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Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Here, we develop a mechanical model to understand active cell intercalation behaviours in the context of an epithelial tissue. Extending existing descriptions, such as vertex models, the junctional actomyosin cortex of every cell is modelled as a continuum morphoelastic rod, explicitly representing cortices facing each other at bicellular junctions. Cells are described directly in terms of the key subcellular constituents that drive dynamics, with localised stresses from the contractile actomyosin cortex and adhesion molecules coupling apposed cortices. This multi-scale apposed-cortex formulation reveals key behaviours that drive tissue dynamics, such as cell-cell shearing and flow of junctional material past cell vertices. We show that cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and viscous turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, the 4-way vertex is resolved and a new, orthogonal junction extends passively. The adhesion timescale defines a frictional viscosity that is an important regulator of these dynamics, modulating tension transmission in the tissue as well as the speeds of junction shrinkage and growth. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are likely to occur in active tissues with high adhesive friction.SIGNIFICANCECell intercalation, or neighbour exchange, is a crucial behaviour that can drive tissue deformations, dissipate stress and facilitate wound healing. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study the continuous dynamics of intercalation, involving shear between coupled cell cortices. Deriving a continuum description of the cell cortex, explicitly coupling neighbouring cortices with adhesions, we define the biophysical conditions required for successful neighbour exchanges. Furthermore, we show how the turnover of adhesion molecules specifies a viscous friction that regulates active tissue dynamics.

International audience; We propose a variational method for joint motion estimation and source identification in one-dimensional image sequences. The problem is motivated by fluorescence microscopy data of laser nanoablations of cell membranes in live Drosophila embryos, which can be conveniently—and without loss of significant information—represented in space-time plots, so called kymographs. Based on mechanical models of tissue formation, we propose a variational formulation that is based on the nonhomogenous continuity equation and investigate the solution of this ill-posed inverse problem using convective regularisation. We show existence of a minimiser of the minimisation problem, derive the associated Euler–Lagrange equations, and numerically solve them using a finite element discretisation together with Newton’s method. Based on synthetic data, we demonstrate that source estimation can be crucial whenever signal variations can not be explained by advection alone. Furthermore, we perform an extensive evaluation and comparison of various models, including standard optical flow, based on manually annotated kymographs that measure velocities of visible features. Finally, we present results for data generated by a mechanical model of tissue formation and demonstrate that our approach reliably estimates both a velocity and a source.

We review recent developments in the understanding of the biomechanics of apicomedial actomyosin and how its contractility can tense and deform tissue. Myosin pulses are driven by a biochemical oscillator but how they are modulated by the mechanical context remains unclear. On the other hand, the emergence of tissue behaviour is highly dependent on the material properties of actin, on how strongly components are connected and on the influence of neighbouring tissues. We further review the use of constitutive equations in exploring the mechanics of epithelial apices dominated by apicomedial Myosin contractility. Sin financiación 5.288 JCR (2018) Q1, 22/174 Genetics & Heredity, 47/193 Cell Biology 3.954 SJR (2018) Q1, 5/87 Developmental Biology, 18/351 Genetics No data IDR 2018 UEM

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell ‘footprint’ is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

[Background] Force generation and the material properties of cells and tissues are central to morphogenesis but remain difficult to measure in vivo. Insight is often limited to the ratios of mechanical properties obtained through disruptive manipulation, and the appropriate models relating stress and strain are unknown. The Drosophila amnioserosa epithelium progressively contracts over 3 hours of dorsal closure, during which cell apices exhibit area fluctuations driven by medial myosin pulses with periods of 1.5–6 min. Linking these two timescales and understanding how pulsatile contractions drive morphogenetic movements is an urgent challenge., [Results] We present a novel framework to measure in a continuous manner the mechanical properties of epithelial cells in the natural context of a tissue undergoing morphogenesis. We show that the relationship between apicomedial myosin fluorescence intensity and strain during fluctuations is consistent with a linear behaviour, although with a lag. We thus used myosin fluorescence intensity as a proxy for active force generation and treated cells as natural experiments of mechanical response under cyclic loading, revealing unambiguous mechanical properties from the hysteresis loop relating stress to strain. Amnioserosa cells can be described as a contractile viscoelastic fluid. We show that their emergent mechanical behaviour can be described by a linear viscoelastic rheology at timescales relevant for tissue morphogenesis. For the first time, we establish relative changes in separate effective mechanical properties in vivo. Over the course of dorsal closure, the tissue solidifies and effective stiffness doubles as net contraction of the tissue commences. Combining our findings with those from previous laser ablation experiments, we show that both apicomedial and junctional stress also increase over time, with the relative increase in apicomedial stress approximately twice that of other obtained measures., [Conclusions] Our results show that in an epithelial tissue undergoing net contraction, stiffness and stress are coupled. Dorsal closure cell apical contraction is driven by the medial region where the relative increase in stress is greater than that of stiffness. At junctions, by contrast, the relative increase in the mechanical properties is the same, so the junctional contribution to tissue deformation is constant over time. An increase in myosin activity is likely to underlie, at least in part, the change in medioapical properties and we suggest that its greater effect on stress relative to stiffness is fundamental to actomyosin systems and confers on tissues the ability to regulate contraction rates in response to changes in external mechanics., We thank the following funding bodies for their support: Herchel Smith Fund (PFM), Ministerio de Ciencia e Innovación (NG and JD, BFU2011-25828 and Ramón y Cajal fellowship award), Marie Curie Career Integration Grant (NG, PCIG09-GA-2011-293479), Biotechnology and Biological Sciences Research Council (GBB, grant BB/J010278/1) and Rhône-Alpes Complex System Institute (JE).

