Jocelyn Étienne

Cells as liquid motors: Mechanosensitivity emerges from collective dynamics of actomyosin cortex

Significance Animals have muscles to act on their environment. The molecules endowing them with this faculty are actin and myosin and are also present in nonmuscle cells. Our modelling breaks down the motor-like properties of the actomyosin network in single nonmuscle cells, which show striking similarity to the properties of muscles. In particular, an internal friction sets the maximum speed of contraction of both cells and muscles when myosins do not have time to detach after pulling, just as rowers lifting their oars too slowly after their stroke. The same modelling explains cell-scale mechanosensing: the combination of myosin-driven contraction and actin polymerization-driven protrusivity regulates cell length in a force-dependent manner, making response to rigidity a property of the very material of the cell cortex. 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.

Numerical simulations of high density ratio lock-exchange flows

In this paper direct numerical simulations of exchange flows of large density ratios are presented and are compared with experiments by Grobelbauer 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...

Emergent material properties of developing epithelial tissues.

BackgroundForce 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.ResultsWe 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.ConclusionsOur 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.

Initial dynamics of cell spreading are governed by dissipation in the actin cortex

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.

Numerical simulations of dense clouds on steep slopes: application to powder-snow avalanches

Abstract In this paper, two-dimensional direct numerical simulations (DNS) of dense clouds moving down steep slopes are presented for the first time. The results obtained are in good agreement with the overall characteristics, i.e. the spatial growth rate and velocity variations, of clouds studied in the laboratory. In addition to the overall flow structure, DNS provide local density and velocity variations inside the cloud, not easily accessible in experiments. The validity of two-dimensional simulations as a first approach is confirmed by the dynamics of the flow and by comparison with experimental results. The interest of the results for powder-snow avalanches is discussed; it is concluded that two-dimensionality is acceptable and that large density differences need to be taken into account in future simulations.

Geometry can provide long-range mechanical guidance for embryogenesis

Downstream of gene expression, effectors such as the actomyosin contractile machinery drive embryo morphogenesis. During Drosophila embryonic axis extension, actomyosin has a specific planar-polarised organisation, which is responsible for oriented cell intercalation. In addition to these cell rearrangements, cell shape changes also contribute to tissue deformation. While cell-autonomous dynamics are well described, understanding the tissue-scale behaviour challenges us to solve the corresponding mechanical problem at the scale of the whole embryo, since mechanical resistance of all neighbouring epithelia will feedback on individual cells. Here we propose a novel numerical approach to compute the whole-embryo dynamics of the actomyosin-rich apical epithelial surface. We input in the model specific patterns of actomyosin contractility, such as the planar-polarisation of actomyosin in defined ventro-lateral regions of the embryo. Tissue strain rates and displacements are then predicted over the whole embryo surface according to the global balance of stresses and the material behaviour of the epithelium. Epithelia are modelled using a rheological law that relates the rate of deformation to the local stresses and actomyosin anisotropic contractility. Predicted flow patterns are consistent with the cell flows observed when imaging Drosophila axis extension in toto, using light sheet microscopy. The agreement between model and experimental data indicates that the anisotropic contractility of planar-polarised actomyosin in the ventro-lateral germband tissue can directly cause the tissue-scale deformations of the whole embryo. The three-dimensional mechanical balance is dependent on the geometry of the embryo, whose curved surface is taken into account in the simulations. Importantly, we find that to reproduce experimental flows, the model requires the presence of the cephalic furrow, a fold located anteriorly of the extending tissues. The presence of this geometric feature, through the global mechanical balance, guides the flow and orients extension towards the posterior end.

Inverse problems for the determination of traction forces by cells on a substrate: a comparison of two methods

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.

Prediction of traction forces of motile cells

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.

From pulsatile apicomedial contractility to effective epithelial mechanics

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.