or a shell, see Structural mechanics*).
For example, flexural rigidity (or bending stiffness) is the amount of torque needed to produce a unit change in curvature.
Flexural rigidity influences buckling instability* and the resistance to active tropic bending of tree trunks. It is also involved
in the storing of elastic potential energy used to power fast motions. The opposite of stiffness is compliance.
Strain: the degree to which the length of a small virtual cube of material changes in a particular direction relative to its original
length (normal strain), or to which the cube’s angle changes (shear strain). Deformation is defined using strain. When subjected
to the action of forces, a deformable body will strain. This deformation will stretch bonds and slide/shear internal elements,
allowing internal reaction forces or stresses* to be set up until an internal and external mechanical equilibrium is achieved. The
link between strains, strain rates, and stresses is analysed in rheology*. In plants, the analysis of strains and deformations are
central to the kinematics* of motion, cell morphogenesis and growth, and mechanosensing and thigmomorphogenesis.
Strength: the limit of a material’s or a structure’s capacity to withstand stresses or strains before it weakens or breaks.
In materials, the strength is described by failure criteria, the simplest being the maximum stress* or strain* at which failure
starts under uniaxial stress. But more complex failure criteria may be necessary to describe multiaxial stresses and anisotropic rheologies*. In solid structures, strength is often analysed by localizing stresses through integrative modelling* and
by assuming that the material fails when one stress component exceeds the uniaxial tensile or compressive limit. Note that
water and many fluids also have tensile strength.
Strength of materials: a set of simplified models of solid mechanics* specifically adapted to a set of engineering situations. ‘Strength of materials’ provides methods for calculating stresses in structural members, such as beams, columns,
shafts, plates, and shells of regular shapes and comparing them with the strength of their constitutive material (‘strength
of structures’ might be a more appropriate name). The relationship between strength of materials and solid mechanics is
analogous to the relationship between hydraulics and fluid mechanics. Strength-of-material models and the closed-form
expression that they provide have been used widely in plant biomechanics. However, care should be taken when using
them, as plant systems are open systems with free energy and change in the mass of material and rheology* over time (see
Growth*). Not to be confused with fracture mechanics*.
Stress: density of reaction forces per unit area acting on an oriented surface and measured in Pascal (Pa) or N m–2. The
surface may be a physical interface (e.g. between neighbouring cells or at the boundary of an organ) or a virtual slice through
Biomechanics and mechanobiology | 4621
Box 1. Continued
a block of tissue or cell wall. A normal stress is one that acts perpendicularly to the surface. A shear stress acts tangentially
to the surface. Pressure is therefore a normal stress and a positive pressure is considered as compression. In general, a
surface will be subject to both normal and shear stresses. For a small virtual cube of material (e.g. within a cell wall or within
a fluid inside or outside cells), normal and shear stresses act on each of the cube’s six faces. The stress exerted on the cube
by a uniform external pressure is isotropic (the pressure has the same magnitude on each face) as is usually the case in
fluids. In many solids occurring in plants, however, the shear and normal stresses acting on the different faces of the cube
will have different magnitudes, making the local stress distribution anisotropic (Baskin and Jensen, 2013). However, if the
cube is at rest (or at least not accelerating rapidly), then the net forces acting on the surfaces of the cube must balance.
Stress cannot be measured directly (it is not observable and can only be estimated using a model). Stress analysis is
at the very heart of mechanics and biomechanics. It has been central, for example, in the biomechanical analysis of the
micromechanical behaviour of plant cells, expansion growth*, plant morphogenesis, plant mechanosensing, functional
ecology, and evolutionary biophysics.
It is important to note that the semantics of the concept of ‘stress’ can generate confusion in the interdisciplinary
context of biomechanics and mechanobiology. Originally deriving from the noun ‘distress’, the word ‘stress’ has since
been adopted in mechanics, biology, and psychology. Stress has been strictly defined in mechanics and is the clear dual
opposite of strain. The current biological definition of stress, ‘any strain that disturbs the functioning of an organism’
(Encyclopaedia Britannica, 2009), is much more vague and contradicts the mechanics definition. This has led many biologists to assume that ‘mechanical’ stress is the variable of interest, but this is not always appropriate (see discussion by
Moulia et al., 2011).
Structural mechanics, Structural analysis: the branch of solid mechanics dealing with structures like beams, columns,
plates, shells, and assemblies thereof (e.g. trees, trusses). In plants, principles of structural mechanics have been applied
in order to mechanistically integrate the behaviour of: (i) macromolecules in a subcellular complex; (ii) cell walls in the
behaviour of a tissue viewed as a cellular solid*; (iii) tissues inside a complex organ; and (iv) a set of organs, such as the
dynamics* of a complex tree vibrating in the wind.
Thigmomorphogenesis: the plant physiological response to external mechanical stimuli, which in natural conditions
come mostly from the drag by wind or currents, raindrops, and the contact and rubbing by neighbouring objects, plants,
or passing animals (from the Greek word thigma meaning ‘touch’). Thigmomorphogenesis was first demonstrated by
submitting plants to artificial mechanical loads. A syndrome of responses is then observed in a large number of species,
involving: (i) a reduction in longitudinal stem growth; (ii) a stimulation of secondary cambial growth (if present), possibly
with differentiation of a more flexible but stronger ‘flexure wood’; and (iii) a reallocation of biomass to the root system. This
mechanosensitive control of growth allometries results in stunting and more anchored shoots, while conserving most of
the capacity for wind drag reduction through reconfiguration made possible by the more flexible wood. The thigmomorphogenetic syndrome thus improves plant acclimation to its mechanical environment. Studies under natural conditions
on isolated plants as well as on forest and crop dense stands have indeed shown that thigmomorphogenesis is a major
process in the control of plant canopy growth in the ecological range of natural chronic winds or water currents.
Toughness: Amount of mechanical energy (work) per volume that a material can absorb and/or dissipate before rupturing
(unit J/m3). The toughness of a material depends on (i) the type and amount of defects existing in the material, and there possible control through mechanobiological wounding reactions, (ii) the balance between elastic and plastic deformation of the
material depending on its content and ultrastructure, and (iii) the existence of crack-stopping anatomical features (holes and
lumens, inclusions of soft materials)—see Fracture mechanics*. The study of the rheological and anatomical bases of toughness in plant is central to the understanding of the mechanical stability of plants and the resistance to pathogens or herbivory.
It is also important for the use of plant-derived materials by animals and humans (e.g. texture and taste of fruits and vegetables, safety of wooden or bamboo constructions, and so on), and therefore studied in ecological and engineering sciences.
Tribology: an interdisciplinary field at the intersection of mechanics*, rheology*, soft matter* sciences, and chemistry
that studies the phenomena of friction, adhesion, cohesion, abrasion, erosion, and corrosion at the interfaces between the
surfaces of two systems. In plant biomechanics, tribology may be essential in understanding, for example, lubrication in
root growth, cell-to-cell adhesion, insect-to-leaf adhesion, and insect trapping.
