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Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

The forces that cells, tissues, and organisms exert on the surface of a soft substrate can be measured using Traction Force Microscopy (TFM), an important and well-established technique in Mechanobiology. The usual TFM technique (two-dimensional, 2D TFM) treats only the in-plane component of the traction forces and omits the out-of-plane forces at the substrate interfaces (2.5D) that turn out to be important in many biological processes such as tissue migration and tumour invasion. Here, we review the imaging, material, and analytical tools to perform "2.5D TFM" and explain how they are different from 2D TFM. Challenges in 2.5D TFM arise primarily from the need to work with a lower imaging resolution in the z-direction, track fiducial markers in three-dimensions, and reliably and efficiently reconstruct mechanical stress from substrate deformation fields. We also discuss how 2.5D TFM can be used to image, map, and understand the complete force vectors in various important biological events of various length-scales happening at two-dimensional interfaces, including focal adhesions forces, cell diapedesis across tissue monolayers, the formation of three-dimensional tissue structures, and the locomotion of large multicellular organisms. We close with future perspectives including the use of new materials, imaging and machine learning techniques to continuously improve the 2.5D TFM in terms of imaging resolution, speed, and faithfulness of the force reconstruction procedure., Competing Interests: Declaration of Competing Interest We declare that there is no conflict of interest regarding the preparation of this manuscript., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Mechanical cues such as stresses and strains are now recognized as essential regulators in many biological processes like cell division, gene expression or morphogenesis. Studying the interplay between these mechanical cues and biological responses requires experimental tools to measure these cues. In the context of large scale tissues, this can be achieved by segmenting individual cells to extract their shapes and deformations which in turn inform on their mechanical environment. Historically, this has been done by segmentation methods which are well known to be time consuming and error prone. In this context however, one doesn't necessarily require a cell-level description and a coarse-grained approach can be more efficient while using tools different from segmentation. The advent of machine learning and deep neural networks has revolutionized the field of image analysis in recent years, including in biomedical research. With the democratization of these techniques, more and more researchers are trying to apply them to their own biological systems. In this paper, we tackle a problem of cell shape measurement thanks to a large annotated dataset. We develop simple Convolutional Neural Networks (CNNs) which we thoroughly optimize in terms of architecture and complexity to question construction rules usually applied. We find that increasing the complexity of the networks rapidly no longer yields improvements in performance and that the number of kernels in each convolutional layer is the most important parameter to achieve good results. In addition, we compare our step-by-step approach with transfer learning and find that our simple, optimized CNNs give better predictions, are faster in training and analysis and don't require more technical knowledge to be implemented. Overall, we offer a roadmap to develop optimized models and argue that we should limit the complexity of such models. We conclude by illustrating this strategy on a similar problem and dataset., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Combe et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

In the heart, cardiac function is regulated by the autonomic nervous system (ANS) that extends through the myocardium and establishes junctions at the sinus node and ventricular levels. Thus, an increase or decrease in neuronal activity acutely affects myocardial function and chronically affects its structure through remodeling processes. The neuro-cardiac junction (NCJ), which is the major structure of this system, is poorly understood and only a few cell models allow us to study it. Here, we present an innovant neuro-cardiac organ-on-chip model to study this structure to better understand the mechanisms involved in the establishment of NCJ. To create such a system, we used microfluidic devices composed of two separate cell culture compartments interconnected by asymmetric microchannels. Rat PC12 cells were differentiated to recapitulate the characteristics of sympathetic neurons, and cultivated with cardiomyocytes derived from human induced pluripotent stem cells (hiPSC). We confirmed the presence of a specialized structure between the two cell types that allows neuromodulation and observed that the neuronal stimulation impacts the excitation-contraction coupling properties including the intracellular calcium handling. Finally, we also co-cultivated human neurons (hiPSC-NRs) with human cardiomyocytes (hiPSC-CMs), both obtained from the same hiPSC line. Hence, we have developed a neuro-cardiac compartmentalized in vitro model system that allows us to recapitulate the structural and functional properties of the neuro-cardiac junction and that can also be used to better understand the interaction between the heart and brain in humans, as well as to evaluate the impact of drugs on a reconstructed human neuro-cardiac system.

Mechanical constraints have a high impact on development processes, and there is a need for new tools to investigate the role of mechanosensitive pathways in tissue reorganization during development. We present here experiments in which embryonic cell aggregates are aspired through constrictions in microfluidic channels, generating highly heterogeneous flows and large cell deformations that can be imaged using two-photon microscopy. This approach provides a way to measure in situ local viscoelastic properties of 3D tissues and connect them to intracellular and intercellular events, such as cell shape changes and cell rearrangements. These methods could be applied to organoids to investigate and quantify rheological properties of tissues, and to understand how constraints affect development., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2022. Published by The Company of Biologists Ltd.)

