Modulation of tissue growth heterogeneity by responses to mechanical stress

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elasticity map in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) by inferring the heterogeneous elasticity maps across three materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. We further applied our improved architecture to three additional examples of breast cancer tissue and extended our analysis to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Our selected network architecture consistently produced highly accurate estimations of heterogeneous elasticity maps, even when there was up to 10% noise present in the training data.

Self-organization underlies developmental robustness in plants

Development is a self-organized process that builds on cells and their interactions. Cells are heterogeneous in gene expression, growth, and division; yet how development is robust despite such heterogeneity is a fascinating question. Here, we review recent progress on this topic, highlighting how developmental robustness is achieved through self-organization. We will first discuss sources of heterogeneity, including stochastic gene expression, heterogeneity in growth rate and direction, and heterogeneity in division rate and precision. We then discuss cellular mechanisms that buffer against such noise, including Paf1C- and miRNA-mediated denoising, spatiotemporal growth averaging and compensation, mechanisms to improve cell division precision, and coordination of growth rate and developmental timing between different parts of an organ. We also discuss cases where such heterogeneity is not buffered but utilized for development. Finally, we highlight potential directions for future studies of noise and developmental robustness.

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 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 lengthscale of variation of this quantity. 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 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 an 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.

The dynamics and biophysics of shape formation: Common themes in plant and animal morphogenesis

The emergence of tissue form in multicellular organisms results from the complex interplay between genetics and physics. In both plants and animals, cells must act in concert to pattern their behaviors. Our understanding of the factors sculpting multicellular form has increased dramatically in the past few decades. From this work, common themes have emerged that connect plant and animal morphogenesis-an exciting connection that solidifies our understanding of the developmental basis of multicellular life. In this review, we will discuss the themes and the underlying principles that connect plant and animal morphogenesis, including the coordination of gene expression, signaling, growth, contraction, and mechanical and geometric feedback.

Stiffness transitions in new walls post-cell division differ between Marchantia polymorpha gemmae and Arabidopsis thaliana leaves

Plant morphogenesis is governed by the mechanics of the cell wall-a stiff and thin polymeric box that encloses the cells. The cell wall is a highly dynamic composite material. New cell walls are added during cell division. As the cells continue to grow, the properties of cell walls are modulated to undergo significant changes in shape and size without breakage. Spatial and temporal variations in cell wall mechanical properties have been observed. However, how they relate to cell division remains an outstanding question. Here, we combine time-lapse imaging with local mechanical measurements via atomic force microscopy to systematically map the cell wall's age and growth, with their stiffness. We make use of two systems, Marchantia polymorpha gemmae, and Arabidopsis thaliana leaves. We first characterize the growth and cell division of M. polymorpha gemmae. We then demonstrate that cell division in M. polymorpha gemmae results in the generation of a temporary stiffer and slower-growing new wall. In contrast, this transient phenomenon is absent in A. thaliana leaves. We provide evidence that this different temporal behavior has a direct impact on the local cell geometry via changes in the junction angle. These results are expected to pave the way for developing more realistic plant morphogenetic models and to advance the study into the impact of cell division on tissue growth.

How to Grow a Flat Leaf

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

Cycling in a crowd: Coordination of plant cell division, growth, and cell fate

The reiterative organogenesis that drives plant growth relies on the constant production of new cells, which remain encased by interconnected cell walls. For these reasons, plant morphogenesis strictly depends on the rate and orientation of both cell division and cell growth. Important progress has been made in recent years in understanding how cell cycle progression and the orientation of cell divisions are coordinated with cell and organ growth and with the acquisition of specialized cell fates. We review basic concepts and players in plant cell cycle and division, and then focus on their links to growth-related cues, such as metabolic state, cell size, cell geometry, and cell mechanics, and on how cell cycle progression and cell division are linked to specific cell fates. The retinoblastoma pathway has emerged as a major player in the coordination of the cell cycle with both growth and cell identity, while microtubule dynamics are central in the coordination of oriented cell divisions. Future challenges include clarifying feedbacks between growth and cell cycle progression, revealing the molecular basis of cell division orientation in response to mechanical and chemical signals, and probing the links between cell fate changes and chromatin dynamics during the cell cycle.

Mechanobiology of cell division in plant growth

Cell division in plants is particularly important as cells cannot rearrange. It therefore determines the arrangement of cells (topology) and their size and shape (geometry). Cell division reduces mechanical stress locally by producing smaller cells and alters mechanical properties by reinforcing the mechanical wall network, both of which can alter overall tissue morphology. Division orientation is often regarded as following geometric rules, however recent work has suggested that divisions align with the direction of maximal tensile stress. Mechanical stress has already been shown to feed into many processes of development including those that alter mechanical properties. Such an alignment may enable cell division to selectively reinforce the cell wall network in the direction of maximal tensile stress. Therefore there exists potential feedback between cell division, mechanical stress and growth. Improving our understanding of this topic will help to shed light on the debated role of cell division in organ scale growth.

