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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.

Coordinating mitotic spindle and cytokinetic furrow positioning is essential to ensure proper DNA segregation. Here we present a novel mechanism, which corrects DNA segregation defects due to cytokinetic furrow mispositioning. We show that DNA segregation defects following the abnormal displacement of the cytokinetic furrow towards the anterior side of C. elegans one-cell embryos are unexpectedly corrected at the end of cytokinesis. This correction relies on the concomitant displacement of the furrow and of the anterior nucleus towards the posterior and anterior poles, respectively. It also coincides with cortical blebbing and an anteriorly directed flow of cytoplasmic particles. While microtubules contribute to nuclear displacement, relaxation of an excessive tension at the anterior cortex plays a central role in the correction process and simultaneously regulates cytoplasmic flow as well as nuclear and furrow displacements. This work thus reveals the existence of a so far uncharacterized correction mechanism, which is critical to correct DNA segregation defects due to cytokinetic furrow mispositioning.

This paper deals with the Traction Force Microscopy (TFM) problem. It consists in obtaining stresses by solving an inverse problem in an elastic medium, from known experimentally measured displacements. In this article, the application is the determination of the stresses exerted by a living cell at the surface of an elastic gel. We propose an abstract framework which formulates this inverse problem as a constrained minimization one. The mathematical constraints express the biomechanical conditions that the stress field must satisfy. From this framework, two methods currently used can be derived, the adjoint method (AM) and the Fourier Transform Traction Cytometry (FTTC) method. An improvement of the FTTC method is also derived using this framework. The numerical results are compared and show the advantage of the AM, in particular its ability to capture details more accurately. Cet article est consacré au problème de la Microscopie à Force de Traction (TFM). Ce problème consiste à déterminer les contraintes exercées par une cellule lors de sa migration sur un substrat élastique à partir d’une mesure expérimentale des déplacements induits dans ce substrat. Mathématiquement, il s’agit de résoudre un problème inverse pour lequel nous proposons une formulation abstraite de type optimisation sous contraintes. Les contraintes mathématiques expriment les constraintes biomécaniques que doit satisfaire le champ de contraintes exercé par la cellule. Ce cadre abstrait permet de retrouver deux des méthodes de résolution utilisées en pratique, à savoir la méthode adjointe (AM) et la méthode de Cytométrie de Traction par Transformée de Fourier (FTTC). Il permet aussi d’ameliorer la méthode FTTC. Les résultats numériques obtenus sont ensuite comparés et démontrent l’avantage de la méthode adjointe, en particulier par sa capacité à capturer des détails avec une meilleure précision.

[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; Traction forces exerted by cells on soft elastic substrates are important for characterizing the types of mechanisms used for cell migration. Classical tools for the determination of traction forces include the knowledge of the displacement field thanks to fluorescent beads embedded into the substrate. Then, from the discrete beads displacements, an inverse problem is solved to obtain the stress field. Two currently used methods in the literature are the well-known Fourier Transform Traction Cytometry (FTTC) method and the adjoint method (AM), which are compared here. A real case is presented where the displacement field is known from cancer cell migration study. The two methods allow the recovery of the traction stresses and their results are compared. Similar results are seen as long as an adequate projection technique is used (zero force imposed outside the cell). It is found that the AM allows a finer resolution of the traction forces, in particular at the cell edge. This is a strong incentive to use this method for the investigation of cancer cell migration on soft substrates.

11 pages; International audience; The initial stages of spreading of a suspended cell onto a substrate under the effect of (specific or nonspecific) adhesion exhibit a universal behavior, which is cell-type independent. We show that this behavior is governed only by cell-scale phenomena. This can be understood if the main retarding force that opposes cell adhesion is of mechanical origin, that is, dissipation occurring during the spreading. By comparing several naive models that generate different patterns of dissipation, we show by numerical simulation that only dissipation due to the deformation of the actin cortex is compatible with the experimental observations. This viscous-like dissipation corresponds to the energetic cost of rearranging the cytoskeleton, and is the trace of all dissipative events occurring in the cell cortex during the early spreading, such as the binding and unbinding of cross-linkers and molecular friction.