Animal cells are active, contractile objects. While bioassays address the molecular characterization of cell contractility, the mechanical characterization of the active forces in cells remains challenging. Here by confronting theoretical analysis and experiments, we calculated both the resistive and the active components of the intracellular stresses that build up following cell adhesion. We obtained a linear relationship between the divergence of the passive stress and the traction forces, which we show is the consequence of the cell adhering and applying forces on the surface only through very localized adhesion points (whose size is inferior to our best resolution, of 400 nm). This entails that there are no measurable forces outside of these active point sources, and also that the passive stresses and active stresses inside cells are proportional.

To understand cell migration, it is crucial to gain knowledge on how cells exert and integrate forces on and from their environment. A quantity of prime interest for biophysicists interested in cell movements modeling is the intracellular stresses. Up to now, three different methods have been proposed to calculate it, they are all in the regime of the thin plate approximation. Two are based on solving the mechanical equilibrium equation inside the cell material (monolayer stress microscopy and Bayesian inference stress microscopy) and one is based on the continuity of displacement at the cell-substrate interface (intracellular stress microscopy). We show here using 3D FEM modeling that these techniques do not calculate the same quantities (as was previously assumed), the first techniques calculate the sum of the active and resistive stresses within the cell, whereas the last one only calculates the resistive component. Combining these techniques should, in principle, permit access to the active stress alone.

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices, do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement, and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers., Competing Interests: AG, ML, JC, TG, ML, HD, AO, SH, DR No competing interests declared, PS Reviewing editor, eLife, (© 2022, Godeau, Leoni et al.)

We present an in-depth investigation of a fully automated Fourier-based analysis to determine the cell size and the width of its distribution in 3D biological tissues. The results are thoroughly tested using generated images, and we offer valuable criteria for image acquisition settings to optimize accuracy. We demonstrate that the most important parameter is the number of cells in the field of view, and we show that accurate measurements can already be made on volume only containing [Formula: see text] cells. The resolution in z is also not so important, and a reduced number of in-depth images, of order of one per cell, already provides a measure of the mean cell size with less than 5% error. The technique thus appears to be a very promising tool for very fast live local volume cell measurement in 3D tissues in vivo while strongly limiting photobleaching and phototoxicity issues., (© 2022. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

Cell rigidity sensing-a basic cellular process allowing cells to adapt to mechanical cues-involves cell capabilities exerting force on the extracellular environment. In vivo, cells are exposed to multi-scaled heterogeneities in the mechanical properties of the surroundings. Here, we investigate whether cells are able to sense micron-scaled stiffness textures by measuring the forces they transmit to the extracellular matrix. To this end, we propose an efficient photochemistry of polyacrylamide hydrogels to design micron-scale stiffness patterns with kPa/µm gradients. Additionally, we propose an original protocol for the surface coating of adhesion proteins, which allows tuning the surface density from fully coupled to fully independent of the stiffness pattern. This evidences that cells pull on their surroundings by adjusting the level of stress to the micron-scaled stiffness. This conclusion was achieved through improvements in the traction force microscopy technique, e.g., adapting to substrates with a non-uniform stiffness and achieving a submicron resolution thanks to the implementation of a pyramidal optical flow algorithm. These developments provide tools for enhancing the current understanding of the contribution of stiffness alterations in many pathologies, including cancer.

Motivation: Cardiomyocytes derived from stem cells are closely followed, notably since the discovery in 2007 of human induced pluripotent stem cells (hiPSC). Cardiomyocytes (hiPSC-CM) derived from hiPSC are indeed more and more used to study specific cardiac diseases as well as for developing novel applications such as drug safety experiments. Robust dedicated tools to characterize hiPSC-CM are now required. The hiPSC-CM morphology constitutes an important parameter since these cells do not demonstrate the expected rod shape, characteristic of native human cardiomyocytes. Similarly, the presence, the density and the organization of contractile structures would be a valuable parameter to study. Precise measurements of such characteristics would be useful in many situations: for describing pathological conditions, for pharmacological screens or even for studies focused on the hiPSC-CM maturation process., Results: For this purpose, we developed a MATLAB based image analysis toolbox, which gives accurate values for cellular morphology parameters as well as for the contractile cell organization., Availability and Implementation: To demonstrate the power of this automated image analysis, we used a commercial maturation medium intended to promote the maturation status of hiPSC-CM, and compare the parameters with the ones obtained with standard culture medium, and with freshly dissociated mouse cardiomyocytes., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

