Mechanics of biological networks: from the cell cytoskeleton to connective tissue

Bionic Artificial Skin Based on Self-Healable Ionogel Composites with Tailored Mechanics and Robust Interfaces

Bionic artificial skin which imitates the features and functions of human skin, has broad applications in wearable human-machine interfaces. However, equipping artificial materials with skin-like mechanical properties, self-healing ability, and high sensitivity remains challenging. Here, inspired by the structure of human skin, an artificial skin based on ionogel composites with tailored mechanical properties and robust interface is prepared. Combining finite element analysis and direct ink writing (DIW) 3D printing technology, an ionogel composite with a rigid skeleton and an ionogel matrix is precisely designed and fabricated, realizing the mechanical anisotropy and nonlinear mechanical response that accurately mimic human skin. Robust interface is created through co-curing of the skeleton and matrix resins, significantly enhancing the stability of the composite. The realization of self-healing ability and resistance to crack growth further ensure the remarkable durability of the artificial skin for sensing application. In summary, the bionic artificial skin mimics the characteristics of human skin, including mechanical anisotropy, nonlinear mechanical response, self-healing capability, durability and high sensitivity when applied as flexible sensors. These strategies provide strong support for the fabrication of tissue-like materials with adaptive mechanical behaviors.

Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model

In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite. It is observed that in the small strain, linear regime the parallel model leads to errors when the ratio of the individual stiffnesses of the two components is in the range 0.1-10, and the error increases as the matrix approaches the incompressible limit. The data presented can be used to correct the parallel model to improve the accuracy of the overall stiffness prediction. In the non-linear large deformation regime linear superposition does not apply. The data shows that the matrix reduces the stiffening rate of the network, and the response is softer than that predicted by the parallel model. The correction proposed for the linear regime mitigates to a large extent the error in the non-linear regime as well, provided the matrix Poisson ratio is not close to 0.5. The special case in which the matrix is rendered auxetic is also evaluated and it is seen that the auxeticity of the matrix may compensate the stiffening introduced by the network, leading to a composite with linear elastic response over a broad range of strains.

Nonlinear Poisson effect in affine semiflexible polymer networks

Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or, in the incompressible limit, remains constant as the material is stretched. However, in networks of semiflexible or stiff polymers, which are typically highly compressible yet stiffen significantly when stretched, one instead sees a significant reduction in specific volume under finite strains. This volume reduction is accompanied by increasing alignment of filaments along the strain axis and a nonlinear elastic response, with stiffening of the apparent Young's modulus. For semiflexible networks, in which entropic bending elasticity governs the linear elastic regime, the nonlinear Poisson effect is caused by the nonlinear force-extension relationship of the constituent filaments, which produces a highly asymmetric response of the constituent polymers to stretching and compression. The details of this relationship depend on the geometric and elastic properties of the underlying filaments, which can vary greatly in experimental systems. Here, we provide a comprehensive characterization of the nonlinear Poisson effect in an affine network model and explore the influence of filament properties on essential features of both microscopic and macroscopic response, including strain-driven alignment and volume reduction.

Microstructural Evolution and Failure in Fibrous Network Materials: Failure Mode Transition from the Competition between Bond and Fiber

For the complex structure of fibrous network materials, it is a challenge to analyze the network strength and deformation mechanism. Here, we identify a failure mode transition within the network material comprising brittle fibers and bonds, which is related to the strength ratio of the bond to the fiber. A failure criterion for this type of fibrous network is proposed to quantitatively characterize this transition between bond damage and fiber damage. Additionally, tensile experiments on carbon and ceramic fibrous network materials were conducted, and the experimental results show that the failure modes of these network materials satisfy the theoretical prediction. The relationship between the failure mode, the relative density of network and strength of the components is established based on finite element analysis of the 3D network model. The failure mode transforms from bond damage to fiber damage as increasing of bond strength. According to the transition of the failure modes in the brittle fibrous network, it is possible to tailor the mechanical properties of fibrous network material by balancing the competition between bond and fiber properties, which is significant for optimizing material design and engineering applications.

Tailoring Synthetic Polypeptide Design for Directed Fibril Superstructure Formation and Enhanced Hydrogel Properties

The biological significance of self-assembled protein filament networks and their unique mechanical properties have sparked interest in the development of synthetic filament networks that mimic these attributes. Building on the recent advancement of autoaccelerated ring-opening polymerization of amino acid N-carboxyanhydrides (NCAs), this study strategically explores a series of random copolymers comprising multiple amino acids, aiming to elucidate the core principles governing gelation pathways of these purpose-designed copolypeptides. Utilizing glutamate (Glu) as the primary component of copolypeptides, two targeted pathways were pursued: first, achieving a fast fibrillation rate with lower interaction potential using serine (Ser) as a comonomer, facilitating the creation of homogeneous fibril networks; and second, creating more rigid networks of fibril clusters by incorporating alanine (Ala) and valine (Val) as comonomers. The selection of amino acids played a pivotal role in steering both the morphology of fibril superstructures and their assembly kinetics, subsequently determining their potential to form sample-spanning networks. Importantly, the viscoelastic properties of the resulting supramolecular hydrogels can be tailored according to the specific copolypeptide composition through modulations in filament densities and lengths. The findings enhance our understanding of directed self-assembly in high molecular weight synthetic copolypeptides, offering valuable insights for the development of synthetic fibrous networks and biomimetic supramolecular materials with custom-designed properties.