Fluctuations shape plants through proprioception

Plants constantly experience fluctuating internal and external mechanical cues, ranging from nanoscale deformation of wall components, cell growth variability, nutating stems, and fluttering leaves to stem flexion under tree weight and wind drag. Developing plants use such fluctuations to monitor and channel their own shape and growth through a form of proprioception. Fluctuations in mechanical cues may also be actively enhanced, producing oscillating behaviors in tissues. For example, proprioception through leaf nastic movements may promote organ flattening. We propose that fluctuation-enhanced proprioception allows plant organs to sense their own shapes and behave like active materials with adaptable outputs to face variable environments, whether internal or external. Because certain shapes are more amenable to fluctuations, proprioception may also help plant shapes to reach self-organized criticality to support such adaptability.

Growth dynamics of the Arabidopsis fruit is mediated by cell expansion

Fruit have evolved a sophisticated tissue and cellular architecture to secure plant reproductive success. Postfertilization growth is perhaps the most dramatic event during fruit morphogenesis. Several studies have proposed that fertilized ovules and developing seeds initiate signaling cascades to coordinate and promote the growth of the accompanying fruit tissues. This dynamic process allows the fruit to conspicuously increase its size and acquire its final shape and means for seed dispersal. All these features are key for plant survival and crop yield. Despite its importance, we lack a high-resolution spatiotemporal map of how postfertilization fruit growth proceeds at the cellular level. In this study, we have combined live imaging, mutant backgrounds in which fertilization can be controlled, and computational modeling to monitor and predict postfertilization fruit growth in Arabidopsis We have uncovered that, unlike leaves, sepals, or roots, fruit do not exhibit a spatial separation of cell division and expansion domains; instead, there is a separation into temporal stages with fertilization as the trigger for transitioning to cell expansion, which drives postfertilization fruit growth. We quantified the coordination between fertilization and fruit growth by imaging no transmitting tract (ntt) mutants, in which fertilization fails in the bottom half of the fruit. By combining our experimental data with computational modeling, we delineated the mobility properties of the seed-derived signaling cascades promoting growth in the fruit. Our study provides the basis for generating a comprehensive understanding of the molecular and cellular mechanisms governing fruit growth and shape.

FORCE-ing the shape

The plant cell wall is a dynamic structure that mediates cell and organ morphogenesis and provides structural support to the whole plant body. The primary load bearing components of the cell wall are a cellulose-xyloglucan network embedded in a pectin matrix. Plant morphogenesis is regulated by a constant adjustment of the chemical structure and thus mechanical properties of the cell wall components. These modifications are modulated by a variety of different remodeling agents that precisely control cell wall mechanical properties. Here, we briefly review the major recent updates on cell wall mechanics during growth and development.

Statistics of noisy growth with mechanical feedback in elastic tissues

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow [Formula: see text] decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts.

Mechanical Conflicts in Twisting Growth Revealed by Cell-Cell Adhesion Defects

Many plants grow organs and tissues with twisted shapes. Arabidopsis mutants with impaired microtubule dynamics exhibit such a phenotype constitutively. Although the activity of the corresponding microtubule regulators is better understood at the molecular level, how large-scale twisting can emerge in the mutants remains largely unknown. Classically, oblique cortical microtubules would constrain the deposition of cellulose microfibrils in cells, and such conflicts at the cell level would be relaxed at the tissue scale by supracellular torsion. This model implicitly assumes that cell-cell adhesion is a key step to transpose local mechanical conflicts into a macroscopic twisting phenotype. Here we tested this prediction using the quasimodo1 mutant, which displays cell-cell adhesion defects. Using the spriral2/tortifolia1 mutant with hypocotyl helical growth, we found that qua1-induced cell-cell adhesion defects restore straight growth in qua1-1 spr2-2. Detached cells in qua1-1 spr2-2 displayed helical growth, confirming that straight growth results from the lack of mechanical coupling between cells rather than a restoration of SPR2 activity in the qua1 mutant. Because adhesion defects in qua1 depend on tension in the outer wall, we also showed that hypocotyl twisting in qua1-1 spr2-2 could be restored when decreasing the matrix potential of the growth medium, i.e., by reducing the magnitude of the pulling force between adjacent cells, in the double mutant. Interestingly, the induction of straight growth in qua1-1 spr2-2 could be achieved beyond hypocotyls, as leaves also displayed a flat phenotype in the double mutant. Altogether, these results provide formal experimental support for a scenario in which twisted growth in spr2 mutant would result from the relaxation of local mechanical conflicts between adjacent cells via global organ torsion.

Positive charge-dependent cell targeted staining and DNA detection

Fluorescence probes containing pyridinium compounds and different negative ions with the applications of specific tracing of different cell organelles and DNA detection!