The shape of Nature's stingers revealed.

Stinger-like structures in living organisms evolved convergently across taxa for both defensive and offensive purposes, with the main goal being penetration and damage. Our observations over a broad range of taxa and sizes, from microscopic radiolarians to narwhals, reveal a self-similar geometry of the stinger extremity: the diameter (d) increases along the distance from the tip (x) following a power law [Formula: see text] , with the tapering exponent varying universally between 2 and 3. We demonstrate, through analytical and experimental mechanics involving three-dimensional (3D) printing, that this geometry optimizes the stinger's performance; it represents a trade-off between the propensity to buckle, for n smaller than 2, and increased penetration force, for n greater than 3. Moreover, we find that this optimal tapering exponent does not depend on stinger size and aspect ratio (base diameter over length). We conclude that for Nature's stingers, composed of biological materials with moduli ranging from hundreds of megapascals to ten gigapascals, the necessity for a power-law contour increases with sharpness to ensure sufficient stability for penetration of skin-like tissues. Our results offer a solution to the puzzle underlying this universal geometric trait of biological stingers and may provide a new strategy to design needle-like structures for engineering or medical applications.

Experimental observation of near-wall effects during the puncture of soft solids.

Performing conventional mechanical characterization techniques on soft materials can be challenging due to issues such as limited sample volumes and clamping difficulties. Deep indentation and puncture is a promising alternative as it is an information-rich measurement with the potential to be performed in a high-throughput manner. Despite its promise, the method lacks standardized protocols, and open questions remain about its possible limitations. Addressing these shortcomings is vital to ensure consistent methodology, measurements, and interpretation across samples and labs. To fill this gap, we examine the role of finite sample dimensions (and by extension, volume) on measured forces to determine the sample geometry needed to perform and unambiguously interpret puncture tests. Through measurements of puncture on a well-characterized elastomer using systematically varied sample dimensions, we show that the apparent mechanical response of a material is in fact sensitive to near-wall effects, and that additional properties, such as the sliding friction coefficient, can only be extracted in the larger dimension case where such effects are negligible.

Nanolatticed Architecture Mitigates Damage in Shark Egg Cases.

Structural versatility and multifunctionality of biological materials have resulted in countless bioinspired strategies seeking to emulate the properties of nature. The nanostructured egg case of swell sharks is one of the toughest permeable membranes known and, thus, presents itself as a model system for materials where the conflicting properties, strength and porosity, are desirable. The egg case possesses an intricately ordered structure that is designed to protect delicate embryos from the external environment while enabling respiratory and metabolic exchange, achieving a tactical balance between conflicting properties. Herein, structural analyses revealed an enabling nanolattice architecture that constitutes a Bouligand-like nanoribbon hierarchical assembly. Three distinct hierarchical architectural adaptations enhance egg case survival: Bouligand-like organization for in-plane isotropic reinforcement, noncylindrical nanoribbons maximizing interfacial stress distribution, and highly ordered nanolattices enabling permeability and lattice-governed toughening mechanisms. These discoveries provide fundamental insights for the improvement of multifunctional membranes, fiber-reinforced soft composites, and mechanical metamaterials.

Role of boundary conditions in determining cell alignment in response to stretch.

The ability of cells to orient in response to mechanical stimuli is essential to embryonic development, cell migration, mechanotransduction, and other critical physiologic functions in a range of organs. Endothelial cells, fibroblasts, mesenchymal stem cells, and osteoblasts all orient perpendicular to an applied cyclic stretch when plated on stretchable elastic substrates, suggesting a common underlying mechanism. However, many of these same cells orient parallel to stretch in vivo and in 3D culture, and a compelling explanation for the different orientation responses in 2D and 3D has remained elusive. Here, we conducted a series of experiments designed specifically to test the hypothesis that differences in strains transverse to the primary loading direction give rise to the different alignment patterns observed in 2D and 3D cyclic stretch experiments ("strain avoidance"). We found that, in static or low-frequency stretch conditions, cell alignment in fibroblast-populated collagen gels correlated with the presence or absence of a restraining boundary condition rather than with compaction strains. Cyclic stretch could induce perpendicular alignment in 3D culture but only at frequencies an order of magnitude greater than reported to induce perpendicular alignment in 2D. We modified a published model of stress fiber dynamics and were able to reproduce our experimental findings across all conditions tested as well as published data from 2D cyclic stretch experiments. These experimental and model results suggest an explanation for the apparently contradictory alignment responses of cells subjected to cyclic stretch on 2D membranes and in 3D gels.

