Crawling in a fluid

There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a non-motile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends

Dynamics of initial cell spreading : a hydrodynamics-governed process

The initial stages of spreading of a suspended cell onto a substrate under the effect of adhesion are systematically compared to the behaviour of model objects, simulated by finite elements. It has been reported that in different cell and adhesion types the spread area initially grows linearly and then as the square root of elapsed time. In addition our experiments show that the transition between these power-laws is triggered by geometry rather than absolute value of the area or elapsed time. This is shown to mean that mechanics rather than biochemistry govern the dynamics

The flapping of a flag. Numerical investigation of a Kelvin-Helmholtz type instability

L'interaction d'une structure fine et inextensible avec un écoulement est connu pour donner lieu à une déstabilisation en-deça de la transition turbulente dans le fluide. Lorsque l'élasticité de courbure de la structure est faible, cette instabilité est de type Kelvin-Helmholtz. Elle est excitée par la différence d'inertie entre fluide et structure mais elle est stabilisée par la tension. Par simulation numérique, utilisant une approche de multiplicateur de Lagrange pour la tension, et approches analytiques, nous décrivons la déstabilisation qui en résulte

Inextensible membranes or threads immersed in a fluid : a Lagrange multiplier approach

The inextensibility constraint is encountered in many physical problems involving thin solids interacting with a fluid. It is generally imposed in numerical simulations by means of a penalty method. Here, we propose a novel saddle-point approach allowing to impose it through a Lagrange multiplier defined on the thin structure, the tension. The forces originating from the structure appear as a boundary condition for the fluid problem, defined on a moving boundary which represents the structure. The problem is discretised with mixed finite elements, various computation examples are presented

Écoulements tangentiels à des surfaces courbes: application à la morphogenèse de l'embryon

Nous développons une nouvelle approche éléments finis pour des équations aux dérivées partielles elliptiques de type Stokes sur une surface fermée de R3. La surface considérée est décrite par le zéro d'une fonction de niveau assez régulière. Le problème se ramène à la minimisation d'une fonctionnelle énergie pour le champ de vitesse sous contraintes. Les contraintes sont de deux types : (i) la vitesse est tangentielle à la surface, (ii) la surface est inextensible. Cette deuxième contrainte équivaut à l'incompressibilité surfacique du champ de vitesse. Nous abordons ce problème de deux façcons : la pénalisation et l'introduction de deux multiplicateurs de Lagrange. Cette dernière méthode a l'avantage de traiter le cas de la limite incompressible d'un écoulement compressible en surface dont nous présentons pour la première fois l'analyse théorique et numérique. Nous montrons des estimations d'erreurs sur la solution discrète et les tests numériques pour la validation. L'implémentation utilise la librairie libre d'éléments finis [1]. Nous présentons aussi des résultats de simulations numériques pour une application en biologie : la morphogenèse de l'embryon de la drosophile, durant laquelle des déformations tangentielles d'une monocouche de cellules, avec une faible variation de l'aire des cellules. La rhéologie des cellules est décrite dans [2]. Ce phénomène est connu sous le nom de l'extension de la bande germinale

3D migration of cells solving an inverse problem

International audienceTraction Force Microscopy (TFM) is an inverse method that allows to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself during its migration. This biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled in a variational framework. In such a case, a suitable penalty functional has to be minimized. The resulting Euler-Lagrange equations include both the direct problem based on the linear elasticity operator as well as an equation built on its adjoint. Results from a two-dimensional model, i.e. where living cancer cells are migrating on a plane substrate, are briefly presented. While the mathematics is well established also in the three-dimensional case, i.e. where cells are completely embedded in the gel matrix, the experimental data needed are more difficult to obtain than the two-dimensional counterpart. First steps towards the complete three-dimensional traction reconstruction are reported

Mathematical framework for Traction Force Microscopy

International audienceThis 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 problem. The mathematical constraints express the biomechanical conditions that the cell 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 it can capture details more accurately

How the cell got its shape : A visco-elasto-active model of the cytoskeleton

Living cells cytoskeleton is made of polymers which are constantly being re-modelled by polymerisation and depolymerisation, and which are bound to one another (crosslinked) through even more unstable molecules, lasting for about one second. With such a dynamic structure, one may wonder how cells can maintain a given shape over time ranges several orders of magnitude larger than the turn-over time of their constituents. We propose a rheological model which features crosslink turn-over, polymerisation and molecular motor-generated contractile forces, and provides answers to these questions

Addressing climate change with behavioral science:A global intervention tournament in 63 countries

Effectively reducing climate change requires marked, global behavior change. However, it is unclear which strategies are most likely to motivate people to change their climate beliefs and behaviors. Here, we tested 11 expert-crowdsourced interventions on four climate mitigation outcomes: beliefs, policy support, information sharing intention, and an effortful tree-planting behavioral task. Across 59,440 participants from 63 countries, the interventions' effectiveness was small, largely limited to nonclimate skeptics, and differed across outcomes: Beliefs were strengthened mostly by decreasing psychological distance (by 2.3%), policy support by writing a letter to a future-generation member (2.6%), information sharing by negative emotion induction (12.1%), and no intervention increased the more effortful behavior-several interventions even reduced tree planting. Last, the effects of each intervention differed depending on people's initial climate beliefs. These findings suggest that the impact of behavioral climate interventions varies across audiences and target behaviors.</p

Addressing climate change with behavioral science: a global intervention tournament in 63 countries

Effectively reducing climate change requires marked, global behavior change. However, it is unclear which strategies are most likely to motivate people to change their climate beliefs and behaviors. Here, we tested 11 expert-crowdsourced interventions on four climate mitigation outcomes: beliefs, policy support, information sharing intention, and an effortful tree-planting behavioral task. Across 59,440 participants from 63 countries, the interventions’ effectiveness was small, largely limited to nonclimate skeptics, and differed across outcomes: Beliefs were strengthened mostly by decreasing psychological distance (by 2.3%), policy support by writing a letter to a future-generation member (2.6%), information sharing by negative emotion induction (12.1%), and no intervention increased the more effortful behavior—several interventions even reduced tree planting. Last, the effects of each intervention differed depending on people’s initial climate beliefs. These findings suggest that the impact of behavioral climate interventions varies across audiences and target behaviors