Genetic and Mechanical Regulation of Intestinal Smooth Muscle Development.

The gastrointestinal tract is enveloped by concentric and orthogonally aligned layers of smooth muscle; however, an understanding of the mechanisms by which these muscles become patterned and aligned in the embryo has been lacking. We find that Hedgehog acts through Bmp to delineate the position of the circumferentially oriented inner muscle layer, whereas localized Bmp inhibition is critical for allowing formation of the later-forming, longitudinally oriented outer layer. Because the layers form at different developmental stages, the muscle cells are exposed to unique mechanical stimuli that direct their alignments. Differential growth within the early gut tube generates residual strains that orient the first layer circumferentially, and when formed, the spontaneous contractions of this layer align the second layer longitudinally. Our data link morphogen-based patterning to mechanically controlled smooth muscle cell alignment and provide a mechanistic context for potentially understanding smooth muscle organization in a wide variety of tubular organs.

Excitable Dynamics and Yap-Dependent Mechanical Cues Drive the Segmentation Clock.

The periodic segmentation of the vertebrate body axis into somites, and later vertebrae, relies on a genetic oscillator (the segmentation clock) driving the rhythmic activity of signaling pathways in the presomitic mesoderm (PSM). To understand whether oscillations are an intrinsic property of individual cells or represent a population-level phenomenon, we established culture conditions for stable oscillations at the cellular level. This system was used to demonstrate that oscillations are a collective property of PSM cells that can be actively triggered in vitro by a dynamical quorum sensing signal involving Yap and Notch signaling. Manipulation of Yap-dependent mechanical cues is sufficient to predictably switch isolated PSM cells from a quiescent to an oscillatory state in vitro, a behavior reminiscent of excitability in other systems. Together, our work argues that the segmentation clock behaves as an excitable system, introducing a broader paradigm to study such dynamics in vertebrate morphogenesis.

Bending gradients: how the intestinal stem cell gets its home.

We address the mechanism by which adult intestinal stem cells (ISCs) become localized to the base of each villus during embryonic development. We find that, early in gut development, proliferating progenitors expressing ISC markers are evenly distributed throughout the epithelium, in both the chick and mouse. However, as the villi form, the putative stem cells become restricted to the base of the villi. This shift in the localization is driven by mechanically influenced reciprocal signaling between the epithelium and underlying mesenchyme. Buckling forces physically distort the shape of the morphogenic field, causing local maxima of epithelial signals, in particular Shh, at the tip of each villus. This induces a suite of high-threshold response genes in the underlying mesenchyme to form a signaling center called the "villus cluster." Villus cluster signals, notably Bmp4, feed back on the overlying epithelium to ultimately restrict the stem cells to the base of each villus.

The sex of organ geometry.

Organs have a distinctive yet often overlooked spatial arrangement in the body1-5. We propose that there is a logic to the shape of an organ and its proximity to its neighbours. Here, by using volumetric scans of many Drosophila melanogaster flies, we develop methods to quantify three-dimensional features of organ shape, position and interindividual variability. We find that both the shapes of organs and their relative arrangement are consistent yet differ between the sexes, and identify unexpected interorgan adjacencies and left-right organ asymmetries. Focusing on the intestine, which traverses the entire body, we investigate how sex differences in three-dimensional organ geometry arise. The configuration of the adult intestine is only partially determined by physical constraints imposed by adjacent organs; its sex-specific shape is actively maintained by mechanochemical crosstalk between gut muscles and vascular-like trachea. Indeed, sex-biased expression of a muscle-derived fibroblast growth factor-like ligand renders trachea sexually dimorphic. In turn, tracheal branches hold gut loops together into a male or female shape, with physiological consequences. Interorgan geometry represents a previously unrecognized level of biological complexity which might enable or confine communication across organs and could help explain sex or species differences in organ function.

The developmental mechanics of divergent buckling patterns in the chick gut.