Asymmetric response emerges between creation and disintegration of force-bearing subcellular structures as revealed by percolation analysis

Cells dynamically remodel their internal structures by modulating the arrangement of actin filaments (AFs). In this process, individual AFs exhibit stochastic behavior without knowing the macroscopic higher-order structures they are meant to create or disintegrate, but the mechanism allowing for such stochastic process-driven remodeling of subcellular structures remains incompletely understood. Here we employ percolation theory to explore how AFs interacting only with neighboring ones without recognizing the overall configuration can nonetheless create a substantial structure referred to as stress fibers (SFs) at particular locations. We determined the interaction probabilities of AFs undergoing cellular tensional homeostasis, a fundamental property maintaining intracellular tension. We showed that the duration required for the creation of SFs is shortened by the increased amount of preexisting actin meshwork, while the disintegration occurs independently of the presence of actin meshwork, suggesting that the coexistence of tension-bearing and non-bearing elements allows cells to promptly transition to new states in accordance with transient environmental changes. The origin of this asymmetry between creation and disintegration, consistently observed in actual cells, is elucidated through a minimal model analysis by examining the intrinsic nature of mechano-signal transmission. Specifically, unlike the symmetric case involving biochemical communication, physical communication to sense environmental changes is facilitated via AFs under tension, while other free AFs dissociated from tension-bearing structures exhibit stochastic behavior. Thus, both the numerical and minimal models demonstrate the essence of intracellular percolation, in which macroscopic asymmetry observed at the cellular level emerges not from microscopic asymmetry in the interaction probabilities of individual molecules, but rather only as a consequence of the manner of the mechano-signal transmission. These results provide novel insights into the role of the mutual interplay between distinct subcellular structures with and without tension-bearing capability. Insight: Cells continuously remodel their internal elements or structural proteins in response to environmental changes. Despite the stochastic behavior of individual structural proteins, which lack awareness of the larger subcellular structures they are meant to create or disintegrate, this self-assembly process somehow occurs to enable adaptation to the environment. Here we demonstrated through percolation simulations and minimal model analyses that there is an asymmetry in the response between the creation and disintegration of subcellular structures, which can aid environmental adaptation. This asymmetry inherently arises from the nature of mechano-signal transmission through structural proteins, namely tension-mediated information exchange within cells, despite the stochastic behavior of individual proteins lacking asymmetric characters in themselves.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Role of supramolecular polymers in photo-actuation of spiropyran hydrogels

Supramolecular-covalent hybrid polymers have been shown to be interesting systems to generate robotic functions in soft materials in response to external stimuli. In recent work supramolecular components were found to enhance the speed of reversible bending deformations and locomotion when exposed to light. The role of morphology in the supramolecular phases integrated into these hybrid materials remains unclear. We report here on supramolecular-covalent hybrid materials that incorporate either high-aspect-ratio peptide amphiphile (PA) ribbons and fibers, or low-aspect-ratio spherical peptide amphiphile micelles into photo-active spiropyran polymeric matrices. We found that the high-aspect-ratio morphologies not only play a significant role in providing mechanical reinforcement to the matrix but also enhance photo-actuation for both light driven volumetric contraction and expansion of spiropyran hydrogels. Molecular dynamics simulations indicate that water within the high-aspect-ratio supramolecular polymers exhibits a faster draining rate as compared to those in spherical micelles, which suggests that the high-aspect-ratio supramolecular polymers effectively facilitate the transport of trapped water molecules by functioning as channels and therefore enhancing actuation of the hybrid system. Our simulations provide a useful strategy for the design of new functional hybrid architectures and materials with the aim of accelerating response and enhancing actuation by facilitating water diffusion at the nanoscopic level.

The Fractal Network Structure of Silk Fibroin Molecules and Its Effect on Spinning of Silkworm Silk

Animal silk is usually considered to exist as a solid fiber with a highly ordered structure, formed by the hierarchical assembly starting from a single silk fibroin (SF) chain. However, this study showed that silk protein molecules existed in the form of a fractal network structure in aqueous solution, rather than as a single chain. This type of network was relatively rigid with low fractal dimension. Finite element analysis revealed that this network structure significantly helped in the stable storage of SF prior to the spinning process and in the rapid formation of a β-sheeted nanocrystalline and nematic texture during spinning. Further, the strong but brittle mechanical properties of Bombyx mori silk could also be well-explained through the fractal network model of silk fibroin. The strength was mainly derived from the dual network structure, consisting of nodes and β-sheet cross-links, whereas the brittleness could be attributed to the rigidity of the SF chains between these nodes and cross-links. In summary, this study presents insights from network topology for understanding the spinning process of natural silk and the structure-property relationship in silk materials.

