Stress controls the mechanics of collagen networks

Red Phosphorus: An Elementary Semiconductor for Room-Temperature NO2 Gas Sensing

Black and blue phosphorus (both allotropes of elementary phosphorus) have recently been widely explored as an active material for electronic devices, and their potential in gas sensing applications has been demonstrated. On the other hand, amorphous red phosphorus (a-RP), a much cheaper and readily available phosphorus allotrope, has seldom been investigated as an electronic material, and its gas sensing properties have never been studied. In this work we have investigated these properties of a-RP by combining experimental characterizations with theoretical calculations. We found that a-RP exhibited an amphoteric character for detecting both commonly regarded reducing and oxidizing gas molecules, featuring a negative correlation between the electrical resistance of a-RP and the gas concentration. Interestingly, the a-RP based sensors appear to be particularly suitable for room-temperature NO₂ detection, exhibiting excellent sensitivity and selectivity, as well as fast temporal response and recovery. A unique sensing feature of a-RP toward NO₂ was identified, which is associated with the expansion of P-P bonds upon NO₂ chemisorption. Based on density functional theory calculations we proposed a physiochemical model to elaborate the synergistic effects of the P-P bond expansion and Langmuir isotherm adsorption on the electronic properties and gas sensing processes of a-RP.

Fibril bending stiffness of 3D collagen matrices instructs spreading and clustering of invasive and non-invasive breast cancer cells

Extracellular matrix stiffening of breast tissues has been clinically correlated with malignant transformation and poor prognosis. An increase of collagen fibril diameter and lysyl-oxidase mediated crosslinking has been observed in advanced tumor stages. Many current reports suggest that the local mechanical properties of single fibrillar components dominantly regulate cancer cell behavior. Here, we demonstrate by an independent control of fibril diameter and intrafibrillar crosslinking of three-dimensional (3D) collagen matrices that fibril bending stiffness instructs cell behavior of invasive and non-invasive breast cancer cells. Two types of collagen matrices with fibril diameter of either 650 nm or 800 nm at a similar pore size of 10 μm were reconstituted and further modified with the zero-length crosslinker 1-ethyl-3-(3-dimethyl aminopropyl)-carbodiimide (EDC) at concentrations of 0, 20, 100 and 500 mM. This approach yields two sets of collagen matrices with overlapping variation of matrix elasticity. With these matrices we could prove the common assumption that matrix elasticity of collagen networks is bending dominated with a linear dependence on fibril bending stiffness. We derive that the measured variation of matrix elasticity is directly correlated to the variation of fibril bending stiffness, being independently controlled either by fibril diameter or by intrafibrillar crosslinking. We use these defined matrices to demonstrate that the adjustment of fibril bending stiffness allows to instruct the behavior of two different breast cancer cell lines, invasive MDA-MB-231 (human breast carcinoma) and non-invasive MCF-7 cells (human breast adenocarcinoma). Invasiveness and spreading of invasive MDA-MB-231 cells as well as clustering of non-invasive MCF-7 cells is thereby investigated over a broad parameter range. Our results demonstrate and quantify the direct dependence of cancer cell phenotypes on the matrix mechanical properties on the scale of single fibrils.

Strain-Stiffening in Dynamic Supramolecular Fiber Networks

The cytoskeleton is a highly adaptive network of filamentous proteins capable of stiffening under stress even as it dynamically assembles and disassembles with time constants of minutes. Synthetic materials that combine reversibility and strain-stiffening properties remain elusive. Here, strain-stiffening hydrogels that have dynamic fibrous polymers as their main structural components are reported. The fibers form via self-assembly of bolaamphiphiles (BA) in water and have a well-defined cross-section of 9 to 10 molecules. Fiber length recovery after sonication, H/D exchange experiments, and rheology confirm the dynamic nature of the fibers. Cross-linking of the fibers yields strain-stiffening, self-healing hydrogels that closely mimic the mechanics of biological networks, with mechanical properties that can be modulated by chemical modification of the components. Comparison of the supramolecular networks with covalently fixated networks shows that the noncovalent nature of the fibers limits the maximum stress that fibers can bear and, hence, limits the range of stiffening.