Tropic, Tropism, -tropy: the term ‘tropic’ comes from the Greek word trepein meaning ‘to turn, to change direction’. It
has been used in mechanics to describe the dependency of a material’s properties on direction. Isotropic means that the
property is the same in all directions, while anisotropic means the property differs with angular orientation within the material. This can also be extended to the stress* state. In botany, the same etymology has been used to name active motion
oriented towards a vectorial stimulus (e.g. gravity→gravitropism, light intensity gradients→phototropism, contact or oriented drag→thigmotropism). Compare with nastic movement*.
4622 | Moulia
Plant systems that might by studied from a biomechanical
perspective range from molecular and cellular structures (like
DNA, stretch-activated channels, the cytoskeleton, cell membranes, nuclei, cytoplasm, and cell walls) up to tissues, organs,
and the whole plant itself, and on up to entire communities
(like forests, grassland, crops, and landscapes). The biological functions that are being studied from biomechanical and
mechanobiological perspectives cover most of the physiological functions of plants—growth*, sensing, morphogenesis,
differentiation, water relations, sap flow and osmoregulation,
support and posture control, above- and below-ground exploration, mating and seed dispersal, acclimation, and resistance
to wind and currents and to drought, gravity, pathogens, and
herbivory (Table 1).
Reasons for studying plant biomechanics and mechanobiology are often to extend our fundamental understanding of
biological functions and their acclimation and adaptation to
the physical environment. However, ‘real-world’ issues related
to forestry, crop sciences, and ecological management may
also be the motivation for turning to these approaches, e.g.
to cope with the problems of windthrow and lodging (e.g. Py
et al., 2006; de Langre, 2008; Fourcaud et al., 2008; Gardiner
et al., 2008). Another practical purpose is in studying material
derived from plants (like wood, bamboo, textile fibres, fruits,
and vegetables) and relating their properties to the biomechanical history of the plant before harvest (e.g. Thibaut et al.,
2001; Bargel and Neinhuis, 2005; Wanga and Jeronimidis,
2008; Yamamoto et al., 2010, Gibson, 2013). More recently,
researchers in mechanical engineering and technology have
turned to plants for inspiration. What might be termed evolutionary plant mechanical ‘design’ is usually different from
standard engineering practices, so studying plants may open
the minds of engineers and designers to novel design solutions
(e.g. in the domains of soft and anisotropic matter, deformable and foldable structures, actuation, and smart materials).
Coming full circle then, some biomechanical studies are stemming directly from biomimetics (e.g. Burgert and Fratzl, 2009;
Johnson et al. 2009; Martone et al., 2010, Rampf et al., 2011).
Table 1. Biomechanical and mechanobiological studies of plant functions
Functions
Useful introductions to the topic
Mechanosensing and gravisensing, and
mechanotransduction and gene regulation
Braam, 2005; Telewski, 2006; Monshausen and Gilroy, 2009;
Merret et al. 2010; Morita, 2010; Moulia et al., 2011, Wojtsasek,
2011; Hamant, 2013; Monshausen and Haswell, 2013; Toyota and
Gilroy, 2013
Silk, 1984, 2006; Baskin, 2005; Schopfer, 2006; Goriely and Ben
Amar 2007; Geitmann and Ortega, 2009; Jordan and Dumais,
2010; Merret et al. 2010; Baskin and Jensen, 2013
Clair et al., 2011; Mirabet et al., 2011; Burgert and Keplinger, 2013;
Dumais, 2013; Milani et al., 2013; Routier-Kierzkowska and
Smith, 2013
Sharon et al., 2004; Boudaoud, 2010; Mirabet et al., 2011;
Hamant, 2013, Robinson et al., 2013
Angeles et al., 2004; Sperry et al., 2008; Cochard et al., 2009,
2013; Jensen et al., 2011
Niklas, 1992; Fournier et al., 2006, 2013
Growth including cell expansion, cell division,
wall synthesis and exocytosis, water influxes,
and gene regulation
Cell-wall mechanics, and cell and tissue
differentiation
Pattern formation and morphogenesis
Sap and internal fluid circulation
Support and risk of breakage under selfweight or external loads
Active movements (tropism, nastic
movements, and twining)
Posture control
Penetration in soils and tissues
Anchorage and drag resistance to wind and
currents (static and dynamic aspects)
Water relations and drought resistance
Biomechanical acclimation through
mechanobiological processes including
osmoregulation and thigmomorphogenesis
Fast motion and seed dispersal
Resistance to biotic injuries such as herbivory
or pathogen attack
Metabolic ecology and scaling laws
Functional ecology and ecological strategies
Evolutionary biomechanical adaptations and inference
of extinct plant stature and biomechanical functions
from paleobotanical records
Skotheim and Mahadevan, 2005; Isnard and Silk, 2009; Moulia and
Fournier, 2009
Moulia et al., 2006; Bastien et al., 2013
Goriely and Tabor, 2006; Bengough et al., 2011; Winship et al.,
2011; Jin et al., 2013; Nezhad and Geitmann, 2013
Ennos, 2000; Spatz et al., 2007; de Langre, 2008; Fourcaud et al.,
2008; Gardiner et al., 2008; Koehl et al., 2008; Puijalon et al., 2011
Tyree and Hammel, 1972; Franks et al., 1998; Boyer and Silk,
2004; Sperry et al., 2008; Cochard et al., 2009, 2013
Braam, 2005; Telewski, 2006; Coutand, 2010; Moulia et al., 2011;
Wojtsasek, 2011
Niklas, 1992; Forterre et al., 2005; de Langre, 2008; Forterre, 2013
Goriely and Tabor, 2006; Sanson, 2006; Onoda et al., 2011
McMahon, 1976; Niklas and Spatz, 2004; Price et al., 2007; Olson
et al., 2009
Ennos, 1997; Fournier et al., 2006, 2013; Read and Stokes, 2006
Mosbrugger, 1990; Rowe and Speck, 2005; Niklas and Kutschera,
2009; Niklas, 2013
Biomechanics and mechanobiology | 4623
It should finally be stressed that, in using mechanical concepts and tools to study plant systems, it is not sufficient
just to apply sets of models that have already been developed for engineering, such as in strength of materials* or
hydraulics*. Plant systems display numerous non-linearities
in their mechanical behaviour. Many plant organs are very
slender. They therefore display large reconfigurations under
load (e.g. de Langre, 2008) and are prone to mechanical
instabilities*. Their constitutive tissues may display complex rheologies* (Dumais, 2013), high levels of anisotropy
(Baskin, 2005), and behave as soft matter*. But there is
more. The theoretical handling of the mechanics of growth*
is quite specific. It needs to deal with the existence of internal sources of free energy (such as ATP and osmotic pressure) that are used to produce active work (e.g. Moulia and
Fournier, 2009; Forterre, 2013; Baskin and Jensen 2013). At
the same time, new material is synthesized and added at the
inner side of an existing cell wall or forms a new wall in a
dividing cell (Dumais, 2013). The rheology* of the growing
cell walls can also be regulated very rapidly in response to
changes in the mechanical state of the plant (Dumais, 2013;
Monshausen and Haswell, 2013). Finally, water needs to flow
into the expanding cells to maintain the internal pressurization required for their growth (Boyer and Silk, 2004). All
these characteristics make the calculation of stress* distribution and of changes in shape in plant biomechanics very
different from standard strength of material calculations*
when growth needs to be taken into account. Specific theoretical developments have been necessary (see also Goriely
and Ben Amar, 2007; Geitmann and Ortega, 2009; Moulia
and Fournier, 2009; Jordan and Dumais, 2010; Moulia et al.,
2011) and have allowed the field to advance such that some
of these studies of special features of plant systems are setting plant biomechanics at the frontier of modern mechanics
and physics, as well as of systems biology. However, as we
shall see, the use of mechanical tools in advancing plant science is in fact as old as plant science itself.
