Jocelyn Étienne’s research while affiliated with Grenoble Alpes University and other places

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Publications (100)


Allometric spreading and focal adhesion collective organization are coordinated by cell-scale geometrical constraints
  • Preprint

January 2025

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8 Reads

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Ali-Alhadi Wahhod

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Démosthène Mitrossilis

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[...]

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Jonathan Fouchard

Focal adhesions are protein complexes that transmit actin cytoskeleton forces to the extracellular matrix and serve as signaling hubs that regulate cell physiology. While their growth is achieved through a local force-dependent process, the requirement of sustaining stress at the cell scale suggests a global regulation of the collective organization of focal adhesions. To investigate evidence of such large-scale regulation, we compared changes in cell shape and the organization of focal adhesion-like structures during the early spreading of fibroblasts either on a two-dimensional substrate or confined between two parallel plates, and for cells of different volumes. In this way, we reveal that the areal density of focal adhesions is conserved regardless of cell size or third-dimensional confinement, despite different absolute values of the surface covered by adhesion clusters. In particular, the width of the focal adhesions ring, which fills the flat lamella at the cell front, adapts to cell size and third-dimensional confinement and scales with cell-substrate contact radius. We find that this contact radius also adapts in the parallel-plate geometry so that the cumulated area of cell-substrate contact is conserved at the cell scale. We suggest that this behavior is the result of 3D cell shape changes which govern spreading transitions. Indeed, because of volume conservation constraints, the evolution of cell-body contact angle adjusts according to cell size and confinement, whereas the rate of early spreading at the cell-substrate contact is not affected by third-dimensional geometry. Overall, our data suggest that a coordination between global and local scales mediates the adaptation of cell-substrate contacts and focal adhesions distribution to large scale geometrical constraints, which allows an invariant cell-substrate adhesive energy.


Network model. A, Chains made of a finite number of freely-jointed segments. Each is described by an end-to-end vector R∼ and can be modelled as a spring. They can connect to other chains at their ends. B, If a global deformation ∇∼v∼ exists, bound chains are affinely deformed, Eq. (1). The additional active flux j∼a is described in Sect. 2.3. C, Unbound end of a chain is submitted to spring force F∼s and to a Brownian force F∼b. Unbound chains relax extremely fast to a configuration where those forces balance. Bound ends (configuration 1) unbind at rate ku\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k_{\mathrm{u}}$\end{document} and the chain thus relaxes (configuration 2). They will then quickly rebind at rate kb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k_{\mathrm{b}}$\end{document} (configuration 3) but do so in their relaxed state
Multiplicative decomposition of the deformation gradient for viscoelastic active fluids
Uniaxially contractile beam interacting with an elastic environment. A, The initial configuration Ω0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega _{0}$\end{document} of the beam, before the active strain E≈a has been applied, is chosen here at equilibrium with the external springs. The visco-active deformation F≈va(t) gives the intermediate virtual configuration Ωva(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega _{\mathrm{va}}(t)$\end{document}, a configuration which is not compatible with the external forces and does not obey incompressibility. The elastic deformation F≈e(t) restores both of these requirements in the current configuration Ω(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega (t)$\end{document}. The time evolution of F≈va(t) is prescribed by the relaxation dynamics of the microstructure A≈ towards a state where the elastic stress is equal to the active stress, σ≈(teq)=νκ(A≈(teq)−A≈0)=−GE≈a. B-D, Dynamics for a contractile strain E≈a=−a2e∼xe∼x for different values of a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document} and G/Es=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G/E_{s}=1$\end{document}. In all cases, the contractile strain drives an initial decreasing γx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma _{x}$\end{document} (active shortening) which is partly balanced by an increasing αx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _{x}$\end{document} (elastic stretch), resulting in a lesser shortening of the current configuration λx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{x}$\end{document}. Incompressibility imposes a swelling in the radial direction, λr>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{r}>1$\end{document}, which after a transient elastic stretch αr>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _{r}>1$\end{document} drives a viscoelastic relaxation towards γr=λr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma _{r}=\lambda _{r}$\end{document}. B, for a=0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a=0.1$\end{document}, the contraction is 90% of the final contraction at t≈17τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\approx 17\tau $\end{document}. C, for a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document} equal to the critical value ac≈0.35\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a_{c}\approx 0.35$\end{document}, the contraction is 90% of the final contraction at t≈195τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\approx 195\tau $\end{document}. D, for a contractility slightly above the critical value, the contraction reaches the critical value 0.5 at t≈229τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\approx 229\tau $\end{document}, the beam then collapses tending to 0 length while the radial stretch diverges
Tangentially contractile sphere bound elastically to a fixed sphere. A, The initial, intermediate and current configurations of the contractile sphere. In the current configuration, mechanical balance with the Winkler foundation which binds it to a fixed sphere of radius ρ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho _{0}$\end{document} has to be verified. B,C, Dynamics for ac=2/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a_{c} = \sqrt{2}/2$\end{document} and an orthoradial contractile strain E≈a=−12a2(I≈−e∼re∼r) with two different magnitudes of a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document}, respectively below and above the critical value ac\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a_{c}$\end{document}. Transient behaviours similar to the case of the contractile beam are observed, although the axes in which they appear differs due to the different geometry and active stress orientation
Mechanics and Thermodynamics of Contractile Entropic Biopolymer Networks
  • Article
  • Publisher preview available