Single-Molecule Study of Peptide Gel Dynamics Reveals States of Prestress

De novo peptide surfactant (I₃K) gels provide an ideal system to study the complex dynamics of lightly cross-linked semiflexible fibers because of their large contour lengths, simple chemistry, and slow dynamics. We used single-molecule fluorescence microscopy to record individual fibers and Fourier decomposition of the fiber dynamics to separate thermal contributions to the persistence length from compressive states of prestress (SPS). Our results show that SPS in the network depend strongly on peptide concentration, buffer, and pH and that the fibril energies in SPS follow a Lévy distribution. The presence of SPS in the network imply that collective states of self-stress are also present. Therefore, semiflexible polymer gels need to be considered as complex load-bearing structures and the mean field models for polymer gel elasticity and dynamics often applied to them will not be fully representative of the behavior at the nanoscale. We quantify the impact of cross-links on reptation tube dynamics, which provides a second population of tube fluctuations in addition to those expected for uncross-linked entangled solutions.

Heterogeneity and nonaffinity of cell-induced matrix displacements

Cell contractile forces deform and reorganize the surrounding matrix, but the relationship between the forces and the resulting displacements is complicated by the fact that the fibrous structure brings about a complex set of mechanical properties. Many studies have quantified nonlinear and time-dependent properties at macroscopic scales, but it is unclear whether macroscopic properties apply to the scale of a cell, where the matrix is composed of a heterogeneous network of fibers. To address this question, we mimicked the contraction of a cell embedded within a fibrous collagen matrix and quantified the resulting displacements. The data revealed displacements that were heterogeneous and nonaffine. The heterogeneity was reproducible during cyclic loading, and it decreased with decreasing fiber length. Both the experiments and a fiber network model showed that the heterogeneous displacements decayed over distance at a rate no faster than the average displacement field, indicating no transition to homogeneous continuum behavior. Experiments with cells fully embedded in collagen matrices revealed the presence of heterogeneous displacements as well, exposing the dramatic heterogeneity in matrix reorganization that is induced by cells at different positions within the same fibrous matrix.

Inelastic behaviour of cellulose microfibril networks

Cellulose microfibrils (CMF) are a unique class of shape anisotropic bio-nanomaterials, already finding many applications in diverse fields owing to their advantageous material properties and abundant availability. The rich non-linear mechanical behaviour of CMF networks has been under-studied due to the complex nature of this system, being influenced by many factors such as strong inter-fibril interactions, a heterogeneous microstructure, and process conditions. In this work, we systematically explore the non-linear rheological behaviour of these networks using a CMF model system with controlled process conditions and fibril interactions. The microfibrils were dispersed in dimethyl sulfoxide to minimise the attractive van der Waals interactions and thereby also the network heterogeneity. We show that the networks exhibit a transition with increasing shear stress from a predominantly elastic to a plastic deformation where they undergo softening. We find that the network stiffness and plasticity are dependent on the loading rate. Finally, we observed that the networks regain their original viscoelastic moduli on cessation of shear. These findings form a basis towards understanding and ultimately modelling the mechanics of CMF networks, which is a prerequisite for the rational design of novel bio-based materials.

Nonlinear Elasticity of the ECM Fibers Facilitates Efficient Intercellular Communication

Biological cells embedded in fibrous matrices have been observed to form intercellular bands of dense and aligned fibers through which they mechanically interact over long distances. Such matrix-mediated cellular interactions have been shown to regulate various biological processes. This study aimed to explore the effects of elastic nonlinearity of the fibers contained in the extracellular matrix (ECM) on the transmission of mechanical loads between contracting cells. Based on our biological experiments, we developed a finite-element model of two contracting cells embedded within a fibrous network. The individual fibers were modeled as showing linear elasticity, compression microbuckling, tension stiffening, or both of the latter two. Fiber compression buckling resulted in smaller loads in the ECM, which were primarily directed toward the neighboring cell. These loads decreased with increasing cell-to-cell distance; when cells were >9 cell diameters apart, no such intercellular interaction was observed. Tension stiffening further contributed to directing the loads toward the neighboring cell, though to a smaller extent. The contraction of two neighboring cells resulted in mutual attraction forces, which were considerably increased by tension stiffening and decayed with increasing cell-to-cell distances. Nonlinear elasticity contributed also to the onset of force polarity on the cell boundaries, manifested by larger contractile forces pointing toward the neighboring cell. The density and alignment of the fibers within the intercellular band were greater when fibers buckled under compression, with tension stiffening further contributing to this structural remodeling. Although previous studies have established the role of the ECM nonlinear mechanical behavior in increasing the range of force transmission, our model demonstrates the contribution of nonlinear elasticity of biological gels to directional and efficient mechanical signal transfer between distant cells, and rehighlights the importance of using fibrous gels in experimental settings for facilitating intercellular communication. VIDEO ABSTRACT.