A potted history of plant mechanics
research
Over the 18th and 19th centuries, the pioneers of plant biology showed a clear interest in the mechanics of plants. Stephen
Hales called his major work Vegetable Staticks (1727), a sign
of Isaac Newton’s influence on thinking in plant physiology in
Cambridge at the time. This work in turn influenced Duhamel
du Monceau in France, who published his Traité de la physique
des arbres (Handbook of tree physics) in 1758 extending biomechanics to trees. In Germany, in the 19th century, Wilhelm
Hofmeister (1824–1877), Julius von Sachs (1832–1897), and
Wilhelm Pfeffer (1845–1920) pioneered the biomechanical
analysis of root and shoot growth, and of water relations and
particularly turgor pressure. In 1868, Hofmeister also postulated the idea of mechanical control of morphogenesis at the
shoot apex, while Simon Schwendener (1874) extended the
analysis of plant mechanical design in relation to the functional anatomy of grasses in his book Das mechanische Prinzip
in Anatomie Bau der Monokotylen (The mechanical principle in
the anatomical structure of monocots), establishing that fibres
had a mechanical function and that cross-section shape and tissue position influence organ stiffness* and strength*. Greenhill
(1881) and Metzger (1893) pioneered the idea of adaptive
mechanical design in plants (defining optimal shapes of tree
trunks to resist wind drag or buckling* under self-weight), as
well as the use of formal mechanical models in plant biomechanics (see Fournier et al., 2013). Even before that, Knight
(1803) in England followed by Metzger (1893) in Germany
noted the influence of wind mechanosensing on plant growth
and its importance for arboriculture and forestry, establishing
fundamental and applied approaches to mechanobiology and
plant mechanical acclimation. Similarly, in Ireland, the interdisciplinary collaboration between plant biologist Henry Dixon
and physicist John Joly led to the identification of the driving
force for sap ascent in xylem and the subsequent postulation of
the cohesion–­tension theory (Dixon and Joly, 1895; see Brown,
2013). It was not until the 1930s, however, that a convincing
biophysical explanation of the more complex phloem transport was given in the osmotic gradient-pressure flow model by
Ernst Münch (1930). The relationship between water status
and the biomechanics of plant cells and tissues was refined by
Karl Höfler, who, in the 1920s, drew pressure–volume curves
of water storage (Biebl, 1974) that led to the description of
the bulk modulus of elasticity of plant tissues and its control
over water capacitance (although the theoretical and experimental development awaited Tyree and Hammel, 1972).This
completed the biomechanical bases of water flow and storage
in plants (at least in non-growing tissues). In parallel, Charles
Darwin and his third son, Francis Darwin, both turned their
botanical interest to study the kinematics of growth* in plants
in their evocatively entitled The power of movement in plants,
published in 1880. This was among the first attempts to record
tropic*, nastic*, and nutational* movements, thus linking
plant biomechanics to the study of evolution at the outset.
For all these pioneers, it was very clear that the mechanics of both fluids and solids were of utmost importance in
plant biology. Activity in the field proceeded until the 1940s,
sometimes aided by the interest of distinguished mathematicians and physicists (e.g. Airy in 1873, Greenhill in 1881,
and Fietzerald in 1894), but partly hampered by the lack of
experimental and mechanical tools capable of handling such
complex systems as plants. For more details of all these pioneering works, see Kramer (1988), Peters and Tomos (1996),
Niklas (1992), Nachtigall (1994), Telewski (2006), Moulia
and Fournier (2009), Isnard and Silk (2009), Jordan and
Dumais (2010), and Brown (2013).
After World War II, progress in genetics and later the birth
of molecular biology shifted the main research agenda away
from the mechanics of plant life. However, interest in the
biomechanics of cell expansion was rekindled in the 1950s.
Work on plant cell wall growth and differentiation featured a
strong mechanical and rheological component (e.g. Preston,
1952), and since then cell wall micromechanics has developed
greatly (see Cosgrove and Jarvis, 2012; Burgert and Keplinger,
2013 and Dumais, 2013, in this volume). Lockhart (1965) put
forward the first formal model of plant cell growth, joining fluid and solid mechanics to cell biology and generating
4624 | Moulia
predictions that could be assessed experimentally. For the first
time, a quantitative understanding of the relative influences
of cell size and shape, cell wall, cell membranes, and osmotic
adjustment on expansion growth was established, a new paradigm that aptly would see the research field grow too (see
Green, 1999; Boyer and Silk, 2004; Geitmann and Ortega,
2009; Baskin and Jensen, 2013; Dumais, 2013; Forterre 2013;
Robinson et al., 2013). Almost simultaneously, quantitative
studies of the kinematics* of plant growth, based on concepts and tools from continuum mechanics, were initiated by
Erickson (1966), providing strong impetus for the quantitative spatiotemporal analysis of cell expansion and division
(reviewed by Silk, 1984, 2006) and developmental gene regulation in growing tissues (Merret et al. 2010), as well as growthsustaining water influxes and gradients in water potential (see
Boyer and Silk, 2004). At the same time, this also started a
longstanding debate about the physical constraints of organ
growth, namely the relative contributions of wall extensibility and water conductivity (see review by Cosgrove, 1999;
Boyer and Silk, 2004; Moulia and Fournier, 2009) that more
recently was reflected in the relative influence of water pores
as aquaporins and of wall-loosening agents such as expansins
and pectin methylesterase over growth (see reviews by Boyer
and Silk, 2004; Band et al., 2012; Cosgrove and Jarvis, 2012;
Peaucelle et al., 2012). The biomechanical study of plant morphogenesis developed in parallel (e.g. Green, 1962; Lintilhac
and Vesecky, 1984; Green, 1999; see Robinson et al., 2013,
for a review), leading to a systems biology view of the plant
meristem (to be discussed further below). Water relations and
drought effects in plants were viewed from a biomechanical perspective by considering turgor pressure and how it is
balanced by cell-wall reaction stresses, in both growing and
non-growing cells (see reviews by Tyree and Hammel, 1972;
Kramer, 1988; Nobel, 2005), thus providing new insights into
adaptation strategies to drought.