The huge gap between 2D in vitro assays used for drug screening and the in vivo 3D physiological environment hampered reliable predictions for the route and accumulation of nanotherapeutics in vivo. For such nanotherapeutics, multi-cellular tumour spheroids (MCTS) are emerging as a good alternative in vitro model. However, the classical approaches to produce MCTS suffer from low yield, slow process, difficulties in MCTS manipulation and compatibility with high-magnification fluorescence optical microscopy. On the other hand, spheroid-on-chip set-ups developed so far require a practical knowledge of microfluidics difficult to transfer to a cell biology laboratory. We present here a simple yet highly flexible 3D model microsystem consisting of agarose-based microwells. Fully compatible with the multi-well plate format conventionally used in cell biology, our simple process enables the formation of hundreds of reproducible spheroids in a single pipetting. Immunostaining and fluorescence imaging including live high-resolution optical microscopy can be performed in situ, with no manipulation of spheroids. As a proof of principle of the relevance of such an in vitro platform for nanotherapeutic evaluation, this study investigates the kinetics and localisation of nanoparticles within colorectal cancer MCTS cells (HCT-116). The nanoparticles chosen are sub-5 nm ultrasmall nanoparticles made of polysiloxane and gadolinium chelates that can be visualized in MRI (AGuIX®, currently implicated in clinical trials as effective radiosensitizers for radiotherapy) and confocal microscopy after addition of Cy5.5. We show that the amount of AGuIX® nanoparticles within cells is largely different in 2D and 3D. Using our flexible agarose-based microsystems, we are able to resolve spatially and temporally the penetration and distribution of AGuIX® nanoparticles within MCTS. The nanoparticles are first found in both extracellular and intracellular space of MCTS. While the extracellular part is washed away after a few days, we evidenced intracellular localisation of AGuIX®, mainly within the lysosomal compartment, but also occasionally within mitochondria. Hence, our agarose-based microsystem appears as a promising 3D in vitro user-friendly platform for investigation of nanotherapeutic transport, ahead of in vivo studies.

While many cellular mechanisms leading to chemotherapeutic resistance have been identified, there is an increasing realization that tumor-stroma interactions also play an important role. In particular, mechanical alterations are inherent to solid cancer progression and profoundly impact cell physiology. Here, we explore the influence of compressive stress on the efficacy of chemotherapeutics in pancreatic cancer spheroids. We find that increased compressive stress leads to decreased drug efficacy. Theoretical modeling and experiments suggest that mechanical stress decreases cell proliferation which in turn reduces the efficacy of chemotherapeutics that target proliferating cells. Our work highlights a mechanical form of drug resistance and suggests new strategies for therapy.

Cell migration is involved in key phenomena in biology, ranging from development to cancer. Fibroblasts move between organs in 3D polymeric networks. So far, motile cells were mainly tracked in vitro on Petri dishes or on coverslips, i.e., 2D flat surfaces, which made the extrapolation to 3D physiological environments difficult. We therefore prepared 3D Cell Derived Matrices (CDM) with specific characteristics with the goal of extracting the main readouts required to measure and characterize cell motion: cell specific matrix deformation through the tracking of fluorescent fibronectin within CDM, focal contacts as the cell anchor and acto-myosin cytoskeleton which applies cellular forces. We report our method for generating this assay of physiological-like gel with relevant readouts together with its potential impact in explaining cell motility in vivo., (© 2020 Elsevier Inc. All rights reserved.)

The structure of tumors can be recapitulated as an elastic frame formed by the connected cytoskeletons of the cells invaded by interstitial and intracellular fluids. The low-frequency mechanics of this poroelastic system, dictated by the elastic skeleton only, control tumor growth, penetration of therapeutic agents, and invasiveness. The high-frequency mechanical properties containing the additional contribution of the internal fluids have also been posited to participate in tumor progression and drug resistance, but they remain largely unexplored. Here we use Brillouin light scattering to produce label-free images of tumor microtissues based on the high-frequency viscoelastic modulus as a contrast mechanism. In this regime, we demonstrate that the modulus discriminates between tissues with altered tumorigenic properties. Our micrometric maps also reveal that the modulus is heterogeneously altered across the tissue by drug therapy, revealing a lag of efficacy in the core of the tumor. Exploiting high-frequency poromechanics should advance present theories based on viscoelasticity and lead to integrated descriptions of tumor response to drugs.

Collective cell migration contributes to embryogenesis, wound healing and tumour metastasis. Cell monolayer migration experiments help in understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length scales and time scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers, which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation., Competing Interests: We have no competing interests.