Effect of crosslink torsional stiffness on elastic behavior of semiflexible polymer networks

Networks of semiflexible filaments are building blocks of different biological and structural materials such as cytoskeleton and extracellular matrix. The mechanical response of these systems when subjected to an applied strain at zero temperature is often investigated numerically using networks composed of filaments, which are either rigidly welded or pinned together at their crosslinks. In the latter, filaments during deformation are free to rotate about their crosslinks while the relative angles between filaments remain constant in the former. The behavior of crosslinks in actual semiflexible networks is different than these idealized models and there exists only partial constraint on torques at crosslinks. The present work develops a numerical model in which two intersecting filaments are connected to each other by torsional springs with arbitrary stiffness. We show that fiber networks composed of rigid and freely rotating crosslinks are the limiting case of the present model. Furthermore, we characterize the effects of stiffness of crosslinks on effective Young's modulus of semiflexible networks as a function of filament flexibility and crosslink density. The effective Young's modulus is determined as a function of the mechanical properties of crosslinks and is found to vanish for networks composed of very weak torsional springs. Independent of the stiffness of crosslinks, it is found that the effective Young's modulus is a function of fiber flexibility and crosslink density. In low density networks, filaments primarily bend and the effective Young's modulus is much lower than the affine estimate. With increasing filament bending stiffness and/or crosslink density, the mechanical behavior of the networks becomes more affine and the stretching of filaments depicts itself as the dominant mode of deformation. The torsional stiffness of the crosslinks significantly affects the effective Young's modulus of the semiflexible random fiber networks.

Cellulose crystals plastify by localized shear

While most attention has so far been devoted to the tensile properties of crystalline cellulose, the main elementary building block of plants, we show here using atomistic simulations that their shear is also an important mode of deformation, occurring at stress levels lower than tension with much larger ductility. We also demonstrate how crystalline defects like dislocations drastically facilitate plasticity. This analysis can be used as a basis for the micromechanical modeling of cellulose microfibrils that are currently considered as promising eco-friendly alternatives to synthetic fibers for structural materials.

Cellulose microfibrils are the principal structural building blocks of wood and plants. Their crystalline domains provide outstanding mechanical properties. Cellulose microfibrils have thus a remarkable potential as eco-friendly fibrous reinforcements for structural engineered materials. However, the elastoplastic properties of cellulose crystals remain poorly understood. Here, we use atomistic simulations to determine the plastic shear resistance of cellulose crystals and analyze the underpinning atomic deformation mechanisms. In particular, we demonstrate how the complex and adaptable atomic structure of crystalline cellulose controls its anisotropic elastoplastic behavior. For perfect crystals, we show that shear occurs through localized bands along with noticeable dilatancy. Depending on the shear direction, not only noncovalent interactions between cellulose chains but also local deformations, translations, and rotations of the cellulose macromolecules contribute to the response of the crystal. We also reveal the marked effect of crystalline defects like dislocations, which decrease both the yield strength and the dilatancy, in a way analogous to that of metallic crystals.

The Role of Network Architecture in Collagen Mechanics

Collagen forms fibrous networks that reinforce tissues and provide an extracellular matrix for cells. These networks exhibit remarkable strain-stiffening properties that tailor the mechanical functions of tissues and regulate cell behavior. Recent models explain this nonlinear behavior as an intrinsic feature of disordered networks of stiff fibers. Here, we experimentally validate this theoretical framework by measuring the elastic properties of collagen networks over a wide range of self-assembly conditions. We show that the model allows us to quantitatively relate both the linear and nonlinear elastic behavior of collagen networks to their underlying architecture. Specifically, we identify the local coordination number (or connectivity) 〈z〉 as a key architectural parameter that governs the elastic response of collagen. The network elastic response reveals that 〈z〉 decreases from 3.5 to 3 as the polymerization temperature is raised from 26 to 37°C while being weakly dependent on concentration. We furthermore infer a Young's modulus of 1.1 MPa for the collagen fibrils from the linear modulus. Scanning electron microscopy confirms that 〈z〉 is between three and four but is unable to detect the subtle changes in 〈z〉 with polymerization conditions that rheology is sensitive to. Finally, we show that, consistent with the model, the initial stress-stiffening response of collagen networks is controlled by the negative normal stress that builds up under shear. Our work provides a predictive framework to facilitate future studies of the regulatory effect of extracellular matrix molecules on collagen mechanics. Moreover, our findings can aid mechanobiological studies of wound healing, fibrosis, and cancer metastasis, which require collagen matrices with tunable mechanical properties.