Starting from an applied mechanical engineering standpoint with a view to biomimetics, the study of the mechanics
of cellular* solids with composite cell walls, like woody and
non-woody plant tissues, began to gain momentum in the late
1970s (see reviews by Niklas and Spatz 2012; Gibson, 2013),
and included the specific case of hydrostatic living tissues
(e.g. Nilsson et al., 1958; Niklas, 1992; Spatz et al. 1999). This
made it possible to understand quantitatively the functional
significance of different ultrastructural and anatomical settings in both herbaceous and lignified organs. By this point,
the biomechanical significance and origin of growth stresses
during tree growth and wood formation became much more
clearly specified (e.g. Wilson and Archer, 1977), establishing the source of the ‘power of movement’ in woody organs.
This fed into detailed studies of secondary cell-wall formation (Yamamoto et al. 2010; Clair et al., 2011; Burgert and
Keplinger, 2013) and the biomechanics of gravitropism and
posture control in woody stems (see reviews by Thibaut et al.,
2001; Moulia and Fournier, 2009; Fournier et al., 2013, this
issue). The homologous subject of the so-called ‘tissue tensions’ in non-woody stems received more episodic attention
despite its significance (Peters and Tomos, 1996; Hejnowicz,
1997; Kutschera and Niklas, 2007; Moulia and Fournier,
2009; Baskin and Jensen, 2013, this issue). Valuable quantitative insights into how plants resist breakage, penetration by pathogens, and herbivory introduced the important
issue of fracture mechanics and the concept of toughness*
to botany (see reviews by Sanson, 2006; Farquhar and Zhao,
2006). Unfortunately, this area has remained isolated from
the mechanobiological work on wounding, except in recent
research on the biomechanics and biomimetics of self-repair
(e.g. Rampf et al., 2011).
The persistent challenge of understanding the fluid
mechanics of sap transport has seen much progress since
the 1980s with analysis of the inherent instabilities of xylem
transport, cavitation, and embolism (e.g. Sperry and Tyree,
1988; reviewed by Cochard et al., 2013), and bolstering up
of the cohesion–tension theory in the face of criticism and
alternative theories (Angeles et al., 2004). More recently
modelling of the transport of phloem sap (Jensen et al., 2011)
provided a mechanistic and integrated overview of phloem
sap flow and how it is coupled to xylem flow (Lacointe and
Minchin, 2008). The loads due to wind flow, the risk of lodging, windthrow, and windbreaks also became the focus of
research starting with Esser (1946), with increasing attention
being paid to the dynamics* of the interaction between plants
and turbulent winds, including instability* (see complementary reviews by Moulia and Fournier, 1997; Py et al., 2006; de
Langre, 2008; Gardiner et al., 2008). The equivalent action
of water streams and waves on aquatic plants received somewhat less attention (but see Denny, 1988), but this situation is
now rapidly changing (e.g. Koehl et al., 2008; Nikora, 2010;
Puijalon et al., 2011).
Root biomechanics and mechanobiology has been studied
less (except for the growth of roots in hydroponics) due to
the complexity of soils and the practical difficulties in visualizing roots in soils or digging them out intact. The problem
of anchorage nevertheless received a clearer biomechanical
foundation in the late 1990s (Ennos, 2000; Danjon et al.,
2005). The mechanical functions of the diverse morphologies
of root systems and their adaptation to given soil conditions
have been analysed. Colonization of the soil by roots has
indeed become an exciting topic over recent years in considering how roots deal with physical impediment. The detailed
mechanics of roots penetrating or skirting round soil aggregates and the mechanosensing of changes in soil resistance
to penetration are being analysed as well as their feedback
on root growth, lateral root initiation (Ditengou et al., 2008),
and root–shoot signalling (reviewed by Bengough et al., 2011;
Jin et al., 2013, this issue).
The field of thigmomorphogenesis*, how shoot and root
growth responds to external mechanical loads, underwent a
revival through physiological approaches in the 1970s, and
took a more cellular and molecular bent in the late 1990s
with the discovery of mechanosensitive channels, calcium signalling, touch genes, and transcription factors (for complementary reviews, see Braam, 2005; Telewski, 2006; Coutand,
2010; Moulia et al., 2011; Monshausen and Haswell, 2013).
More recently, the importance of wind as a major ecological factor was established, even in environments with moderate winds (Ennos, 1997; Moulia et al., 2011). Wind sensing
Biomechanics and mechanobiology | 4625
has been looked at from a biomechanical and integrative
mechanobiological perspective (see review by Moulia et al.,
2011). This has revealed the effects of plant structure and
size on the distribution of the mechanical load to the mechanosensitive tissues and subsequent quantitative expression
of mechanosensitive genes, but also on the integration of
mechanosensing for the building up of the thigmomorphogenetic growth responses in the meristematic tissues. And a
fine tuning (accommodation) of the cellular mechanosensitive pathway itself over the history of multiple mechanical
loading was evidenced (Martin et al., 2010). Gravisensing and
gravitropism* were mostly considered to be under the remit
of physiology, but this is changing somewhat following live
kinematic imaging of statolith motion (e.g. Saito et al., 2005;
Morita, 2010), the study of how the bending–straightening
movement is coordinated (Bastien et al. 2013), and the comparative biomechanical analysis of tropic bending of woody
and non-woody stems (see Moulia and Fournier, 2009). For
the specific case of root gravitropism, the obvious interaction of roots with the soil means that barrier mechanosensing
and soil effects are now being taken into account (Toyota and
Gilroy, 2013; Jin et al., 2013, this issue). By contrast, studies
of nutating*, coiling, and winding organs got their mechanical twist much earlier on and are still mostly seen from that
point of view. Indeed, the mere description of these 3D movements requires advanced kinematic tools (Isnard and Silk,
2009). Biomechanics has started to reveal the motors and
controls of such exploratory motion, the grasping action of
vines (Isnard and Silk, 2009; Gerbode et al., 2012), and the
ecological diversity of climbing strategies (Rowe and Speck,
2005).
