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Studies of fate patterning during development typically emphasize cell-cell communication via diffusible chemical signals. Recent experiments on stem cell colonies, however, suggest that in some cases mechanical stresses, rather than secreted chemicals, enable long-ranged cell-cell interactions that specify positional information and pattern cell fates. These findings inspire a model of mechanical patterning: fate affects cell contractility, and pressure in the cell layer biases fate. Cells at the colony edge, more contractile than cells at the center, seed a pattern that propagates via force transmission. Strikingly, our model implies that the width of the outer fate domain varies nonmonotonically with substrate stiffness, a prediction that we confirm experimentally; we argue that a similar dependence on substrate stiffness can be achieved by a chemical morphogen only if strong constraints on the signaling pathway's mechanobiology are met. Our findings thus support the idea that mechanical stress can mediate patterning in the complete absence of chemical morphogens, even in nonmotile cell layers, thus expanding the repertoire of possible roles for mechanical signals in development and morphogenesis. Future tests of additional model predictions, like the effect of anisotropic substrate rigidity, will further broaden the range of achievable fate patterns. Published by the American Physical Society2025 

Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM. 

Abstract All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ 0 of an elastic medium is approximately $$\delta {\lambda }_{0}/{\lambda }_{0} \sim ({\Delta }_{\lambda }^{1/2}/{\lambda }_{0}){(d/a)}^{D/2}{(\xi /a)}^{D/2}$$ δ λ 0 / λ 0 ~ ( Δ λ 1 / 2 / λ 0 ) ( d / a ) D / 2 ( ξ / a ) D / 2 for a  ≫  d  ≫  ξ , $${\lambda }_{0}\gg {\Delta }_{\lambda }^{1/2}$$ λ 0 ≫ Δ λ 1 / 2 , and D  > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ 0 , Δ λ is the local variability of λ 0 , and D is the dimension of the medium. Our results reveal how one can construct devices capable of sensing near these limits, e.g. for medical diagnostics. We use our theoretical framework to estimate the limits of mechanosensing in a biopolymer network, a sensory process involved in cellular behavior, medical diagnostics, and material fabrication. 

The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called “Y-Junctions”, form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.