Simulation of the mechanical behavior of random fiber networks with different microstructure

Filamentous protein networks are broadly encountered in biological systems such as cytoskeleton and extracellular matrix. Many numerical studies have been conducted to better understand the fundamental mechanisms behind the striking mechanical properties of these networks. In most of these previous numerical models, the Mikado algorithm has been used to represent the network microstructure. Here, a different algorithm is used to create random fiber networks in order to investigate possible roles of architecture on the elastic behavior of filamentous networks. In particular, random fibrous structures are generated from the growth of individual fibers from random nucleation points. We use computer simulations to determine the mechanical behavior of these networks in terms of their model parameters. The findings are presented and discussed along with the response of Mikado fiber networks. We demonstrate that these alternative networks and Mikado networks show a qualitatively similar response. Nevertheless, the overall elasticity of Mikado networks is stiffer compared to that of the networks created using the alternative algorithm. We describe the effective elasticity of both network types as a function of their line density and of the material properties of the filaments. We also characterize the ratio of bending and axial energy and discuss the behavior of these networks in terms of their fiber density distribution and coordination number.

Multicompartment cell-based modeling of confined migration: regulation by cell intrinsic and extrinsic factors

Though cell and nuclear deformability are expected to influence efficiency of confined migration, their individual and collective influence on migration efficiency remains incompletely understood. In addition to cell intrinsic properties, the relevance of cell extrinsic factors on confined migration, if any, has not been adequately explored. Here we address these questions using a statistical mechanics-based stochastic modeling approach where cell/nuclear dimensions and their deformability are explicitly taken into consideration. In addition to demonstrating the importance of cell softness in sustaining confined migration, our results suggest that dynamic tuning of cell and nuclear properties at different stages of migration is essential for maximizing migration efficiency. Our simulations also implicate confinement shape and confinement history as two important cell extrinsic regulators of cell invasiveness. Together, our findings illustrate the strength of a multicompartment model in dissecting the contributions of multiple factors that collectively influence confined cell migration.

Combined experimental and computational characterization of crosslinked collagen-based hydrogels

Collagen hydrogels are widely used for in-vitro experiments and tissue engineering applications. Their use has been extended due to their biocompatibility with cells and their capacity to mimic biological tissues; nevertheless their mechanical properties are not always optimal for these purposes. Hydrogels are formed by a network of polymer filaments embedded on an aqueous substrate and their mechanical properties are mainly defined by the filament network architecture and the individual filament properties. To increase properties of native collagen, such as stiffness or strain-stiffening, these networks can be modified by adding crosslinking agents that alter the network architecture, increasing the unions between filaments. In this work, we have investigated the effect of one crosslinking agent, transglutaminase, in collagen hydrogels with varying collagen concentration. We have observed a linear dependency of the gel rigidity on the collagen concentration. Moreover, the addition of transglutaminase has induced an earlier strain-stiffening of the collagen gels. In addition, to better understand the mechanical implications of collagen concentration and crosslinkers inclusion, we have adapted an existing computational model, based on the worm-like chain model (WLC), to reproduce the mechanical behavior of the collagen gels. With this model we can estimate the parameters of the biopolymer networks without more sophisticated techniques, such as image processing or network reconstruction, or, inversely, predict the mechanical properties of a defined collagen network.

Elasticity in Physically Cross-Linked Amyloid Fibril Networks

We provide a constitutive model of semiflexible and rigid amyloid fibril networks by combining the affine thermal model of network elasticity with the Derjaguin-Landau-Vervey-Overbeek (DLVO) theory of electrostatically charged colloids. When compared to rheological experiments on β-lactoglobulin and lysozyme amyloid networks, this approach provides the correct scaling of elasticity versus both concentration (G∼c^{2.2} and G∼c^{2.5} for semiflexible and rigid fibrils, respectively) and ionic strength (G∼I^{4.4} and G∼I^{3.8} for β-lactoglobulin and lysozyme, independent from fibril flexibility). The pivotal role played by the screening salt is to reduce the electrostatic barrier among amyloid fibrils, converting labile physical entanglements into long-lived cross-links. This gives a power-law behavior of G with I having exponents significantly larger than in other semiflexible polymer networks (e.g., actin) and carrying DLVO traits specific to the individual amyloid fibrils.

