Compression of a pressurized spherical shell by a spherical or flat probe.

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere or compression between two plates. Different theoretical approaches have been developed to retrieve material parameters (e.g., elastic modulus) or state variables (e.g., pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

Systematic mapping of cell wall mechanics in the regulation of cell morphogenesis.

Walled cells of plants, fungi, and bacteria come with a large range of shapes and sizes, which are ultimately dictated by the mechanics of their cell wall. This stiff and thin polymeric layer encases the plasma membrane and protects the cells mechanically by opposing large turgor pressure derived mechanical stresses. To date, however, we still lack a quantitative understanding for how local and/or global mechanical properties of the wall support cell morphogenesis. Here, we combine subresolution imaging and laser-mediated wall relaxation to quantitate subcellular values of wall thickness (h) and bulk elastic moduli (Y) in large populations of live mutant cells and in conditions affecting cell diameter in the rod-shaped model fission yeast. We find that lateral wall stiffness, defined by the surface modulus, σ = hY, robustly scales with cell diameter. This scaling is valid across tens of mutants spanning various functions-within the population of individual isogenic strains, along single misshaped cells, and even across the fission yeasts clade. Dynamic modulations of cell diameter by chemical and/or mechanical means suggest that the cell wall can rapidly adapt its surface mechanics, rendering stretched wall portions stiffer than unstretched ones. Size-dependent wall stiffening constrains diameter definition and limits size variations; it may also provide an efficient means to keep elastic strains in the wall below failure strains, potentially promoting cell survival. This quantitative set of data impacts our current understanding of the mechanics of cell walls and its contribution to morphogenesis.

Mechanical control of morphogenesis at the shoot apex.

Morphogenesis does not just require the correct expression of patterning genes; these genes must induce the precise mechanical changes necessary to produce a new form. Mechanical characterization of plant growth is not new; however, in recent years, new technologies and interdisciplinary collaborations have made it feasible in young tissues such as the shoot apex. Analysis of tissues where active growth and developmental patterning are taking place has revealed biologically significant variability in mechanical properties and has even suggested that mechanical changes in the tissue can feed back to direct morphogenesis. Here, an overview is given of the current understanding of the mechanical dynamics and its influence on cellular and developmental processes in the shoot apex. We are only starting to uncover the mechanical basis of morphogenesis, and many exciting questions remain to be answered.

Abaxial growth and steric constraints guide leaf folding and shape in Acer pseudoplatanus.

PREMISE OF THE STUDY: How leaf shape is regulated is a long-standing question in botany. For diverse groups of dicotyledon species, lamina folding along the veins and geometry of the space available for the primordia can explain the palmate leaf morphology. Dubbed the kirigami theory, this hypothesis of fold-dependent leaf shape regulation has remained largely theoretical. Using Acer pseudoplatanus, we investigated the mechanisms behind the two key processes of kirigami leaf development. METHODS: Cytological examination and quantitative analyses were used to examine the course of the vein-dependent lamina folding. Surgical ablation and tissue culturing were employed to test the effects of physical constraints on primordia growth. The final morphology of leaves growing without steric constraints were predicted mathematically. KEY RESULTS: The cytological examination showed that the lamina's abaxial side along the veins grows substantially more than the adaxial side. The abaxial hypergrowth along the veins and the lamina extension correlated with the lamina folding. When a primordium was released from the physical constraints imposed by the other primordia, it rapidly grew into the newly available space, while maintaining the curvature inward. The morphology of such a leaf was predicted to lack symmetry in the lobe shapes. CONCLUSIONS: The enhanced growth on the abaxial side of the lamina along the veins is likely to drive lamina folding. The surgical ablation provided clear support for the space-filling nature of leaf growth; thus, steric constraints play a role in determination of the shapes of folded leaves and probably also of the final leaf morphology.

Plant root growth against a mechanical obstacle: the early growth response of a maize root facing an axial resistance is consistent with the Lockhart model.

