Mechanisms of regulating tissue elongation in Drosophila wing: impact of oriented cell divisions, oriented mechanical forces, and reduced cell size

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Self-sustained planar intercalations due to mechanosignaling feedbacks lead to robust axis extension during morphogenesis

Tissue elongation is a necessary process in metazoans to implement their body plans that is not fully understood. Here we propose a mechanism based on the interplay between cellular mechanics and primordia patterning that results in self-sustained planar intercalations. Thus, we show that a location-dependent modulation of the mechanical properties of cells leads to robust axis extension. To illustrate the plausibility of this mechanism, we test it against different patterning models by means of computer simulations of tissues where we implemented mechano-signaling feedbacks. Our results suggest that robust elongation relies on a trade-off between cellular and tissue strains that is orchestrated through the cleavage orientation. In the particular context of axis extension in Turing-patterned tissues, we report that different directional cell activities cooperate synergetically to achieve elongation. Altogether, our findings help to understand how the axis extension phenomenon emerges from the dynamics of individual cells.

Apical Constriction Reversal upon Mitotic Entry Underlies Different Morphogenetic Outcomes of Cell Division

During development, coordinated cell shape changes and cell divisions sculpt tissues. While these individual cell behaviors have been extensively studied, how cell shape changes and cell divisions that occur concurrently in epithelia influence tissue shape is less understood. We addressed this question in two contexts of the early Drosophila embryo: premature cell division during mesoderm invagination, and native ectodermal cell divisions with ectopic activation of apical contractility. Using quantitative live-cell imaging, we demonstrated that mitotic entry reverses apical contractility by interfering with medioapical RhoA signaling. While premature mitotic entry inhibits mesoderm invagination, which relies on apical constriction, mitotic entry in an artificially contractile ectoderm induced ectopic tissue invaginations. Ectopic invaginations resulted from medioapical myosin loss in neighboring mitotic cells. This myosin loss enabled nonmitotic cells to apically constrict through mitotic cell stretching. Thus, the spatial pattern of mitotic entry can differentially regulate tissue shape through signal interference between apical contractility and mitosis.

Growth control in the Drosophila wing disk

The regulation of size and shape is a fundamental requirement of biological development and has been a subject of scientific study for centuries, but we still lack an understanding of how organisms know when to stop growing. Imaginal wing disks of the fruit fly Drosophila melanogaster, which are precursors of the adult wings, are an archetypal tissue for studying growth control. The growth of the disks is dependent on many inter- and intra-organ factors such as morphogens, mechanical forces, nutrient levels, and hormones that influence gene expression and cell growth. Extracellular signals are transduced into gene-control signals via complex signal transduction networks, and since cells typically receive many different signals, a mechanism for integrating the signals is needed. Our understanding of the effect of morphogens on tissue-level growth regulation via individual pathways has increased significantly in the last half century, but our understanding of how multiple biochemical and mechanical signals are integrated to determine whether or not a cell decides to divide is still rudimentary. Numerous fundamental questions are involved in understanding the decision-making process, and here we review the major biochemical and mechanical pathways involved in disk development with a view toward providing a basis for beginning to understand how multiple signals can be integrated at the cell level, and how this translates into growth control at the level of the imaginal disk. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Cellular Models.

Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium

Cell division, movement and differentiation contribute to pattern formation in developing tissues. This is the case in the vertebrate neural tube, in which neurons differentiate in a characteristic pattern from a highly dynamic proliferating pseudostratified epithelium. To investigate how progenitor proliferation and differentiation affect cell arrangement and growth of the neural tube, we used experimental measurements to develop a mechanical model of the apical surface of the neuroepithelium that incorporates the effect of interkinetic nuclear movement and spatially varying rates of neuronal differentiation. Simulations predict that tissue growth and the shape of lineage-related clones of cells differ with the rate of differentiation. Growth is isotropic in regions of high differentiation, but dorsoventrally biased in regions of low differentiation. This is consistent with experimental observations. The absence of directional signalling in the simulations indicates that global mechanical constraints are sufficient to explain the observed differences in anisotropy. This provides insight into how the tissue growth rate affects cell dynamics and growth anisotropy and opens up possibilities to study the coupling between mechanics, pattern formation and growth in the neural tube.

Summary: A mechanical model of the vertebrate neuroepithelium, based on experimental observations, suggests that the rate of neuronal differentiation influences tissue growth and the shape of lineage-related clones.

Biological Tissues as Active Nematic Liquid Crystals

Live tissues can self-organize and be described as active materials composed of cells that generate active stresses through continuous injection of energy. In vitro reconstituted molecular networks, as well as single-cell cytoskeletons show that their filamentous structures can portray nematic liquid crystalline properties and can promote nonequilibrium processes induced by active processes at the microscale. The appearance of collective patterns, the formation of topological singularities, and spontaneous phase transition within the cell cytoskeleton are emergent properties that drive cellular functions. More integrated systems such as tissues have cells that can be seen as coarse-grained active nematic particles and their interaction can dictate many important tissue processes such as epithelial cell extrusion and migration as observed in vitro and in vivo. Here, a brief introduction to the concept of active nematics is provided, and the main focus is on the use of this framework in the systematic study of predominantly 2D tissue architectures and dynamics in vitro. In addition how the nematic state is important in tissue behavior, such as epithelial expansion, tissue homeostasis, and the atherosclerosis disease state, is discussed. Finally, how the nematic organization of cells can be controlled in vitro for tissue engineering purposes is briefly discussed.

Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization

Computational modelling of cells can reveal insight into the mechanisms of the important processes of tissue development. However, current cell models have limitations and are challenged to model detailed changes in cellular shapes and physical mechanics when thousands of migrating and interacting cells need to be modelled. Here we describe a novel dynamic cellular finite-element model (DyCelFEM), which accounts for changes in cellular shapes and mechanics. It also models the full range of cell motion, from movements of individual cells to collective cell migrations. The transmission of mechanical forces regulated by intercellular adhesions and their ruptures are also accounted for. Intra-cellular protein signalling networks controlling cell behaviours are embedded in individual cells. We employ DyCelFEM to examine specific effects of biochemical and mechanical cues in regulating cell migration and proliferation, and in controlling tissue patterning using a simplified re-epithelialization model of wound tissue. Our results suggest that biochemical cues are better at guiding cell migration with improved directionality and persistence, while mechanical cues are better at coordinating collective cell migration. Overall, DyCelFEM can be used to study developmental processes when a large population of migrating cells under mechanical and biochemical controls experience complex changes in cell shapes and mechanics.

A quantitative approach to understanding vertebrate limb morphogenesis at the macroscopic tissue level

To understand organ morphogenetic mechanisms, it is essential to clarify how spatiotemporally-regulated molecular/cellular dynamics causes physical tissue deformation. In the case of vertebrate limb development, while some of the genes and oriented cell behaviors underlying morphogenesis have been revealed, tissue deformation dynamics remains incompletely understood. We here introduce our recent work on the reconstruction of tissue deformation dynamics in chick limb development from cell lineage tracing data. This analysis has revealed globally-aligned anisotropic tissue deformation along the proximo-distal axis not only in the distal region but also in the whole limb bud. This result points to a need, as a future challenge, to find oriented molecular/cellular behaviors for realizing the observed anisotropic tissue deformation in both proximal and distal regions, which will lead to systems understanding of limb morphogenesis.

Effects of mechanical properties on tumor invasion: insights from a cellular model

Understanding the regulating mechanism of tumor invasion is of crucial importance for both fundamental cancer research and clinical applications. Previous in vivo experiments have shown that invasive cancer cells dissociate from the primary tumor and invade into the stroma, forming an irregular invasive morphology. Although cell movements involved in tumor invasion are ultimately driven by mechanical forces of cell-cell interactions and tumor-host interactions, how these mechanical properties affect tumor invasion is still poorly understood. In this study, we use a recently developed two-dimensional cellular model to study the effects of mechanical properties on tumor invasion. We study the effects of cell-cell adhesions as well as the degree of degradation and stiffness of extracellular matrix (ECM). Our simulation results show that cell-cell adhesion relationship must be satisfied for tumor invasion. Increased adhesion to ECM and decreased adhesion among tumor cells result in invasive tumor behaviors. When this invasive behavior occurs, ECM plays an important role for both tumor morphology and the shape of invasive cancer cells. Increased stiffness and stronger degree of degradation of ECM promote tumor invasion, generating more aggressive tumor invasive morphologies. It can also generate irregular shape of invasive cancer cells, protruding towards ECM. The capability of our model suggests it a useful tool to study tumor invasion and might be used to propose optimal treatment in clinical applications.

Patterning of wound-induced intercellular Ca(2+) flashes in a developing epithelium

Differential mechanical force distributions are increasingly recognized to provide important feedback into the control of an organ's final size and shape. As a second messenger that integrates and relays mechanical information to the cell, calcium ions (Ca(2+)) are a prime candidate for providing important information on both the overall mechanical state of the tissue and resulting behavior at the individual-cell level during development. Still, how the spatiotemporal properties of Ca(2+) transients reflect the underlying mechanical characteristics of tissues is still poorly understood. Here we use an established model system of an epithelial tissue, the Drosophila wing imaginal disc, to investigate how tissue properties impact the propagation of Ca(2+) transients induced by laser ablation. The resulting intercellular Ca(2+) flash is found to be mediated by inositol 1,4,5-trisphosphate and depends on gap junction communication. Further, we find that intercellular Ca(2+) transients show spatially non-uniform characteristics across the proximal-distal axis of the larval wing imaginal disc, which exhibit a gradient in cell size and anisotropy. A computational model of Ca(2+) transients is employed to identify the principle factors explaining the spatiotemporal patterning dynamics of intercellular Ca(2+) flashes. The relative Ca(2+) flash anisotropy is principally explained by local cell shape anisotropy. Further, Ca(2+) velocities are relatively uniform throughout the wing disc, irrespective of cell size or anisotropy. This can be explained by the opposing effects of cell diameter and cell elongation on intercellular Ca(2+) propagation. Thus, intercellular Ca(2+) transients follow lines of mechanical tension at velocities that are largely independent of tissue heterogeneity and reflect the mechanical state of the underlying tissue.

Mechanical model of geometric cell and topological algorithm for cell dynamics from single-cell to formation of monolayered tissues with pattern

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly available.

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

Genome sequences provide the overall genetic blueprint of cells, but cells possessing the same genome can exhibit diverse phenotypes. There is a multitude of mechanisms controlling cellular epigenetic states and that dictate the behavior of cells. Among these, networks of interacting molecules, often under stochastic control, depending on the specific wirings of molecular components and the physiological conditions, can have a different landscape of cellular states. In addition, chromosome folding in three-dimensional space provides another important control mechanism for selective activation and repression of gene expression. Fully differentiated cells with different properties grow, divide, and interact through mechanical forces and communicate through signal transduction, resulting in the formation of complex tissue patterns. Developing quantitative models to study these multi-scale phenomena and to identify opportunities for improving human health requires development of theoretical models, algorithms, and computational tools. Here we review recent progress made in these important directions.