January 2025

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14 Reads

Journal of Elasticity

Contractile biopolymer networks, such as the actomyosin meshwork of animal cells, are ubiquitous in living organisms. The active gel theory, which provides a thermodynamic framework for these materials, has been mostly used in conjunction with the assumption that the microstructure of the biopolymer network is based on rigid rods. However, experimentally, crosslinked actin networks exhibit entropic elasticity. Here we combine an entropic elasticity kinetic theory, in the spirit of the Green and Tobolsky model of transiently crosslinked networks, with an active flux modelling biological activity. We determine this active flux by applying Onsager reciprocal relations to the corresponding microscopic dynamics. We derive the macroscopic active stress that arises from the resulting dynamics and obtain a closed-form model of the macroscopic mechanical behaviour. We show how this model can be rewritten using the framework of multiplicative deformation gradient decomposition, which is convenient for the resolution of such problems.

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Disentangling the contributions of stress fibres and the unbundled actin meshwork to the anisotropy of cortical tension in response to cell shape

October 2024

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20 Reads

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1 Citation

Many fundamental biological processes, in particular development and morphogenetic movements, involve tissue and cell deformation, as well as the generation of anisotropic mechanical stresses. They are often accompanied by the appearance of oriented contractile actomyosin structures resembling the stress fibres (SF) observed in vitro. Here, we investigate, at the single cell level, how cell shape - by itself - could control the structure and tension of the actomyosin cortex. Using a unique combination of 3D micropatterning, single peripheral SF (PSF) tension measurement, laser ablation and image analysis, we show that cell shape anisotropy, e.g. its 2D aspect ratio, is indeed sufficient to induce anisotropy of the cortical structure and tension. In particular, taking into account the experimentally measured anisotropy of the cortical meshwork, we could quantify cortical tension and decouple the contribution originating from bundled actin (oriented cortical stress fibres, CSF) and the contribution of the unbundled actin meshwork (UAM). We show that the increase of cortical tension anisotropy with the cell's aspect ratio depends on the CSF alignment and orientation, the contribution of the isotropic mesh being independent of cell shape. Remarkably, while experimental data from single stress fibre measurements and laser ablation were analysed through different theoretical frameworks, namely that of negative pressure in nematics and hole drilling in prestressed materials, we found quantitatively the same composite material behaviour. In sum, we decipher here the very material properties of the actomyosin cortex, and its sensitivity to cell shape which is at the root of many mechanobiological processes, in particular morphogenesis.



Initiation of motility on a compliant substrate

March 2023

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15 Reads

The conditions under which biological cells switch from a static to a motile state are fundamental to the understanding of many healthy and pathological processes. We show that even in the presence of a fully symmetric protrusive activity at the cell edges, such a spontaneous transition can result solely from the mechanical interaction of the cell traction forces with an elastic substrate. The loss of symmetry of the traction forces leading to the cell propulsion is rooted in the fact that the surface loading follows the substrate deformation. We analytically characterize the bifurcation between the static and motile states and, considering the measurements performed on two cell types, we show that such an instability can realistically occur on soft in vivo substrates.