Plant root growth is dramatically reduced in compacted soils, affecting the growth of the whole plant. Through a model experiment coupling force and kinematics measurements, we probed the force-growth relationship of a primary root contacting a stiff resisting obstacle, which mimics the strongest soil impedance variation encountered by a growing root. The growth of maize roots just emerging from a corseting agarose gel and contacting a force sensor (acting as an obstacle) was monitored by time-lapse imaging simultaneously to the force. The evolution of the velocity field along the root was obtained from kinematics analysis of the root texture with a particle image velocimetry derived technique. A triangular fit was introduced to retrieve the elemental elongation rate or strain rate. A parameter-free model based on the Lockhart law quantitatively predicts how the force at the obstacle modifies several features of the growth distribution (length of the growth zone, maximal elemental elongation rate and velocity) during the first 10 min. These results suggest a strong similarity of the early growth responses elicited either by a directional stress (contact) or by an isotropic perturbation (hyperosmotic bath).

The filling law: a general framework for leaf folding and its consequences on leaf shape diversity.

Leaves are packed in a bud in different ways, being flat, rolled, or folded, but always filling the whole bud volume. This "filling law" has many consequences, in particular on the shapes of growing folded leaves. This is shown here for different types of folding and packing. The folded volume is roughly a part of an ellipsoid, with the veins on the outside rounded face and the lamina margin on the adaxial plane. The veins on the abaxial side protect the fragile lamina inside. The first general consequence of the folds and the space limitation of the lamina growth is the presence of symmetries on the leaf shape, and the second is the quantitative relationships between the sizes of the lobes and sinuses. For particular geometries, the leaf lamina can be limited by lateral veins, creating spoon-like lobes, or tangent cuts, creating asymmetrical wavy perimeters. Changes in the packing between different cultivars correspond to changes in the mature leaf shapes. Each particular case shows how pervasive the geometrical consequences of the filling law are.

Fluttering of growing leaves as a way to reach flatness: experimental evidence on Persea americana.

Simple leaves show unexpected growth motions: the midrib of the leaves swings periodically in association with buckling events of the leaf blade, giving the impression that the leaves are fluttering. The quantitative kinematic analysis of this motion provides information about the respective growth between the main vein and the lamina. Our three-dimensional reconstruction of an avocado tree leaf shows that the conductor of the motion is the midrib, presenting continuous oscillations and inducing buckling events on the blade. The variations in the folding angle of the leaf show that the lamina is not passive: it responds to the deformation induced by the connection to the midrib to reach a globally flat state. We model this movement as an asymmetric growth of the midrib, which directs an inhomogeneous growth of the lamina, and we suggest how the transition from the folded state to the flat state is mechanically organized.

Mechanosensation Dynamically Coordinates Polar Growth and Cell Wall Assembly to Promote Cell Survival.

How growing cells cope with size expansion while ensuring mechanical integrity is not known. In walled cells, such as those of microbes and plants, growth and viability are both supported by a thin and rigid encasing cell wall (CW). We deciphered the dynamic mechanisms controlling wall surface assembly during cell growth, using a sub-resolution microscopy approach to monitor CW thickness in live rod-shaped fission yeast cells. We found that polar cell growth yielded wall thinning and that thickness negatively influenced growth. Thickness at growing tips exhibited a fluctuating behavior with thickening phases followed by thinning phases, indicative of a delayed feedback promoting thickness homeostasis. This feedback was mediated by mechanosensing through the CW integrity pathway, which probes strain in the wall to adjust synthase localization and activity to surface growth. Mutants defective in thickness homeostasis lysed by rupturing the wall, demonstrating its pivotal role for walled cell survival.

Folded isometric deformations and banana-shaped seedpod.

Thin vegetal shells have recently been a significant source of inspiration for the design of smart materials and soft actuators. Herein is presented a novel analytical family of isometric deformations with a family of θ-folds crossing a family of parallel z-folds; it contains the isometric deformations of a banana-shaped surface inspired by a seedpod, which converts a vertical closing into either an horizontal closing or an opening depending on the location of the fold. Similarly to the seedpod, optimum shapes for opening ease are the most elongated ones.