Tissue buckling is an increasingly appreciated mode of morphogenesis in the embryo, but it is often unclear how geometric and material parameters are molecularly determined in native developmental contexts to generate diverse functional patterns. Here, we study the link between differential mechanical properties and the morphogenesis of distinct anteroposterior compartments in the intestinal tract-the esophagus, small intestine, and large intestine. These regions originate from a simple, common tube but adopt unique forms. Using measured data from the developing chick gut coupled with a minimal theory and simulations of differential growth, we investigate divergent lumen morphologies along the entire early gut and demonstrate that spatiotemporal geometries, moduli, and growth rates control the segment-specific patterns of mucosal buckling. Primary buckling into wrinkles, folds, and creases along the gut, as well as secondary buckling phenomena, including period-doubling in the foregut and multiscale creasing-wrinkling in the hindgut, are captured and well explained by mechanical models. This study advances our existing knowledge of how identity leads to form in these regions, laying the foundation for future work uncovering the relationship between molecules and mechanics in gut morphological regionalization.

Direct force measurement and loading on developing tissues in intact avian embryos.

Developmental morphogenesis is driven by tissue stresses acting on tissue rheology. Direct measurements of forces in small tissues (100 µm-1 mm) in situ, such as in early embryos, require high spatial precision and minimal invasiveness. Here, we introduce a control-based approach, tissue force microscopy (TiFM), that integrates a mechanical cantilever probe and live imaging with closed-loop feedback control of mechanical loading in early chicken embryos. By testing previously qualitatively characterized force-producing tissues in the elongating body axis, we show that TiFM quantitatively captures stress dynamics with high sensitivity. TiFM also provides the means to apply stable, minimally invasive and physiologically relevant loads to drive tissue deformation and to follow the resulting morphogenetic progression associated with large-scale cell movements. Together, TiFM allows us to control tissue force measurement and manipulation in small developing embryos, and promises to contribute to the quantitative understanding of complex multi-tissue mechanics during development.

Rectified random cell motility as a mechanism for embryo elongation.

The body of vertebrate embryos forms by posterior elongation from a terminal growth zone called the tail bud. The tail bud is a source of highly motile cells that eventually constitute the presomitic mesoderm (PSM), a tissue that plays an important role in elongation movements. PSM cells establish an anterior-posterior cell motility gradient that parallels a gradient associated with the degradation of a specific cellular signal (FGF) known to be implicated in cell motility. Here, we combine the electroporation of fluorescent reporters in the PSM with time-lapse imaging in the chicken embryo to quantify cell diffusive movements along the motility gradient. We show that a simple microscopic model for random cell motility induced by FGF activity along with geometric confinement leads to rectified tissue elongation consistent with our observations. A continuum analog of the microscopic model leads to a macroscopic mechano-chemical model for tissue extension that couples FGF activity-induced cell motility and tissue rheology, and is consistent with the experimentally observed speed and extent of elongation. Together, our experimental observations and theoretical models explain how the continuous addition of cells at the tail bud combined with lateral confinement can be converted into oriented movement and drive body elongation.

Molecular control of macroscopic forces drives formation of the vertebrate hindgut.

The embryonic gut tube is a cylindrical structure from which the respiratory and gastrointestinal tracts develop1. Although the early emergence of the endoderm as an epithelial sheet2,3 and later morphogenesis of the definitive digestive and respiratory organs4-6 have been investigated, the intervening process of gut tube formation remains relatively understudied7,8. Here we investigate the molecular control of macroscopic forces underlying early morphogenesis of the gut tube in the chick embryo. The gut tube has been described as forming from two endodermal invaginations-the anterior intestinal portal (AIP) towards the rostral end of the embryo and the caudal intestinal portal (CIP) at the caudal end-that migrate towards one another, internalizing the endoderm until they meet at the yolk stalk (umbilicus in mammals)1,6. Migration of the AIP to form foregut has been descriptively characterized8,9, but the hindgut is likely to form by a distinct mechanism that has not been fully explained10. We find that the hindgut is formed by collective cell movements through a stationary CIP, rather than by movement of the CIP itself. Further, combining in vivo imaging, biophysics and mathematical modelling with molecular and embryological approaches, we identify a contractile force gradient that drives cell movements in the hindgut-forming endoderm, enabling tissue-scale posterior extension of the forming hindgut tube. The force gradient, in turn, is established in response to a morphogenic gradient of fibroblast growth factor signalling. As a result, we propose that an important positive feedback arises, whereby contracting cells draw passive cells from low to high fibroblast growth factor levels, recruiting them to contract and pull more cells into the elongating hindgut. In addition to providing insight into the early gut development, these findings illustrate how large-scale tissue level forces can be traced to developmental signals during vertebrate morphogenesis.