MultiCellular Tumor Spheroids (MCTS), which mimic the 3-Dimensional (3D) organization of a tumor, are considered as better models than conventional cultures in 2-Dimensions (2D) to study cancer cell biology and to evaluate the response to chemotherapeutic drugs. A real time and quantitative follow-up of MCTS with simple and robust readouts to evaluate drug efficacy is still missing. Here, we evaluate the chemotherapeutic drug 5-Fluorouracil (5-FU) response on the growth and integrity of MCTS two days after treatment of MCTS and for three colorectal carcinoma cell lines with different cohesive properties (HT29, HCT116 and SW480). We found different sensitivity to 5-FU for the three CRC cell lines, ranging from high (SW480), intermediate (HCT116) and low (HT29) and the same hierarchy of CRC cell lines sensitivity is conserved in 2D. We also evidence that 5-FU has a strong impact on spheroid cohesion, with the apparition of a number of single detaching cells from the spheroid in a 5-FU dose- and cell line-dependent manner. We propose an innovative methodology for the chemosensitivity evaluation in 3D MCTS that recapitulates and regionalizes the 5-FU-induced changes within MCTS over time. These robust phenotypic read-outs could be easily scalable for high-throughput drug screening that may include different types of cancer cells to take into account tumor heterogeneity and resistance to treatment.

Understanding the relationship between the material structural details, the geometrical confining constraints, the local dynamical events and the global rheological response is at the core of present investigations on complex fluid properties. In the present article, this problem is addressed on a model yield stress fluid made of highly entangled polymer gels of Carbopol which follows at the macroscopic scale the well-known Herschel-Bulkley rheological law. First, performing local rheology measurements up to high shear rates ([Formula: see text] s -1 )and under confinement, we evidence unambiguously the breakdown of bulk rheology associated with cooperative processes under flow. Moreover, we show that these behaviors are fully captured with a unique cooperativity length [Formula: see text] over the whole range of experimental conditions. Second, we introduce an original optical microscopy method to access structural properties of the entangled polymer gel in the direct space. Performing image correlation spectroscopy of fluorophore-loaded gels, the characteristic size D of carbopol gels microstructure is determined as a function of preparation protocol. Combining both dynamical and structural information shows that the measured cooperative length [Formula: see text] corresponds to 2-5 times the underlying structural size D, thus providing a strong grounding to the "Shear Transformation Zones" modeling approach.

We have performed surface tension measurements on carbopol gels of different concentrations and yield stresses. Our setup, based on the force exerted by a capillary bridge on two parallel plates, allows us to measure an apparent surface tension of the complex fluid and to investigate the influence of flow history. More precisely the apparent surface tension measured after stretching the bridge is always higher than after compressing it. The difference between the two values is due to the existence of a yield stress in the fluid. The experimental observations are successfully reproduced with a simple elasto-plastic model. The shape of successive stretching-compression cycles can be described by taking into account the yield stress and the elasticity of the gel. We show that the surface tension γLV of yield stress fluids is the mean of the apparent surface tension values only if the elastic modulus is high compared to the yield stress. This work highlights that measurements of thermodynamic quantities are challenged by the fluid out-of-equilibrium state implied by jamming, even at small scales where the shape of the bridge is driven by surface energy. Therefore setups allowing for deformation in opposite directions are relevant for surface tension measurements on yield stress fluids.

The slime mould Physarum polycephalum is a giant multinucleated cell exhibiting well-known Ca(2+)-dependent actomyosin contractions of its vein network driving the so-called cytoplasmic shuttle streaming. Its actomyosin network forms both a filamentous cortical layer and large fibrils. In order to understand the role of each structure in the locomotory activity, we performed birefringence observations and traction force microscopy on excised fragments of Physarum. After several hours, these microplasmodia adopt three main morphologies: flat motile amoeba, chain types with round contractile heads connected by tubes and motile hybrid types. Each type exhibits oscillations with a period of about 1.5 min of cell area, traction forces and fibril activity (retardance) when fibrils are present. The amoeboid types show only peripheral forces while the chain types present a never-reported force pattern with contractile rings far from the cell boundary under the spherical heads. Forces are mostly transmitted where the actomyosin cortical layer anchors to the substratum, but fibrils maintain highly invaginated structures and contribute to forces by increasing the length of the anchorage line. Microplasmodia are motile only when there is an asymmetry in the shape and/or the force distribution., (© 2015 The Author(s) Published by the Royal Society. All rights reserved.)