Nonaffine Deformation of Semiflexible Polymer and Fiber Networks

Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such nonaffine deformation have been shown to be much stronger than for flexible polymers. To date, our understanding of nonaffinity in such systems is limited to simulations or specific 2D models of athermal fibers. Here, we present an effective medium theory for nonaffine deformation of semiflexible polymer and fiber networks, which is general to both 2D and 3D and in both thermal and athermal limits. The predictions of this model are in good agreement with both prior computational and experimental results for linear elasticity. Moreover, the framework we introduce can be extended to address nonlinear elasticity and network dynamics.

Nanochitin and Nanochitosan: Chitin Nanostructure Engineering with Multiscale Properties for Biomedical and Environmental Applications

Nanochitin and nanochitosan (with random-copolymer-based multiscale architectures of glucosamine and N-acetylglucosamine units) have recently attracted immense attention for the development of green, sustainable, and advanced functional materials. Nanochitin and nanochitosan are multiscale materials from small oligomers, rod-shaped nanocrystals, longer nanofibers, to hierarchical assemblies of nanofibers. Various physical properties of chitin and chitosan depend on their molecular- and nanostructures; translational research has utilized them for a wide range of applications (biomedical, industrial, environmental, and so on). Instead of reviewing the entire extensive literature on chitin and chitosan, here, recent developments in multiscale-dependent material properties and their applications are highlighted; immune, medical, reinforcing, adhesive, green electrochemical materials, biological scaffolds, and sustainable food packaging are discussed considering the size, shape, and assembly of chitin nanostructures. In summary, new perspectives for the development of sustainable advanced functional materials based on nanochitin and nanochitosan by understanding and engineering their multiscale properties are described.

Atomic force microscopy identifies the alteration of rheological properties of the cardiac fibroblasts in idiopathic restrictive cardiomyopathy

Restrictive cardiomyopathy (RCM) is a rare disease characterized by increased ventricular stiffness and preserved ventricular contraction. Various sarcomere gene variants are known to cause RCM; however, more than a half of patients do not harbor such pathogenic variants. We recently demonstrated that cardiac fibroblasts (CFs) play important roles in inhibiting the diastolic function of cardiomyocytes via humoral factors and direct cell–cell contact regardless of sarcomere gene mutations. However, the mechanical properties of CFs that are crucial for intercellular communication and the cardiomyocyte microenvironment remain less understood. In this study, we evaluated the rheological properties of CFs derived from pediatric patients with RCM and healthy control CFs via atomic force microscopy. Then, we estimated the cellular modulus scale factor related to the cell stiffness, fluidity, and Newtonian viscosity of single cells based on the single power-law rheology model and analyzed the comprehensive gene expression profiles via RNA-sequencing. RCM-derived CFs showed significantly higher stiffness and viscosity and lower fluidity compared to healthy control CFs. Furthermore, RNA-sequencing revealed that the signaling pathways associated with cytoskeleton elements were affected in RCM CFs; specifically, cytoskeletal actin-associated genes (ACTN1, ACTA2, and PALLD) were highly expressed in RCM CFs, whereas several tubulin genes (TUBB3, TUBB, TUBA1C, and TUBA1B) were down-regulated. These results implies that the signaling pathways associated with cytoskeletal elements alter the rheological properties of RCM CFs, particularly those related to CF–cardiomyocyte interactions, thereby leading to diastolic cardiac dysfunction in RCM.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Biomimetic Strain-Stiffening in Chitosan Self-Healing Hydrogels

The strain-stiffening and self-healing capabilities of biological tissues enable them to preserve the structures and functions from deformation and damage. However, biodegradable hydrogel materials with both of these biomimetic characteristics have not been explored. Here, a series of strain-stiffened, self-healing hydrogels are developed through dynamic imine crosslinking of semiflexible O-carboxymethyl chitosan (main chain) and flexible dibenzaldehyde-terminated telechelic poly(ethylene glycol) (crosslinker). The biomimetic hydrogels can be reversibly stiffened to resist the deformation and can even recover to their original state after repeated damages. The mechanical properties and stiffening responses of the hydrogels are tailored by varying the component contents (1-3%) and the crosslinker length (4 or 8 kDa). A combinatorial system of in situ coherent small-angle X-ray scattering with rheological testing is developed to investigate the network structures (in sizes 1.5-160 nm) of hydrogels under shear strains and reveals that the strain-stiffening originates from the fibrous chitosan network with poly(ethylene glycol) crosslinking fixation. The biomimetic hydrogels with biocompatibility and biodegradability promote wound healing. The study provides an insight into the nanoscale design of biomimetic strain-stiffening self-healing hydrogels for biomedical applications.

Acquiring structural and mechanical information of a fibrous network through deep learning

Fibrous networks play an essential role in the structure and properties of a variety of biological and engineered materials, such as cytoskeletons, protein filament-based hydrogels, and entangled or crosslinked polymer chains. Therefore, insight into the structural features of these fibrous networks and their constituent filaments is critical for discovering the structure-property-function relationships of these material systems. In this paper, a fibrous network-deep learning system (FN-DLS) is established to extract fibrous network structure information from atomic force microscopy images. FN-DLS accurately assesses the structural and mechanical characteristics of fibrous networks, such as contour length, number of nodes, persistence length, mesh size and fractal dimension. As an open-source system, FN-DLS is expected to serve a vast community of scientists working on very diverse disciplines and pave the way for new approaches on the study of biological and synthetic polymer and filament networks found in current applied and fundamental sciences.

