Epithelial cells exhibit strong interconnections that are crucial for tissue mechanical properties. In homeostasis, these properties, termed mechanical homeostasis, depend on the balance between intercellular tension and extracellular matrix (ECM) adhesion forces. While age-related ECM remodeling is linked to outer retinal disease, its fundamental role in mechanical homeostasis remains unclear. In our study, we quantified changes in the mechanical state of retinal pigment epithelium (RPE), revealing a correlation with gradients of basement membrane laminins and their integrin receptors, β1 and β4. This relationship is related to regional phagocytic demand for recycling photoreceptor outer segments. Using a reductionist approach, we found that laminin 332 and laminin 511 isoforms differentially influence engagement with β1 and β4 integrins at low densities. Notably, laminin 511 enhances RPE contractility by reducing the β4 to β1 integrin engagement ratio, which subsequently diminishes phagocytic efficiency. Our findings suggest that the ECM-defined mechanical status of RPE serves as a novel parameter for visual function.

Metachronal coordination is a highly efficient natural strategy for swimming across scales, yet mimetic systems replicating this form of propulsion remain rare, limiting our ability to explore its underlying physics. Here, we investigate a minimal magneto-capillary system consisting of seven beads that exhibit metachronal-like motion when actuated by either a rotating or Lissajous-type oscillating magnetic field, resulting in net rotation or translation of the assembly, respectively. By systematically varying the driving frequency, we identify two distinct swimming regimes, both experimentally and theoretically. At low frequencies and negligible Reynolds numbers, propulsion arises from individual bead rotations phase-locked to the external field, constituting a linear, quasi-static regime. At higher frequencies, where the Reynolds number of the appendages exceeds unity, the dynamics transition to a deformation-dominated metachronal regime. Notably, optimized propulsion emerges near a mechanical resonance, underscoring the increasing role of inertia. While demonstrated on a specific design, we hypothesize that the existence of these regimes and the crossover between them may be a general feature of mesoscopic swimmers in nature.

Despite the primary role of cell proliferation in tissue development and homeostatic maintenance, the interplay between cell density, cell mechanoresponse, and cell growth and division is not yet understood. In this article we address this issue by reporting on an experimental investigation of cell proliferation on all time- and length-scales of the development of a model tissue, grown on collagen-coated glass or deformable substrates. Through extensive data analysis, we demonstrate the relation between mechanoresponse and probability for cell division, as a function of the local cell density. Motivated by these results, we construct a minimal model of cell proliferation that can recover the data. By parametrizing the growth and the dividing phases of the cell cycle, and introducing such a proliferation model in dissipative particle dynamics simulations, we recover the mechanoresponsive, time-dependent density profiles in 2D tissues growing to macroscopic scales. The importance of separating the cell population into growing and dividing cells, each characterized by a particular time scale, is further emphasized by calculations of density profiles based on adapted Fisher-Kolmogorov equations. Together, these results show that the mechanoresponse on the level of a constitutive cell and its proliferation results in a matrix-sensitive active pressure. The latter evokes massive cooperative displacement of cells in the invading tissue and is a key factor for developing large-scale structures in the steady state.

In nature, metachronal coordination is an efficient strategy for fluid pumping and self-propulsion. Yet, mimetic systems for this type of organization are scarce. Recently, metachronal motion was observed in a bead-based magnetocapillary mesoswimmer, but the mechanism of such device's behavior remained unclear. Here, we combine theory and experiments to explain two swimming regimes that we identify by modulation of the driving frequency. In the linear, low-frequency regime, the swimmer motion originates from individual bead rotations. However, the high-frequency, metachronal regime is dominated by deformations of the device near a mechanical resonance, which highlights the role of bead inertia for optimized self-propulsion.

Epithelial cells are highly interconnected, whereby they acquire mesoscale mechanical properties to accomplish specific tissue functions. In homeostasis, this mechanical status can be summarised as mechanical homeostasis, regulated by the balance of intercellular tension and extracellular matrix adhesion forces. In the outer retina, the significance of this force balance and its consequences for vision remains poorly understood. The retinal pigmented epithelium (RPE) is located at the base of the retina and supports vision by ensuring the light sensitivity and lifespan of photoreceptor cells. Given the varying photoreceptor densities along the visual angle, the functional demand on the RPE varies from the most illuminated macula to the retinal periphery and corresponds to a significant difference in RPE homeostatic state. In this work, we hypothesised that extracellular matrix (ECM) cues define the relation between RPE mechanical status and functional capacity. We found that the density of basement membrane laminins modulates the level of RPE contractility, which directly controls the efficiency of the epithelium in phagocytosing photoreceptor outer segments. In vivo, the density gradient of laminin α5 and 332 follows retinal functional demand, supporting the physiological role of laminins in controlling RPE mechanical homeostasis. Our data suggest that laminin density and isoforms can differentially engage integrins β1 and β4, the ratio of which determines the contribution of actin vs keratin cytoskeleton in balancing tissue mechanics. With this work, we suggest that the ECM-defined mechanical status of RPE is a novel parameter for visual function, opening new paths of investigation and treatment for sight-threatening diseases such as high myopia and age-related macular degeneration.