How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

October 2022

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131 Reads

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6 Citations

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress—topological prestress—can result from active processes altering the microstructure of tissue.


Figure 1: Prestrain and prestress in simple 1D systems. (a) Illustration of deformation gradient decomposition for contractile prestrain. An active element (red) and a passive one (gray) are put in parallel in between force-bearing walls (black vertical lines). The active element is composed of a spring whose length is actively decreased (or increased) from L 0 to L, with an anelastic stretch, or prestrain, λ a (here λ a < 1) imposed via a crank. In the virtual configuration, both elements remain stress-free but the system's topology (dashed line connections) is not respected. In the current configuration, even at equilibrium (no net force on the walls), the structure is under stress. Operating the crank the other way, λ a > 1, gives the effect of growth prestrain. (b) A system equivalent to the one in a can be obtained by replacing the active crank and spring element by a stress generator element (pulleys and weight system) whose magnitude is the prestress. (c) For topological prestress, no active spring is necessary; the activity consists of disconnecting and reconnecting elements into a new network. Initially, springs k 1 and k 2 are in parallel, and the pair is connected in series with k 3 . The topological change reconnects the springs, such that k 1 and k 3 are in series, this pair connected in parallel with k 2 . Due to the change of topology (see directed graph insets) the initially stress-free structure becomes prestressed; spring k 2 is in tension, springs k 1 and k 3 are in compression. (d ) A viscous passive element (dashpot) in parallel with a stress generator gives a permanent regime of contraction at a constant strain rate.
Figure 4: Growth and/or contractile prestress governs the shape of subcellular, cellular and tissue-scale structures through mechanical connection between active and passive elements. (a) In podosomes, protruding forces applied by the actin core (growing at a rate v p ) onto the substrate are balanced by a contractile actomyosin network of prestress (σ a ), organised as a dome and attached to the substrate at the periphery via adhesion proteins [Labernadie et al., 2014]. (b) In adherent cells, actomyosin prestress (σ a ) is balanced by cytosol pressure (∆P) and substrate deformation. Cell shape is further refined by anisotropic and heterogeneous actomyosin network contraction. Here, orthoradial stress fibres are connected to radial stress fibres, which are attached to the substrate via adhesion proteins at the cell periphery [Burnette et al., 2014]. (c) In the zebrafish semicircular canal, pressure (∆P) is generated within the ECM via synthesis of hyaluronan, pumping in interstitial fluid. This deforms the overlying epithelium which is further shaped by an anisotropic prestress (σ a ) generated by actin-and cadherin-rich protrusions [Munjal et al., 2021].
Figure 5: Example biophysical systems where mechanics is governed by heterogeneous, anisotropic or differential prestress of either sign, corresponding to contraction or growth. (a) Contractile actomyosin with local accumulation, in parallel with a length-regulating element and in continuous adhesion with a substrate, generates a friction pattern that enables motility [Recho et al., 2013]. (b) Anisotropic pretension of the apical surface of cells regulates their shape [Burnette et al., 2014]. (c) Differential prestress between the weakly contractile apical (top) surface and strongly contractile basal (bottom) surface causes tissue curling [Recho et al., 2020] (d ) Residual stress due to heterogeneous growth is characterised by cutting experiments in tumours, revealing tensile hoop stress at the periphery [Stylianopoulos et al., 2012] (e) The core of podosomes grows within a confined space, generating anisotropic prestress [Labernadie et al., 2014] (f ) Arteries change curvature if cut, this is believed to be caused by differential growth and remodelling of concentric layers [Goriely and Vandiver, 2010]
Review: How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

September 2022

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574 Reads

Cells and tissues change shape both to {carry out} their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualise the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularised tissues. Despite the diversity of scale and organisation, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorised as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress -- topological prestress -- can result from active processes altering the microstructure of tissue.


