The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but there is no unifying framework to describe all these behaviors. Here we develop a general computational framework that enables the description of embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and tension fluctuations. In addition to previously reported rigidity transitions, we find a distinct rigidity transition governed by the magnitude of tension fluctuations. Our results indicate that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. Comparing simulation results to experimental data, we show that tension fluctuations do control rigidity transitions in embryonic tissues, highlighting a key role of non-equilibrium tension dynamics in developmental processes.Many essential processes in multicellular organisms, from organ formation to tissue homeostasis, require a tight control of the tissue physical state 1, 2 . While tissue mechanics and structure at supracellular scales emerge from the collective physical interactions among the constituent cells, their control occurs at cell and subcellular levels. Bridging these scales is essential to understand the physical nature of active (non-equilibrium) multicellular systems and to identify the processes that cells use to control the physical state of embryonic tissues.In vitro experiments of cell monolayers on substrates have revealed characteristics of glassy .

1The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but there is no unifying framework to describe all these behaviors. Here we develop a general computational framework that enables the description of embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and tension fluctuations. In addition to previously reported rigidity transitions, we find a distinct rigidity transition governed by the magnitude of tension fluctuations. Our results indicate that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. Comparing simulation results to experimental data, we show that tension fluctuations do control rigidity transitions in embryonic tissues, highlighting a key role of non-equilibrium tension dynamics in developmental processes.Many essential processes in multicellular organisms, from organ formation to tissue homeostasis, require a tight control of the tissue physical state 1, 2 . While tissue mechanics and structure at supracellular scales emerge from the collective physical interactions among the constituent cells, their control occurs at cell and subcellular levels. Bridging these scales is essential to understand the physical nature of active (non-equilibrium) multicellular systems and to identify the processes that cells use to control the physical state of embryonic tissues.In vitro experiments of cell monolayers on substrates have revealed characteristics of glassy 2 dynamics 3, 4 and rigidity transitions 5-7 , which are thought to be linked to biological function and multiple pathologies. In contrast, suspended epithelial monolayers are largely solid-like in vitro 8 and show evidence of fracture in vivo 9 . Experiments in embryonic tissues have shown characteristics of glassy dynamics in cell movements 10 , viscous behavior at long-timescales 11 and also structural signatures reminiscent of jamming transitions 12 . Recent in vivo experiments in developing zebrafish embryos showed the existence of a rigidity (fluid-to-solid) transition underlying the formation of the vertebrate body axis, revealing a functional role of rigidity transitions in embryonic development 13 . It is, however, unclear how cells control rigidity transitions in multicellular systems and, more generally, whether all these observed phenomena share a common physical origin.The physical behavior of multicellular systems has been studied theoretically using various approaches. Vertex models [14][15][16][17][18][19] and Cellular Potts models 20, 21 , which account for cell geometry and use equilibrium formulations to describe the physical state of the system, predict a densityindependent rigidity transition in confluent systems that is solely controlled by cell...

Tissue morphogenesis, homoeostasis and repair require cells to constantly monitor their three-dimensional microenvironment and adapt their behaviours in response to local biochemical and mechanical cues. Yet the mechanical parameters of the cellular microenvironment probed by cells in vivo remain unclear. Here, we report the mechanics of the cellular microenvironment that cells probe in vivo and in situ during zebrafish presomitic mesoderm differentiation. By quantifying both endogenous cell-generated strains and tissue mechanics, we show that individual cells probe the stiffness associated with deformations of the supracellular, foam-like tissue architecture. Stress relaxation leads to a perceived microenvironment stiffness that decreases over time, with cells probing the softest regime. We find that most mechanical parameters, including those probed by cells, vary along the anteroposterior axis as mesodermal progenitors differentiate. These findings expand our understanding of in vivo mechanosensation and might aid the design of advanced scaffolds for tissue engineering applications.

Wave-like beating of eukaryotic cilia and flagella-threadlike protrusions found in many cells and microorganisms-is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending.Here we show that in the presence of myosin motors, polymerizing actin filaments selfassemble into polar bundles which exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin-bundle shape, providing a feedback mechanism between myosin activity and filament deformations for the self-organization of large motor-filament assemblies.