From a more general and transversal perspective, the
adaptive mechanical design of plants has received continued
attention since the 1970s (e.g. McMahon, 1976; Niklas and
Spatz, 2004: Olson et al., 2009; Eloy, 2011; Lopez et al., 2011;
reviewed by Moulia and Fournier, 1997; Niklas and Spatz,
2012). Ecological aspects of biomechanics began to attract
interest in the 1990s, continuing into this century (reviews by
Read and Stokes, 2006; Fournier et al., 2013), with anchorage, support, and posture maintenance during height growth
being recognized as major ecological functions. In parallel,
there was development in the use of biomechanical analysis
in paleobotany initially to infer the stature and habit of fossil
species from geological records and, more generally, the evolution of plant growth forms and body plans (e.g. Mosbrugger,
1990; Rowe and Speck, 2005; Niklas and Kutschera, 2009;
Niklas, 2013). The mechanical protection of leaves and fruits
and apparent trade-offs with other functions have also been
described (Read and Stokes, 2006; Sanson, 2006; Onoda
et al., 2011).
Finally an impressive effort to synthetize much of plant biomechanics (e.g. Niklas, 1992; Niklas et al., 2006; Wojtaszek,
2011; Niklas and Spatz, 2012) and comparative biomechanics
including some aspects of plant life (e.g. Vogel, 2003; Herrel
et al., 2006; Ennos, 2011) was very instrumental in developing
a common biomechanical culture, and in highlighting major
results and theories. Another impetus in 1994 for harmonizing plant biomechanics research was the first in a series of
international congresses that has continued every 3 years, the
most recent being Plant-BioMech in 2012.
A meeting of the ways
Biomechanics and mechanobiology: two tribes
The previous chronological description of the development
of plant biomechanics and mechanobiology research is
lacking one important aspect that is required to understand
some of the very recent breakthroughs. It may seem that
mechanobiology is just the part of plant biomechanics that
deals with mechanoperception and mechanical responses of
growth and morphogenesis. However, the two terms reflect
very distinct foci of research starting around the end of the
20th century and initiated by distinct research communities.
To assess what is happening now, it is important to understand how the whole field started and developed. The use of
‘plant biomechanics’ as a keyword to define research really
came back into use over the 1990s by an interdisciplinary
community of plant biologists and mechanical engineers.
Most work focused on the organizational levels from tissue to the whole plant, particularly zooming in on cell-wall
mechanics (as the cell wall, a defining feature of plants, is
particularly important for tissue stiffness* and strength*
and for growth*-stress* building). Independently, ‘mechanobiology’ mainly gained momentum in plant molecular
biology in the late 1990s when it was found that mechanical stimuli regulate the expression of specific genes (Braam,
2005) and transgenic plants could be used to monitor signalling in planta (Knight et al., 1992). The focus was thus
mostly on subcellular, cellular, and tissue levels of organization (Braam, 2005; Monshausen and Haswell, 2013, in this
issue). Amidst the coining of biomechanics and mechanobiology as specific keywords, studies of cell expansion and
division, sap flow, thigmomorphogenesis, and gravitropism
continued as specific subfields of plant physiology that nevertheless relied on the use of mechanical concepts and tools.
Heading towards systems
Connections between plant physiology, mechanobiology,
and biomechanical studies were reinforced as physiologists
specializing in growth and thigmomorphogenesis started to
join the plant biomechanics community, using the term ‘biomechanics’ to describe their own work (e.g. Telewski, 2006;
Isnard and Silk, 2009; Cosgrove and Jarvis, 2012). More
recently, the new wave of integrative biology, systems biology, and systems ecology fostered the creation of multilateral
connections between mechanical engineers, physicists, and
biologists, and thereby between biomechanics and mechanobiology. Four open questions in particular are currently
structuring these collaborations: (i) What brings about plant
morphogenesis and pattern formation? (ii) How are growth
and differentiation controlled? (iii) How are cell walls deposited and how do they stretch and differentiate? (iv) How do
plants acclimate to wind as in thigmomorphogenetic growth
responses and gravitropic recovery after wind lodging?
4626 | Moulia
Concerning the shoot apex, mechanical aspects were shown
to be essential in the transformation of 2D patterns of diffusible hormones and transcription factors into complex and
dynamic 3D morphogenesis of bulges, hinges, and tubular
structures that finally shapes the different organs (leaves, stamens, etc.) and their phyllotactic pattern (Hamant and Traas,
2010; Mirabet et al., 2011). Mechanosensitive responses
of the cytoskeleton, cell-wall-remodelling enzymes, auxin
transporters, and gene expression were found to be involved
(Milani et al., 2013; Robinson et al., 2013). The complexity
of the structural, dynamic, and regulatory aspects required
deep interdisciplinary interactions fostering the establishment of large and highly interdisciplinary groups. At the
same time, there was a renewal of interest in growth mechanics as the interplay between plant hormones and the mechanical behaviour of cell walls turned out to be central (e.g. Band
et al., 2012; Kierzkowski et al., 2012; Peaucelle et al., 2012;
Braybrook and Peaucelle, 2013). More complex effects such
as growth anisotropy, intrusive growth, and root growth in
real soils were considered (Bengough et al., 2011; Baskin
and Jensen, 2013; Dumais, 2013; Nezhad and Geitmann,
2013; Jin et al., 2013). Similarly the study of the synthesis,
growth, remodelling, and differentiation of cell walls has
become decidedly interdisciplinary (Dumais, 2013; Burgert
and Keplinger, 2013, this issue).
Wind acclimation and plant recovery from growth and
wind-induced tilting (posture control) also involve a complex interaction between mechanical load distribution,
mechanosensing of local strain and gravity, and the development of integrative but differential growth responses (for
recent reviews, see Moulia and Fournier, 2009; Moulia et al.,
2011). Here again, a two-way interaction between load distribution and mechanotransduction was found, resulting in
a developmental loop throughout plant growth for which
both biomechanical and mechanobiological arguments had
to be invoked. Therefore, integrative interdisciplinary models
had to be developed, which needed the formation of large
interdisciplinary groups and collaborations. The field of sap
conduction (Cochard et al., 2013) and, more recently, that
of functional ecology (Read and Stokes, 2006; Onoda et al.,
2011; Fournier et al., 2013) are currently undergoing a similar
spurt in interdisciplinarity.
All this interdisciplinary cross-talk and networking of ideas
were consolidated by the explosion on to the scene, almost literally, of a new field, the physics of living systems, with some
major studies focused on plants. Starting with fast motions
and actuation that are mostly driven by pure physics (e.g.
Forterre et al., 2005), physicists soon started to tackle many
other botanical and physiological phenomena (e.g. Skotheim
and Mahadevan, 2005; de Langre, 2008; Burgert and Fratzl,
2009; Boudaoud, 2010; Bastien et al., 2013; Dumais, 2013;
Forterre, 2013).