Using IR fs laser ablation to demonstrate the necessity and building of a model to test the sufficiency of apical contraction to drive VFF
a Recoil and recovery of the ventral apical actomyosin network after laser ablation. The ablation is performed along the DV axis across the ventral tissue. MyoII is depleted along the ablated region while membrane signal density eventually decreases as a consequence of cell dilation. Panel shows representative experiment. Experiment repeated 5 times on 5 different embryos. Scale bar 10 μm. b Cross-sectional view of the embryo ventral side just before (t0 and t1) and just after (t2) laser ablation, and (t3) after actomyosin recovery. Time between t0 and t3 is 3 min. Laser ablations were performed similarly as in (a). Panel shows representative experiment. Experiment repeated 4 times on 4 different embryos. Scale bar 20 μm. c Curvature analysis before and after laser ablation and during actomyosin network recovery as shown in (b). n = 4 embryos, data are presented as mean values ± standard deviation. The statistical test performed was Kruskal–Wallis test for multiple comparisons, *p ≤ 0.05 and ns (non-significant), p > 0.05. d Digital mid-cross-sections before and during furrow formation in wild-type and slam⁻dunk⁻ acellular embryos. Panel shows representative case, n = 4 embryos. Scale bar 50 μm. e Representation of the embryo geometry with the mesoderm region highlighted. f Finite element mesh of an embryo-shaped elastic surface where some facets will be pre-strained to mimic MyoII activity (colour code, log scale, nondim. nondimensional units). g Circles, MyoII profile at different phases of VFF as a function of distance from the ventral midline, normalized using the intensity of cells at midline (row 0, see the “Methods” section), in experiments (average of n = 3 embryos, confocal microscopy). Line, pre-stress profile chosen for simulations. This profile is also similar to the one reported by ref. ³³.
Actomyosin contractility drives tension anisotropy on the ventral side of the embryo
a Strain angular profile (current size relative to initial size) along the AP and DV axes for midline pre-strain εam=0.43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }_{{{{{{{{\rm{a}}}}}}}}}^{{{{{{{{\rm{m}}}}}}}}}=0.43$$\end{document}. b Mechanical stress (sum of the two principal stresses) resulting from the area pre-strain. Midline pre-strain εam=0.43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }_{{{{{{{{\rm{a}}}}}}}}}^{{{{{{{{\rm{m}}}}}}}}}=0.43$$\end{document}. Black line corresponds to the boundary of the pre-strained region in the current configuration. See tensor components in Supplementary Fig. 1b. c Angular profiles of the pre-stress σa and of the two principal stresses along the AP and DV axes for εam=0.43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }_{{{{{{{{\rm{a}}}}}}}}}^{{{{{{{{\rm{m}}}}}}}}}=0.43$$\end{document}. d Same as (b) for εam=5.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }_{{{{{{{{\rm{a}}}}}}}}}^{{{{{{{{\rm{m}}}}}}}}}=5.25$$\end{document}. See tensor components in Supplementary Fig. 1d and profiles in Supplementary Fig. 1e, f. e Isotropic pre-strain pattern (left) yields anisotropic mechanical response, with a greater stress and strain along the AP and DV axes, respectively. The cells at the periphery of the mesoderm move towards it, arrows, which generates a hoop stress along the dotted line. f Colour code for panels (b) and (d). All panels are for nondimensional mechanical parameters χ̃2D=50\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde{\chi }}_{{{{{{{{\rm{2D}}}}}}}}}=50$$\end{document} and ν2D = 0, see Supplementary Information.
In vivo apical area changes are reproduced by the computational model
