Fluidization of tissues by cell division and apoptosis (original) (raw)
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Dynamics of anisotropic tissue growth
New Journal of Physics, 2008
We study the mechanics of tissue growth via cell division and cell death (apoptosis). The rearrangements of cells can on large scales and times be captured by a continuum theory which describes the tissue as an effective viscous material with active stresses generated by cell division. We study the effects of anisotropies of cell division on cell rearrangements and show that average cellular trajectories exhibit anisotropic scaling behaviors. If cell division and apoptosis balance, there is no net growth, but for anisotropic cell division the tissue undergoes spontaneous shear deformations. Our description is relevant for the study of developing tissues such as the imaginal disks of the fruit fly Drosophila melanogaster, which grow anisotropically.
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The Differential Adhesion Hypothesis (DAH) posits that differences in adhesion provide the driving force for morphogenetic processes. A manifestation of differential adhesion is tissue liquidity and a measure for it is tissue surface tension. In terms of this property, DAH correctly predicts global developmental tissue patterns. However, it provides little information on how these patterns arise from the movement and shape changes of cells. We provide strong qualitative and quantitative support for tissue liquidity both in true developmental context and in vitro assays. We follow the movement and characteristic shape changes of individual cells in the course of specific tissue rearrangements leading to liquid-like configurations. Finally, we relate the measurable tissue-liquid properties to molecular entities, whose direct determination under realistic three-dimensional culture conditions is not possible. Our findings confirm the usefulness of tissue liquidity and provide the scientific underpinning for a novel tissue engineering technology. Developmental Dynamics 237:2438 -2449, 2008.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
For many organisms, shapes emerge from growth, which generates stresses, which in turn can feedback on growth. In this review, theoretical methods to analyse various aspects of morphogenesis are discussed with the aim to determine the most adapted method for tissue mechanics. We discuss the need to work at scales intermediate between cells and tissues and emphasize the use of finite elasticity for this. We detail the application of these ideas to four systems: active cells embedded in tissues, brain cortical convolutions, the cortex of Caenorhabditis elegans during elongation and finally the proliferation of epithelia on extracellular matrix. Numerical models well adapted to inhomogeneities are also presented. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.
Mechanical formalism 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 can ultimately lead to predictions. The newly accessible local information thus urges 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 constitutive equation. We also recall the mathematical framework developped for continuum materials and how to transform a constitutive equation into a system of partial differential equations amenable to numerical resolution. The present article thus groups together mechanical elements and theoretical methods that are ready to enhance the significance of the data extracted from recent or future high throughput biomechanical experiments.
A Sub-Cellular Viscoelastic Model for Cell Population Mechanics
PLoS ONE, 2010
Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and 'in silico' (computational) models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue.
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Although collective cell migration (CCM) is a highly coordinated and ordered migratory mode, perturbations in the form of mechanical waves appear even in 2D. These perturbations caused by the viscoelastic nature of cell rearrangement are involved in various biological processes, such as embryogenesis, wound healing and cancer invasion. The mechanical waves, as a product of the active turbulence occurred at low Reynolds number, represent an oscillatory change in cell velocity and the relevant rheological parameters. The velocity oscillations, in the form of forward and backward flows, are driven by: viscoelastic force, surface tension force, and traction force. The viscoelastic force represents a consequence of inhomogeneous distribution of cell residual stress accumulated during CCM. This cause-consequence relation is considered on a model system such as the cell monolayer free expansion. The collision of forward and backward flows causes an increase in cell packing density which ha...
Emergent morphogenesis: Elastic mechanics of a self-deforming tissue
Journal of Biomechanics, 2010
Multicellular organisms are generated by coordinated cell movements during morphogenesis. Convergent extension is a key tissue movement that organizes mesoderm, ectoderm, and endoderm in vertebrate embryos. The goals of researchers studying convergent extension, and morphogenesis in general, include understanding the molecular pathways that control cell identity, establish fields of cell types, and regulate cell behaviors. Cell identity, the size and boundaries of tissues, and the behaviors exhibited by those cells shape the developing embryo; however, there is a fundamental gap between understanding the molecular pathways that control processes within single cells and understanding how cells work together to assemble multi-cellular structures. Theoretical and experimental biomechanics of embryonic tissues are increasingly being used to bridge that gap. The efforts to map molecular pathways and the mechanical processes underlying morphogenesis are crucial to understanding: 1) the source of birth defects, 2) the formation of tumors and progression of cancer, and 3) basic principles of tissue engineering. In this paper, we first review the process of tissue convergent-extension of the vertebrate axis and then review models used to study the selforganizing movements from a mechanical perspective. We conclude by presenting a relatively simple "wedge-model" that exhibits key emergent properties of convergent extension such as the coupling between tissue stiffness, cell intercalation forces, and tissue elongation forces.
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Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jammingunjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological processes including cancer. However, most analysis of these mechanical properties and UJT have sidestepped the effect of cellular death and division in these systems. Cellular apoptosis (programmed cell death) and mitosis (cell division) can drive significant changes in tissue properties. The balance between the two is crucial in maintaining tissue function, and an imbalance between the two is seen in situations such as cancer progression, wound healing and necrosis. In this work we investigate the impact of cell death and division on tissue mechanical properties, by incorporating specific mechanosensitive triggers of cell death and division based on the size and geometry of the cell within in silico models of tissue dynamics. Specifically, we look a...