Growth couples temporal and spatial fluctuations of tissue properties during morphogenesis.

Living tissues display fluctuations-random spatial and temporal variations of tissue properties around their reference values-at multiple scales. It is believed that such fluctuations may enable tissues to sense their state or their size. Recent theoretical studies developed specific models of fluctuations in growing tissues and predicted that fluctuations of growth show long-range correlations. Here, we elaborated upon these predictions and we tested them using experimental data. We first introduced a minimal model for the fluctuations of any quantity that has some level of temporal persistence or memory, such as concentration of a molecule, local growth rate, or mechanical property. We found that long-range correlations are generic, applying to any such quantity, and that growth couples temporal and spatial fluctuations, through a mechanism that we call "fluctuation stretching"-growth enlarges the length scale of variation of this quantity. We then analyzed growth data from sepals of the model plant Arabidopsis and we quantified spatial and temporal fluctuations of cell growth using the previously developed cellular Fourier transform. Growth appears to have long-range correlations. We compared different genotypes and growth conditions: mutants with lower or higher response to mechanical stress have lower temporal correlations and longer-range spatial correlations than wild-type plants. Finally, we used theoretical predictions to merge experimental data from all conditions and developmental stages into a unifying curve, validating the notion that temporal and spatial fluctuations are coupled by growth. Altogether, our work reveals kinematic constraints on spatiotemporal fluctuations that have an impact on the robustness of morphogenesis.

Growth couples temporal and spatial fluctuations of tissue properties during morphogenesis.

Living tissues display fluctuations - random spatial and temporal variations of tissue properties around their reference values - at multiple scales. It is believed that such fluctuations may enable tissues to sense their state or their size. Recent theoretical studies developed specific models of fluctuations in growing tissues and predicted that fluctuations of growth show long-range correlations. Here we elaborated upon these predictions and we tested them using experimental data. We first introduced a minimal model for the fluctuations of any quantity that has some level of temporal persistence or memory, such as concentration of a molecule, local growth rate, or mechanical properties. We found that long-range correlations are generic, applying to to any such quantity, and that growth couples temporal and spatial fluctuations. We then analysed growth data from sepals of the model plant Arabidopsis and we quantified spatial and temporal fluctuations of cell growth using the previously developed Cellular Fourier Transform. Growth appears to have long-range correlations. We compared different genotypes and growth conditions: mutants with altered response to mechanical stress have lower temporal correlations and longer-range spatial correlations than wild-type plants. Finally, we used a theoretical prediction to collapse experimental data from all conditions and developmental stages, validating the notion that temporal and spatial fluctuations are coupled by growth. Altogether, our work reveals kinematic constraints on spatiotemporal fluctuations that have an impact on the robustness of morphogenesis.

Spatial consistency of cell growth direction during organ morphogenesis requires CELLULOSE SYNTHASE INTERACTIVE1.

Extracellular matrices contain fibril-like polymers often organized in parallel arrays. Although their role in morphogenesis has been long recognized, it remains unclear how the subcellular control of fibril synthesis translates into organ shape. We address this question using the Arabidopsis sepal as a model organ. In plants, cell growth is restrained by the cell wall (extracellular matrix). Cellulose microfibrils are the main load-bearing wall component, thought to channel growth perpendicularly to their main orientation. Given the key function of CELLULOSE SYNTHASE INTERACTIVE1 (CSI1) in guidance of cellulose synthesis, we investigate the role of CSI1 in sepal morphogenesis. We observe that sepals from csi1 mutants are shorter, although their newest cellulose microfibrils are more aligned compared to wild-type. Surprisingly, cell growth anisotropy is similar in csi1 and wild-type plants. We resolve this apparent paradox by showing that CSI1 is required for spatial consistency of growth direction across the sepal.

Mechanobiology of the cell wall - insights from tip-growing plant and fungal cells.

The cell wall (CW) is a thin and rigid layer encasing the membrane of all plant and fungal cells. It ensures mechanical integrity by bearing mechanical stresses derived from large cytoplasmic turgor pressure, contacts with growing neighbors or growth within restricted spaces. The CW is made of polysaccharides and proteins, but is dynamic in nature, changing composition and geometry during growth, reproduction or infection. Such continuous and often rapid remodeling entails risks of enhanced stress and consequent damages or fractures, raising the question of how the CW detects and measures surface mechanical stress and how it strengthens to ensure surface integrity? Although early studies in model fungal and plant cells have identified homeostatic pathways required for CW integrity, recent methodologies are now allowing the measurement of pressure and local mechanical properties of CWs in live cells, as well as addressing how forces and stresses can be detected at the CW surface, fostering the emergence of the field of CW mechanobiology. Here, using tip-growing cells of plants and fungi as case study models, we review recent progress on CW mechanosensation and mechanical regulation, and their implications for the control of cell growth, morphogenesis and survival.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development.

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Feeling Stressed or Strained? A Biophysical Model for Cell Wall Mechanosensing in Plants.