a MyoII average intensity and mesoderm apical area changes as a function of time, for in vivo analysis and simulations, averaged over all cells within five rows of the ventral midline. b Apical area fold-change relative to the initial area (t = −4 min) of cells at different lateral distances from the midline at t = −1 min, in observations for in vivo analysis and simulations. (c) Apical AP size fold-change relative to the initial size (t = −4 min) of cells at different lateral distances from the midline at t = −1 min, d Apical DV size fold-change relative to the initial size (t = − 4 min) of cells at different lateral distances from the midline at t = −1 min, for in vivo analysis and simulations. Panels (a–d), n = 3 embryos using multi-view light sheet and n = 3 embryos using confocal microscopy, shaded areas in (a) and error bars in (b–d), minimum and maximum values among the corresponding embryos. e, f Time evolution of AP stripes of apical surface in simulation and MuVi SPIM, respectively.
VFF results from tissue curvature changes along the DV and AP axes
a Embryo shape during VFF in simulations at t=4′12″\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=4^{\prime} 12^{\prime\prime}$$\end{document}. Shading reveals furrow shape, blue arrowheads. Dotted lines are transverse cuts, solid lines give the furrow apex offset from a reference z position at different x positions. b Furrow apex position at different AP positions as a function of time in MuVi SPIM experiments (solid lines, posterior side, dotted lines, anterior side, n = 6) and simulations (dashed lines and arrow showing slope at t=3′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t={3}^{\prime}$$\end{document}). c Rate of furrow formation at different AP positions at t=3′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t={3}^{\prime}$$\end{document}. d Digital cross-sections at different AP positions. White arrowheads indicate VFF initiation. Scale bar 100 μm. e Digital mid-sagittal section of the embryo. Red line indicates ventral tissue flattening. Scale bars 100 μm, zoom 50 μm. f Curvature of the ventral tissue along the AP and DV axes as a function of time (MuVi SPIM, n = 6 embryos, shaded area denotes minimum and maximum).
Embryo poles function as anchoring sites for ventral midline flattening and furrow formation
a Distance map of the apical surface to the vitelline membrane at different phases of VFF. b Forces exerted on the poles by the rest of the tissue (red arrows), and pressure forces exerted by the incompressible cytoplasms (grey arrowheads), pole tissue deformation (compare shape of solid-filled regions) and displacement of the pole (solid and dashed lines) in simulations. c Digital mid-sagittal section showing inward displacement of the pole tissue during VFF. Scale bar 100 μm, zoom 5 μm. d Tension distribution at different DV positions from the ventral midline in simulations at t=0′30″\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0^{\prime} 30^{\prime\prime}$$\end{document}. e Recoil velocity distribution after DV-oriented IR fs laser ablation at different DV positions from the ventral midline. n = 6 embryos, data are presented as mean values ± standard deviation; the statistical test performed was Kruskal–Wallis test for multiple comparisons, *p ≤ 0.05; ***p ≤ 0.001 and n.s. (not significant), p > 0.05. f Digital mid-sagittal and cross sections of an embryo on which two cauterizations (red arrowheads), acting as fixed points, have been performed at the ventral side (tc indicates time of cauterization). The red line indicates tissue straightening along the embryo mid-sagittal section in between the two cauterized regions. Experiment performed and result reproduced 3 times. Scale bar sagittal view 100 μm. Scale bar cross-section 50 μm.
Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation

June 2022

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329 Reads

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32 Citations

Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation.


Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

January 2022

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46 Reads

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18 Citations

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. 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 cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.


Cell crawling on a compliant substrate: a biphasic relation with linear friction

December 2021

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125 Reads

A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the cell dynamics. By considering a cell constrained to move along a one-dimensional thin track, we take advantage of the problem geometry to explicitly derive the effective law that describes the non-local frictional contact between the cell and the deformable substrate. We then couple such a law with one of the simplest model of the active flow within the cell cytoskeleton. This offers a paradigm that does not invoke any local non-linear friction law to explain that the relation between the cell steady state velocity and the substrate elasticity is non linear as experimentally observed. Additionally, we present an experimental platform to test our theoretical predictions. While our efforts are still not conclusive in this respect as more cell types need to be investigated, our analysis of the coupling between the substrate displacement and the actin flow leads to friction coefficient estimates that are in-line with some previously reported results.


Citations (24)


... The relevance of this model for actomyosin-based systems is discussed in [28], where we also find that a viscoelastic liquid material with an internal active stress adapts in length to the external stiffness E s . It may also be seen as a modelling framework for the so-called actin ventral stress fibres [53,54]. ...

Reference:

Mechanics and Thermodynamics of Contractile Entropic Biopolymer Networks
Disentangling the contributions of stress fibres and the unbundled actin meshwork to the anisotropy of cortical tension in response to cell shape
  • Citing Preprint
  • October 2024

... Continuum modelling approaches have been able to reproduce a number of the behaviours of the actomyosin cytoskeleton by the introduction of an active stress as a driving force within a liquid-like material modelling the network [11]. This active stress can be interpreted as a dynamic prestress [12], allowing to draw analogies with the residual stress which is observed in solid-like tissue [13,14]. The theory of active gels [15,16], drawing from the hydrodynamics of suspensions of orientable objects endowed with active stresses [17], has provided a sound thermodynamic framework for the generation of this active stress by molecular motors. ...

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

... According to a simulation study, an actomyosin ring is likely responsible for epithelial folding [127]. Gastrulation is initiated by a propagating furrow, which is initiated by epithelial buckling in Drosophila embryos [128]. Importantly, to drive this buckling, embryo-scale force balance is necessary and sufficient [128]. ...

Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation

... For liquid-like systems, an additional phenomenon is the microstructure relaxation. Many numerical models that aim at reproducing the phenomenology of microstructure relaxation use an algorithm that can formally be likened to morphoelasticity: at each time step, solve [48,49]. However this approach is very crude in the sense that it cannot describe any dynamics at a characteristic time close or smaller than the relaxation time of the material, and of course that its thermodynamics are uncontrolled. ...

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

... By taking into account the role of adhesions, membrane tension and polymerization in a simple way Lin shows that at low speeds the adhesive force increases linearly in a viscous-like manner, while at high speeds, it falls off exponentially. Chelly et al. [26] provide the following intuitive explanation for a biphasic traction stress-velocity relation: when the actin velocity is sufficiently small, the force in the bound springs increases slowly and this leads to a linear increase in the traction stress with velocity. When the actin velocity is sufficiently large, the bonds break rapidly and the traction stress decreases with velocity. ...

Cell crawling on a compliant substrate: A biphasic relation with linear friction
  • Citing Article
  • December 2021

International Journal of Non-Linear Mechanics

... The latter, variational methods featuring explicit motion models, can be divided in two categories. The first ones model the motion as an evolutionary PDE (Burger et al. 2017Dirks 2015;Frerking 2016) using optical flow (Horn and Schunck 1981) or a continuity equation Lang et al. 2019a), either as a constraint or in the form of a penalty term in the variational reconstruction model. Some prominent applications of this approach are in dynamic photoacoustic tomography (Lucka et al. 2018) and 3D computed tomography (Djurabekova et al. 2019), just to name a few. ...

Joint Motion Estimation and Source Identification Using Convective Regularisation with an Application to the Analysis of Laser Nanoablations
  • Citing Chapter
  • January 2021

... To imitate the intrinsic asymmetry of flagellates and other microorganisms, active colloids are designed with fore-aft asymmetric chemical activity, which defines their polar axis and their preferential direction of motion [11,12]. Alternatively, in the absence of a built-in asymmetry, a polar axis defining the direction of motion of an isotropic active particle can emerge from a spontaneous symmetry-breaking instability [13][14][15][16][17][18][19] that is reminiscent of that used by cells to migrate [20][21][22]. However, unlike their biological counterparts that have evolved internal mechanochemical processes to actively change the direction of motion [23], active colloids can only rely on passive rotational diffusion [12]. ...

Crawling in a Fluid
  • Citing Article
  • September 2019

Physical Review Letters

... gin of the pulsations, contrasting emergence versus upstream signalling [15,33]. In favour of pulsations being emergent, it has been argued that advection, caused by myosin-induced contractions, can by itself produce enough of a positive feedback mechanism to sustain actomyosin oscillations [11,31]. ...

From pulsatile apicomedial contractility to effective epithelial mechanics
  • Citing Article
  • August 2018

Current Opinion in Genetics & Development

... There is no physical picture of how the intricate geometry of the Volvox ECM arises through what must be a self-organized process of polymer crosslinking [37]. While information on a structure's growth dynamics can be inferred from its evolving shape, as done for animal epithelial cells [38], this connection has not been made for Volvox. ...

Geometry can provide long-range mechanical guidance for embryogenesis