Tether-guided lamellipodia enable rapid wound healing

Adhesion between animal cells and the underlying extracellular matrix is challenged during wounding, cell division, and a variety of pathological processes. How cells recover adhesion in the immediate aftermath of detachment from the extracellular matrix remains incompletely understood, due in part to technical limitations. Here, we used acute chemical and mechanical perturbations to examine how epithelial cells respond to partial delamination events. In both cases, we found that cells extended lamellipodia to establish readhesion within seconds of detachment. These lamellipodia were guided by sparse membrane tethers whose tips remained attached to their original points of adhesion, yielding lamellipodia that appear to be qualitatively distinct from those observed during cell migration. In vivo measurements in the context of a zebrafish wound assay showed a similar behavior, in which membrane tethers guided rapidly extending lamellipodia. In the case of mechanical wounding events, cells selectively extended tether-guided lamellipodia in the direction opposite of the pulling force, resulting in the rapid reestablishment of contact with the substrate. We suggest that membrane tether-guided lamellipodial respreading may represent a general mechanism to reestablish tissue integrity in the face of acute disruption.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

Real-time visualization of morphology-dependent self-motion of hyaluronic acid nanomaterials in water

Drug delivery to target sites is often limited by inefficient particle transport through biological media. Herein, motion behaviors of spherical and nonspherical nanomaterials composed of hyaluronic acid were studied in water using real-time multiple particle tracking technology. The two types of nanomaterials have comparable surface compositions and surface potentials, and they have equivalent diameters. The analysis of nanomaterial trajectories revealed that particles with flattened morphology and a high aspect ratio, designated nanoplatelets, exhibited more linear trajectories and faster diffusion in water than nanospheres. Fitting the plots of mean square displacement vs. time scale suggests that nanoplatelets exhibited hyperdiffusive behavior, which is similar to the motion of living microorganisms. Furthermore, at 37 °C, the surface explored by a nanoplatelet was up to 33-fold higher than that explored by a nanosphere. This investigation on morphology-dependent self-motion of nanomaterials could have a significant impact on drug delivery applications by increasing particle transport through biological media.

Effect of random fiber networks on bubble growth in gelatin hydrogels

In hydrodynamics, the event of dynamic bubble growth in a pure liquid under tensile pressure is known as cavitation. The same event can also be observed in soft materials (e.g., elastomers and hydrogels). However, for soft materials, bubble/cavity growth is either defined as cavitation if the bubble growth is elastic and reversible or as fracture if the cavity growth is by material failure and irreversible. In any way, bubble growth can cause damage to soft materials (e.g., tissue) by inducing high strain and strain-rate deformation. Additionally, a high-strength pressure wave is generated upon the collapse of the bubble. Therefore, it is crucial to identify the critical condition of spontaneous bubble growth in soft materials. Experimental and theoretical observations have agreed that the onset of bubble growth in soft materials requires higher tensile pressure than pure water. The extra tensile pressure is required since the cavitating bubble needs to overcome the elastic and surface energy in soft materials. In this manuscript, we developed two models to study and quantify the extra tensile pressure for different gelatin concentrations. Both the models are then compared with the existing cavitation onset criteria of rubber-like materials. Validation is done with the experimental results of threshold tensile pressure for different gelatin concentrations. Both models can moderately predict the extra tensile pressure within the intermediate range of gelatin concentrations (3-7% [w/v]). For low concentration (∼1%), the network's non-affinity plays a significant role and must be incorporated. On the other hand, for higher concentrations (∼10%), the entropic deformation dominates, and the strain energy formulation is not adequate.

Nonlinear stress relaxation of transiently crosslinked biopolymer networks

A long-standing puzzle in the rheology of living cells is the origin of the experimentally observed long-time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.

Fingerprints of viscoelastic subdiffusion in random environments: Revisiting some experimental data and their interpretations

Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and colloidal solutions, cytosol and plasma membrane of biological cells, which are viscoelastic and, at the same time, highly inhomogeneous randomly fluctuating environments. The observed subdiffusion often combines features of ergodic fractional Brownian motion (reflecting viscoelasticity) and nonergodic jumplike non-Markovian diffusional processes (reflecting disorder). Accordingly, several theories were proposed to explain puzzling experimental findings. Below we show that some of the significant and profound published experimental results are better rationalized within the viscoelastic subdiffusion approach in random environments, which is based on generalized Langevin dynamics in random potentials, than some earlier proposed theories.

How Structural Features of a Spring-Based Model of Fibrous Collagen Tissue Govern the Overall Young's Modulus

While much study has been dedicated to investigating biopolymers' stress-strain response at low strain levels, little research has been done to investigate the linear region of biopolymers' stress-strain response and how the microstructure affects it. We propose a mathematical model of fibrous networks which reproduces qualitative features of collagen gel's stress-strain response and provides insight into the key features which impact the Young's Modulus of similar fibrous tissues. This model analyzes the relationship of the Young's Modulus of the lattice to internodal fiber length, number of connection points or nodes per unit area, and average number of connections to each node. Our results show that fiber length, nodal density, and level of connectivity each uniquely impact the Young's Modulus of the lattice. Furthermore, our model indicates that the Young's Modulus of a lattice can be estimated using the effective resistance of the network, a graph theory technique that measures distances across a network. Our model thus provides insight into how the organization of fibers in a biopolymer impact its linear Young's Modulus.

