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.

Mechanical force sensing in tissues

Tissue size, shape, and organization reflect individual cell behaviors such as proliferation, shape change, and movement. Evidence suggests that mechanical signals operate in tandem with biochemical cues to properly coordinate cell behavior and pattern tissues. The objective of this chapter is to present recent evidence demonstrating that forces transmitted between cells act as signals that coordinate cell behavior across tissues. We first briefly summarize molecular and cellular mechanisms by which forces are sensed by cells with an emphasis on forces generated and transmitted by cytoskeletal networks. We then discuss evidence for these mechanisms operating in multicellular contexts to coordinate complex cell and tissue behaviors that occur during embryonic development: specifically growth and morphogenesis.

The Spectrin cytoskeleton regulates the Hippo signalling pathway

The Spectrin cytoskeleton is known to be polarised in epithelial cells, yet its role remains poorly understood. Here, we show that the Spectrin cytoskeleton controls Hippo signalling. In the developing Drosophila wing and eye, loss of apical Spectrins (alpha/beta-heavy dimers) produces tissue overgrowth and mis-regulation of Hippo target genes, similar to loss of Crumbs (Crb) or the FERM-domain protein Expanded (Ex). Apical beta-heavy Spectrin binds to Ex and co-localises with it at the apical membrane to antagonise Yki activity. Interestingly, in both the ovarian follicular epithelium and intestinal epithelium of Drosophila, apical Spectrins and Crb are dispensable for repression of Yki, while basolateral Spectrins (alpha/beta dimers) are essential. Finally, the Spectrin cytoskeleton is required to regulate the localisation of the Hippo pathway effector YAP in response to cell density human epithelial cells. Our findings identify both apical and basolateral Spectrins as regulators of Hippo signalling and suggest Spectrins as potential mechanosensors.

Control of cell-cell forces and collective cell dynamics by the intercellular adhesome

Dynamics of epithelial tissues determine key processes in development, tissue healing and cancer invasion. These processes are critically influenced by cell-cell adhesion forces. However, the identity of the proteins that resist and transmit forces at cell-cell junctions remains unclear, and how these proteins control tissue dynamics is largely unknown. Here we provide a systematic study of the interplay between cell-cell adhesion proteins, intercellular forces and epithelial tissue dynamics. We show that collective cellular responses to selective perturbations of the intercellular adhesome conform to three mechanical phenotypes. These phenotypes are controlled by different molecular modules and characterized by distinct relationships between cellular kinematics and intercellular forces. We show that these forces and their rates can be predicted by the concentrations of cadherins and catenins. Unexpectedly, we identified different mechanical roles for P-cadherin and E-cadherin; whereas P-cadherin predicts levels of intercellular force, E-cadherin predicts the rate at which intercellular force builds up.

Making quantitative morphological variation from basic developmental processes: Where are we? The case of the Drosophila wing

One of the aims of evolutionary developmental biology is to discover the developmental origins of morphological variation. The discipline has mainly focused on qualitative morphological differences (e.g., presence or absence of a structure) between species. Studies addressing subtle, quantitative variation are less common. The Drosophila wing is a model for the study of development and evolution, making it suitable to investigate the developmental mechanisms underlying the subtle quantitative morphological variation observed in nature. Previous reviews have focused on the processes involved in wing differentiation, patterning and growth. Here, we investigate what is known about how the wing achieves its final shape, and what variation in development is capable of generating the variation in wing shape observed in nature. Three major developmental stages need to be considered: larval development, pupariation, and pupal development. The major cellular processes involved in the determination of tissue size and shape are cell proliferation, cell death, oriented cell division and oriented cell intercalation. We review how variation in temporal and spatial distribution of growth and transcription factors affects these cellular mechanisms, which in turn affects wing shape. We then discuss which aspects of the wing morphological variation are predictable on the basis of these mechanisms. Developmental Dynamics 244:1058-1073, 2015. © 2015 Wiley Periodicals, Inc.

Size control: the developmental physiology of body and organ size regulation

The developmental regulation of final body and organ size is fundamental to generating a functional and correctly proportioned adult. Research over the last two decades has identified a long list of genes and signaling pathways that, when perturbed, influence final body size. However, body and organ size are ultimately a characteristic of the whole organism, and how these myriad genes and pathways function within a physiological context to control size remains largely unknown. In this review, we first describe the major size-regulatory signaling pathways: the Insulin/IGF-, RAS/RAF/MAPK-, TOR-, Hippo-, and JNK-signaling pathways. We then explore what is known of how these pathways regulate five major aspects of size regulation: growth rate, growth duration, target size, negative growth and growth coordination. While this review is by no means exhaustive, our goal is to provide a conceptual framework for integrating the mechanisms of size control at a molecular-genetic level with the mechanisms of size control at a physiological level.

High-resolution imaging of cellular processes across textured surfaces using an indexed-matched elastomer

Understanding and controlling how cells interact with the microenvironment has emerged as a prominent field in bioengineering, stem cell research and in the development of the next generation of in vitro assays as well as organs on a chip. Changing the local rheology or the nanotextured surface of substrates has proved an efficient approach to improve cell lineage differentiation, to control cell migration properties and to understand environmental sensing processes. However, introducing substrate surface textures often alters the ability to image cells with high precision, compromising our understanding of molecular mechanisms at stake in environmental sensing. In this paper, we demonstrate how nano/microstructured surfaces can be molded from an elastomeric material with a refractive index matched to the cell culture medium. Once made biocompatible, contrast imaging (differential interference contrast, phase contrast) and high-resolution fluorescence imaging of subcellular structures can be implemented through the textured surface using an inverted microscope. Simultaneous traction force measurements by micropost deflection were also performed, demonstrating the potential of our approach to study cell-environment interactions, sensing processes and cellular force generation with unprecedented resolution.

Tug of war--the influence of opposing physical forces on epithelial cell morphology

The shape of a single animal cell is determined both by its internal cytoskeleton and through physical interactions with its environment. In a tissue context, this extracellular environment is made up largely of other cells and the extracellular matrix. As a result, the shape of cells residing within an epithelium will be determined both by forces actively generated within the cells themselves and by their deformation in response to forces generated elsewhere in the tissue as they propagate through cell-cell junctions. Together these complex patterns of forces combine to drive epithelial tissue morphogenesis during both development and homeostasis. Here we review the role of both active and passive cell shape changes and mechanical feedback control in tissue morphogenesis in different systems.

Cell division and the maintenance of epithelial order

Epithelia are polarized layers of adherent cells that are the building blocks for organ and appendage structures throughout animals. To preserve tissue architecture and barrier function during both homeostasis and rapid growth, individual epithelial cells divide in a highly constrained manner. Building on decades of research focused on single cells, recent work is probing the mechanisms by which the dynamic process of mitosis is reconciled with the global maintenance of epithelial order during development. These studies reveal how symmetrically dividing cells both exploit and conform to tissue organization to orient their mitotic spindles during division and establish new adhesive junctions during cytokinesis.

Canonical Wnt signalling regulates epithelial patterning by modulating levels of laminins in zebrafish appendages

The patterning and morphogenesis of body appendages – such as limbs and fins – is orchestrated by the activities of several developmental pathways. Wnt signalling is essential for the induction of limbs. However, it is unclear whether a canonical Wnt signalling gradient exists and regulates the patterning of epithelium in vertebrate appendages. Using an evolutionarily old appendage – the median fin in zebrafish – as a model, we show that the fin epithelium exhibits graded changes in cellular morphology along the proximo-distal axis. This epithelial pattern is strictly correlated with the gradient of canonical Wnt signalling activity. By combining genetic analyses with cellular imaging, we show that canonical Wnt signalling regulates epithelial cell morphology by modulating the levels of laminins, which are extracellular matrix components. We have unravelled a hitherto unknown mechanism involved in epithelial patterning, which is also conserved in the pectoral fins – evolutionarily recent appendages that are homologous to tetrapod limbs.

Highlighted article: In the zebrafish fin, a Wnt gradient dictates the expression of laminin α5, which signals via integrin α3 to control epithelial cell morphology.

Sensing the local environment: actin architecture and Hippo signalling

The Hippo network is a major conserved growth suppressor pathway that participates in organ size control during development and prevents tumour formation during adult homeostasis. Recent evidence has implicated the actin cytoskeleton as a link between tissue architecture and Hippo signalling. In this review, we will consider the evidence and models proposed for the regulation of Hippo signalling by actin dynamics and structure. We cover aspects of signalling regulation by mechanotransduction, cytoskeletal tethering and the spatial reorganization of signalling components. We also examine the physiological and pathological contexts in which these mechanisms are relevant.

Cytoskeletal tension inhibits Hippo signaling through an Ajuba-Warts complex

Mechanical forces have been proposed to modulate organ growth, but a molecular mechanism that links them to growth regulation in vivo has been lacking. We report that increasing tension within the cytoskeleton increases Drosophila wing growth, whereas decreasing cytoskeletal tension decreases wing growth. These changes in growth can be accounted for by changes in the activity of Yorkie, a transcription factor regulated by the Hippo pathway. The influence of myosin activity on Yorkie depends genetically on the Ajuba LIM protein Jub, a negative regulator of Warts within the Hippo pathway. We further show that Jub associates with α-catenin and that its localization to adherens junctions and association with α-catenin are promoted by cytoskeletal tension. Jub recruits Warts to junctions in a tension-dependent manner. Our observations delineate a mechanism that links cytoskeletal tension to regulation of Hippo pathway activity, providing a molecular understanding of how mechanical forces can modulate organ growth.

Towards long term cultivation of Drosophila wing imaginal discs in vitro

The wing imaginal disc of Drosophila melanogaster is a prominent experimental system for research on control of cell growth, proliferation and death, as well as on pattern formation and morphogenesis during organogenesis. The precise genetic methodology applicable in this system has facilitated conceptual advances of fundamental importance for developmental biology. Experimental accessibility and versatility would gain further if long term development of wing imaginal discs could be studied also in vitro. For example, culture systems would allow live imaging with maximal temporal and spatial resolution. However, as clearly demonstrated here, standard culture methods result in a rapid cell proliferation arrest within hours of cultivation of dissected wing imaginal discs. Analysis with established markers for cells in S- and M phase, as well as with RGB cell cycle tracker, a novel reporter transgene, revealed that in vitro cultivation interferes with cell cycle progression throughout interphase and not just exclusively during G1. Moreover, quantification of EGFP expression from an inducible transgene revealed rapid adverse effects of disc culture on basic cellular functions beyond cell cycle progression. Disc transplantation experiments confirmed that these detrimental consequences do not reflect fatal damage of imaginal discs during isolation, arguing clearly for a medium insufficiency. Alternative culture media were evaluated, including hemolymph, which surrounds imaginal discs during growth in situ. But isolated larval hemolymph was found to be even less adequate than current culture media, presumably as a result of conversion processes during hemolymph isolation or disc culture. The significance of prominent growth-regulating pathways during disc culture was analyzed, as well as effects of insulin and disc co-culture with larval tissues as potential sources of endocrine factors. Based on our analyses, we developed a culture protocol that prolongs cell proliferation in cultured discs.

Force and the spindle: mechanical cues in mitotic spindle orientation

The mechanical environment of a cell has a profound effect on its behaviour, from dictating cell shape to driving the transcription of specific genes. Recent studies have demonstrated that mechanical forces play a key role in orienting the mitotic spindle, and therefore cell division, in both single cells and tissues. Whilst the molecular machinery that mediates the link between external force and the mitotic spindle remains largely unknown, it is becoming increasingly clear that this is a widely used mechanism which could prove vital for coordinating cell division orientation across tissues in a variety of contexts.

Dynamic clonal analysis based on chronic in vivo imaging allows multiscale quantification of growth in the Drosophila wing disc

In the course of morphogenesis, tissues change shape and grow. How this is orchestrated is largely unknown, partly owing to the lack of experimental methods to visualize and quantify growth. Here, we describe a novel experimental approach to investigate the growth of tissues in vivo on a time-scale of days, as employed to study the Drosophila larval imaginal wing disc, the precursor of the adult wing. We developed a protocol to image wing discs at regular intervals in living anesthetized larvae so as to follow the growth of the tissue over extended periods of time. This approach can be used to image cells at high resolution in vivo. At intermediate scale, we tracked the increase in cell number within clones as well as the changes in clone area and shape. At scales extending to the tissue level, clones can be used as landmarks for measuring strain, as a proxy for growth. We developed general computational tools to extract strain maps from clonal shapes and landmark displacements in individual tissues, and to combine multiple datasets into a mean strain. In the disc, we use these to compare properties of growth at the scale of clones (a few cells) and at larger regional scales.

