Chemically mediated mechanical expansion of the pollen tube cell wall

Morphogenesis of plant cells is tantamount to the shaping of the stiff cell wall that surrounds them. To this end, these cells integrate two concomitant processes: 1), deposition of new material into the existing wall, and 2), mechanical deformation of this material by the turgor pressure. However, due to uncertainty regarding the mechanisms that coordinate these processes, existing models typically adopt a limiting case in which either one or the other dictates morphogenesis. In this report, we formulate a simple mechanism in pollen tubes by which deposition causes turnover of cell wall cross-links, thereby facilitating mechanical deformation. Accordingly, deposition and mechanics are coupled and are both integral aspects of the morphogenetic process. Among the key experimental qualifications of this model are: its ability to precisely reproduce the morphologies of pollen tubes; its prediction of the growth oscillations exhibited by rapidly growing pollen tubes; and its prediction of the observed phase relationships between variables such as wall thickness, cell morphology, and growth rate within oscillatory cells. In short, the model captures the rich phenomenology of pollen tube morphogenesis and has implications for other plant cell types.     

Polar growth in pollen tubes is associated with spatially confined dynamic changes in cell mechanical properties

Cellular morphogenesis involves changes to cellular size and shape which in the case of walled cells implies the mechanical deformation of the extracellular matrix. So far, technical challenges have made quantitative mechanical measurements of this process at subcellular scale impossible. We used micro-indentation to investigate the dynamic changes in the cellular mechanical properties during the onset of spatially confined growth activities in plant cells. Pollen tubes are cellular protuberances that have a strictly unidirectional growth pattern. Micro-indentation of these cells revealed that the initial formation of a cylindrical protuberance is preceded by a local reduction in cellular stiffness. Similar cellular softening was observed before the onset of a rapid growth phase in cells with oscillating growth pattern. These findings provide the first quantitative cytomechanical data that confirm the important role of the mechanical properties of the cell wall for local cellular growth processes. They are consistent with a conceptual model that explains pollen tube oscillatory growth based on the relationship between turgor pressure and tensile resistance in the apical cell wall. To further confirm the significance of cell mechanics, we artificially manipulated the mechanical cell wall properties as well as the turgor pressure. We observed that these changes affected the oscillation profile and were able to induce oscillatory behavior in steadily growing tubes.     

In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy

Whereas the morphogenesis of developing organisms is relatively well understood at the molecular level, the contribution of the mechanical properties of the cells to shape changes remains largely unknown, mainly because of the lack of quantified biophysical parameters at cellular or subcellular resolution. Here we designed an atomic force microscopy approach to investigate the elastic modulus of the outer cell wall in living shoot apical meristems (SAMs). SAMs are highly organized structures that contain the plant stem cells, and generate all of the aerial organs of the plant. Building on modeling and experimental data, we designed a protocol that is able to measure very local properties, i.e. within 40-100 nm deep into the wall of living meristematic cells. We identified three levels of complexity at the meristem surface, with significant heterogeneity in stiffness at regional, cellular and even subcellular levels. Strikingly, we found that the outer cell wall was much stiffer at the tip of the meristem (5 ± 2 MPa on average), covering the stem cell pool, than on the flanks of the meristem (1.5 ± 0.7 MPa on average). Altogether, these results demonstrate the existence of a multiscale spatialization of the mechanical properties of the meristem surface, in addition to the previously established molecular and cytological zonation of the SAM, correlating with regional growth rate distribution.     

Mechanical Control of Bacterial Cell Shape

In bacteria, cytoskeletal filament bundles such as MreB control the cell morphology and determine whether the cell takes on a spherical or a rod-like shape. Here we use a theoretical model to describe the interplay of cell wall growth, mechanics, and cytoskeletal filaments in shaping the bacterial cell. We predict that growing cells without MreB exhibit an instability that favors rounded cells. MreB can mechanically reinforce the cell wall and prevent the onset of instability. We propose that the overall bacterial shape is determined by a dynamic turnover of cell wall material that is controlled by mechanical stresses in the wall. The model affirms that morphological transformations with and without MreB are reversible, and quantitatively describes the growth of irregular shapes and cells undergoing division. The theory also suggests a unique coupling between mechanics and chemistry that can control organismal shapes in general.     