International audience; Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodeling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerization at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn, regulates the cell length in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena, which are of the same nature as those taking place during the contraction of a whole muscle. This similarity explains the fact that single nonmuscle cell and whole-muscle contraction both follow a Hill-like force–velocity relationship.; Parmi les nombreuses énigmes posées par les cellules vivantes, leurcapacité à se déplacer et à changer de forme a attiré notre attention entant que physiciens. Une double approche de modélisation et d'expériencesnous conduit à expliquer deux observations troublantes : premièrement, lacellule adapte l'intensité des forces avec lesquelles elle tire sur sonenvironnement selon la rigidité de celui-ci. Et deuxièmement, pendantqu'une cellule progresse dans une direction en développant uneprotrusion, son squelette interne s'écoule en fait dans l'autre direction,dans un mouvement apparemment contre-productif, appelé écoulementrétrograde. Nous montrons que ces deux phénomènes émanent d'une mêmepropriété paradoxale du squelette interne de la cellule, qui est fait defilaments d'actine assemblés en un réseau. Cet assemblage est bâtipar des liens dont la durée de vie est très courte, ce qui en fait enréalité un liquide qui va lentement s'écouler. À première vue, cela paraîtincompatible avec l'observation, puisque la forme d'un liquide est dictéepar son environnement, alors que les cellules déforment activement leurmilieu. Cependant, parmi les liens formant le réseau d'actine se trouventdes moteurs moléculaires, appelés myosines, capables de tirer sur lesfilaments d'actine et ainsi d'engendrer un écoulement de l'intérieur. Nousmontrons que c'est l'interaction de ces myosines avec la rigidité del'extérieur qui détermine la forme que la cellule prendra. Cela impliqueune consommation continuelle d'énergie par les myosines même lorsque lacellule est globalement immobile, mais nous montrons que ce fonctionnementdote le squelette cellulaire de deux avantages cruciaux : l'agilité d'unliquide pour s'adapter et accomplir les multiples rôles physiologiques dela cellule, et simultanément la résistance d'un solide élastique qui répondinstantanément à des sollicitations mécaniques.

International audience; Finite volume release gravity currents of large density contrast on steep slopes, representing powder-snow avalanches, are simulated numerically using a dynamic mesh adaptation technique. This technique allows one to treat large Reynolds numbers and large density contrast flows, but it is (presently) restricted to two dimensions. Comparison of numerical results with experiments in the Boussinesq limit shows that 2D simulations capture the essential dynamics. The physics of powder-snow avalanches is analysed on hand of the similarity model developed by Rastello and Hopfinger (2004) and briefly reproduced here. The numerical simulations provide the closure parameters required in this model and give access to the flow structure. The non-Boussinesq effect is to decrease substantially the spatial growth in height and to increase the aspect ratio, hence the overall flow structure.

International audience; In this paper direct numerical simulations of exchange flows of large density ratios are presented and are compared with experiments by Gröbelbauer et al. [J. Fluid Mech. 250, 669 (1993)]. These simulations, which make use of a dynamic mesh adaptation technique, cover the whole density ratio range of the experiments and very good agreement with the experimental front velocities and the Froude number variations is obtained. Moreover, in order to establish more definitely the Froude number dependency on density ratio, the simulations were carried up to ratios of 100 compared with 21.6 accessible in experiments. An empirical law for the dense front Froude number as a function of the density parameter is proposed. The mathematical difficulty of the problem is discussed. This difficulty arises because, when the density ratio is large, the existence of a solution is dependent on a compatibility condition between the diffusion and viscous terms model. Moreover, a specific numerical technique is required to treat the finite, nonuniform divergence of the mass-averaged velocity field described by the continuity equation.