Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model

Structure and growth of plant cell walls

Plant cells build nanofibrillar walls that are central to plant growth, morphogenesis and mechanics. Starting from simple sugars, three groups of polysaccharides, namely, cellulose, hemicelluloses and pectins, with very different physical properties are assembled by the cell to make a strong yet extensible wall. This Review describes the physics of wall growth and its regulation by cellular processes such as cellulose production by cellulose synthase, modulation of wall pH by plasma membrane H+-ATPase, wall loosening by expansin and signalling by plant hormones such as auxin and brassinosteroid. In addition, this Review discusses the nuanced roles, properties and interactions of cellulose, matrix polysaccharides and cell wall proteins and describes how wall stress and wall loosening cooperatively result in cell wall growth.

Revisiting the relationship between turgor pressure and plant cell growth

Growth is central to plant morphogenesis. Plant cells are encased in rigid cell walls, and they must overcome physical confinement to grow to specific sizes and shapes. Cell wall tension and turgor pressure are the main mechanical components impacting plant cell growth. Cell wall mechanics has been the focus of most plant biomechanical studies, and turgor pressure was often considered as a constant and largely passive component. Nevertheless, it is increasingly accepted that turgor pressure plays a significant role in plant growth. Numerous theoretical and experimental studies suggest that turgor pressure can be both spatially inhomogeneous and actively modulated during morphogenesis. Here, we revisit the pressure-growth relationship by reviewing recent advances in investigating the interactions between cellular/tissular pressure and growth.

A dive into the cell wall with Arabidopsis

One of the many legacies of the work of Michel Caboche is our understanding of plant cell wall synthesis and metabolism thanks to the use of Arabidopsis mutants. Here I describe how he was instrumental in initiating the genetic study of plant cell walls. I also show, with a few examples for cellulose and pectins, how this approach has led to important new insights in cell wall synthesis and how the metabolism of pectins contributes to plant growth and morphogenesis. I also illustrate the limitations of the use of mutants to explain processes at the scale of cells, organs or whole plants in terms of the physico-chemical properties of cell wall polymers. Finally, I sketch how new approaches can cope with these limitations.

Building an extensible cell wall

This article recounts, from my perspective of four decades in this field, evolving paradigms of primary cell wall structure and the mechanism of surface enlargement of growing cell walls. Updates of the structures, physical interactions, and roles of cellulose, xyloglucan, and pectins are presented. This leads to an example of how a conceptual depiction of wall structure can be translated into an explicit quantitative model based on molecular dynamics methods. Comparison of the model's mechanical behavior with experimental results provides insights into the molecular basis of complex mechanical behaviors of primary cell wall and uncovers the dominant role of cellulose-cellulose interactions in forming a strong yet extensible network.

What shoots can teach about theories of plant form

Plants generate a large variety of shoot forms with regular geometries. These forms emerge primarily from the activity of a stem cell niche at the shoot tip. Recent efforts have established a theoretical framework of form emergence at the shoot tip, which has empowered the use of modelling in conjunction with biological approaches to begin to disentangle the biochemical and physical mechanisms controlling form development at the shoot tip. Here, we discuss how these advances get us closer to identifying the construction principles of plant shoot tips. Considering the current limits of our knowledge, we propose a roadmap for developing a general theory of form development at the shoot tip.

Microtubule-Mediated Wall Anisotropy Contributes to Leaf Blade Flattening

Plant organs can adopt a wide range of shapes, resulting from highly directional cell growth and divisions. We focus here on leaves and leaf-like organs in Arabidopsis and tomato, characterized by the formation of thin, flat laminae. Combining experimental approaches with 3D mechanical modeling, we provide evidence that leaf shape depends on cortical microtubule mediated cellulose deposition along the main predicted stress orientations, in particular, along the adaxial-abaxial axis in internal cell walls. This behavior can be explained by a mechanical feedback and has the potential to sustain and even amplify a preexisting degree of flatness, which in turn depends on genes involved in the control of organ polarity and leaf margin formation.

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Microtubules and cellulose microfibrils align along the ad-abaxial direction

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Microtubule-mediated cell growth anisotropy contributes to leaf flattening

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Mechanical feedback accounts for microtubule alignments in the ad-abaxial direction

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Final organ shape depends on the degree of initial asymmetry of primordia

Disentangling loosening from softening: insights into primary cell wall structure

How cell wall elasticity, plasticity, and time-dependent extension (creep) relate to one another, to plant cell wall structure and to cell growth remain unsettled topics. To examine these issues without the complexities of living tissues, we treated cell-free strips of onion epidermal walls with various enzymes and other agents to assess which polysaccharides bear mechanical forces in-plane and out-of-plane of the cell wall. This information is critical for integrating concepts of wall structure, wall material properties, tissue mechanics and mechanisms of cell growth. With atomic force microscopy we also monitored real-time changes in the wall surface during treatments. Driselase, a potent cocktail of wall-degrading enzymes, removed cellulose microfibrils in superficial lamellae sequentially, layer-by-layer, and softened the wall (reduced its mechanical stiffness), yet did not induce wall loosening (creep). In contrast Cel12A, a bifunctional xyloglucanase/cellulase, induced creep with only subtle changes in wall appearance. Both Driselase and Cel12A increased the tensile compliance, but differently for elastic and plastic components. Homogalacturonan solubilization by pectate lyase and calcium chelation greatly increased the indentation compliance without changing tensile compliances. Acidic buffer induced rapid cell wall creep via endogenous α-expansins, with negligible effects on wall compliances. We conclude that these various wall properties are not tightly coupled and therefore reflect distinctive aspects of wall structure. Cross-lamellate networks of cellulose microfibrils influenced creep and tensile stiffness whereas homogalacturonan influenced indentation mechanics. This information is crucial for constructing realistic molecular models that define how wall mechanics and growth depend on primary cell wall structure.

Feedback from Tissue Mechanics Self-Organizes Efficient Outgrowth of Plant Organ

Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions during outgrowth is still puzzling, especially when cells are tightly connected as in plant tissue. In plants, the mechanics of cells within a tissue is particularly well-defined because individual cell growth is essentially the mechanical yielding of the cell wall in response to internal turgor pressure. Cell-wall stiffness is controlled by biological signaling, which is impacted by stresses, and hence, cell growth is observed to respond to mechanical stresses building up within a tissue. What is the role of the mechanical feedback during morphing of tissue in three dimensions? Here, we develop a three-dimensional vertex model to investigate tissue mechanics at the onset of organ outgrowth at the tip of a plant shoot. We find that organ height is primarily governed by the ratio of growth rates of faster-growing cells initiating the organ versus slower-growing cells surrounding them. Remarkably, the outgrowth rate is higher when cell growth responds to the tissue-wide mechanical stresses. Our quantitative analysis of simulation data shows that tissue mechanical feedback on cell growth can act via a twofold mechanism. First, the feedback guides patterns of cellular growth. Second, the feedback modifies the stress patterns on the cells, consequently amplifying and propagating growth anisotropies. This mechanism may allow plants to grow organs efficiently out of the meristem by reorganizing the cellular growth rather than inflating growth rates.

Discrete mechanical growth model for plant tissue

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall’s microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke’s law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.

How water flow, geometry, and material properties drive plant movements

Plants are dynamic. They adjust their shape for feeding, defence, and reproduction. Such plant movements are critical for their survival. We present selected examples covering a range of movements from single cell to tissue level and over a range of time scales. We focus on reversible turgor-driven shape changes. Recent insights into the mechanisms of stomata, bladderwort, the waterwheel, and the Venus flytrap are presented. The underlying physical principles (turgor, osmosis, membrane permeability, wall stress, snap buckling, and elastic instability) are highlighted, and advances in our understanding of these processes are summarized.

MorphoNet: an interactive online morphological browser to explore complex multi-scale data

Powerful novel imaging and image-processing methods are revolutionizing many fields of biology, at scales ranging from the molecule to the functional organ. To support this big-data revolution, we develop a concept of generic web-based morphodynamic browser to interactively visualize complex image datasets, with applications in research and education. MorphoNet handles a broad range of natural or simulated morphological data, onto which quantitative geometric or genetic data can be projected.

Most morphological visualization platforms are not designed to share research data, or are limited to data visualization. Here the authors present MorphoNet, an open-source, web-based tool for interactive visualization and sharing of complex morphodynamic datasets, onto which users can project their own data.