Polyacrylamide Hydrogel Composite E-skin Fully Mimicking Human Skin

Transparent e-skin that can fully mimic human skin with J-shaped mechanical-behavior and tactile sensing attributes have not yet been reported. In this work, the skin-like hydrogel composite with J-shaped mechanical behavior and highly transparent, tactile, soft but strong, flexible, and stretchable attributes is developed as structural strain sensing element for e-skin. Piezo-resistive polyacrylamide (PAAm) hydrogel is used as supporting matrix to endow high transparency, softness, flexibility, stretch-ability and strain sensing capability desired for e-skin. Ultrahigh molecular weight polyethylene (UHMWPE) fiber with a wavy configuration is designed as reinforcement filler to provide the tunable strain-limiting effect. As a result, the as-prepared UHMWPE fiber/PAAm composite e-skin presents unique "J-shape" stress-strain behavior akin to human skin. And the PAAm composite can switch from supersoft to highly stiff in the designed strain range up to 100% with a prominent tensile strength of 48.3 MPa, which enables it to have the high stretch-ability and excellent load-bearing ability, simultaneously. Moreover, finite element model is developed to clarify the stress distribution and damage evolution for the UHMWPE fiber/PAAm composite during the tensile process. The PAAm composite exhibits not only an excellent strain sensing performance with a long-term reliability up to 5000 loading-unloading cycles but also an extraordinary softness and mechanical strength with a low initial modulus of 6.7 kPa, which is matchable with soft human epidermis. Finally, the e-skin is used for demonstrations in monitoring various human activities and protecting structural integrity in designed strain ranges. The strategy for reinforcing piezo-resistive hydrogel with wavy-shaped UHMWPE fibers proposed here is promising for the development of transparent, flexible, soft but strong e-skin with a tunable strain-limiting effect akin to human skin.

Biophysical interactions between components of the tumor microenvironment promote metastasis

During metastasis, tumor cells need to adapt to their dynamic microenvironment and modify their mechanical properties in response to both chemical and mechanical stimulation. Physical interactions occur between cancer cells and the surrounding matrix including cell movements and cell shape alterations through the process of mechanotransduction. The latter describes the translation of external mechanical cues into intracellular biochemical signaling. Reorganization of both the cytoskeleton and the extracellular matrix (ECM) plays a critical role in these spreading steps. Migrating tumor cells show increased motility in order to cross the tumor microenvironment, migrate through ECM and reach the bloodstream to the metastatic site. There are specific factors affecting these processes, as well as the survival of circulating tumor cells (CTC) in the blood flow until they finally invade the secondary tissue to form metastasis. This review aims to study the mechanisms of metastasis from a biomechanical perspective and investigate cell migration, with a focus on the alterations in the cytoskeleton through this journey and the effect of biologic fluids on metastasis. Understanding of the biophysical mechanisms that promote tumor metastasis may contribute successful therapeutic approaches in the fight against cancer.

Rheology of rounded mammalian cells over continuous high-frequencies

Understanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1-40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

Microrheology of semiflexible filament solutions based on relaxation simulations

We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the dynamical properties of probe particles immersed in solutions of semiflexible filaments from relaxation simulations with a relatively low computational cost and higher precision in comparison to those based on stochastic dynamics. We used a microrheological approach to obtain the complex shear modulus and the complex viscosity of the solution through its compliance which was obtained directly from the dynamical properties of a probe particle attached to an effective medium described by a mesoscopic model, i.e., an effective filament model (EFM). The relaxation simulations were applied to assess the effects of the bending energy on the viscoelasticity of the semiflexible filament solutions, and our methodology was validated by comparing the numerical results to the experimental data on DNA and collagen solutions.

Anomalous mechanics of Zn2+-modified fibrin networks

Fibrin is the main component of blood clots. The mechanical properties of fibrin are therefore of critical importance in successful hemostasis. One of the divalent cations released by platelets during hemostasis is Zn2+; however, its effect on the network structure of fibrin gels and on the resultant mechanical properties remains poorly understood. Here, by combining mechanical measurements with three-dimensional confocal microscopy imaging, we show that Zn2+ can tune the fibrin network structure and alter its mechanical properties. In the presence of Zn2+, fibrin protofibrils form large bundles that cause a coarsening of the fibrin network due to an increase in fiber diameter and reduction of the total fiber length. We further show that the protofibrils in these bundles are loosely coupled to one another, which results in a decrease of the elastic modulus with increasing Zn2+ concentrations. We explore the elastic properties of these networks at both low and high stress: At low stress, the elasticity originates from pulling the thermal slack out of the network, and this is consistent with the thermal bending of the fibers. By contrast, at high stress, the elasticity exhibits a common master curve consistent with the stretching of individual protofibrils. These results show that the mechanics of a fibrin network are closely correlated with its microscopic structure and inform our understanding of the structure and physical mechanisms leading to defective or excessive clot stiffness.