Cell contraction induces long-ranged stress stiffening in the extracellular matrix

Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing nonlinear stress inference microscopy (NSIM), a technique to infer stress fields in a 3D matrix from nonlinear microrheology measurements with optical tweezers. Using NSIM and simulations, we reveal large long-ranged cell-generated stresses capable of buckling filaments in the matrix. These stresses give rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which can provide a mechanism for mechanical communication between cells.

Mechanical signaling through the discoidin domain receptor 1 plays a central role in tissue fibrosis

The preservation of tissue and organ architecture and function depends on tightly regulated interactions of cells with the extracellular matrix (ECM). These interactions are maintained in a dynamic equilibrium that balances intracellular, myosin-generated tension with extracellular resistance conferred by the mechanical properties of the extracellular matrix. Disturbances of this equilibrium can lead to the development of fibrotic lesions that are associated with a wide repertoire of high prevalence diseases including obstructive cardiovascular diseases, muscular dystrophy and cancer. Mechanotransduction is the process by which mechanical cues are converted into biochemical signals. At the core of mechanotransduction are sensory systems, which are frequently located at sites of cell-ECM and cell-cell contacts. As integrins (cell-ECM junctions) and cadherins (cell-cell contacts) have been extensively studied, we focus here on the properties of the discoidin domain receptor 1 (DDR1), a tyrosine kinase that mediates cell adhesion to collagen. DDR1 expression is positively associated with fibrotic lesions of heart, kidney, liver, lung and perivascular tissues. As the most common end-point of all fibrotic disorders is dysregulated collagen remodeling, we consider here the mechanical signaling functions of DDR1 in processing of fibrillar collagen that lead to tissue fibrosis.

The role of extracellular matrix stiffness in megakaryocyte and platelet development and function

The extracellular matrix (ECM) is a key acellular structure in constant remodeling to provide tissue cohesion and rigidity. Deregulation of the balance between matrix deposition, degradation, and crosslinking results in fibrosis. Bone marrow fibrosis (BMF) is associated with several malignant and nonmalignant pathologies severely affecting blood cell production. BMF results from abnormal deposition of collagen fibers and enhanced lysyl oxidase-mediated ECM crosslinking within the marrow, thereby increasing marrow stiffness. Bone marrow stiffness has been recently recognized as an important regulator of blood cell development, notably by modifying the fate and differentiation process of hematopoietic or mesenchymal stem cells. This review surveys the different components of the ECM and their influence on stem cell development, with a focus on the impact of the ECM composition and stiffness on the megakaryocytic lineage in health and disease. Megakaryocyte maturation and the biogenesis of their progeny, the platelets, are thought to respond to environmental mechanical forces through a number of mechanosensors, including integrins and mechanosensitive ion channels, reviewed here.

Displacement Propagation in Fibrous Networks Due to Local Contraction

The extracellular matrix provides macroscale structure to tissues and microscale guidance for cell contraction, adhesion, and migration. The matrix is composed of a network of fibers, which each deform by stretching, bending, and buckling. Whereas the mechanics has been well characterized in uniform shear and extension, the response to more general loading conditions remains less clear, because the associated displacement fields cannot be predicted a priori. Studies simulating contraction, such as due to a cell, have observed displacements that propagate over a long range, suggesting mechanisms such as reorientation of fibers toward directions of tensile force and nonlinearity due to buckling of fibers under compression. It remains unclear which of these two mechanisms produces the long-range displacements and how properties like fiber bending stiffness and fiber length affect the displacement field. Here, we simulate contraction of an inclusion within a fibrous network and fit the resulting radial displacements to ur ∼ r−n where the power n quantifies the decay of displacements over distance, and a value of n less than that predicted by classical linear elasticity indicates displacements that propagate over a long range. We observed displacements to propagate over a longer range for greater contraction of the inclusion, for networks having longer fibers, and for networks with lower fiber bending stiffness. Contraction of the inclusion also caused fibers to reorient into the radial direction, but, surprisingly, the reorientation was minimally affected by bending stiffness. We conclude that both reorientation and nonlinearity are responsible for the long-range displacements.

