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Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell-cell and cell-substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.

International audience; In most instances, the growth of solid tumors occurs in constrained environments and requires a competition for space. A mechanical crosstalk can arise from this competition. In this article, we dissect the biomechanical sequence caused by a controlled compressive stress on multicellular spheroids (MCSs) used as a tumor model system. On timescales of minutes, we show that a compressive stress causes a reduction of the MCS volume, linked to a reduction of the cell volume in the core of the MCS. On timescales of hours, we observe a reversible induction of the proliferation inhibitor, p27Kip1, from the center to the periphery of the spheroid. On timescales of days, we observe that cells are blocked in the cell cycle at the late G1 checkpoint, the restriction point. We show that the effect of pressure on the proliferation can be antagonized by silencing p27Kip1. Finally, we quantify a clear correlation between the pressure-induced volume change and the growth rate of the spheroid. The compression-induced proliferation arrest that we studied is conserved for five cell lines, and is completely reversible. It demonstrates a generic crosstalk between mechanical stresses and the key players of cell cycle regulation. Our results suggest a role of volume change in the sensitivity to pressure, and that p27Kip1 is strongly influenced by this change.

The mechanical and dynamical properties of the actin network are essential for many cellular processes like motility or division, and there is a growing body of evidence that they are also important for adhesion and trafficking. The leading edge of migrating cells is pushed out by the polymerization of actin networks, a process orchestrated by cross-linkers and other actin-binding proteins. In vitro physical characterizations show that these same proteins control the elastic properties of actin gels. Here we use a biomimetic system of Listeria monocytogenes, beads coated with an activator of actin polymerization, to assess the role of various actin-binding proteins in propulsion. We find that the properties of actin-based movement are clearly affected by the presence of cross-linkers. By monitoring the evolution of marked parts of the comet, we provide direct experimental evidence that the actin gel continuously undergoes deformations during the growth of the comet. Depending on the protein composition in the motility medium, deformations arise from either gel elasticity or monomer diffusion through the actin comet. Our findings demonstrate that actin-based movement is governed by the mechanical properties of the actin network, which are fine-tuned by proteins involved in actin dynamics and assembly.

Processive motor proteins such as kinesin and myosin-V are enzymes that use the energy of ATP hydrolysis to travel along polar cytoskeletal filaments. One of the functions of these proteins is the transport of vesicles and protein complexes that are linked to the light chains of the motors. Modeling the light chain by a linear elastic spring, and using the two-state model for one- and two-headed molecular motors, we study the influence of thermal fluctuations of the cargo on the motion of the motor-cargo complex. We solve numerically the Fokker-Planck equations of motor motion, and find that the mean velocity of the motor-cargo complex decreases monotonously as the spring becomes softer. This effect is due to the random force of thermal fluctuations of the cargo disrupting the operation of the motor. Increasing the size (thus, the friction coefficient) of the cargo also decreases the velocity. Surprisingly, we find that for a given size of the cargo, the velocity has a maximum for a certain friction of the motor. We explain this effect by the interplay between the characteristic length of thermal fluctuations of the cargo on a spring, the motor diffusion length, and the filament period. Our results may be relevant for the interpretation of single-molecule experiments with molecular motors (bead assays), where the motor motion is observed by tracking of a bead attached to the motor.

We give a simple picture of transient and stationary transport in lipid nanotubes connecting two vesicles, when a difference of membrane tension is imposed at time t = 0, either by pressing one vesicle with a micro-fiber, or by adding a surplus of membrane lipid. The net result is a transport of membrane from the tense towards the floppy vesicle. In the early stage, the tube remains cylindrical, and the gradient of surface tension gives rise to two opposite flows of the internal liquid: a Marangoni flow towards the direction of high tension, and a Poiseuille flow (induced by Laplace pressures) in the opposite direction. At longer time, the tube reaches a stationary state, where curvature and Laplace pressure are balanced. Marangoni flows dominate for giant vesicles, where Laplace pressure is negligible.

We discuss theoretically the relaxation of charge fluctuations in polyampholyte solutions. It has been shown previously by some of us (J. Wittmer et al. Europhys. Lett. 24, 263 (1993)) that the charge distribution along the polyampholyte backbone has a dramatic influence on the polarization energy and hence on the solubility. Here it is demonstrated that a similar effect exists for the charge relaxation. The charge relaxation mechanism qualitatively depends on the statistics: for alternating polyampholytes the relaxation is mainly due to local dipole inversion and is not primarily driven by electrostatic interactions, whereas for random polyampholytes it is driven by electrostatic interactions. Intermediate statistics (with short-ranged (exponential) correlations) appear as a combination of these two limiting cases: short-wavelength modes are insensitive to the loss of correlations along the backbone, whereas long-wavelength modes correspond to a random statistics with renormalized charges. The relaxation of the dielectric constant is also calculated.

International audience; Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.

In previous theories of sheared grafted polymer layers, the chain configurations are stationary. Formally, the shear stress is thus always supported by the same chains. These models predict that the response to the flow (in plane tension at the wall, free end deflection) is larger than the thermodynamic fluctuations for Deborah numbers De 1. Here we take into account the exchange of the chain configurations so that an individual chain on average does not support the shear stress long enough to reach a steady-state configuration. This effect smears out the response to flow over a larger number of chains, those with ends within one coil radius from the edge. The response only reaches the magnitude of the thermal fluctuations for De = 1. This corresponds in practice to shear rates as high as several 104s−1. Recent experiments by Baker et al. indeed show that self-assembled copolymer layers are very stable against steady shear flow, shear-induced desorption is only detected for De ~ 1.

In this paper we discuss the elements of a recent mean-field theory developed to describe the structure of an adsorbed polymer layer. Recently it has been shown by Semenov and Joanny that the central part of an adsorbed polymer layer does not display a self-similar structure but the profiles depend on a characteristic length-scale z*. This length separates the region domainted by the loops from the region where tails are dominant and it is only dependent on the size of the chain and on the dimension of the space. The results of the mean-field calculation are compared with the numerical solution of the full self-consistent field calculations.

The influence of a weak shear flow on the micellization of diblock copolymers in selective solvents is investigated. The micelles are described as small microgel beads and the hydrodynamic fields calculated within the Brinkman approximation. The critical micellar concentration is shown to decrease in the shear flow, leading to the possibility of shear-induced micellization. It is also shown that the aggregation number of the micelles is modified by the flow: it increases for micelles with a large asymmetry but decreases for more symmetric micelles

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We study some dynamical aspects of grafted polymer layers in a solvent. The structure of the brush is described in a θ solvent by the self‐consistent mean field theory and in a good solvent using scaling laws. The Rouse–Zimm model including hydrodynamic interactions is used for the dynamic properties. A given chain end explores the entire thickness of a free grafted layer in a time Te proportional to the cube of the thickness. The exploration time is much larger than the Rouse time that characterizes the relaxation of the fluctuations of the chains conformations. In a θ‐solvent we give a detailed study of the relaxation of the density of a few labeled chain ends towards its equilibrium value. The bridging kinetics between a grafting plate and a plate adsorbing the free ends is also discussed. When adsorption proceeds, an exclusion zone grows in the vicinity of the adsorbing plate. To cross the exclusion zone and adsorb, a chain end must overcome an energy barrier. The typical adsorption time is the first ...

We study the adsorption of a polymer brush on a solid plate parallel to the plate where the chains are grafted in the limit where only the free-end monomers of the grafted chains adsorb. In the vicinity of the adsorbing plate, there exists a dead zone where no free chain ends are found; the monomer concentration is constant in this region and parabolic close to the grafting plate. In the absence of external force, the equilibrium distance between the two plates is smaller than the natural brush size. The fraction of chains forming bridges increases linearly with the adsorption energy at small adsorption energy and reaches one for a finite adsorption energy. The effect of an external force is also briefly discussed.

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.

Contact angle hysteresis on weakly heterogeneous surfaces is studied using an extension of Imry and Ma's analysis of the random field problem. Deformations of the liquid-vapor interface in response to the heterogeneity are characterized by a length Ld which increases as the magnitude of the heterogeneity decreases. The characteristic energy associated with these deformations is used to find the scale of contact angle hysteresis. In the absence of gravity, contact angle hysteresis occurs for arbitrarily weak heterogeneity. Hysteresis disappears when Ld exceeds the gravitational capillary length, while systems with characteristic size less than Ld show increased hysteresis.

We review some recent results on phase separation of polymer mixtures and on mesophase formation of diblock copolymers in solution. Mixtures of two chemically different polymers most often segregate in solution. Their phase diagram and the related critical properties are studied in a solvent that can be either a good solvent for both polymers or a θ-solvent for both polymers or a selective solvent (good for one polymer, θ for the other). Diblock copolymers in dilute or semidilute solutions form several kinds of mesophases with different symmetries. The onset of formation of some of these phases is discussed in a highly selective solvent good for one block and poor for the other, and in a common good solvent.

We report a study of a fingering instability which occurs during the spreading of a spinning drop. We measure the time evolution of the drop profile, the critical radius for instability onset, and the fastest growing instability wavelength. The experimental results are compatible with the predictions of lubrication theory when the centrifugal effect is not too large compared to the capillary one.

The wetting properties of a solid surface by a liquid are very sensitive to surface heterogeneities: the contact line becomes wiggly, and the final equilibrium structure of the liquid droplet or liquid film on the surface is history dependent on a heterogeneous surface (in the case of partial wetting, this phenomenon is known as contact angle hysteresis). We study here the statistics of a wiggly contact line on a heterogeneous solid, both for totally or partially wetting fluids.

Insoluble monolayers in the presence of dipolar forces have been predicted to fcrm lamellar and hexagonal supercrystal phases at the liquid-gas or liquid-expanded — liquid-condensed transition. We study here the dynamics of the initial stages of the formation of these supercrystal phases including the flow induced in the supporting liquid in three different geometries a) free films b) films on a solid c) film on a bulk liquid phase.

The interaction between two plates coated by adsorbed polymer layers is considered theoretically in the marginal solvent regime. A novel mean-field approach that takes into account the effect of chain ends is proposed. The approach generalizes the well-known ground-state dominance theory. It is shown that the effect of polymer chain ends is important even if there is no specific interaction between the ends and the adsorbing plates. Both cases of polymer layers in equilibrium with a bulk dilute or semidilute solution and of fixed amount of polymer between the plates are considered. In all the cases the effect of polymer chain ends changes the interaction between the plates from an attraction to a repulsion if the plates are far enough from each other. This additional repulsive interaction can be qualitatively interpreted as being due to an ideal-gas pressure of chain ends.

We study the effect of electrostatic interactions on the membrane bending energies of weakly charged, swollen, lamellar phases of surfactant solutions. We treat the surface charge density of the lamellae as a constant and consider only situations where it is low enough so that the distance 2d between lamellae is the smallest relevant length scale in the problem. In the presence of salt (the short-distance DebyeHuckel regime) we show that the electrostatic contribution to the bending energy of a membrane is in general small, in disagreement with a previous result, is proportional to d3, and is independent of ionic strength. Identical results are obtained for membranes undulating sinusoidally in phase and for concentric cylindrical membranes. The bending constant is also calculated for membranes held at constant electric potential and is compared to the constant charge density case. In the absence of salt, continuity arguments predict an electrostatic contribution to the bending energy that scales as d3. Furthermore, a direct calculation for concentric cylindrical membranes gives exactly the same scaling behavior (including the numerical prefactor) as in the presence of salt.

We present a detailed analysis of the dynamical instabilities appearing in two kinetic theories for the collective behavior of molecular motors: the rigid two-state model and the two-state crossbridge (or power-stroke) model with continuous binding sites. We calculate force-velocity relations, discuss their stability, plot a diagram that summarizes the oscillation regimes, identify the location of the Hopf bifurcation with a memory effect, discuss the oscillation frequency and make a link with single-molecule experiments. We show that the instabilities present in these models naturally translate into non-linearities in force-displacement relations, and at linear order give forces that are similar to the delayed stretch activation observed in oscillating muscles. We also find that instabilities can appear for both apparent load-decelerated and load-accelerated detachment rates in a 3-state crossbridge model.

Studies of the mechanism of cytokinesis, the process by which a mother cell undergoes cleavage to form two separated daughter cells, often focus on the action of the contractile actomyosin ring at the cell equator. Ewa Paluch and colleagues instead investigate the mechanics of the actomyosin cortex found at the cell poles during cytokinesis. They find that the presence of a contractile polar cortex makes cytokinesis an inherently unstable process that can result in misalignment of the constriction ring. They propose that the membrane blebs forming at the poles of dividing cells stabilize the position by releasing cortical contractility. These findings reveal an inherent instability in the shape of a dividing cell and demonstrate a novel mechanism that helps to limit shape instability. Cytokinesis, the physical separation of daughter cells at the end of mitosis, requires precise regulation of the mechanical properties of the cell periphery1,2. Although studies of cytokinetic mechanics mostly focus on the equatorial constriction ring3, a contractile actomyosin cortex is also present at the poles of dividing cells2,4. Whether polar forces influence cytokinetic cell shape and furrow positioning remains an open question. Here we demonstrate that the polar cortex makes cytokinesis inherently unstable. We show that limited asymmetric polar contractions occur during cytokinesis, and that perturbing the polar cortex leads to cell shape oscillations, resulting in furrow displacement and aneuploidy. A theoretical model based on a competition between cortex turnover and contraction dynamics accurately accounts for the oscillations. We further propose that membrane blebs, which commonly form at the poles of dividing cells5 and whose role in cytokinesis has long been enigmatic, stabilize cell shape by acting as valves releasing cortical contractility. Our findings reveal an inherent instability in the shape of the dividing cell and unveil a novel, spindle-independent mechanism ensuring the stability of cleavage furrow positioning.