Atomic force microscopy for revealing micro/nanoscale mechanics in tumor metastasis: from single cells to microenvironmental cues

Mechanics are intrinsic properties which appears throughout the formation, development, and aging processes of biological systems. Mechanics have been shown to play important roles in regulating the development and metastasis of tumors, and understanding tumor mechanics has emerged as a promising way to reveal the underlying mechanisms guiding tumor behaviors. In particular, tumors are highly complex diseases associated with multifaceted factors, including alterations in cancerous cells, tissues, and organs as well as microenvironmental cues, indicating that investigating tumor mechanics on multiple levels is significantly helpful for comprehensively understanding the effects of mechanics on tumor progression. Recently, diverse techniques have been developed for probing the mechanics of tumors, among which atomic force microscopy (AFM) has appeared as an excellent platform enabling simultaneously characterizing the structures and mechanical properties of living biological systems ranging from individual molecules and cells to tissue samples with unprecedented spatiotemporal resolution, offering novel possibilities for understanding tumor physics and contributing much to the studies of cancer. In this review, we survey the recent progress that has been achieved with the use of AFM for revealing micro/nanoscale mechanics in tumor development and metastasis. Challenges and future progress are also discussed.

Correlative Imaging of Motoneuronal Cell Elasticity by Pump and Probe Spectroscopy

Because of their role of information transmitter between the spinal cord and the muscle fibers, motor neurons are subject to physical stimulation and mechanical property modifications. We report on motoneuron elasticity investigated by time-resolved pump and probe spectroscopy. A dual picosecond geometry simultaneously probing the acoustic impedance mismatch at the cell-titanium transducer interface and acoustic wave propagation inside the motoneuron is presented. Such noncontact and nondestructive microscopy, correlated to standard atomic force microscopy or a fluorescent labels approach, has been carried out on a single cell to address some physical properties such as bulk modulus of elasticity, dynamical longitudinal viscosity, and adhesion.

Molecular Regulators of Cellular Mechanoadaptation at Cell-Material Interfaces

Diverse essential cellular behaviors are determined by extracellular physical cues that are detected by highly orchestrated subcellular interactions with the extracellular microenvironment. To maintain the reciprocity of cellular responses and mechanical properties of the extracellular matrix, cells utilize a variety of signaling pathways that transduce biophysical stimuli to biochemical reactions. Recent advances in the micromanipulation of individual cells have shown that cellular responses to distinct physical and chemical features of the material are fundamental determinants of cellular mechanosensation and mechanotransduction. In the process of outside-in signal transduction, transmembrane protein integrins facilitate the formation of focal adhesion protein clusters that are connected to the cytoskeletal architecture and anchor the cell to the substrate. The linkers of nucleoskeleton and cytoskeleton molecular complexes, collectively termed LINC, are critical signal transducers that relay biophysical signals between the extranuclear cytoplasmic region and intranuclear nucleoplasmic region. Mechanical signals that involve cytoskeletal remodeling ultimately propagate into the nuclear envelope comprising the nuclear lamina in assistance with various nuclear membrane proteins, where nuclear mechanics play a key role in the subsequent alteration of gene expression and epigenetic modification. These intracellular mechanical signaling cues adjust cellular behaviors directly associated with mechanohomeostasis. Diverse strategies to modulate cell-material interfaces, including alteration of surface rigidity, confinement of cell adhesive region, and changes in surface topology, have been proposed to identify cellular signal transduction at the cellular and subcellular levels. In this review, we will discuss how a diversity of alterations in the physical properties of materials induce distinct cellular responses such as adhesion, migration, proliferation, differentiation, and chromosomal organization. Furthermore, the pathological relevance of misregulated cellular mechanosensation and mechanotransduction in the progression of devastating human diseases, including cardiovascular diseases, cancer, and aging, will be extensively reviewed. Understanding cellular responses to various extracellular forces is expected to provide new insights into how cellular mechanoadaptation is modulated by manipulating the mechanics of extracellular matrix and the application of these materials in clinical aspects.

Dynamics of undulatory fluctuations of semiflexible filaments in a network

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-De Dominicis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength sqrt[κ/τ_{R}], set by the filament's bending modulus κ and spring-renormalized tension τ_{R}, are changed by the boundary spring. This occurs near the crossover frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from ω^{1/2} to ω^{3/4}, but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.

Strain Stiffening and Negative Normal Force of Agarose Hydrogels

Inspired by the specific strain stiffening and negative normal force phenomena in several biological networks, herein, we show strain stiffening and negative normal force in agarose hydrogels. We use both pre-strain and strain amplitude sweep protocols in dynamic rheological measurements where the gel slip was suppressed by the in situ gelation in the cross-hatched parallel plate rheometer geometry. Within the stiffening region, we show the scaling relation for the differential modulus K ∝ σ1, where σ is stress. The strain at the onset of stiffening is almost constant throughout the concentration range. The gels show negative apparent normal stress difference when sheared as a result of the gel contraction. The pore size of the hydrogel is large enough to allow water to move with respect to the network to balance the pressure difference caused by the hoop stress. The rheological analysis together with scanning electron microscopy suggests that the agarose gels can be described using subisostatic athermal network models where the connectivity dictates the stiffening behavior. Therefore, the simple agarose gels appear to capture several of the viscoelastic properties, which were previously thought to be characteristic to biological protein macromolecules.