Poisson's Contraction and Fiber Kinematics in Tissue: Insight From Collagen Network Simulations

Connective tissue mechanics is highly nonlinear, exhibits a strong Poisson's effect, and is associated with significant collagen fiber re-arrangement. Although the general features of the stress-strain behavior have been discussed extensively, the Poisson's effect received less attention. In general, the relationship between the microscopic fiber network mechanics and the macroscopic experimental observations remains poorly defined. The objective of the present work is to provide additional insight into this relationship. To this end, results from models of random collagen networks are compared with experimental data on reconstructed collagen gels, mouse skin dermis, and the human amnion. Attention is devoted to the mechanism leading to the large Poisson's effect observed in experiments. The results indicate that the incremental Poisson's contraction is directly related to preferential collagen orientation. The experimentally observed downturn of the incremental Poisson's ratio at larger strains is associated with the confining effect of fibers transverse to the loading direction and contributing little to load bearing. The rate of collagen orientation increases at small strains, reaches a maximum, and decreases at larger strains. The peak in this curve is associated with the transition of the network deformation from bending dominated, at small strains, to axially dominated, at larger strains. The effect of fiber tortuosity on network mechanics is also discussed, and a comparison of biaxial and uniaxial loading responses is performed.

Fibril growth kinetics link buffer conditions and topology of 3D collagen I networks

Three-dimensional fibrillar networks reconstituted from collagen I are widely used as biomimetic scaffolds for in vitro and in vivo cell studies. Various physicochemical parameters of buffer conditions for in vitro fibril formation are well known, including pH-value, ion concentrations and temperature. However, there is a lack of a detailed understanding of reconstituting well-defined 3D network topologies, which is required to mimic specific properties of the native extracellular matrix. We screened a wide range of relevant physicochemical buffer conditions and characterized the topology of the reconstituted 3D networks in terms of mean pore size and fibril diameter. A congruent analysis of fibril formation kinetics by turbidimetry revealed the adjustment of the lateral growth phase of fibrils by buffer conditions to be key in the determination of pore size and fibril diameter of the networks. Although the kinetics of nucleation and linear growth phase were affected by buffer conditions as well, network topology was independent of those two growth phases. Overall, the results of our study provide necessary insights into how to engineer 3D collagen matrices with an independent control over topology parameters, in order to mimic in vivo tissues in in vitro experiments and tissue engineering applications.

STATEMENT OF SIGNIFICANCE

The study reports a comprehensive analysis of physicochemical conditions of buffer solutions to reconstitute defined 3D collagen I matrices. By a combined analysis of network topology, i.e., pore size and fibril diameter, and the kinetics of fibril formation we can reveal the dependence of 3D network topology on buffer conditions, such as pH-value, phosphate concentration and sodium chloride content. With those results we are now able to provide engineering strategies to independently tune the topology parameters of widely used 3D collagen scaffolds based on the buffer conditions. By that, we enable the straightforward mimicking of extracellular matrices of in vivo tissues for in vitro cell culture experiments and tissue engineering applications.

Network Topology in Soft Gels: Hardening and Softening Materials

The structural complexity of soft gels is at the origin of a versatile mechanical response that allows for large deformation, controlled elastic recovery, and toughness in the same material. A limit to exploiting the potential of such materials is the insufficient fundamental understanding of the microstructural origin of the bulk mechanical properties. Here we investigate the role of the network topology in a model gel through 3D numerical simulations. Our study links the topology of the network organization in space to its nonlinear rheological response preceding yielding and damage: our analysis elucidates how the network connectivity alone could be used to modify the gel mechanics at large strains, from strain-softening to hardening and even to a brittle response. These findings provide new insight for smart material design and for understanding the nontrivial mechanical response of a potentially wide range of technologically relevant materials.

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.

Hindrances to precise recovery of cellular forces in fibrous biopolymer networks

How cells move through the three-dimensional extracellular matrix (ECM) is of increasing interest in attempts to understand important biological processes such as cancer metastasis. Just as in motion on flat surfaces, it is expected that experimental measurements of cell-generated forces will provide valuable information for uncovering the mechanisms of cell migration. However, the recovery of forces in fibrous biopolymer networks may suffer from large errors. Here, within the framework of lattice-based models, we explore possible issues in force recovery by solving the inverse problem: how can one determine the forces cells exert to their surroundings from the deformation of the ECM? Our results indicate that irregular cell traction patterns, the uncertainty of local fiber stiffness, the non-affine nature of ECM deformations and inadequate knowledge of network topology will all prevent the precise force determination. At the end, we discuss possible ways of overcoming these difficulties.

Conditional deletion of RB1 in the Tie2 lineage leads to aortic valve regurgitation

Objective

Aortic valve disease is a complex process characterized by valve interstitial cell activation, disruption of the extracellular matrix culminating in valve mineralization occurring over many years. We explored the function of the retinoblastoma protein (pRb) in aortic valve disease, given its critical role in mesenchymal cell differentiation including bone development and mineralization.

