Assessing the mechanical energy costs of various tissue reshaping mechanisms

Elongated Cells Drive Morphogenesis in a Surface-Wrapped Finite-Element Model of Germband Retraction

During Drosophila embryogenesis, the germband first extends to curl around the posterior end of the embryo and then retracts back; however, retraction is not simply the reversal of extension. At a tissue level, extension is coincident with ventral furrow formation, and at a cellular level, extension occurs via convergent cell neighbor exchanges in the germband, whereas retraction involves only changes in cell shape. To understand how cell shapes, tissue organization, and cellular forces drive germband retraction, we investigate this process using a whole-embryo, surface-wrapped cellular finite-element model. This model represents two key epithelial tissues-amnioserosa and germband-as adjacent sheets of two-dimensional cellular finite elements that are wrapped around an ellipsoidal three-dimensional approximation of an embryo. The model reproduces the detailed kinematics of in vivo retraction by fitting just one free model parameter, the tension along germband cell interfaces; all other cellular forces are constrained to follow ratios inferred from experimental observations. With no additional parameter adjustments, the model also reproduces quantitative assessments of mechanical stress using laser dissection and failures of retraction when amnioserosa cells are removed via mutations or microsurgery. Surprisingly, retraction in the model is robust to changes in cellular force values but is critically dependent on starting from a configuration with highly elongated amnioserosa cells. Their extreme cellular elongation is established during the prior process of germband extension and is then used to drive retraction. The amnioserosa is the one tissue whose cellular morphogenesis is reversed from germband extension to retraction, and this reversal coordinates the forces needed to retract the germband back to its pre-extension position and shape. In this case, cellular force strengths are less important than the carefully established cell shapes that direct them. VIDEO ABSTRACT.

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Segment-specific adhesion as a driver of convergent extension

Convergent extension, the simultaneous extension and narrowing of tissues, is a crucial event in the formation of the main body axis during embryonic development. It involves processes on multiple scales: the sub-cellular, cellular and tissue level, which interact via explicit or intrinsic feedback mechanisms. Computational modelling studies play an important role in unravelling the multiscale feedbacks underlying convergent extension. Convergent extension usually operates in tissue which has been patterned or is currently being patterned into distinct domains of gene expression. How such tissue patterns are maintained during the large scale tissue movements of convergent extension has thus far not been investigated. Intriguingly, experimental data indicate that in certain cases these tissue patterns may drive convergent extension rather than requiring safeguarding against convergent extension. Here we use a 2D Cellular Potts Model (CPM) of a tissue prepatterned into segments, to show that convergent extension tends to disrupt this pre-existing segmental pattern. However, when cells preferentially adhere to cells of the same segment type, segment integrity is maintained without any reduction in tissue extension. Strikingly, we demonstrate that this segment-specific adhesion is by itself sufficient to drive convergent extension. Convergent extension is enhanced when we endow our in silico cells with persistence of motion, which in vivo would naturally follow from cytoskeletal dynamics. Finally, we extend our model to confirm the generality of our results. We demonstrate a similar effect of differential adhesion on convergent extension in tissues that can only extend in a single direction (as often occurs due to the inertia of the head region of the embryo), and in tissues prepatterned into a sequence of domains resulting in two opposing adhesive gradients, rather than alternating segments.

The process of convergent extension is a major contributor to the formation of the anterior-posterior body axis in the early embryo. Convergent extension refers to the directed movement of cells that leads to the extension of tissue in one direction and narrowing of the tissue in the perpendicular direction. Often, convergent extension occurs in tissue which already contains distinct domains of gene expression such as segments, and it is unclear how these patterns are maintained despite extensive cell movement. Interestingly, experimental evidence suggests that these tissue patterns may drive rather than be compromised by convergent extension. However, existing computational models aimed at unravelling the mechanisms of convergent extension have thus far only studied the process in homogeneous tissues. With our model, we demonstrate that in a segmented tissue, preferential adhesion of cells to other cells within the same segment type is required to maintain the tissue pattern during convergent extension. Furthermore, such segment-specific adhesion is by itself capable of driving convergent extension.

The interplay between cell signalling and mechanics in developmental processes

Force production and the propagation of stress and strain within embryos and organisms are crucial physical processes that direct morphogenesis. In addition, there is mounting evidence that biomechanical cues created by these processes guide cell behaviours and cell fates. In this Review we discuss key roles for biomechanics during development to directly shape tissues, to provide positional information for cell fate decisions and to enable robust programmes of development. Several recently identified molecular mechanisms suggest how cells and tissues might coordinate their responses to biomechanical cues. Finally, we outline long-term challenges in integrating biomechanics with genetic analysis of developing embryos.

A multiscale road map of cancer spheroids – incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.