Employing Nanostructured Scaffolds to Investigate the Mechanical Properties of Adult Mammalian Retinae Under Tension

Numerous eye diseases are linked to biomechanical dysfunction of the retina. However, the underlying forces are almost impossible to quantify experimentally. Here, we show how biomechanical properties of adult neuronal tissues such as porcine retinae can be investigated under tension in a home-built tissue stretcher composed of nanostructured TiO₂ scaffolds coupled to a self-designed force sensor. The employed TiO₂ nanotube scaffolds allow for organotypic long-term preservation of adult tissues ex vivo and support strong tissue adhesion without the application of glues, a prerequisite for tissue investigations under tension. In combination with finite element calculations we found that the deformation behavior is highly dependent on the displacement rate which results in Young’s moduli of (760–1270) Pa. Image analysis revealed that the elastic regime is characterized by a reversible shear deformation of retinal layers. For larger deformations, tissue destruction and sliding of retinal layers occurred with an equilibration between slip and stick at the interface of ruptured layers, resulting in a constant force during stretching. Since our study demonstrates how porcine eyes collected from slaughterhouses can be employed for ex vivo experiments, our study also offers new perspectives to investigate tissue biomechanics without excessive animal experiments.

Computational models of melanoma

Genes, proteins, or cells influence each other and consequently create patterns, which can be increasingly better observed by experimental biology and medicine. Thereby, descriptive methods of statistics and bioinformatics sharpen and structure our perception. However, additionally considering the interconnectivity between biological elements promises a deeper and more coherent understanding of melanoma. For instance, integrative network-based tools and well-grounded inductive in silico research reveal disease mechanisms, stratify patients, and support treatment individualization. This review gives an overview of different modeling techniques beyond statistics, shows how different strategies align with the respective medical biology, and identifies possible areas of new computational melanoma research.

Cytoskeleton-inspired artificial protein design to enhance polymer network elasticity

Reducing topological network defects to enhance elasticity in polymeric materials remains a grand challenge. Efforts to control network topology, primarily focused on crosslinking junctions, continue to underperform compared to theoretical estimations from idealized networks using affine and phantom network theories. Here, artificial protein technology was adapted for the design of polymer-network hydrogels with precisely defined coil-like and rod-like strands to observe the impact of strand rigidity on the mechanical properties of polymeric materials. Cytoskeleton-inspired polymer-network hydrogels incorporated with rod-like protein strands nearly tripled the gel shear elastic modulus and relaxation time compared to coil-like protein strands, indicating an enhanced effective crosslinking density. Furthermore, asymmetric rod-coil protein designs in network strands with an optimal rod:coil ratio improved the hydrogel relaxation time, enhancing the stability of physical macromolecular associations by modulating crosslinker mobility. The careful design of strand rigidity presents a new direction to reduce topological defects for optimizing polymeric materials.

Why Are Viscosity and Nonlinearity Bound to Make an Impact in Clinical Elastographic Diagnosis?

The adoption of multiscale approaches by the biomechanical community has caused a major improvement in quality in the mechanical characterization of soft tissues. The recent developments in elastography techniques are enabling in vivo and non-invasive quantification of tissues' mechanical properties. Elastic changes in a tissue are associated with a broad spectrum of pathologies, which stems from the tissue microstructure, histology and biochemistry. This knowledge is combined with research evidence to provide a powerful diagnostic range of highly prevalent pathologies, from birth and labor disorders (prematurity, induction failures, etc.), to solid tumors (e.g., prostate, cervix, breast, melanoma) and liver fibrosis, just to name a few. This review aims to elucidate the potential of viscous and nonlinear elastic parameters as conceivable diagnostic mechanical biomarkers. First, by providing an insight into the classic role of soft tissue microstructure in linear elasticity; secondly, by understanding how viscosity and nonlinearity could enhance the current diagnosis in elastography; and finally, by compounding preliminary investigations of those elastography parameters within different technologies. In conclusion, evidence of the diagnostic capability of elastic parameters beyond linear stiffness is gaining momentum as a result of the technological and imaging developments in the field of biomechanics.

100th Anniversary of Macromolecular Science Viewpoint: Synthetic Protein Hydrogels

Our bodies are composed of soft tissues made of various proteins. In contrast, most hydrogels designed for biological applications are made of synthetic polymers. Recently, it is increasingly recognized that genetically synthesized proteins can be tailored as building blocks of hydrogels with biological, chemical, and mechanical properties similar to native soft tissues. In this Viewpoint, we summarize recent progress in synthetic protein hydrogels. We compare the structural and mechanical properties of different protein building blocks. We discuss various biocompatible cross-linking strategies based on covalent chemical reactions and noncovalent physical interactions. We introduce how stimulus-responsive conformational changes or intermolecular interactions at the molecular level can be used to engineer responsive hydrogels. We highlight that hydrogel network structures are as important as the protein sequences for the properties and functions of protein hydrogels and should be carefully designed. Despite great progress and potentials of synthetic protein hydrogels, there are still quite a few unsettled challenges and unexploited opportunities, providing abundant room for future investigation and development, particularly as this field is quickly expanding beyond its initial stage. We discuss a number of possible directions, including optimizing protein production and reducing cost, engineering anisotropic hydrogels to better mimic native tissues, rationally designing hydrogel mechanical properties, investigating interplays of hydrogels and residing cells for 3D cell culture and organoid construction, and evaluating long-term cytotoxicity and immune response.