Contraction of polymer gels created by the activity of molecular motors.

We propose a theory based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent. When activated, these motors attach to the chains of the polymer network and shorten them creating a global contraction of the gel, which mimics the active behavior of a cytoskeleton. The power generated by these motors is obtained by an ATP hydrolysis reaction, which transduces chemical energy into mechanical work. The latter is described by an increment of strain energy in the gel due to an increased stiffness. This effect is described with an increment of the cross-link density in the polymer network, which reduces its entropy. The theory then considers polymer network swelling and species diffusion to describe the transient passive behavior of the gel. We finally formulate the problem of uniaxial contraction of a slab of gel and compare the results with experiments, showing good agreement.

Ferroelectric properties of composites containing BaTiO3 nanoparticles of various sizes.

Size effects, including the occurrence of superparaelectric phases associated with small scale, are a significant research topic for ferroelectrics. Relevant phenomena have been explored in detail, e.g. for homogeneous, thin ferroelectric films, but the related effects associated with nanoparticles are usually only inferred from their structural properties. In contrast, this paper describes all the steps and concepts necessary for the direct characterization and quantitative assessment of the ferroelectric properties of as-synthesized and as-received nanoparticles. The method adopted uses electrical polarization measurements on polymer matrix composites containing ferroelectric nanoparticles. It is applied to ten different BaTiO3 particle types covering a size range from 10 nm to 0.8 µm. The influence of variations of particle characteristics such as tetragonality and dielectric constant is considered based on measurements of these properties. For composites containing different particle types a clearly differing polarization behaviour is found. For decreasing particle size, increasing electric field is required to achieve a given level of polarization. The size dependence of a measure related to the coercive field revealed by this work is qualitatively in line with the state of the knowledge for ferroelectrics having small dimensions. For the first time, such results and size effects are described based on data from experiments on collections of actual nanoparticles.

On the generation of force required for actin-based motility.

The fundamental question of how forces are generated in a motile cell, a lamellipodium, and a comet tail is the subject of this note. It is now well established that cellular motility results from the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone around the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed, departing from the well-known theory of Larché-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.

Simulation of the mechanical response of cells on micropost substrates.

Experimental studies where cells are seeded on micropost arrays in order to quantify their contractile behavior are becoming increasingly common. Interpretation of the data generated by this experimental technique is difficult, due to the complexity of the processes underlying cellular contractility and mechanotransduction. In the current study, a coupled framework that considers strain rate dependent contractility and remodeling of the cytoskeleton is used in tandem with a thermodynamic model of tension dependent focal adhesion formation to investigate the biomechanical response of cells adhered to micropost arrays. Computational investigations of the following experimental studies are presented: cell behavior on different sized arrays with a range of post stiffness; stress fiber and focal adhesion formation in irregularly shaped cells; the response of cells to deformations applied locally to individual posts; and the response of cells to equibiaxial stretching of micropost arrays. The predicted stress fiber and focal adhesion distributions; in addition to the predicted post tractions are quantitatively and qualitatively supported by previously published experimental data. The computational models presented in this study thus provide a framework for the design and interpretation of experimental micropost studies.

Cataglyphis desert ants improve their mobility by raising the gaster.

We analyze theoretically the moment of inertia of the desert ant Cataglyphis (C. bicolor and C. fortis) around a vertical axis through its own center of mass when the animal raises its gaster to a vertical position. Compared to the value when the gaster is horizontal, the moment of inertia is reduced to one half; this implies that when increasing its angular acceleration the ant need apply only half the level of torque when the gaster is raised, compared to when the gaster is lowered. As an example, we analyze the cases of an ant running on circular and sinusoidal paths. In both cases, the ant must apply a sideways thrust, anti-roll and anti-pitch torques to avoid toppling, and, on the circular path when accelerating and throughout the sinusoidal trajectory, a torque to enable turning as the path curves. When the ant is accelerating in a very tight circle or running on a very narrow sinusoidal path, in which the amplitude of the sinusoid is less than the length of the ant's body, the forces required for the turning torque can equal and exceed those required for the sideways thrust, and can be reduced significantly by the ant raising the gaster, whereas the foot-thrust for the anti-roll and anti-pitch torques rises only modestly when the gaster is up. This suggests that there may be an evolutionary advantage for employing the gaster-raising mode of locomotion, since this habit will allow desert ants to use lower forces and less energy, and perhaps run faster on more tortuous paths.

Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues.

Physical forces generated by cells drive morphologic changes during development and can feedback to regulate cellular phenotypes. Because these phenomena typically occur within a 3-dimensional (3D) matrix in vivo, we used microelectromechanical systems (MEMS) technology to generate arrays of microtissues consisting of cells encapsulated within 3D micropatterned matrices. Microcantilevers were used to simultaneously constrain the remodeling of a collagen gel and to report forces generated during this process. By concurrently measuring forces and observing matrix remodeling at cellular length scales, we report an initial correlation and later decoupling between cellular contractile forces and changes in tissue morphology. Independently varying the mechanical stiffness of the cantilevers and collagen matrix revealed that cellular forces increased with boundary or matrix rigidity whereas levels of cytoskeletal and extracellular matrix (ECM) proteins correlated with levels of mechanical stress. By mapping these relationships between cellular and matrix mechanics, cellular forces, and protein expression onto a bio-chemo-mechanical model of microtissue contractility, we demonstrate how intratissue gradients of mechanical stress can emerge from collective cellular contractility and finally, how such gradients can be used to engineer protein composition and organization within a 3D tissue. Together, these findings highlight a complex and dynamic relationship between cellular forces, ECM remodeling, and cellular phenotype and describe a system to study and apply this relationship within engineered 3D microtissues.

A bioinspired snap-through metastructure for manipulating micro-objects.

Micro-objects stick tenaciously to each other-a well-known show-stopper in microtechnology and in handling micro-objects. Inspired by the trigger plant, we explore a mechanical metastructure for overcoming adhesion involving a snap-action mechanism. We analyze the nonlinear mechanical response of curved beam architectures clamped by a tunable spring, incorporating mono- and bistable states. As a result, reversible miniaturized snap-through devices are successfully realized by micron-scale direct printing, and successful pick-and-place handling of a micro-object is demonstrated. The technique is applicable to universal scenarios, including dry and wet environment, or smooth and rough counter surfaces. With an unprecedented switching ratio (between high and low adhesion) exceeding 104, this concept proposes an efficient paradigm for handling and placing superlight objects.

Viscoelastic analysis of mussel threads reveals energy dissipative mechanisms.

Mussels use byssal threads to secure themselves to rocks and as shock absorbers during cyclic loading from wave motion. Byssal threads combine high strength and toughness with extensibility of nearly 200%. Researchers attribute tensile properties of byssal threads to their elaborate multi-domain collagenous protein cores. Because the elastic properties have been previously scrutinized, we instead examined byssal thread viscoelastic behaviour, which is essential for withstanding cyclic loading. By targeting protein domains in the collagenous core via chemical treatments, stress relaxation experiments provided insights on domain contributions and were coupled with in situ small-angle X-ray scattering to investigate relaxation-specific molecular reorganizations. Results show that when silk-like domains in the core were disrupted, the stress relaxation of the threads decreased by nearly 50% and lateral molecular spacing also decreased, suggesting that these domains are essential for energy dissipation and assume a compressed molecular rearrangement when disrupted. A generalized Maxwell model was developed to describe the stress relaxation response. The model predicts that maximal damping (energy dissipation) occurs at around 0.1 Hz which closely resembles the wave frequency along the California coast and implies that these materials may be well adapted to the cyclic loading of the ambient conditions.

A simple 3-point flexural method for measuring fracture toughness of the dental porcelain to zirconia bond and other brittle bimaterial interfaces.

PURPOSE: Porcelain fused to zirconia prostheses are widely used, but porcelain chipping, fracture, spalling and delamination are common clinical problems. Conventional bond strength testing is inherently unsuited for studying interfacial failure by cracking in brittle materials. Instead, fracture toughness is a more meaningful parameter because it can assess the robustness of the interface when subjected to loading, but fracture mechanics approaches have only rarely been used. Our purpose was to develop a novel, simple, 3-point flexural methodology and mathematical analysis to measure the fracture toughness of the porcelain to zirconia interface. METHODS: Equations were derived to estimate the fracture toughness of the bond by computing the interfacial energy release rate for a novel simple 3-point flexural test model. The test was validated using two different configurations of layered zirconia/porcelain beams (n = 10), approximating the dimensions of a fixed dental prosthesis, fabricated from a tetragonal polycrystalline zirconium dioxide partially stabilized with yttria and a feldspathic dental porcelain. RESULTS: Cracking along the bimaterial interface was produced and measured as a discrete event. Fracture toughness means (standard deviations) computed from the measured energy release rate, for the porcelain to zirconia interface in two different specimen configurations were 7.9 (1.3) and 5.3 (1.6) J/m2. CONCLUSIONS: Equations were derived to measure interfacial fracture toughness of brittle materials using a novel simple 3-point flexural test method. The test was then validated; estimates for the fracture toughness for the porcelain to zirconia bond, overlapped with previously published data derived from more complex 4-point notched tests.

A microscopically motivated model for the remodeling of cardiomyocytes.

We present a thermodynamically based model that captures the remodeling effects in cardiac muscle cells. This work begins with the formulation of the kinematics of a cardiomyocyte resulting from a prescribed macroscopic deformation and the reorganization of the internal structure. Specifically, relations between the macroscopic deformation and the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell are determined. The remodeling process is split into two separate phases-(1) elongation/shortening of the existing myofibrils by addition/detachment of sarcomeres and (2) formation of new myofibrils. The remodeling associated with each phase is modeled through a dissipation postulate. We show that remodeling is based on a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources to drive the remodeling process, and dissipation mechanisms. While the variations in entropy associated with phase (1) are neglected, the substantial entropy loss associated with the formation of new myofibrils is determined. To illustrate the merit of the proposed framework, we compute the response of cardiomyocytes subjected to isometric axial stretch that are either free to deform or fixed in the transverse direction. We also examine the predictions of this model for cardiomyocytes subjected to various cyclic loadings. The proposed framework is capable of capturing a wide range of remodeling effects and agrees with experimental observations.

Force distribution and multiscale mechanics in the mussel byssus.

The byssi of sessile mussels have the extraordinary ability to adhere to various surfaces and withstand static and dynamic loadings arising from hostile environmental conditions. Many investigations aimed at understanding the unique properties of byssal thread-plaque structures have been conducted and have inspired the enhancement of fibre coatings and adhesives. However, a systems-level analysis of the mechanical performance of the composite materials is lacking. In this work, we discuss the anatomy of the byssus and the function of each of the three components (the proximal thread portion, the distal thread portion and the adhesive plaque) of its structures. We introduce a basic nonlinear system of springs that describes the contribution of each component to the overall mechanical response and use this model to approximate the elastic modulus of the distal thread portion as well as the plaque, the response of which cannot be isolated through experiment alone. We conclude with a discussion of unresolved questions, highlighting areas of opportunity where additional experimental and theoretical work is needed. This article is part of the theme issue 'Transdisciplinary approaches to the study of adhesion and adhesives in biological systems'.

Statistical properties of defect-dependent detachment strength in bioinspired dry adhesives.

Dry adhesives using surface microstructures inspired by climbing animals have been recognized for their potentially novel capabilities, with relevance to a range of applications including pick-and-place handling. Past work has suggested that performance may be strongly dependent on variability in the critical defect size among fibrillar sub-contacts. However, it has not been directly verified that the resulting adhesive strength distribution is well described by the statistical theory of fracture used. Using in situ contact visualization, we characterize adhesive strength on a fibril-by-fibril basis for a synthetic fibrillar adhesive. Two distinct detachment mechanisms are observed. The fundamental, design-dependent mechanism involves defect propagation from within the contact. The secondary mechanism involves defect propagation from fabrication imperfections at the perimeter. The existence of two defect populations complicates characterization of the statistical properties. This is addressed by using the mean order ranking method to isolate the fundamental mechanism. The statistical properties obtained are subsequently used within a bimodal framework, allowing description of the secondary mechanism. Implications for performance are discussed, including the improvement of strength associated with elimination of fabrication imperfections. This statistical analysis of defect-dependent detachment represents a more complete approach to the characterization of fibrillar adhesives, offering new insight for design and fabrication.

The simulation of stress fibre and focal adhesion development in cells on patterned substrates.