A Computational Framework for 3D Mechanical Modeling of Plant Morphogenesis with Cellular Resolution

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.     

The problem of morphogenesis: unscripted biophysical control systems in plants

The relative simplicity of plant developmental systems, having evolved within the universal constraints imposed by the plant cell wall, may allow us to outline a consistent developmental narrative that is not currently possible in the animal kingdom. In this article, I discuss three aspects of the development of the mature form in plants, approaching them in terms of the role played by the biophysics and mechanics of the cell wall during growth. First, I discuss axis extension in terms of a loss of stability-based model of cell wall stress relaxation and I introduce the possibility that cell wall stress relaxation can be modeled as a binary switch. Second, I consider meristem shape and surface conformation as a controlling element in the morphogenetic circuitry of plant organogenesis at the apex. Third, I approach the issue of reproductive differentiation and propose that the multicellular sporangium, a universal feature of land plants, acts as a stress–mechanical lens, focusing growth-induced stresses to create a geometrically precise mechanical singularity that can serve as an inducing developmental signal triggering the initiation of reproductive differentiation. Lastly, I offer these three examples of biophysically integrated control processes as entry points into a narrative that provides an independent, nongenetic context for understanding the evolution of the apoplast and the morphogenetic ontogeny of multicellular land plants.     

Coupling mechanical deformations and planar cell polarity to create regular patterns in the zebrafish retina

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish lrp2 mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis.     

Cellular force microscopy for in vivo measurements of plant tissue mechanics

Although growth and morphogenesis are controlled by genetics, physical shape change in plant tissue results from a balance between cell wall loosening and intracellular pressure. Despite recent work demonstrating a role for mechanical signals in morphogenesis, precise measurement of mechanical properties at the individual cell level remains a technical challenge. To address this challenge, we have developed cellular force microscopy (CFM), which combines the versatility of classical microindentation techniques with the high automation and resolution approaching that of atomic force microscopy. CFM's large range of forces provides the possibility to map the apparent stiffness of both plasmolyzed and turgid tissue as well as to perform micropuncture of cells using very high stresses. CFM experiments reveal that, within a tissue, local stiffness measurements can vary with the level of turgor pressure in an unexpected way. Altogether, our results highlight the importance of detailed physically based simulations for the interpretation of microindentation results. CFM's ability to be used both to assess and manipulate tissue mechanics makes it a method of choice to unravel the feedbacks between mechanics, genetics, and morphogenesis.     

A computational approach for inferring the cell wall properties that govern guard cell dynamics

Guard cells dynamically adjust their shape in order to regulate photosynthetic gas exchange, respiration rates and defend against pathogen entry. Cell shape changes are determined by the interplay of cell wall material properties and turgor pressure. To investigate this relationship between turgor pressure, cell wall properties and cell shape, we focused on kidney‐shaped stomata and developed a biomechanical model of a guard cell pair. Treating the cell wall as a composite of the pectin‐rich cell wall matrix embedded with cellulose microfibrils, we show that strong, circumferentially oriented fibres are critical for opening. We find that the opening dynamics are dictated by the mechanical stress response of the cell wall matrix, and as the turgor rises, the pectinaceous matrix stiffens. We validate these predictions with stomatal opening experiments in selected Arabidopsis cell wall mutants. Thus, using a computational framework that combines a 3D biomechanical model with parameter optimization, we demonstrate how to exploit subtle shape changes to infer cell wall material properties. Our findings reveal that proper stomatal dynamics are built on two key properties of the cell wall, namely anisotropy in the form of hoop reinforcement and strain stiffening.     