We investigate the formation and maintenance of the homeostatic state in the case of 2D epithelial tissues following an induction of hyperosmotic conditions, using media enriched with 80 to 320 mOsm of mannitol, NaCl, and urea. We characterise the changes in the tissue immediately after the osmotic shock, and follow it until the new homeostatic state is formed. We characterise changes in cooperative motility and proliferation pressure in the tissue upon treatment with the help of a theoretical model based on the delayed Fisher-Kolmogorov formalism, where the delay in density evolution is induced by the the finite time of the cell division. Finally we explore the adaptation of the homeostatic tissue to highly elevated osmotic conditions by evaluating the morphology and topology of cells after 20 days in incubation. We find that hyperosmotic environments together with changes in the extracellular matrix induce different mechanical states in viable tissues, where only some remain functional. The perspective is a relation between tissue topology and function, which could be explored beyond the scope of this manuscript.Experimental investigation of morphological effect of change of osmotic conditions on long-term tissue morphology and topology Effect of osmotic changes on transient tissue growth behaviour Analysis of recovery process of tissues post-osmotic-shock Toxicity limits of osmolytes in mid-to long-term tissue evolution Tissue adaptation to physiological changes in environment Long-term tissue stabilisation under altered osmotic conditions.

Epithelial cells are highly interconnected, whereby they acquire mesoscale mechanical properties to accomplish specific tissue functions. In homeostasis, this mechanical status can be summarised as mechanical homeostasis, regulated by the balance of intercellular tension and extracellular matrix adhesion forces. In the outer retina, the significance of this force balance and its consequences for vision remains poorly understood. The retinal pigmented epithelium (RPE) is located at the base of the retina and supports vision by ensuring the light sensitivity and lifespan of photoreceptor cells. Given the varying photoreceptor densities along the visual angle, the functional demand on the RPE varies from the most illuminated macula to the retinal periphery and corresponds to a significant difference in RPE homeostatic state. In this work, we hypothesised that extracellular matrix (ECM) cues define the relation between RPE mechanical status and functional capacity. We found that the density of basement membrane laminins modulates the level of RPE contractility, which directly controls the efficiency of the epithelium in phagocytosing photoreceptor outer segments. In vivo , the density gradient of laminin α5 and 332 follows retinal functional demand, supporting the physiological role of laminins in controlling RPE mechanical homeostasis. Our data suggest that laminin density and isoforms can differentially engage integrins β1 and β4, the ratio of which determines the contribution of actin vs keratin cytoskeleton in balancing tissue mechanics. With this work, we suggest that the ECM-defined mechanical status of RPE is a novel parameter for visual function, opening new paths of investigation and treatment for sight-threatening diseases such as high myopia and age-related macular degeneration.### Competing Interest StatementThe authors have declared no competing interest.

The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves. We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of two separable parts. Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid. The two components couple via an immersed boundary method. We present data for a single swimmer system and our data also show the onset of collective effects and, in particular, an overall velocity increment of clusters of swimmers.

Information storage is a key element of autonomous, out-of-equilibrium dynamics, especially for biological and synthetic active matter. In synthetic active matter however, the implementation of internal memory in self-propelled systems is often absent, limiting our understanding of memory-driven dynamics. Recently, a system comprised of a droplet generating its guiding wavefield appeared as a prime candidate for such investigations. Indeed, the wavefield, propelling the droplet, encodes information about the droplet trajectory and the amount of information can be controlled by a single scalar experimental parameter. In this work, we show numerically and experimentally that the accumulation of information in the wavefield induces the loss of time correlations, where the dynamics can then be described by a memory-less process. We rationalize the resulting statistical behavior by defining an effective temperature for the particle dynamics where the wavefield acts as a thermostat of large dimensions, and by evidencing a minimization principle of the generated wavefield.

Despite recent efforts to understand homeostasis in epithelial tissues, there are many unknowns surrounding this steady state. It is considered to be regulated by mechanoresponse, but unlike for single cells, this idea remains heavily debated for tissues. Here, we show that changes in matrix stiffness induce a nonequilibrium transition from tubular to squamous Madin-Darby Canine Kidney II tissues. Nonetheless, despite different cell morphologies and densities, all homeostatic tissues display equivalent topologies, which, hence, must be actively targeted and regulated. On the contrary, the mechanoresponse induces dramatic changes in the large-scale organization of the colonies. On stiff gels, this yields an unreported cooperative state of motile cells displaying higher densities than in the arrested homeostatic state, which suggests a more complex relation between cell density and motility than previously anticipated. Our results unequivocally relate the mechanosensitive properties of individual cells to the evolving macroscopic structures, an effect that could be important for understanding the emergent pathologies of living tissues.

The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer's maximum velocity centred around the particle's inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations.

By comparing theoretical modeling, simulations, and experiments, we show that there exists a swimming regime at low Reynolds numbers solely driven by the inertia of the swimmer itself. This is demonstrated by considering a dumbbell with an asymmetry in coasting time in its two spheres. Despite deforming in a reciprocal fashion, the dumbbell swims by generating a nonreciprocal Stokesian flow, which arises from the asymmetry in coasting times. This asymmetry acts as a second degree of freedom, which allows the scallop theorem to be fulfilled at the mesoscopic scale.

Hydrodynamic interactions are crucial for determining the cooperative behavior of microswimmers at low Reynolds numbers. Here we provide a comprehensive analysis of the scaling laws and the strength of the interactions in the case of a pair of three-sphere swimmers. Both stroke-based and force-based elastic microswimmers are analyzed using an analytic perturbative approach, focusing on passive and active interactions. The former are governed by the cycle-averaged flow field of a single swimmer, which is dipolar at long range. However, at intermediate distances, with a cross-over at the order of 102 swimmer lengths, the quadrupolar field dominates which, notably, yields an increase of the swimming velocity compared to individual swimmers, even when the swimmers are one behind another. Furthermore, we find that active rotations resulting from the interplay of the time-resolved swimming stroke and the ambient flow fields and, even more prominently, active translations are model-dependent. A mapping between the stroke-based and force-based swimmers is only possible for the low driving frequency regime where the characteristic time scale is smaller than the viscous one. Finally, we find that the long-term behavior of the swimmers, while sensitive to the initial relative positioning, does not depend on the pusher or puller nature of the swimmer. These results clearly indicate that the behavior of swarms will depend on the swimmer model, which was hitherto not well appreciated.

Hydrodynamic interactions are crucial for determining the cooperative behavior of microswimmers at low Reynolds numbers. Here we provide a comprehensive analysis of the scaling and strength of the interactions in the case of a pair of three-sphere swimmers with intrinsic elasticity. Both stroke-based and force-based microswimmers are analyzed using an analytic perturbative approach. Following a detailed analysis of the passive interactions, as well as active translations and rotations, we find that the mapping between the stroke-based and force-based swimmers is only possible in a low driving frequency regime where the characteristic time scale is smaller than the viscous one. Furthermore, we find that for swimmers separated by up to hundreds of swimmer lengths, swimming in pairs speeds up the self propulsion, due to the dominant quadrupolar hydrodynamic interactions. Finally, we find that the long term behavior of the swimmers, while sensitive to initial relative positioning, does not depend on the pusher or puller nature of the swimmer.

A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two, and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing interparticle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.

Small objects floating on a fluid have a tendency to aggregate due to capillary forces. This effect has been used, with the help of a magnetic induction field, to assemble submillimeter metallic spheres into a variety of structures, whose shape and size can be tuned. Under time-varying fields, these assemblies can propel themselves due to a breaking of time reversal symmetry in their adopted shapes. In this article, we study the influence of an in-plane rotation of the magnetic field on these structures. Various rotational modes have been observed with different underlying mechanisms. The magnetic properties of the particles cause them to rotate individually. Dipole-dipole interactions in the assembly can cause the whole structure to align with the field. Finally, non-reciprocal deformations can power the rotation of the assembly. Symmetry plays an important role in the dynamics, as well as the frequency and amplitude of the applied field. Understanding the interplay of these effects is essential, both to explain previous observations and to develop new functions for these assemblies.

Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials and via hydrodynamics, driven by an arbitrary force protocol. The approach can be used with mobility matrices of arbitrary accuracy, and we illustrate it with the Oseen and Rotne–Prager approximations. We validate our approach by using 3 bead assemblies and comparing the results with the numerically obtained full-solutions of the governing equations of motion, as well as with existing analytic models for the linear and the triangular swimmer geometry. While recovering the relation between the force and swimming velocity, our detailed analysis and the controlled level of approximation allow us to find qualitative differences already in the far field flow of the devices. Consequently, we are able to identify a behavior of the swimmer that is richer than predicted in previous models. Given its generality, the framework can be applied to any swimmer geometry, driving protocol and bead interactions, as well as in problems involving many swimmers.

Correction for ‘Capillary assemblies in a rotating magnetic field’ by Galien Grosjean et al., Soft Matter, 2019, DOI: 10.1039/c9sm01414d.

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes: linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.