At the same time, there have been extraordinary developments in techniques and tools. Methods to specify the
geometry of plant structures now range from atomic force
microscopy and nano- and microindentation (Peaucelle
et al., 2012; Routier-Kierzkowska et al., 2012) to synchrotron X-ray diffraction of cells (e.g. Clair et al., 2011; Eder
et al., 2013), and from 3D confocal microscopy (e.g. Hamant
et al., 2008) and 3D microcomputerized X-ray tomography
(e.g. Charra-Vaskou et al., 2012) to the digitization of entire
trees using magnetic digitizers (Rodriguez et al., 2008) and
LiDARs (Dassot et al., 2011). In parallel, kinematic live
imaging at the subcellular (e.g. Saito et al., 2005), cellular,
tissue, and organ levels (e.g. Forterre et al., 2005; Bastien
et al., 2013; Spalding and Miller, 2013) up to the whole
plant (Barbacci et al., 2013) and plant canopy (Py et al.,
2006) levels has made it possible to quantify growth rate
distribution, deformation modes, and movements as never
before. Methods to assess the spatial distribution of cellwall mechanical properties, especially using microindentation and atomic force microscopy, have been of great help
in probing both primary and secondary tissues (for recent
reviews, see Eder et al., 2013; Milani et al., 2013, this issue;
Routier-Kierzkowska and Smith, 2013).
Finally, methods of integrative* biomechanical modelling*
were found to be necessary to: (i) extract relevant parameters
from complex experiments (e.g. Milani et al., 2013); (ii) integrate behaviours between scales (e.g. Boudaoud, 2010; Band
et al., 2012); and (iii) experimentally assess novel mechanobiological hypotheses in complex biological systems in which
falsifiable predictions can no longer be handled by simple
deduction (e.g. Hamant et al., 2008; Moulia et al., 2011;
Bastien et al., 2013). All these methods include a lot of biomechanics, and turn out to be instrumental in the development of a system mechanobiology.
It is thus becoming clear that biomechanics and mechanobiology are converging aspects of the same interdisciplinary
field and in many cases are fully coupled. Plant biomechanics is instrumental in shedding light on how mechanical load
is distributed over organs, tissues, cells, organelles, and ultimately macromolecules, so is very important for mechanobiology. And conversely, mechanobiology gives insights into
how the biomechanical properties of cell walls, cells, tissues,
and organs are built in response to the mechanosensitive
history of the plant along its morphogenesis and growth
(Moulia et al., 2011; Hamant, 2013). The apparently mirrorimage names ‘biomechanics’ and ‘mechanobiology’ are complementary perspectives of the system of responses of plants
to mechanical loads and cues. This synergy is being enhanced
by the sharing of concepts and definitions, as well as a crossknowledge on the overall history and recent breakthroughs
in the field.
A special issue to discover recent
breakthroughs in plant biomechanics and
mechanobiology
Plant biomechanics and mechanobiology research is flourishing such that it can barely be summarized in an introductory
review. The purpose of this special issue is to give an updated,
broad, and critical review of many of the recent and exciting
developments in the field, and to illustrate how these interdisciplinary approaches provide new insights into major issues
in plant sciences. I would like now to highlight some of the
Biomechanics and mechanobiology | 4627
recent breakthroughs that are covered in the reviews commissioned for this issue. I will emphasize both the different fields
of plant sciences relating to these studies and the extensive
cross-talk between them. I will also take: (i) a knowledgebased point of view, pointing at some of the insights gathered
in recent years of different biological functions and at different scales, and (ii) a methodological point of view, discussing
how biomechanics and mechanobiology may contribute to a
novel approach to experimental botany. Please note that to
limit the number of references, I will mostly refer to relevant
reviews in this issue (or eventually elsewhere) to redirect the
reader to more in depth coverage and the original citations.
Scaling plant structure and function
The mechanics of cell walls at nano- and microscopic scales
are reviewed by Burgert and Keplinger (2013). Both primary
and secondary walls are analysed together, emphasizing
the common principles in cell-wall assembly and the resulting structure–function relationships. Diverse functions and
structures in different cell types or over the development of
a single cell are considered. The authors analyse, for example, how the distribution of cellulose microfibril angles is central in determining the stiffness and mechanical stability of
cell-wall layers and hence cells (see also Baskin and Jensen,
2013). They show how in situ methods in which mechanical
loading is combined with simultaneous imaging of nano- and
microstructural deformation in genetically distinct plants
(mutants) has made it possible to distinguish between classes
of hemicelluloses in terms of how they interact with cellulose
microfibrils or lignins. Hence, their distinct functions in cellwall rheology, and eventually growth, have been discovered.
The rheological and biological independence of stiffness and
strength is also demonstrated by mechanical analysis of pectin and xyloglucan mutants. The role of pectin sol–gel alteration through methyl esterification is explained, as well as the
possible mechanosensitive feedback on cell-wall assembly
during cell-wall growth and differentiation (see also Robinson
et al., 2013).
Exciting progress in the physiology and genetics of plant
mechanosensing and cell-wall integrity monitoring are
reviewed by Monshausen and Haswell (2013). They especially
focus on novel findings about mechanoreceptors, such as the
mechanosensitive ion channels (MSL, MCA, and PIEZO)
and the receptor-like kinases (WAK family, and CrRLK1L
family including THESEUS and FERONIA), and how the
second-messenger Ca2+ operates at the crossroads of many
of these mechanical signal transduction paths. They show
how structural mechanical changes in the conformation of
the mechanoreceptors can be transduced into ionic currents,
and that (tissue-level) tensile strain appears to be much more
effective than compressive strain. They also explain some of
the genetic and physiological control over these steps. Besides
Ca2+ signalling and its direct action on Ca2+–pectate crossbridging and hence rheological changes in the cell wall, Ca2+dependent pH signalling in conjunction with production of
reactive oxygen species is involved in thigmomorphogenetic
responses, possibly through pH-dependent cell-wall loosening
and oxidative cross-linking of cell-wall components. The
model of action of hormones, including ethylene, brassinosteroids, auxin, and abscisic acid, in the thigmomorphogenetic
syndrome has been adjusted to accommodate the finding that
jasmonic acid can respond incredibly rapidly to mechanical
stimulation (a >10-fold increase in jasmonic acid level within
60 s) and jasmonic acid mutants mimic many thigmomorphogenetic responses (see also Robinson et al., 2013, on this
topic).
The central processes of ‘growth and form’ have always
been paramount in research and they are now being analysed
in terms of their biomechanics and mechanobiology, as demonstrated in several reviews. Standing on d’Arcy Thompson’s
shoulders by picturing the walled cell as a diagram of forces
in equilibrium, Dumais (2013) presents a very novel but comprehensive view of the five different modes of deformation of
walled cells, from the inextensional shear of euglenoid algae
to the chemorheology of plant cell growth. He also shows
how rheological analysis is shedding new light on the longlasting discussion of the possible mechanisms of plant cell
growth including intussuception, viscoplastic behaviour, and
(physiologically tuned) chemorheology.
Also at the cell level, Nezhad and Geitmann (2013) analyse intrusive growth, a very specific but important aspect of
cell growth, either by plant cells themselves or by intruders
such as fungi or even non-walled cells. The different sources
of invasive force (cytoskeletal forces and hydrostatic pressure)
are discussed in relation to cell types and the function of invasion. The physics of invasion also shows how the hardness
and toughness* of the invaded tissues are crucial. We arrive
rapidly, however, at the limit of our knowledge of the fracture mechanics of soft and cellular materials* such as plant
tissues.
The crucial issue of growth anisotropy for stem growth and
morphogenesis is then revisited by Baskin and Jensen (2013),
who reinterpret a set of important but neglected experiments
and discuss stress distribution and growth in organs, integrating from the cell to the whole-organ level. It is argued that the
anisotropy of autostressing at the organ scale, and not the
anisotropy of cell-wall compliance at the cell scale, is likely
to be central in explaining directional growth. Another longstanding debate about the control of organ growth, namely
the relative contributions of wall extension and water influxes
is receiving a new formal statement by Forterre (2013), by
considering the limitation of growth velocity due to the
poroviscoelastic behaviour of water flow across tissues.
Going underground, Jin et al. (2013) dive into the hidden
but coupled mechanics, hydraulics, and mechanosensitivity
of root growth in real soils, and the implications for crops.
Roots provide another example of intrusive anisotropic
growth into a complex and heterogeneous granular medium,
the soil. To grow in soil, roots need to simultaneously overcome soil friction and to penetrate soil aggregates or negotiate existing cracks. This requires an inflow of water from
the soil, not only to power growth and exert axial pressure
on the soil at the root tip but also to maintain the bending
stiffness of the root to limit possible buckling instability*
when penetrating a new soil aggregate after a crack. Studies
4628 | Moulia
of soil structure and mechanics show how the soil strength
and water conductivity are dynamic properties changing
over time and space due to weather, farming, and biological
activities (including root penetration itself). These changes
feed back biomechanically on root growth. In particular,
moderate drying limits root growth via changes in soil resistance rather than through hydraulic effects (another instance
of the issue of mechanical versus hydraulic constraints on
growth). Additionally, the resulting deformation is likely to
be sensed by the roots and to trigger root-to-shoot signalling, allowing the plant to anticipate the onset of real water
stress. The different mechanobiological mechanisms involved
in the penetration of heterogeneous soils by roots (such as
gravitropism), as well as the use of quantitative genetics and
genomics to challenge our models and/or to select crops
with more efficient rooting in non-irrigated farming, are also
discussed.
Besides growth itself and its anisotropy, our understanding
of plant morphogenesis is being remarkably reshaped by biomechanical and mechanobiological insights. First is the practical challenge of performing mechanical experiments on tiny
and fragile plant meristems, and methodological achievements
are critically reviewed by Milani et al. (2013) (see also below
and Burgert and Keplinger, 2013). Robinson et al. (2013)1 then
present far-reaching insights into the shoot apical meristem,
showing how coupling of biomechanical, mechanobiological, and hormonal processes is needed to initiate and control
changes in 3D morphology. The disentangling of the spatiotemporal interplay between auxin transport and mechanical signals to drive the emergence of new primordial at the
shoot apical meristem is currently a focal point of research.
Auxin induces the expression or activity of cell-wall remodelling proteins such as expansins and pectin methylesterases
that dramatically modify the cell-wall rheology of specific
shoot apical meristem layers, especially their elastic compliance and whether or not they may display strain stiffening.
But neither auxin nor pectin demethylesterification alone is
sufficient for organ induction. This is pointing towards a likely
feedback relationship between the mechanical modification of
the cell wall and the auxin-mediated developmental patterning. Indeed, mechanical signals were shown to be involved in
controlling the amount and polarity of the distribution of the
auxin active transporter PIN1 (possibly though Ca2+ signalling that controls the PINOID protein via the calcium-binding
protein TOUCH3). Mechanical signals are also independently
involved in the alignments of microtubules and control of the
orientation of cell division planes, reinforcing the boundaries
between different organs, and hence the salient traits of shoot
1 This paper on the biomechanics and mechanobiology of the shoot
apical meristem is a unique case in this special issue in that it has
been handed over to an outstanding interdisciplinary set of ‘junior’
researchers, from physicists to molecular biologists. Indeed, this novel
approach to a perennial topic in botany is attracting many brilliant junior
researchers. As recent reviews by authoritative groups of researchers
were available (e.g. Hamant and Traas, 2010; Mirabet et al., 2011;
Peaucelle et al., 2012), we thought we should seek a different and
thought-provoking point of view that reflects this vibrancy.
morphogenesis. A positive-feedback loop involving mechanosensing and microtubule dynamics via KATANIN was also
shown to increase the growth heterogeneity necessary for
organogenesis. Moreover, mechanical cues were shown to be
involved throughout the development of young leaves in buds,
so that growth inhibition by contact together with the folding
pattern can fully determine the final shape of the leaf, as for
example in palmate leaves.
Moving on, the physical limits of motion powered by
growth and by reversible pressure changes are then analysed
by Forterre (2013). He contrasts the mechanics of slow versus
rapid motions in plants, highlighting the relevance of recent
physics research on poroelasticity and mechanical instabilities*. He also gives a comprehensive overview of the elegant
mechanisms that some plants have evolved to amplify the
speed and power of motion needed for propagule dispersal or
catching insects. The principle is to impose an ‘energy barrier’
to the system, which can originate from structural mechanics* or from material strength*, allowing elastic potential
energy to be stored. At some point, an instability* is reached,
the barrier is overcome, and all the stored potential energy
is transformed into kinetic energy. The different naturally
selected ‘mechanical designs’ for such mechanisms are then
analysed mechanically, as well as the timescales of movement
compared with the timescales of physiological processes at
the cellular and molecular level.
At even larger scales of integration, biomechanical and
mechanobiological analyses can be applied directly to functional ecology. Cochard et al. (2013) analyse the vulnerability of xylem sap flow to cavitation along its route from the
roots in the soil to leaves held aloft in the atmosphere. They
highlight the methodological challenges, pitfalls, and controversies entailed and the ecological significance for drought
survival. A crucial question today is whether cavitation
and embolism are an everyday occurrence for plants, even
under well-watered conditions, countered every night by an
unknown refilling process, or whether cavitation catastrophes
only develop when the xylem tension drops below a threshold
during periods of significant drought. The physiological and
ecological significance of cavitation and the focusing of new
research depend dramatically on the response to this question,
which will come mostly from understanding the advanced
mechanics and physics of this very sensitive instability.
Integrating information from cell walls on up to plant
populations in temperate and rain forests, Fournier et al.
(2013) explain how integrative mechanical traits associated
with wind or buckling safety, reaction wood, and active
posture control are all relevant for functional tree ecology.
