Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

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A microfluidic platform to investigate the role of mechanical constraints on tissue reorganization

Mechanical constraints have a high impact on development processes, and there is a need for new tools to investigate the role of mechanosensitive pathways in tissue reorganization during development. We present here experiments where embryonic cell aggregates are aspired through constrictions in microfluidic channels, generating highly heterogeneous flows and high cell deformations that can be imaged using two-photon microscopy. This approach provides a way to measure in situ local viscoelastic properties of 3D tissues and connect them to intracellular and intercellular events such as cell shape changes and cell rearrangements. Perspectives include applications on organoids to investigate and quantify rheological properties of tissues, and to understand how constraints affect development

Marangoni-like tissue flows enhance symmetry breaking of embryonic organoids

During early development of multi-cellular animals, cells self-organize to set up the body axes, such as the primary head-to-tail axis, based on which the later body plan is defined. Several signaling pathways are known to control body axis formation. Here, we show, however, that tissue mechanics plays an important role during this process. We focus on the emergence of a primary axis in initially spherical aggregates of mouse embryonic stem cells, which mirrors events in the early mouse embryo. These aggregates break rotational symmetry to establish an axial organization with domains of different expression profiles, e.g. of the transcription factor T/Bra and the adhesion molecule E-cadherin. Combining quantitative microscopy and physical modeling, we identify large-scale tissue flows with a recirculation component and demonstrate that they significantly contribute to symmetry breaking. We show that the recirculating flows are explained by a difference in tissue surface tension across domains, akin to Marangoni flows, which we further confirm by aggregate fusion experiments. Our work highlights that body axis formation is not only driven by biochemical processes, but that it can also be amplified by tissue flows. We expect this type of amplification to operate in many other organoid and in-vivo systems

Erratum to: Colloquium: Mechanical formalisms for tissue dynamics

International audienceThe 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

A detector-independent quality score for cell segmentation without ground truth in 3D live fluorescence microscopy

Deep-learning techniques have enabled a breakthrough in robustness and execution time in automated cell detection in live fluorescence microscopy datasets. However, the heterogeneity, dimensionality and ever-growing size of 3D+time datasets challenge the evaluation of measurements. Here we propose a quality score for the accuracy of cell segmentation maps that is detector-independent and does not need any groundtruth nor priors on object appearance. Our method learns the dynamic parameters of each cell to detect inconsistencies in local displacements induced by segmentation errors. Using simulations that approximate the dynamics of cellular aggregates, we demonstrate the score ability to rank the performance of detectors up to 40% of false positives. On live volumetric imaging of organoids, our score is able to appropriately rank two stateof-the-art pre-trained deep-learning detectors (Stardist3D and Cellpose)

Aster repulsion drives short-ranged ordering in the Drosophila syncytial blastoderm

Biological systems are highly complex, yet notably ordered structures can emerge. During syncytial stage development of the Drosophila melanogaster embryo, nuclei synchronously divide for nine cycles within a single cell, after which most of the nuclei reach the cell cortex. The arrival of nuclei to the cortex occurs with remarkable positional order, which is important for subsequent cellularisation and morphological transformations. Yet, the mechanical principles underlying this lattice-like positional order of nuclei remain untested. Here, utilising quantification of nuclei position and division orientation together with embryo explants we show that short-ranged repulsive interactions between microtubule asters ensure the regular distribution and maintenance of nuclear positions in the embryo. Such ordered nuclear positioning still occurs with the loss of actin caps and even the loss of the nuclei themselves; the asters can self-organise with similar distribution to nuclei in the wild-type embryo. The explant assay enabled us to deduce the nature of the mechanical interaction between pairs of nuclei. We used this to predict how the nuclear division axis orientation changes upon nucleus removal from the embryo cortex, which we confirmed in vivo with laser ablation. Overall, we show that short-ranged microtubule-mediated repulsive interactions between asters are important for ordering in the early Drosophila embryo and minimising positional irregularity

Multicellular aggregates: a model system for tissue rheology

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress

Data from: Collective cell migration without proliferation: density determines cell velocity and wave velocity

Collective cell migration contributes to embryogenesis, wound healing and tumor metastasis. Cell monolayer migration experiments help understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length- and time-scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation