Influence of proliferation on the motions of epithelial monolayers invading adherent strips.

Biological systems integrate dynamics at many scales, from molecules, protein complexes and genes, to cells, tissues and organisms. At every step of the way, mechanics, biochemistry and genetics offer complementary approaches to understand these dynamics. At the tissue scale, in vitro monolayers of epithelial cells provide a model to capture the influence of various factors on the motions of the tissue, in order to understand in vivo processes from morphogenesis, cancer progression and tissue remodelling. Ongoing efforts include research aimed at deciphering the roles of the cytoskeleton, of cell-substrate and cell-cell adhesions, and of cell proliferation-the point we investigate here. We show that confined to adherent strips, and on the time scale of a day or two, monolayers move with a characteristic front speed independent of proliferation, but that the motion is accompanied by persistent velocity waves, only in the absence of cell divisions. Here we show that the long-range transmission of physical signals is strongly coupled to cell density and proliferation. We interpret our results from a kinematic and mechanical perspective. Our study provides a framework to understand density-driven mechanisms of collective cell migration.

Questioning the relationship between the χ4 susceptibility and the dynamical correlation length in a glass former.

Clusters of fast and slow correlated particles, identified as dynamical heterogeneities (DHs), constitute a central aspect of glassy dynamics. A key factor of the glass transition scenario is a significant increase of the cluster size ξ4 as the transition is approached. In need of easy-to-compute tools to measure ξ4, the dynamical susceptibility χ4 was introduced recently, and used in various experimental studies to probe DHs. Here, we investigate DHs in dense microgel suspensions using image correlation analysis, and compute both χ4 and the four-point correlation function G4. The spatial decrease of G4 provides a direct access to ξ4, which is found to grow significantly with increasing volume fraction. However, this increase is not captured by χ4. We show that the assumptions that validate the connection between χ4 and ξ4 are not fulfilled in our experiments.

Colloquium: Mechanical formalisms for tissue dynamics.

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.

Mapping cell cortex rheology to tissue rheology and vice versa.

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

All-in-one rheometry and nonlinear rheology of multicellular aggregates.

Tissues are generally subjected to external stresses, a potential stimulus for their differentiation or remodeling. While single-cell rheology has been extensively studied leading to controversial results about nonlinear response, mechanical tissue behavior under external stress is still poorly understood, in particular, the way individual cell properties translate at the tissue level. Herein, using magnetic cells we were able to form perfectly monitored cellular aggregates (magnetic molding) and to deform them under controlled applied stresses over a wide range of timescales and amplitudes (magnetic rheometer). We explore the rheology of these minimal tissue models using both standard assays (creep and oscillatory response) as well as an innovative broad spectrum solicitation coupled with inference analysis thus being able to determine in a single experiment the best rheological model. We find that multicellular aggregates exhibit a power-law response with nonlinearities leading to tissue stiffening at high stress. Moreover, we reveal the contribution of intracellular (actin network) and intercellular components (cell-cell adhesions) in this aggregate rheology.

Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains.

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

Probing foam with neutrons.

Foams are multiscale materials that have an enormous number of uses. As the relevant structural length-scales span from a few nanometres up to millimetres a number of characterisation methods need to be combined to obtain the full material structure. In this review we explain how foams can be explored using Small Angle Neutron Scattering (SANS). We remind the reader of the basics of SANS and contrast variation before we describe the different types of experiments that have been carried out on foams emphasising the specific role of neutrons in learning about the systems. To date SANS has been used to measure different foam structural parameters, such as the film thickness and the bubble size. Several studies have also been carried out to elucidate the organisation of the stabilising objects in the bulk solution. Finally we show how SANS measurements can be used to measure foam composition. Some of the accessible information is unique to SANS experiments, but as the method is still not very widely used on foams the review is also aimed to act as an introduction on how to carry out such measurements on foams.

A 3D magnetic tissue stretcher for remote mechanical control of embryonic stem cell differentiation.

The ability to create a 3D tissue structure from individual cells and then to stimulate it at will is a major goal for both the biophysics and regenerative medicine communities. Here we show an integrated set of magnetic techniques that meet this challenge using embryonic stem cells (ESCs). We assessed the impact of magnetic nanoparticles internalization on ESCs viability, proliferation, pluripotency and differentiation profiles. We developed magnetic attractors capable of aggregating the cells remotely into a 3D embryoid body. This magnetic approach to embryoid body formation has no discernible impact on ESC differentiation pathways, as compared to the hanging drop method. It is also the base of the final magnetic device, composed of opposing magnetic attractors in order to form embryoid bodies in situ, then stretch them, and mechanically stimulate them at will. These stretched and cyclic purely mechanical stimulations were sufficient to drive ESCs differentiation towards the mesodermal cardiac pathway.The development of embryoid bodies that are responsive to external stimuli is of great interest in tissue engineering. Here, the authors culture embryonic stem cells with magnetic nanoparticles and show that the presence of magnetic fields could affect their aggregation and differentiation.

Extensive collection of femtolitre pad secretion droplets in the beetle Leptinotarsa decemlineata allows nanolitre microrheology.

Pads of beetles are covered with long, deformable setae, each ending in a micrometric terminal plate coated with secretory fluid. It was recently shown that the layer of the pad secretion covering the terminal plates is responsible for the generation of strong attractive forces. However, less is known about the fluid itself because it is produced in an extremely small quantity. We present here the first experimental investigation of the rheological properties of the pad secretion in the Colorado potato beetle Leptinotarsa decemlineata (Coleoptera, Chrysomelidae). Because the secretion is produced in an extremely small amount at the level of the terminal plate, we first developed a procedure based on capillary effects to collect the secretion for rheological experiments. In order to study the collected fluid (less than 1 nl) through passive microrheology, we managed to incorporate micrometric probes (melamine beads) that were initially in the form of a dry powder. Finally, the bead thermal motions were observed optically and recorded to determine the mechanical properties of the surrounding medium. We achieved this quantitative measurement with the collected volume, which is much smaller than the usual 1 µl sample volume required for this technique. Surprisingly, the beetle secretion was found to behave as a purely viscous liquid, of high viscosity (about 100 times that of water). This suggests that no specific complex fluid behaviour is needed by this adhesive system during beetle locomotion. We describe a scenario for the contact formation between the spatula at the setal tip and a smooth substrate, during the insect walk. We show that the attachment dynamics of the insect pad computed from the high measured viscosity is in good agreement with the observed insect pace. We finally discuss the consequences of the viscosity of the secretion on the insect adhesion.

Slippery or sticky boundary conditions: control of wrinkling in metal-capped thin polymer films by selective adhesion to substrates.

Wrinkling patterns at the metallized surface of thin polymer films are shown to be sensitive to the sticky or slippery character of the polymer-substrate interface. Existing theoretical models were expanded to specific boundary conditions (adhesive versus slippery) in order to rationalize these observations. Based on this concept, we were able to propose a new and simple method to orient the wrinkles by chemically patterning the substrate with regions of high and low adhesion.

Some fundamentals of adhesion in synthetic adhesives.

Various adhesion mechanisms that have been understood in the field of synthetic adhesives are described and these are linked with situations relevant to fouling issues. The review mainly deals with mechanical aspects of adhesion phenomena, with an emphasis on the role of the elasticity of the bodies, called substrata, attached by adhesive. The consequences of thin film geometry of the adhesive material are described, such as various heterogeneous deformations upon traction. The importance of the bonding process is discussed, as well as some examples of non-wetting surfaces. Some basic ideas of fracture mechanics are provided and in particular, the behavior of layered systems is discussed. Rolling sticky objects and peeled (flexible) adhesive tapes display similar mechanisms and it is shown how they differ from the normal separation of rigid bodies. Some issues directly related to fouling issues are also discussed, such as forces and torques acting on shells, the advantages of gregarious settlement behavior and concepts for fouling release and antifouling.

Stickiness--some fundamentals of adhesion.

We review some adhesion mechanisms that have been understood in the field of synthetic adhesives, and more precisely for adhesives that adhere instantaneously (a property named tackiness) and whose adhesive strength usually depends on the applied pressure (pressure-sensitive adhesives). The discussion includes effects of surface roughness, elasticity, cavitation, viscous and elastic fingering, substrate flexibility.