Confining cells on adhesive patterns allows performing robust, weakly dispersed, statistical analysis. A priori, adhesive patterns could be efficient tools to analyze intracellular cell stress fields, in particular when patterns are used to force the geometry of the cytoskeleton. This tool could then be very helpful in deciphering the relationship between the internal architecture of the cells and the mechanical, intracellular stresses. However, the quantification of the intracellular stresses is still something delicate to perform. Here we first propose a new, very simple and original method to quantify the intracellular stresses, which directly relates the strain the cells impose on the extracellular matrix to the intracellular stress field. This method is used to analyze how confinement influences the intracellular stress field. As a result, we show that the more confined the cells are, the more stressed they will be. The influence of the geometry of the adhesive patterns on the stress patterns is also discussed.

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress.

What governs tissue organization and movement? If molecular and genetic approaches are able to give some answers on these issues, more and more works are now giving a real importance to mechanics as a key component eventually triggering further signaling events. We chose embryonic cell aggregates as model systems for tissue organization and movement in order to investigate the origin of some mechanical constraints arising from cells organization. Steinberg et al. proposed a long time ago an analogy between liquids and tissues and showed that indeed tissues possess a measurable tissue surface tension and viscosity. We question here the molecular origin of these parameters and give a quantitative measurement of adhesion versus contractility in the framework of the differential interfacial tension hypothesis. Accompanying surface tension measurements by angle measurements (at vertexes of cell-cell contacts) at the cell/medium interface, we are able to extract the full parameters of this model: cortical tensions and adhesion energy. We show that a tunable surface tension and viscosity can be achieved easily through the control of cell-cell contractility compared to cell-medium one. Moreover we show that α-catenin is crucial for this regulation to occur: these molecules appear as a catalyser for the remodeling of the actin cytoskeleton underneath cell-cell contact, enabling a differential contractility between the cell-medium and cell-cell interface to take place.

The Dictyostelium slug is an excellent model system for studying collective movements, as it is comprised of about 10(5) cells all moving together in the same direction. It still remains unclear how this movement occurs and what the physical mechanisms behind it are. By applying our recently developed 3D traction force microscopy, we propose a simple explanation for slug propulsion. Most of the forces are exerted by the sheath surrounding the slug. This secreted shell is under a rather uniform tension (around 50 mN m(-1)) and will give rise to a tissue under pressure. Finally, we propose that this pressure will naturally push the slug tip forwards if a gradient of shell mechanical properties takes place in the very anterior part of the raised tip.

The collective motion of cells in a biological tissue originates from their individual responses to chemical and mechanical signals. The Dictyostelium slug moves as a collective of up to 100,000 cells with prestalk cells in the anterior 10-30% and prespore cells, intermingled with anterior-like cells (AL cells), in the posterior. We used traction force microscopy to measure the forces exerted by migrating slugs. Wild-type slugs exert frictional forces on their substratum in the direction of motion in their anterior, balanced by motive forces dispersed down their length. StlB- mutants lack the signal molecule DIF-1 and hence a subpopulation of AL cells. They produce little if any motive force in their rear and immediately break up. This argues that AL cells, but not prespore cells, are the motive cells in the posterior zone. Slugs also exert large outward radial forces, which we have analyzed during "looping" movement. Each time the anterior touches down after a loop, the outward forces rapidly develop, approximately normal to the almost stationary contact lines. We postulate that these forces result from the immediate binding of the sheath to the substratum and the subsequent application of outward "pressure," which might be developed in several different ways., ((c) 2009 Wiley-Liss, Inc.)

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses ("fluctuation-induced flow"). If not, changing the aggregate's shape requires a sufficiently large applied stress ("stress-induced flow"). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress tau*, the aggregate as a whole flows with an apparent viscosity eta*, and at higher stress it is a shear-thinning fluid. An increasing cell-cell tension results in a higher eta* (and thus a slower stress relaxation time t(c)). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find t(c) of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.

Apparent tissue surface tension allows the quantification of cell-cell cohesion and was reported to be a powerful indicator for the cellular rearrangements that take place during embryonic development or for cancer progression. The measurement is realized with a parallel compression plate tensiometer using the capillary laws. Although it was introduced more than a decade ago, it is based on various geometrical or physical approximations. Surprisingly, these approximations have never been tested. Using a novel tensiometer, we compare the two currently used methods to measure tissue surface tension and propose a third one, based on a local polynomial fit (LPF) of the profile of compressed droplets or cell aggregates. We show the importance of measuring the contact angle between the plate and the dropaggregate to obtain real accurate measurement of surface tension when applying existing methods. We can suspect that many reported values of surface tension are greatly affected because of not handling this parameter properly. We show then the benefit of using the newly introduced LPF method, which is not dependent on this parameter. These findings are confirmed by generating numerically compressed droplet profiles and testing the robustness and the sensitivity to errors of the different methods.