Approach and results

We generated a mouse model of conditional pRb knockout (cKO) in the aortic valve regulated by Tie2-Cre-mediated excision of floxed RB1 alleles. Aged pRb cKO animals showed significantly more aortic valve regurgitation by echocardiography compared to pRb het control animals. The pRb cKO aortic valves had increased leaflet thickness without increased cellular proliferation. Histologic studies demonstrated intense α-SMA expression in pRb cKO leaflets associated with disorganized extracellular matrix and increased leaflet stiffness. The pRb cKO mice also showed increased circulating cytokine levels.

Conclusions

Our studies demonstrate that pRb loss in the Tie2-lineage that includes aortic valve interstitial cells is sufficient to cause age-dependent aortic valve dysfunction.

Biomimetic tumor microenvironments based on collagen matrices

This review provides an overview of the current approaches to engineer defined 3D matrices for the investigation of tumor cell behaviorin vitro, with a focus on collagen-based fibrillar systems.

Collagen structure regulates MSCs behavior by MMPs involved cell–matrix interactions

Various scaffolds have been studied in the formation of cell niches and regulation of mesenchymal stem cells (MSCs) behaviors.

Soft Matter Lubrication: Does Solid Viscoelasticity Matter?

Classical lubrication theory is unable to explain a variety of phenomena and experimental observations involving soft viscoelastic materials, which are ubiquitous and increasingly used in e.g. engineering and biomedical applications. These include unexpected ruptures of the lubricating film and a friction-speed dependence, which cannot be elucidated by means of conventional models, based on time-independent stress-strain constitutive laws for the lubricated solids. A new modeling framework, corroborated through experimental measurements enabled via an interferometric technique, is proposed to address these issues: Solid/fluid interactions are captured thanks to a coupling strategy that makes it possible to study the effect that solid viscoelasticity has on fluid film lubrication. It is shown that a newly defined visco-elasto-hydrodynamic lubrication (VEHL) regime can be experienced depending on the degree of coupling between the fluid flow and the solid hysteretic response. Pressure distributions show a marked asymmetry with a peak at the flow inlet, and correspondingly, the film thickness reveals a pronounced shrinkage at the flow outlet; friction is heavily influenced by the viscoelastic hysteresis which is experienced in addition to the viscous losses. These features show significant differences with respect to the classical elasto-hydrodynamic lubrication (EHL) regime response that would be predicted when solid viscoelasticity is neglected. A simple yet powerful criterion to assess the importance of viscoelastic solid contributions to soft matter lubrication is finally proposed.

Programming the mechanics of cohesive fiber networks by compression

Fibrous networks are ideal functional materials since they provide mechanical rigidity at low weight. Here, we demonstrate that fibrous networks of the blood clotting protein fibrin undergo a strong and irreversible increase in their mechanical rigidity in response to uniaxial compression. This rigidification can be precisely controlled by the level of applied compressive strain, providing a means to program the network rigidity without having to change its composition. To identify the underlying mechanism we measure single fiber-fiber interactions using optical tweezers. We further develop a minimal computational model of cohesive fiber networks that shows that stiffening arises due to the formation of new bonds in the compressed state, which develop tensile stress when the network is re-expanded. The model predicts that the network stiffness after a compression cycle obeys a power-law dependence on tensile stress, which we confirm experimentally. This finding provides new insights into how biological tissues can adapt themselves independently of any cellular processes, offering new perspectives to inspire the design of reprogrammable materials.

Confocal Rheology Probes the Structure and Mechanics of Collagen through the Sol-Gel Transition

Fibrillar type I collagen-based hydrogels are commonly used in tissue engineering and as matrices for biophysical studies. Mechanical and structural properties of these gels are known to be governed by the conditions under which fibrillogenesis occurs, exhibiting variation as a function of protein concentration, temperature, pH, and ionic strength. Deeper understanding of how macroscopic structure affects viscoelastic properties of collagen gels over the course of fibrillogenesis provides fundamental insight into biopolymer gel properties and promises enhanced control over the properties of such gels. Here, we investigate type I collagen fibrillogenesis using confocal rheology-simultaneous confocal reflectance microscopy, confocal fluorescence microscopy, and rheology. The multimodal approach allows direct comparison of how viscoelastic properties track the structural evolution of the gel on fiber and network length scales. Quantitative assessment and comparison of each imaging modality and the simultaneously collected rheological measurements show that the presence of a system-spanning structure occurs at a time similar to rheological determinants of gelation. Although this and some rheological measures are consistent with critical gelation through percolation, additional rheological and structural properties of the gel are found to be inconsistent with this theory. This study clarifies how structure sets viscoelasticity during collagen fibrillogenesis and more broadly highlights the utility of multimodal measurements as critical test-beds for theoretical descriptions of complex systems.