Hydraulic control of mammalian embryo size and cell fate.

Size control is fundamental in tissue development and homeostasis1,2. Although the role of cell proliferation in these processes has been widely studied, the mechanisms that control embryo size-and how these mechanisms affect cell fate-remain unknown. Here we use the mouse blastocyst as a model to unravel a key role of fluid-filled lumen in the control of embryo size and specification of cell fate. We find that there is a twofold increase in lumenal pressure during blastocyst development, which translates into a concomitant increase in cell cortical tension and tissue stiffness of the trophectoderm that lines the lumen. Increased cortical tension leads to vinculin mechanosensing and maturation of functional tight junctions, which establishes a positive feedback loop to accommodate lumen growth. When the cortical tension reaches a critical threshold, cell-cell adhesion cannot be sustained during mitotic entry, which leads to trophectoderm rupture and blastocyst collapse. A simple theory of hydraulically gated oscillations recapitulates the observed dynamics of size oscillations, and predicts the scaling of embryo size with tissue volume. This theory further predicts that disrupted tight junctions or increased tissue stiffness lead to a smaller embryo size, which we verified by biophysical, embryological, pharmacological and genetic perturbations. Changes in lumenal pressure and size can influence the cell division pattern of the trophectoderm, and thereby affect cell allocation and fate. Our study reveals how lumenal pressure and tissue mechanics control embryo size at the tissue scale, which is coupled to cell position and fate at the cellular scale.

Geometric control of topological dynamics in a singing saw.

The common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw's sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory, and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high-quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators and offers a robust principle to design high-quality resonators across scales, from macroscopic instruments to nanoscale devices, simply through geometry.

Optimal transport and control of active drops.

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Statistics and topology of fluctuating ribbons.

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

Active entanglement enables stochastic, topological grasping.

Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here, we circumvent the need for feedback or precise planning by using an array of fluidically actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides options for soft, adaptable grasping.

Matrix viscoelasticity controls spatiotemporal tissue organization.

Biomolecular and physical cues of the extracellular matrix environment regulate collective cell dynamics and tissue patterning. Nonetheless, how the viscoelastic properties of the matrix regulate collective cell spatial and temporal organization is not fully understood. Here we show that the passive viscoelastic properties of the matrix encapsulating a spheroidal tissue of breast epithelial cells guide tissue proliferation in space and in time. Matrix viscoelasticity prompts symmetry breaking of the spheroid, leading to the formation of invading finger-like protrusions, YAP nuclear translocation and epithelial-to-mesenchymal transition both in vitro and in vivo in a Arp2/3-complex-dependent manner. Computational modelling of these observations allows us to establish a phase diagram relating morphological stability with matrix viscoelasticity, tissue viscosity, cell motility and cell division rate, which is experimentally validated by biochemical assays and in vitro experiments with an intestinal organoid. Altogether, this work highlights the role of stress relaxation mechanisms in tissue growth dynamics, a fundamental process in morphogenesis and oncogenesis.

Multifunctional ferrofluid-infused surfaces with reconfigurable multiscale topography.