Qualitative analysis of contribution of intracellular skeletal changes to cellular elasticity

Cells are dynamic structures that continually generate and sustain mechanical forces within their environments. Cells respond to mechanical forces by changing their shape, moving, and differentiating. These reactions are caused by intracellular skeletal changes, which induce changes in cellular mechanical properties such as stiffness, elasticity, viscoelasticity, and adhesiveness. Interdisciplinary research combining molecular biology with physics and mechanical engineering has been conducted to characterize cellular mechanical properties and understand the fundamental mechanisms of mechanotransduction. In this review, we focus on the role of cytoskeletal proteins in cellular mechanics. The specific role of each cytoskeletal protein, including actin, intermediate filaments, and microtubules, on cellular elasticity is summarized along with the effects of interactions between the fibers.

Poroelasticity of (bio)polymer networks during compression: theory and experiment

Soft living tissues like cartilage can be considered as biphasic materials comprising a fibrous complex biopolymer network and a viscous background liquid. Here, we show by a combination of experiment and theoretical analysis that both the hydraulic permeability and the elastic properties of (bio)polymer networks can be determined with simple ramp compression experiments in a commercial rheometer. In our approximate closed-form solution of the poroelastic equations of motion, we find the normal force response during compression as a combination of network stress and fluid pressure. Choosing fibrin as a biopolymer model system with controllable pore size, measurements of the full time-dependent normal force during compression are found to be in excellent agreement with the theoretical calculations. The inferred elastic response of large-pore (μm) fibrin networks depends on the strain rate, suggesting a strong interplay between network elasticity and fluid flow. Phenomenologically extending the calculated normal force into the regime of nonlinear elasticity, we find strain-stiffening of small-pore (sub-μm) fibrin networks to occur at an onset average tangential stress at the gel-plate interface that depends on the polymer concentration in a power-law fashion. The inferred permeability of small-pore fibrin networks scales approximately inverse squared with the fibrin concentration, implying with a microscopic cubic lattice model that the number of protofibrils per fibrin fiber cross-section decreases with protein concentration. Our theoretical model provides a new method to obtain the hydraulic permeability and the elastic properties of biopolymer networks and hydrogels with simple compression experiments, and paves the way to study the relation between fluid flow and elasticity in biopolymer networks during dynamical compression.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Functional DNA-based hydrogel intelligent materials for biomedical applications

Multifunctional intelligent DNA hydrogels have been reviewed for many biomedical applications.

Equilibrium fluctuations of a semiflexible filament cross linked into a network

We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.

A unified rheological model for cells and cellularised materials

The mechanical response of single cells and tissues exhibits a broad distribution of time-scales that often gives rise to a distinctive power-law rheology. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times, derived from the model parameters, delimit different regimes in the materials response. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach to consistently analyse experimental data and uncover similarities and differences in reported behaviour across experimental methods and research groups. It also sets the foundations for more accurate computational models of tissue mechanics.

A unified rheological model for cells and cellularised materials

The mechanical response of single cells and tissues exhibits a broad distribution of time-scales that often gives rise to a distinctive power-law rheology. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times, derived from the model parameters, delimit different regimes in the materials response. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach to consistently analyse experimental data and uncover similarities and differences in reported behaviour across experimental methods and research groups. It also sets the foundations for more accurate computational models of tissue mechanics.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.

Toward Imperfection-Insensitive Soft Network Materials for Applications in Stretchable Electronics

Development of stretchable devices with mechanical responses that mimic those of biological tissues/organs is of particular importance for the long-term biointegration, as the discomfort induced by the mechanical mismatch can be minimized. Recent works have established the bioinspired designs of soft network materials that can precisely reproduce the unconventional J-shaped stress-strain curves of human skin at different regions. Existing studies mostly focused on the design, fabrication, and modeling of perfect soft network materials. When utilized as the substrates of biointegrated electronics, the soft network designs, however, often need to incorporate deterministic holes, a type of imperfection, to accommodate hard, inorganic electronic components. Understanding of the effect of hole imperfections on the mechanical properties of soft network materials is thereby essential in practical applications. This paper presents a combined experimental and computational study of the stretchability and elastic modulus of imperfect soft network materials consisting of circular holes with a variety of diameters. Both the size and location of the circular-hole imperfections are shown to have profound influences on the stretchability. Based on these results, design guidelines of imperfection-insensitive network materials are introduced. For the imperfections that result in an evident reduction of stretchability, an effective reinforcement approach is presented by enlarging the width of horseshoe microstructures at strategic locations, which can enhance the stretchability considerably. A stretchable and imperfection-insensitive integrated device with a light-emitting diode embedded in the network material serves a demonstrative application.