Wall mechanics and exocytosis define the shape of growth domains in fission yeast.

The amazing structural variety of cells is matched only by their functional diversity, and reflects the complex interplay between biochemical and mechanical regulation. How both regulatory layers generate specifically shaped cellular domains is not fully understood. Here, we report how cell growth domains are shaped in fission yeast. Based on quantitative analysis of cell wall expansion and elasticity, we develop a model for how mechanics and cell wall assembly interact and use it to look for factors underpinning growth domain morphogenesis. Surprisingly, we find that neither the global cell shape regulators Cdc42-Scd1-Scd2 nor the major cell wall synthesis regulators Bgs1-Bgs4-Rgf1 are reliable predictors of growth domain geometry. Instead, their geometry can be defined by cell wall mechanics and the cortical localization pattern of the exocytic factors Sec6-Syb1-Exo70. Forceful re-directioning of exocytic vesicle fusion to broader cortical areas induces proportional shape changes to growth domains, demonstrating that both features are causally linked.

A global regulation inducing the shape of growing folded leaves.

Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy Thomson [3], have developed theories where patterns arise spontaneously [4]. Here, we propose that volume constraints restrict the possible shapes of leaves. Focusing on palmate leaves (with lobes), the central observation is that developing leaves first grow folded inside a bud, limited by the previous and subsequent leaves. We show that the lobe perimeters end at the border of this small volume. This induces a direct relationship between the way it was folded and the final unfolded shape of the leaf. These dependencies can be approximated as simple geometrical relationships that we confirm on both folded embryonic and unfolded mature leaves. We find that independent of their position in the phylogenetic tree, these relationships work for folded species, but do not work for non-folded species. This global regulation for the leaf growth could come from a mechanical steric constraint. Such steric regulation should be more general and considered as a new simple means of global regulation.

The structure of gallery networks in the nests of termite Cubitermes spp. revealed by X-ray tomography.

Recent studies have introduced computer tomography (CT) as a tool for the visualisation and characterisation of insect architectures. Here, we use CT to map the three-dimensional networks of galleries inside Cubitermes nests in order to analyse them with tools from graph theory. The structure of these networks indicates that connections inside the nest are rearranged during the whole nest life. The functional analysis reveals that the final network topology represents an excellent compromise between efficient connectivity inside the nest and defence against attacking predators. We further discuss and illustrate the usefulness of CT to disentangle environmental and specific influences on nest architecture.

Replication-associated gene dosage effects shape the genomes of fast-growing bacteria but only for transcription and translation genes.

The bidirectional replication of bacterial genomes leads to transient gene dosage effects. Here, we show that such effects shape the chromosome organisation of fast-growing bacteria and that they correlate strongly with maximal growth rate. Surprisingly the predicted maximal number of replication rounds shows little if any phylogenetic inertia, suggesting that it is a very labile trait. Yet, a combination of theoretical and statistical analyses predicts that dozens of replication forks may be simultaneously present in the cells of certain species. This suggests a strikingly efficient management of the replication apparatus, of replication fork arrests and of chromosome segregation in such cells. Gene dosage effects strongly constrain the position of genes involved in translation and transcription, but not other highly expressed genes. The relative proximity of the former genes to the origin of replication follows the regulatory dependencies observed under exponential growth, as the bias is stronger for RNA polymerase, then rDNA, then ribosomal proteins and tDNA. Within tDNAs we find that only the positions of the previously proposed 'ubiquitous' tRNA, which translate the most frequent codons in highly expressed genes, show strong signs of selection for gene dosage effects. Finally, we provide evidence for selection acting upon genome organisation to take advantage of gene dosage effects by identifying a positive correlation between genome stability and the number of simultaneous replication rounds. We also show that gene dosage effects can explain the over-representation of highly expressed genes in the largest replichore of genomes containing more than one chromosome. Together, these results demonstrate that replication-associated gene dosage is an important determinant of chromosome organisation and dynamics, especially among fast-growing bacteria.