The remodelling of the cytoskeleton and focal adhesion (FA) distributions for cells on substrates with micro-patterned ligand patches is investigated using a bio-chemo-mechanical model. We investigate the effect of ligand pattern shape on the cytoskeletal arrangements and FA distributions for cells having approximately the same area. The cytoskeleton model accounts for the dynamic rearrangement of the actin/myosin stress fibres. It entails the highly nonlinear interactions between signalling, the kinetics of tension-dependent stress-fibre formation/dissolution and stress-dependent contractility. This model is coupled with another model that governs FA formation and accounts for the mechano-sensitivity of the adhesions from thermodynamic considerations. This coupled modelling scheme is shown to capture a variety of key experimental observations including: (i) the formation of high concentrations of stress fibres and FAs at the periphery of circular and triangular, convex-shaped ligand patterns; (ii) the development of high FA concentrations along the edges of the V-, T-, Y- and U-shaped concave ligand patterns; and (iii) the formation of highly aligned stress fibres along the non-adhered edges of cells on the concave ligand patterns. When appropriately calibrated, the model also accurately predicts the radii of curvature of the non-adhered edges of cells on the concave-shaped ligand patterns.

Cooperative contractility: the role of stress fibres in the regulation of cell-cell junctions.

We present simulations of cell-cell adhesion as reported in a recent study [Liu et al., 2010, PNAS, 107(22), 9944-9] for two cells seeded on an array of micro-posts. The micro-post array allows for the measurement of forces exerted by the cell and these show that the cell-cell tugging stress is a constant and independent of the cell-cell junction area. In the current study, we demonstrate that a material model which includes the underlying cellular processes of stress fibre contractility and adhesion formation can capture these results. The simulations explain the experimentally observed phenomena whereby the cell-cell junction forces increase with junction size but the tractions exerted by the cell on the micro-post array are independent of the junction size. Further simulations on different types of micro-post arrays and cell phenotypes are presented as a guide to future experiments.

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion.

Numerous experimental studies have established that cells can sense the stiffness of underlying substrates and have quantified the effect of substrate stiffness on stress fibre formation, focal adhesion area, cell traction, and cell shape. In order to capture such behaviour, the current study couples a mixed mode thermodynamic and mechanical framework that predicts focal adhesion formation and growth with a material model that predicts stress fibre formation, contractility, and dissociation in a fully 3D implementation. Simulations reveal that SF contractility plays a critical role in the substrate-dependent response of cells. Compliant substrates do not provide sufficient tension for stress fibre persistence, causing dissociation of stress fibres and lower focal adhesion formation. In contrast, cells on stiffer substrates are predicted to contain large amounts of dominant stress fibres. Different levels of cellular contractility representative of different cell phenotypes are found to alter the range of substrate stiffness that cause the most significant changes in stress fibre and focal adhesion formation. Furthermore, stress fibre and focal adhesion formation evolve as a cell spreads on a substrate and leading to the formation of bands of fibres leading from the cell periphery over the nucleus. Inhibiting the formation of FAs during cell spreading is found to limit stress fibre formation. The predictions of this mutually dependent material-interface framework are strongly supported by experimental observations of cells adhered to elastic substrates and offer insight into the inter-dependent biomechanical processes regulating stress fibre and focal adhesion formation.

Detachment of compliant films adhered to stiff substrates via van der Waals interactions: role of frictional sliding during peeling.

The remarkable ability of some plants and animals to cling strongly to substrates despite relatively weak interfacial bonds has important implications for the development of synthetic adhesives. Here, we examine the origins of large detachment forces using a thin elastomer tape adhered to a glass slide via van der Waals interactions, which serves as a model system for geckos, mussels and ivy. The forces required for peeling of the tape are shown to be a strong function of the angle of peeling, which is a consequence of frictional sliding at the edge of attachment that serves to dissipate energy that would otherwise drive detachment. Experiments and theory demonstrate that proper accounting for frictional sliding leads to an inferred work of adhesion of only approximately 0.5 J m(-2) (defined for purely normal separations) for all load orientations. This starkly contrasts with the interface energies inferred using conventional interface fracture models that assume pure sticking behaviour, which are considerably larger and shown to depend not only on the mode-mixity, but also on the magnitude of the mode-I stress intensity factor. The implications for developing frameworks to predict detachment forces in the presence of interface sliding are briefly discussed.