Shape and position of the node and notochord along the bilateral plane of symmetry are regulated by cell-extracellular matrix interactions

The node and notochord (and their equivalents in other species) are essential signaling centers, positioned along the plane of bilateral symmetry in developing vertebrate embryos. However, genes and mechanisms regulating morphogenesis of these structures and their placement along the embryonic midline are not well understood. In this work, we provide the first evidence that the position of the node and the notochord along the bilateral plane of symmetry are under genetic control and are regulated by integrin α5β1 and fibronectin in mice. We found that the shape of the node is often inverted in integrin α5-null and fibronectin-null mutants, and that the positioning of node and the notochord is often skewed away from the perceived plane of embryonic bilateral of symmetry. Our studies also show that the shape and position of the notochord are dependent on the shape and embryonic placement of the node. Our studies suggest that fibronectin regulates the shape of the node by affecting apico-basal polarity of the nodal cells. Taken together, our data indicate that cell–extracellular matrix interactions mediated by integrin α5β1 and fibronectin regulate the geometry of the node as well as the placement of the node and notochord along the plane of bilateral symmetry in the mammalian embryo.

Morphology and growth of polarized tissues

We study and classify the time-dependent morphologies of polarized tissues subject to anisotropic but spatially homogeneous growth. Extending previous studies, we model the tissue as a fluid, and discuss the interplay of the active stresses generated by the anisotropic cell division and three types of passive mechanical forces: viscous stresses, friction with the environment and tension at the tissue boundary. The morphology dynamics is formulated as a free-boundary problem, and conformal mapping techniques are used to solve the evolution numerically. We combine analytical and numerical results to elucidate how the different passive forces compete with the active stresses to shape the tissue in different temporal regimes and derive the corresponding scaling laws. We show that in general the aspect ratio of elongated tissues is non-monotonic in time, eventually recovering isotropic shapes in the presence of friction forces, which are asymptotically dominant.

YAP/TAZ as mechanosensors and mechanotransducers in regulating organ size and tumor growth

Organ size is controlled by the concerted action of biochemical and physical processes. Although mechanical forces are known to regulate cell and tissue behavior, as well as organogenesis, the precise molecular events that integrate mechanical and biochemical signals to control these processes are not fully known. The recently delineated Hippo-tumor suppressor network and its two nuclear effectors, YAP and TAZ, shed light on these mechanisms. YAP and TAZ are proto-oncogene proteins that respond to complex physical milieu represented by the rigidity of the extracellular matrix, cell geometry, cell density, cell polarity and the status of the actin cytoskeleton. Here, we review the current knowledge of how YAP and TAZ function as mechanosensors and mechanotransducers. We also suggest that by deciphering the mechanical and biochemical signals controlling YAP/TAZ function, we will gain insights into new strategies for cancer treatment and organ regeneration.

Tension-oriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly

Epithelial spreading is a common and fundamental aspect of various developmental and disease-related processes such as epithelial closure and wound healing. A key challenge for epithelial tissues undergoing spreading is to increase their surface area without disrupting epithelial integrity. Here we show that orienting cell divisions by tension constitutes an efficient mechanism by which the enveloping cell layer (EVL) releases anisotropic tension while undergoing spreading during zebrafish epiboly. The control of EVL cell-division orientation by tension involves cell elongation and requires myosin II activity to align the mitotic spindle with the main tension axis. We also found that in the absence of tension-oriented cell divisions and in the presence of increased tissue tension, EVL cells undergo ectopic fusions, suggesting that the reduction of tension anisotropy by oriented cell divisions is required to prevent EVL cells from fusing. We conclude that cell-division orientation by tension constitutes a key mechanism for limiting tension anisotropy and thus promoting tissue spreading during EVL epiboly.