Persistent Symmetry Frustration in Pollen Tubes

Pollen tubes are extremely rapidly growing plant cells whose morphogenesis is determined by spatial gradients in the biochemical composition of the cell wall. We investigate the hypothesis (MP) that the distribution of the local mechanical properties of the wall, corresponding to the change of the radial symmetry along the axial direction, may lead to growth oscillations in pollen tubes. We claim that the experimentally observed oscillations originate from the symmetry change at the transition zone, where both intervening symmetries (cylindrical and spherical) meet. The characteristic oscillations between resonating symmetries at a given (constant) turgor pressure and a gradient of wall material constants may be identified with the observed growth-cycles in pollen tubes.     

Mechanical Response of Single Plant Cells to Cell Poking： A Numerical Simulation Model

Cell poking is an experimental technique that is widely used to study the mechanical properties of plant cells. A full understanding of the mechanical responses of plant cells to poking force Is helpful for experimental work. The aim of this study was to numerically investigate the stress distribution of the cell wall, cell turgor, and deformation of plant cells in response to applied poking force. Furthermore, the locations damaged during poking were analyzed. The model simulates cell poking, with the cell treated as a spherical, homogeneous, isotropic elastic membrane, filled with incompressible, highly viscous liquid. Equilibrium equations for the contact region and the non-contact regions were determined by using membrane theory. The boundary conditions and continuity conditions for the solution of the problem were found. The forcedeformation curve, turgor pressure and tension of the cell wall under cell poking conditions were obtained. The tension of the cell wall circumference was larger than that of the meridian. In general, maximal stress occurred at the equator around. When cell deformation increased to a certain level, the tension at the poker tip exceeded that of the equator. Breakage of the cell wall may start from the equator or the poker tip, depending on the deformation. A nonlinear model is suitable for estimating turgor, stress, and stiffness, and numerical simulation is a powerful method for determining plant cell mechanical properties.     

Separation anxiety: stress, tension and cytokinesis

Cytokinesis, the physical separation of a mother cell into two daughter cells, progresses through a series of well-defined changes in morphology. These changes involve distinct biochemical and mechanical processes. Here, we review the mechanical features of cells during cytokinesis, discussing both the material properties as well as sources of stresses, both active and passive, which lead to the observed changes in morphology. We also describe a mechanosensory feedback control system that regulates protein localization and shape progression during cytokinesis.     

Kin1 is a plasma membrane‐associated kinase that regulates the cell surface in fission yeast

Cell morphogenesis is a complex process that depends on cytoskeleton and membrane organization, intracellular signalling and vesicular trafficking. The rod shape of the fission yeast Schizosaccharomyces pombe and the availability of powerful genetic tools make this species an excellent model to study cell morphology. Here we have investigated the function of the conserved Kin1 kinase. Kin1‐GFP associates dynamically with the plasma membrane at sites of active cell surface remodelling and is present in the membrane fraction. Kin1Δ null cells show severe defects in cell wall structure and are unable to maintain a rod shape. To explore Kin1 primary function, we constructed an ATP analogue‐sensitive allele kin1‐as1. Kin1 inhibition primarily promotes delocalization of plasma membrane‐associated markers of actively growing cell surface regions. Kin1 itself is depolarized and its mobility is strongly reduced. Subsequently, amorphous cell wall material accumulates at the cell surface, a phenotype that is dependent on vesicular trafficking, and the cell wall integrity mitogen‐activated protein kinase pathway is activated. Deletion of cell wall integrity mitogen‐activated protein kinase components reduces kin1Δ hypersensitivity to stresses such as those induced by Calcofluor white and SDS. We propose that Kin1 is required for a tight link between the plasma membrane and the cell wall.     

Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes

Cells and the tissues they form are not passive material bodies. Cells change their behavior in response to external biochemical and biomechanical cues. Behavioral changes, such as morphological deformation, proliferation and migration, are striking in many multicellular processes such as morphogenesis, wound healing and cancer progression. Cell-based modeling of these phenomena requires algorithms that can capture active cell behavior and their emergent tissue-level phenotypes. In this paper, we report on extensions of the subcellular element model to model active biomechanical subcellular processes. These processes lead to emergent cell and tissue level phenotypes at larger scales, including (i) adaptive shape deformations in cells responding to slow stretching, (ii) viscous flow of embryonic tissues, and (iii) streaming patterns of chemotactic cells in epithelial-like sheets. In each case, we connect our simulation results to recent experiments.     

Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses

We provide a computational comparison of the performance of stentless and stented aortic prostheses, in terms of aortic root displacements and internal stresses. To this aim, we consider three real patients; for each of them, we draw the two prostheses configurations, which are characterized by different mechanical properties and we also consider the native configuration. For each of these scenarios, we solve the fluid–structure interaction problem arising between blood and aortic root, through Finite Elements. In particular, the Arbitrary Lagrangian–Eulerian formulation is used for the numerical solution of the fluid-dynamic equations and a hyperelastic material model is adopted to predict the mechanical response of the aortic wall and the two prostheses. The computational results are analyzed in terms of aortic flow, internal wall stresses and aortic wall/prosthesis displacements; a quantitative comparison of the mechanical behavior of the three scenarios is reported. The numerical results highlight a good agreement between stentless and native displacements and internal wall stresses, whereas higher/non-physiological stresses are found for the stented case.     

The mechanical basis of cell rearrangement. I. Epithelial morphogenesis during Fundulus epiboly

Many morphogenetic processes are accomplished by coordinated cell rearrangements. These rearrangements are accompanied by substantial shifts in the neighbor relationships between cells. Here we propose a model for studying morphogenesis in epithelial sheets by directed cell neighbor change. Our model describes cell rearrangements by accounting for the balance of forces between neighboring cells within an epithelium. Cell rearrangement and cell shape changes occur when these forces are not in mechanical equilibrium. We will show that cell rearrangement within the epidermal enveloping layer (EVL) of the teleost fish Fundulus during epiboly can be explained solely in terms of the balance of forces generated among constituent epithelial cells. Within a cell, we account for circumferential elastic forces and the force generated by hydrostatic and osmotic pressure. The model treats epithelial cells as two-dimensional polygons where the mechanical forces are applied to the polygonal nodes. A cell node protrudes or contracts when the nodal forces are not in mechanical equilibrium. In an epithelial sheet, adjacent cells share common boundary nodes; in this way, mechanical force is transmitted from cell to cell, mimicking junctional coupling. These junctional nodes can slide, and nodes may appear or disappear, so that the number of polygonal sides is variable. Computer graphics allows us to compare numerical simulations of the model with time-lapse cinemicroscopy of cell rearrangements in the living embryo, and data obtained from fixed and silver stained embryos. By manipulating the mechanical properties of the model cells we can study the conditions necessary to reproduce normal cell behavior during Fundulus epiboly. We find that simple stress relaxation is sufficient to account for cell rearrangements among interior cells of the EVL when they are isotropically contractile. Experimental observations show that the number of EVL marginal cells continuously decreases throughout epiboly. In order for the simulation to reproduce this behavior, cells at the EVL boundary must generate protrusive forces rather than contractile tension forces. Therefore, the simulation results suggest that the mechanical properties of EVL marginal cells at their leading edge must be quite different from EVL interior cells.     

Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast

The growth of a tumour in a duct is examined in order to model ductal carcinoma in situ (DCIS) of the breast, the earliest known stage of breast cancer. Interactions between the expansive forces created by tumour cell proliferation and the stresses that develop in the compliant basement membrane are studied using numerical and analytical techniques. Particular attention focuses on the impact that proteolytic enzymes have on the tumour's progression. As the tumour expands and the duct wall deforms, the tumour cells are subjected to mechanical and nutritional stresses caused by high pressures and oxygen deprivation. Such stresses may stimulate the cells to produce proteolytic enzymes that degrade the duct wall, making it more compliant and prone to penetration by the tumour cells. We use our model to compare these two hypotheses for enzyme production and find that mechanical stress is likely the dominant mechanism, with the wall deforming most at the centre of the duct. We then discuss the biological implications of our theoretical results and suggest possible directions for future work.