Mechanical signals have recently emerged as a major cue in plant morphogenesis, notably influencing cytoskeleton organization, gene expression, protein polarity, or cell division. Although many putative mechanosensing proteins have been identified, it is unclear what mechanical cue they might sense and how this would occur. Here we briefly explain the notions of mechanical stress and strain. We present the challenges to understand their sensing by plants, focusing on the cell wall and the plasma membrane, and we review putative mechanosensing structures. We propose minimal biophysical models of mechanosensing, revealing the modes of mechanosensing according to mechanosensor lifetime, threshold force for mechanosensor dissociation, and type of association between the mechanosensor and the cell wall, as the sensor may be associated to a major load-bearing structure such as cellulose or to a minor load-bearing structure such as pectins or the plasma membrane. Permanent strain, permanent expansion, and relatively slow variations thereof are sensed in all cases; variations of stress are sensed in all cases; permanent stress is sensed only in the following specific cases: sensors associated to minor load-bearing structures slowly relaxing in a growing wall, long-lived sensors with high dissociation force and associated to major-load-bearing structures, and sensors with low dissociation force associated to major-load-baring structures behaving elastically. We also find that all sensors respond to variations in the composition or the mechanical properties of the cell wall. The level of sensing is modulated by the properties of all of mechanosensor, cell wall components, and plasma membrane. Although our models are minimal and not fully realistic, our results yield a framework to start investigating the possible functions of putative mechanosensors.

Modulation of tissue growth heterogeneity by responses to mechanical stress.

Morphogenesis often yields organs with robust size and shapes, whereas cell growth and deformation feature significant spatiotemporal variability. Here, we investigate whether tissue responses to mechanical signals contribute to resolve this apparent paradox. We built a model of growing tissue made of fiber-like material, which may account for the cytoskeleton, polar cell-cell adhesion, or the extracellular matrix in animals and for the cell wall in plants. We considered the synthesis and remodeling of this material, as well as the modulation of synthesis by isotropic and anisotropic response to mechanical stress. Formally, our model describes an expanding, mechanoresponsive, nematic, and active fluid. We show that mechanical responses buffer localized perturbations, with two possible regimes-hyporesponsive and hyperresponsive-and the transition between the two corresponds to a minimum value of the relaxation time. Whereas robustness of shapes suggests that growth fluctuations are confined to small scales, our model yields growth fluctuations that have long-range correlations. This indicates that growth fluctuations are a significant source of heterogeneity in development. Nevertheless, we find that mechanical responses may dampen such fluctuations, with a specific magnitude of anisotropic response that minimizes heterogeneity of tissue contours. We finally discuss how our predictions might apply to the development of plants and animals. Altogether, our results call for the systematic quantification of fluctuations in growing tissues.

Mechanical Shielding of Rapidly Growing Cells Buffers Growth Heterogeneity and Contributes to Organ Shape Reproducibility.

A landmark of developmental biology is the production of reproducible shapes, through stereotyped morphogenetic events. At the cell level, growth is often highly heterogeneous, allowing shape diversity to arise. Yet, how can reproducible shapes emerge from such growth heterogeneity? Is growth heterogeneity filtered out? Here, we focus on rapidly growing trichome cells in the Arabidopsis sepal, a reproducible floral organ. We show via computational modeling that rapidly growing cells may distort organ shape. However, the cortical microtubule alignment along growth-derived maximal tensile stress in adjacent cells would mechanically isolate rapidly growing cells and limit their impact on organ shape. In vivo, we observed such microtubule response to stress and consistently found no significant effect of trichome number on sepal shape in wild-type and lines with trichome number defects. Conversely, modulating the microtubule response to stress in katanin and spiral2 mutant made sepal shape dependent on trichome number, suggesting that, while mechanical signals are propagated around rapidly growing cells, the resistance to stress in adjacent cells mechanically isolates rapidly growing cells, thus contributing to organ shape reproducibility.

Mesoscopic formulas of linear and angular momentum fluxes.

Many approaches of coarse graining have been developed under the names of Cosserat theory or polar-fluid theory for those materials in which some component elements undergo nonaffine deformations, such as elastic materials with inclusions or granular matters. For the complex elements such as living cells, however, the microscopic variables and their dynamics are often unknown, and there has been no systematic theory of coarse graining from the microscales nor the formulas like the Irving-Kirkwood formula that constitutes the macroscopic stress or couple stress in terms of some microscale quantities. We show that, for the quasi-steady states, the coarse-graining procedure must generally provide us with the Cosserat-type balance equations as long as the procedure keeps track of the conservation of linear and angular momenta, and that the fluxes of these conserved quantities should generally be expressed in the Irving-Kirkwood-type formulas, where the interparticle distance or forces and torques should be replaced by those associated to the pair of neighboring coarse-graining volumes. This framework, which refers to no particular microvariables or dynamics, is valid for active complex matters out of equilibrium and with any multibody interactions.

Physical role for the nucleus in cell migration.

Cell migration is important for the function of many eukaryotic cells. Recently the nucleus has been shown to play an important role in cell motility. After giving an overview of cell motility mechanisms we review what is currently known about the mechanical properties of the nucleus and the connections between it and the cytoskeleton. We also discuss connections to the extracellular matrix and mechanotransduction. We identify key physical roles of the nucleus in cell migration.

Momentum transfer in nonequilibrium steady states.

When a Brownian object interacts with noninteracting gas particles under nonequilibrium conditions, energy dissipation associated with Brownian motion causes an additional force on the object as a "momentum transfer deficit." This principle is demonstrated first by a new nonequilibrium steady state model and then applied to several known models such as an adiabatic piston for which a simple explanation has been lacking.

Gyroscopic instability of a drop trapped inside an inclined circular hydraulic jump.

A drop of moderate size deposited inside a circular hydraulic jump remains trapped at the shock front and does not coalesce with the liquid flowing across the jump. For a small inclination of the plate on which the liquid is impacting, the drop does not always stay at the lowest position and oscillates around it with a sometimes large amplitude, and a frequency that slightly decreases with flow rate. We suggest that this striking behavior is linked to a gyroscopic instability in which the drop tries to keep constant its angular momentum while sliding along the jump.