The change in scale is shown to be a crucial issue, from the
mechanical and physical properties of wood to real tree-level
traits, combining tree size, shape, and relative position in the
canopy with wood properties. This can be achieved using a
combination of integrative and phenomenological modelling to define ‘hard’ and robust traits that can still be used
to analyse natural variability among plant communities. This
directly feeds into current debate in the ecological community
around the use of wood basic density as a proxy for safety.
It is shown that this neglects other important biomechanical
Biomechanics and mechanobiology | 4629
functions of wood such as its contribution to powering active
tree movement and posture control.
Finally, Niklas (2013) gives a broad perspective of the significance of biomechanical and biophysical traits in the macroevolution of green plants. The central idea is that we may
‘view organic evolution as an extended “experiment” in how
organisms respond to and cope with the laws governing chemical and physical phenomena’. This is tempered, however, with
the recognition that evolution is also the result of historical
accidents and extinctions, thus avoiding the adaptionist view
often taken by newcomers to biology, especially those from
physics or engineering, that any life form might be expected to
display optimal functionality (see also Moulia and Fournier,
1997). In separating historical legacy from true selective pressure, a crucial point is that the effects of physical (especially
mechanical) laws and processes are size dependent. As there
have been numerous changes in plant size through the ages,
scaling relationships may be very informative in studying the
mechanisms and possible trade-offs driving heterologous
organisms to converge at a certain scale. By the same token,
this may also help in testing the ‘universality’ of some of the
rules that have been established for extant plants, and can be
applied to major evolutionary transitions such as the convergent transition from unicellular to multicellular body plans,
or the evolution of secondary growth with the independent
acquisition of cambia by different trees. Interestingly, one of
the physical constraints over multicellular growth of walled
cells is the way anisotropic growth and differential asymmetric cell division are biophysically controlled through a possible microtubule force-sensing system bringing shear stress
minimization. Discussion of how this may have evolved from
a unicellular background feeds back directly on the reviews
by Dumais (2013), Monshausen and Haswell (2013), Baskin
and Jensen (2013), and Robinson et al. (2013). The acquisition of real primary xylem and, later on, of cambial growth
set two other biomechanical constraints in the context of
the evolution of land plant height: limitations on the vertical transport of water and on the mechanical stability of
the stem relative to its cross-sectional area. These topics link
up with the reviews by Cochard et al. (2013) and Fournier
et al. (2013). And, just as stated by Monshausen and Haswell
(2013) and Fournier et al. (2013), it is argued that the evolution of mechanosensitive control over primary and secondary growth (thigmomorphogenesis*) in shoots and roots has
been essential in the adaptation of plants to the variety and
heterogeneity of wind exposure and soil conditions.
A new experimental method for plant sciences
At the frontiers of science, methodological advances are crucial. This often involves refining or inventing new measuring
techniques, and three reviews primarily address these questions. Burgert and Keplinger (2013) detail progress in microand nanoscale measurement of properties of both primary
and secondary cell walls. Milani et al. (2013) cautiously analyse the strengths and limitations of micro- and nanoindentation techniques and related mechanical imaging (atomic,
molecule, and cellular force microscopy) for the measurement
and spatial mapping of both cell-wall rheology and turgor
pressure in meristematic zones. Finally, Cochard et al. (2013)
provide a critical review of different methods used to assess
the vulnerability of xylem to cavitation and embolism and
the current controversy over the sigmoidal versus exponential
hydraulic vulnerability curves and the contrasting ecological conclusions that ensue. Note that, beyond these targeted
methodological reviews, methodological discussion abounds
in this special issue. For example, how much relevant information on medium penetration can be gathered using penetrometry is discussed by Jin et al. (2013) in the context of root
growth in heterogeneous soils, and by Nezhad and Geitmann
(2013) for intrusive growth into plant tissues.
Methodology is not limited to experiments, as it also relates
to modelling. Milani et al. (2013) demonstrate how crucial
integrative mechanical modelling* is in extracting meaningful
mechanical properties from indentation experiments to understand morphogenesis. Fournier et al. (2013) demonstrate how
structural analysis and integrative modelling are central tools
for characterizing ecological functional traits of tree communities. Between the two at the organism level, Baskin and
Jensen (2013), Robinson et al. (2013), and Forterre (2013)
illustrate how integrative modelling* is necessary when investigating the control of directional organ growth, morphogenesis at the shoot apex, the limits of turgor-powered motion
and the mechanisms of rapid motion. Dumais (2013) also
illustrates how rheological phenomenological* modelling can
give insights into the mechanisms of wall growth. In these
examples, modelling in biomechanics and mechanobiology
has become an extension of the ‘hypothesis-driven’ experimental method in cases where the predicted consequences of
the hypothesis can no longer be handled by simple discursive
logic due to the interplay of mechanical and biological aspects
(see also Moulia et al., 2011; Robinson et al., 2013). Only a
model can make biomechanically consistent predictions for
a given hypothesis that can be assessed experimentally. Such
a model-assisted experimental method is particularly suited
to providing plant sciences with a way to deal with size effects
and changes in scales in time and space (Baskin and Jensen,
2013; Forterre, 2013; Fournier et al., 2013; Niklas, 2013), and
this is probably one of the major contributions of plant biomechanics and mechanobiology to plant sciences.
Conclusion
This introductory review began with a quote from Paul
Valéry, a French poet who showed an observant interest in
plant form. I chose it to emphasize the wealth of knowledge
and scientific reward of working in a large interdisciplinary
realm like plant biomechanics and mechanobiology. However,
the quote could equally apply to this review. There is much
more to garner from this special issue than I could possibly
highlight here with my ‘sole point of view’. My purpose was to
provide readers with some background and a global perspective on plant biomechanics and mechanobiology. Rather than
distinct topics, it is useful to consider the reviews that follow
as a network of different perspectives. Whatever your main
4630 | Moulia
research interest, you are likely to find elements related to it in
several reviews. The panorama is incredibly rich and dynamic.
Please enjoy!
Acknowledgements
The author expresses his gratitude to Bernard Thibaut, HannsCristoph Spatz, George Jeronimidis, Thomas Speck, Meriem
Fournier, and Frank Telewski for their commitment to establishing a plant biomechanics and mechanobiology community,
to the contributors of this special issue, and to the participants
of the 7th Plant BioMechanics International Conference in
Clermont-Ferrand, France (2012), for inspiring presentations and discussions, to the JXB editorial board and editorial office for support in bringing together this special issue, to
Christine Girousse, Yoel Forterre, Olivier Pouliquen, Meriem
Fournier, and three anonymous referees for useful feedback
on the manuscript, and to Rachel Carol at Emendo Bioscience
(Boston, USA) for editing the English. This review is dedicated
to Wendy Silk (University of California, Davis, USA), who has
been so influential in building the bridge between growth studies and biomechanics and has been so supportive.
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