Developing adaptive materials with geometries that change in response to external stimuli provides fundamental insights into the links between the physical forces involved and the resultant morphologies and creates a foundation for technologically relevant dynamic systems1,2. In particular, reconfigurable surface topography as a means to control interfacial properties3 has recently been explored using responsive gels4, shape-memory polymers5, liquid crystals6-8 and hybrid composites9-14, including magnetically active slippery surfaces12-14. However, these designs exhibit a limited range of topographical changes and thus a restricted scope of function. Here we introduce a hierarchical magneto-responsive composite surface, made by infiltrating a ferrofluid into a microstructured matrix (termed ferrofluid-containing liquid-infused porous surfaces, or FLIPS). We demonstrate various topographical reconfigurations at multiple length scales and a broad range of associated emergent behaviours. An applied magnetic-field gradient induces the movement of magnetic nanoparticles suspended in the ferrofluid, which leads to microscale flow of the ferrofluid first above and then within the microstructured surface. This redistribution changes the initially smooth surface of the ferrofluid (which is immobilized by the porous matrix through capillary forces) into various multiscale hierarchical topographies shaped by the size, arrangement and orientation of the confining microstructures in the magnetic field. We analyse the spatial and temporal dynamics of these reconfigurations theoretically and experimentally as a function of the balance between capillary and magnetic pressures15-19 and of the geometric anisotropy of the FLIPS system. Several interesting functions at three different length scales are demonstrated: self-assembly of colloidal particles at the micrometre scale; regulated flow of liquid droplets at the millimetre scale; and switchable adhesion and friction, liquid pumping and removal of biofilms at the centimetre scale. We envision that FLIPS could be used as part of integrated control systems for the manipulation and transport of matter, thermal management, microfluidics and fouling-release materials.

Totimorphic assemblies from neutrally stable units.

Inspired by the quest for shape-shifting structures in a range of applications, we show how to create morphable structural materials using a neutrally stable unit cell as a building block. This unit cell is a self-stressed hinged structure with a one-parameter family of morphing motions that are all energetically equivalent. However, unlike kinematic mechanisms, the unit cell is not infinitely floppy and instead exhibits a tunable mechanical response akin to that of an ideal rigid-plastic material. Theory and simulations allow us to explore the properties of planar and spatial assemblies of neutrally stable elements, and solve the inverse problem of designing assemblies that can morph from one given shape into another. Simple experimental prototypes of these assemblies corroborate our theoretical results and show that the addition of switchable hinges allows us to create load-bearing structures. Altogether, totimorphs pave the way for structural materials whose geometry and deformation response can be controlled independently and at multiple scales.

An additive algorithm for origami design.

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

Geometry and dynamics link form, function, and evolution of finch beaks.

Darwin's finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. To quantify their form, we carry out a morphometric analysis of the three-dimensional beak shapes of all of Darwin's finches and find that they can be fit by a transverse parabolic shape with a curvature that increases linearly from the base toward the tip of the beak. The morphological variation of beak orientation, aspect ratios, and curvatures allows us to quantify beak function in terms of the elementary theory of machines, consistent with the dietary variations across finches. Finally, to explain the origin of the evolutionary morphometry and the developmental morphogenesis of the finch beak, we propose an experimentally motivated growth law at the cellular level that simplifies to a variant of curvature-driven flow at the tissue level and captures the range of observed beak shapes in terms of a simple morphospace. Altogether, our study illuminates how a minimal combination of geometry and dynamics allows for functional form to develop and evolve.

Self-organized biotectonics of termite nests.

The termite nest is one of the architectural wonders of the living world, built by the collective action of workers in a colony. Each nest has several characteristic structural motifs that allow for efficient ventilation, cooling, and traversal. We use tomography to quantify the nest architecture of the African termite Apicotermes lamani, consisting of regularly spaced floors connected by scattered linear and helicoidal ramps. To understand how these elaborate structures are built and arranged, we formulate a minimal model for the spatiotemporal evolution of three hydrodynamic fields-mud, termites, and pheromones-linking environmental physics to collective building behavior using simple local rules based on experimental observations. We find that floors and ramps emerge as solutions of the governing equations, with statistics consistent with observations of A. lamani nests. Our study demonstrates how a local self-reinforcing biotectonic scheme is capable of generating an architecture that is simultaneously adaptable and functional, and likely to be relevant for a range of other animal-built structures.

Elastic-instability-enabled locomotion.

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement--via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments--both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales.