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Living systems adopt diversity of shapes. These morphological changes, which range from cell to organismal scales1–4, commonly rely on intrinsic contractile stresses generated by myosin in the cell cytoskeleton, an adaptive active contractile filamentous material, whose molecular constituents, convert chemical energy to produce mechanical work5–7. How these intrinsically active stresses arise in complex 3D shapes and how shape deformation is controlled remains poorly understood. Here, we demonstrate that, initially homogenousnot-prepatternedelastic actomyosin networks spontaneously self-organize in a family of 3D shapes through distinct dynamical patterns. Shape selection is encoded in system size to thickness aspect ratio, indicating shaping scalability. The final configurations show surprisingly simple scaling dependence on system dimensions. Altogether, cytoskeletal networks form a class of adaptive active materials, autonomously designing their own shape in response to system geometry, without needing specific pre-programming. This simplicity present huge advantage for developing bio-soft robots with desired target shapes.

Many bacterial species are helical in form, including the widespread pathogen H. pylori. Motivated by recent experiments on H. pylori showing that cell wall synthesis is not uniform, we investigate the possible formation of helical cell shape induced by elastic heterogeneity. We show, experimentally and theoretically, that helical morphogenesis can be produced by pressurizing an elastic cylindrical vessel with helical reinforced lines. The properties of the pressurized helix are highly dependent on the initial helical angle of the reinforced region. We find that steep angles result in crooked helices with, surprisingly, reduced end-to-end distance upon pressurization. This work helps to explain the possible mechanisms for the generation of helical cell morphologies and may inspire the design of novel pressure-controlled helical actuators.

Confluent epithelial tissues can be viewed as soft active solids, as their individual cells contract in response to local conditions. Little is known about the emergent properties of such materials. Empirical observations have shown contraction waves propagation in various epithelia, yet the governing mechanism, as well as its physiological function, is still unclear. Here we propose an experiment-inspired model for such dynamic epithelia. We show how the widespread cellular response of contraction-under-tension is sufficient to give rise to propagating contraction pulses, by mapping numerically and theoretically the consequences of such a cellular response. The model explains observed phenomena but also predicts enhanced rip-resistance as an emergent property of such cellular sheets. Unlike healing post-rupture, these sheets avoid it by actively re-distributing external stresses across their surface. The mechanism is relevant to a broad class of tissues, especially such under challenging mechanical conditions, and may inspire engineering of synthetic materials. Observations on confluent epithelial tissues show the emergence of dynamic contraction patterns that are suspected to be governed mechanically. Here, the authors propose a model for epithelial sheets and show that cells’ Extension-Induced-Contraction response explains experimentally-observed contraction pulses, that along with a cell softening response enhances epithelial resistance to rupture.

Epithelial tissues in many contexts can be viewed as soft active solids. Their active nature is manifested in the ability of individual cells within the tissue to contract and/or remodel their mechanical properties in response to various conditions. Little is known about the emergent properties of such materials. Specifically, how an individual cellular activity gives rise to collective spatiotemporal patterns is not fully understood. Recently we reported the observation of ultrafast contraction pulses in the dorsal epithelium of T.adhaerens in vivo [1] and speculated these propagate via mechanical fields. Other accumulating evidence suggest mechanics is involved in similar contractile patterns in embryonic development in vivo and in cellular monolayers in vitro. Here we show that a widespread cellular response – activation of contraction in response to stretch – is sufficient to give rise to nonlinear propagating contraction pulses. Using a minimal numerical model and theoretical considerations we show how such mechanical pulses emerge and propagate, spontaneously or in response to external stretch. The model – whose mathematical structure resembles that of reaction-diffusion systems – explains observed phenomena in T. adhaerens (e.g. excitable or spontaneous pulses, pulse interaction) and predicts other phenomena (e.g. symmetric strain profile, “spike trains”). Finally, we show that in response to external tension, such an active two-dimensional sheet lowers and dynamically distributes the strains across its surface, hence facilitating tissue resistance to rupture. Adding a cellular softening-threshold further enhances the tissue resistance to rupture at cell-cell junctions. As cohesion is at the heart of epithelial physiology, our model may be relevant to many other epithelial systems, even if manifested at different time/length scales.SignificanceOur work demonstrates that many observed dynamical phenomena in epithelial tissues can be explained merely by mechanical cell-cell interactions, and do not require chemical diffusion or transport between cells (though chemical activity may participate in relevant intracellular processes). Specifically, we show that single cell extension-induced-contraction (EIC) is sufficient to generate propagating contraction pulses, which also increase the tissue’s resistance to rupture, an essential function of epithelia. Our results may shed light on how epithelial tissues function under challenging physiological conditions, e.g. in lung, gut, vasculature and other biomedical contexts. Our results may also be relevant in the study of early evolution of multicellularity and the nervous-muscular systems. Finally, the work offers guidelines for designing soft synthetic solids with improved mechanical properties.

By definition of multicellularity, all animals need to keep their cells attached and intact, despite internal and external forces. Cohesion between epithelial cells provides this key feature. To better understand fundamental limits of this cohesion, we study the epithelium mechanics of an ultrathin (∼25 μm) primitive marine animal Trichoplax adhaerens , composed essentially of two flat epithelial layers. With no known extracellular matrix and no nerves or muscles, T. adhaerens has been claimed to be the “simplest known living animal,” yet is still capable of coordinated locomotion and behavior. Here we report the discovery of the fastest epithelial cellular contractions known in any metazoan, to be found in T. adhaerens dorsal epithelium (50% shrinkage of apical cell area within one second, at least an order of magnitude faster than other known examples). Live imaging reveals emergent contractile patterns that are mostly sporadic single-cell events, but also include propagating contraction waves across the tissue. We show that cell contraction speed can be explained by current models of nonmuscle actin–myosin bundles without load, while the tissue architecture and unique mechanical properties are softening the tissue, minimizing the load on a contracting cell. We propose a hypothesis, in which the physiological role of the contraction dynamics is to resist external stresses while avoiding tissue rupture (“active cohesion”), a concept that can be further applied to engineering of active materials.

By definition of multi-cellularity, all animals need to keep their cells attached and intact, despite internal and external forces. Cohesion between epithelial cells provides this key feature. In order to better understand fundamental limits of this cohesion, we study the epithelium mechanics of an ultra-thin (~25 um) primitive marine animalTrichoplax adhaerens, composed essentially of two flat epithelial layers. With no known extra-cellular-matrix and no nerves or muscles,T. adhaerenswas claimed the “simplest known living animal”, yet is still capable of coordinated locomotion and behavior. Here we report the discovery of the fastest epithelial cellular contractions to date to be found inT. adhaerensdorsal epithelium (50% shrinkage of apical cell area within one second, at least an order of magnitude faster than known examples). Live imaging reveals emergent contractile patterns that are mostly sporadic single-cell events, but also include propagating contraction waves across the tissue. We show that cell contraction speed can be explained by current models of non-muscle actin-myosin bundles without load, while the tissue architecture and unique mechanical properties are softening the tissue, minimizing the load on a contracting cell. We propose a hypothesis, in which the physiological role of the contraction dynamics is to avoid tissue rupture (“active cohesion”), a novel concept that can be further applied to engineering of active materials.One Sentence SummaryWe report the fastest epithelial cell contractions known to date, show they fit the kinematics arising from current cytoskeletal models, and suggest the extreme tissue dynamics is a means to actively avoid rupture.

Summary Three-dimensional geometry of leaf margins is an important shape characteristic to distinguish different leaf phenotypes. Novel geometrical methods were defined, measured, and used to quantify waviness and lobiness of leaves., The geometry of leaf margins is an important shape characteristic that distinguishes among different leaf phenotypes. Current definitions of leaf shape are qualitative and do not allow quantification of differences in shape between phenotypes. This is especially true for leaves with some non-trivial three-dimensional (3D) configurations. Here we present a novel geometrical method novel geometrical methods to define, measure, and quantify waviness and lobiness of leaves. The method is based on obtaining the curve of the leaf rim from a 3D surface measurement and decomposing its local curvature vector into the normal and geodesic components. We suggest that leaf waviness is associated with oscillating normal curvature along the margins, while lobiness is associated with oscillating geodesic curvature. We provide a way to integrate these local measures into global waviness and lobiness quantities. Using these novel definitions, we analysed the changes in leaf shape of two Arabidopsis genotypes, either as a function of gene mis-expression induction level or as a function of time. These definitions and experimental methods open the way for a more quantitative study of the shape of leaves and other growing slender organs.

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour., 8 pages, 4 figures

We studied the mechanical process of seed pods opening in Bauhinia variegate and found a chirality-creating mechanism, which turns an initially flat pod valve into a helix. We studied configurations of strips cut from pod valve tissue and from composite elastic materials that mimic its structure. The experiments reveal various helical configurations with sharp morphological transitions between them. Using the mathematical framework of "incompatible elasticity," we modeled the pod as a thin strip with a flat intrinsic metric and a saddle-like intrinsic curvature. Our theoretical analysis quantitatively predicts all observed configurations, thus linking the pod's microscopic structure and macroscopic conformation. We suggest that this type of incompatible strip is likely to play a role in the self-assembly of chiral macromolecules and could be used for the engineering of synthetic self-shaping devices.

We provide a geometric-mechanical model for calculating equilibrium configurations of chemical systems that self-assemble into chiral ribbon structures. The model is based on incompatible elasticity and uses dimensionless parameters to determine the equilibrium configurations. As such, it provides universal curves for the shape and energy of self-assembled ribbons. We provide quantitative predictions for the twisted-to-helical transition, which was observed experimentally in many systems, and demonstrate it with synthetic ribbons made of responsive gels. In addition, we predict the bi-stability of wide ribbons and also show how geometrical frustration can cause arrest of ribbon widening. Finally, we show that the model's predictions provide explanations for experimental observations in different chemical systems.