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A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility., Comment: 22 pages and 9 figures

During asymmetrical division of the endomesodermal precursor cell EMS, a cortical flow arises, and the daughter cells, endodermal precursor E and mesodermal precursor MS, have an enduring difference in the levels of F-actin and non-muscular myosin. Ablation of the cell cortex suggests that these observed differences lead to differences in cortical tension. The higher F-actin and myosin levels in the MS daughter coincide with cell shape changes and relatively lower tension, indicating a soft, actively moving cell, whereas the lower signal in the E daughter cell is associated with higher tension and a more rigid, spherical shape. The cortical flow is under control of the Wnt signaling pathway. Perturbing the pathway removes the asymmetry arising during EMS division and induces subtle defects in the cellular movements at the eight-cell stage. The perturbed cellular movement appears to be associated with an asymmetric distribution of E-cadherin across the EMS cytokinesis groove. ABpl forms a lamellipodium which preferentially adheres to MS by the E-cadherin HMR-1. The HMR-1 asymmetry across the groove is complete just at the moment cytokinesis completes. Perturbing Wnt signaling equalizes the HMR-1 distribution across the lamellipodium. We conclude that Wnt signaling induces a cortical flow during EMS division, which results in a transition in the cortical contractile network for the daughter cells, as well as an asymmetric distribution of E-cadherin.

Precisely controlled cell deformations are key to cell migration, division and tissue morphogenesis, and have been implicated in cell differentiation during development, as well as cancer progression. In animal cells, shape changes are primarily driven by the cellular cortex, a thin actomyosin network that lies directly underneath the plasma membrane. Myosin-generated forces create tension in the cortical network, and gradients in tension lead to cellular deformations. Recent studies have provided important insight into the molecular control of cortical tension by progressively unveiling cortex composition and organization. In this Cell Science at a Glance article and the accompanying poster, we review our current understanding of cortex composition and architecture. We then discuss how the microscopic properties of the cortex control cortical tension. While many open questions remain, it is now clear that cortical tension can be modulated through both cortex composition and organization, providing multiple levels of regulation for this key cellular property during cell and tissue morphogenesis., Summary: A summary of the composition, architecture, mechanics and function of the cellular actin cortex, which determines the shape of animal cells, and, thus, provides the foundation for cell and tissue morphogenesis.

By consuming energy from the hydrolysis of ATP, cells are able to exert forces that stem from biochemical reactions. A central element of cells is the cytoskeleton, which is mainly composed of microtubules and actin filaments and accounts for the architecture and most of the mechanical properties of the cells. It is made of crosslinked polymers and, in terms of rheology, has a viscoelastic behavior. Within the cytoskeleton, processes such as actin or microtubule polymerization can exert forces. Proteins from the molecular motor family have the specific role of converting the energy stored in chemical form into mechanical energy. The out-of-equilibrium mechanical activity of the cell is directly related to these forces of biochemical origin. In this work, we studied the statistical distribution of biochemical forces exerted on a micrometer-sized bead attached to the actin cortex through cell adhesion receptors: integrins. The study of the forces of biological origin is inseparable from knowledge of the forces of thermal origin because, at this microscopic scale, the contribution of thermal forces is not negligible. The forces acting on the probe have two possible origins: biological or thermal. Our experimental approach is based on the combination of two microrheology techniques, active and passive, which allows us to calculate the temporal autocorrelation function of the forces exerted on a probe attached to the cortical actin and compare it to the autocorrelation function of the estimated thermal forces via the fluctuation-dissipation theorem. The difference between these two spectra gives us an idea of the contribution of the forces of biological origin to the movement of the bead and a measure of the deviation of the system from thermodynamic equilibrium. To further investigate this system, i.e. a bead undergoing forces from the cortical actin, we studied the effect of varying the ligand coating density on the bead. The question that has driven us throughout this work is the origin of these biological forces or, more precisely the nature of the component of the cytoskeleton that exerts these athermal forces. Initially, we studied the influence of temperature on these biological forces. We then studied the effect of depletion of ATP in the cell, of the depolymerization of actin and of the inhibition of molecular motors of the myosin family., La cellule est capable, en consommant l'énergie issue de l'hydrolyse de l'ATP, d'exercer des forces qui prennent leurs origines dans des réactions biochimiques. Un élément important de la cellule est le cytosquelette, composé principalement de microtubules et de filaments d'actine, il en constitue l'architecture et lui donne l'essentiel de ses propriétés mécaniques. Il est composé de polymères réticulés et, du point de vue de la rhéologie, a un comportement viscoélastique. Au sein du cytosquelette, des processus tels que la polymérisation de l'actine ou des microtubules permettent d'exercer des forces. Des protéines, de la famille des moteurs moléculaires, ont pour rôle spécifique de convertir l'énergie stockée sous forme chimique en énergie mécanique. L'activité mécanique hors-équilibre de la cellule est donc directement reliée à ces forces d'origine biochimique. Dans ce travail, nous avons étudié la distribution statistique des forces d'origine biochimique s'exerçant sur une bille de taille micrométrique attachée au cortex d'actine par l'intermédiaire de récepteurs de l'adhésion cellulaire : les intégrines. L'étude des forces d'origine biologique est inséparable de la connaissance des forces d'origine thermique car à cette échelle microscopique la contribution des forces thermiques n'est pas négligeable. Les forces s'exerçant sur la sonde ont deux origines possibles : biologique ou thermique. Notre approche expérimentale est basée sur la combinaison de deux techniques de microrhéologie, active et passive, ce qui nous permet de calculer la fonction d'autocorrélation temporelle des forces exercées sur une sonde accrochée à l'actine corticale et de la comparer à la fonction d'autocorrélation des forces thermiques estimée via le théorème de fluctuation-dissipation. La différence entre ces deux spectres nous donne une idée de la contribution des forces d'origine biologique au mouvement de la bille et une mesure de l'écart du système à l'équilibre thermodynamique. Afin d'étudier plus en détail ce système de bille subissant des forces de la part de l'actine corticale, nous avons étudié l'effet de la variation de la densité de ligand recouvrant la bille. La question qui nous a animés tout au long de ce travail est l'origine de ces forces biologiques ou plus exactement la nature du composant du cytosquelette qui exerce ces forces athermiques. Dans un premier temps, nous avons étudié l'influence de la température sur ces forces biologiques. Nous avons ensuite étudié l'effet de la déplétion de l'ATP dans la cellule, de la dépolymérisation de l'actine et de l'inhibition des moteurs moléculaires de la famille des myosines.