Functional and Biomimetic Materials for Engineering of the Three-Dimensional Cell Microenvironment

The cell microenvironment has emerged as a key determinant of cell behavior and function in development, physiology, and pathophysiology. The extracellular matrix (ECM) within the cell microenvironment serves not only as a structural foundation for cells but also as a source of three-dimensional (3D) biochemical and biophysical cues that trigger and regulate cell behaviors. Increasing evidence suggests that the 3D character of the microenvironment is required for development of many critical cell responses observed in vivo, fueling a surge in the development of functional and biomimetic materials for engineering the 3D cell microenvironment. Progress in the design of such materials has improved control of cell behaviors in 3D and advanced the fields of tissue regeneration, in vitro tissue models, large-scale cell differentiation, immunotherapy, and gene therapy. However, the field is still in its infancy, and discoveries about the nature of cell-microenvironment interactions continue to overturn much early progress in the field. Key challenges continue to be dissecting the roles of chemistry, structure, mechanics, and electrophysiology in the cell microenvironment, and understanding and harnessing the roles of periodicity and drift in these factors. This review encapsulates where recent advances appear to leave the ever-shifting state of the art, and it highlights areas in which substantial potential and uncertainty remain.

Stress-induced plasticity of dynamic collagen networks

The structure and mechanics of tissues is constantly perturbed by endogenous forces originated from cells, and at the same time regulate many important cellular functions such as migration, differentiation, and growth. Here we show that 3D collagen gels, major components of connective tissues and extracellular matrix (ECM), are significantly and irreversibly remodeled by cellular traction forces, as well as by macroscopic strains. To understand this ECM plasticity, we develop a computational model that takes into account the sliding and merging of ECM fibers. We have confirmed the model predictions with experiment. Our results suggest the profound impacts of cellular traction forces on their host ECM during development and cancer progression, and suggest indirect mechanical channels of cell-cell communications in 3D fibrous matrices.The structure and mechanics of tissues is constantly perturbed by endogenous forces originated from cells. Here the authors show that 3D collagen gels, major components of connective tissues and extracellular matrix, are significantly and irreversibly remodelled by cellular traction forces and by macroscopic strains.

Matrix Mechanosensing: From Scaling Concepts in 'Omics Data to Mechanisms in the Nucleus, Regeneration, and Cancer

Many of the most important molecules of life are polymers. In animals, the most abundant of the proteinaceous polymers are the collagens, which constitute the fibrous matrix outside cells and which can also self-assemble into gels. The physically measurable stiffness of gels, as well as tissues, increases with the amount of collagen, and cells seem to sense this stiffness. An understanding of this mechanosensing process in complex tissues, including fibrotic disease states with high collagen, is now utilizing 'omics data sets and is revealing polymer physics-type, nonlinear scaling relationships between concentrations of seemingly unrelated biopolymers. The nuclear structure protein lamin A provides one example, with protein and transcript levels increasing with collagen 1 and tissue stiffness, and with mechanisms rooted in protein stabilization induced by cytoskeletal stress. Physics-based models of fibrous matrix, cytoskeletal force dipoles, and the lamin A gene circuit illustrate the wide range of testable predictions emerging for tissues, cell cultures, and even stem cell-based tissue regeneration. Beyond the epigenetics of mechanosensing, the scaling in cancer of chromosome copy number variations and other mutations with tissue stiffness suggests that genomic changes are occurring by mechanogenomic processes that now require elucidation.

Mechanical response of collagen networks to nonuniform microscale loads

As force is applied to fibrous proteins such as collagen or fibrin, the fibers respond by bending, stretching, or buckling, which together bring about a nonlinear relationship between force and displacement. The nonlinearity is typically understood in terms of strain stiffening in uniform extension or shear, but there remains a critical lack of data on how fibrous materials respond to other more complicated loadings. Here we study the mechanics of collagen networks in response to nonuniform loads applied on the local scale of the fibers. For this, we use particles made of an active hydrogel that undergoes a temperature-induced phase transition causing a large decrease in volume. We embed these particles in networks of fibrous collagen and use them as microactuators to apply controlled microscale loading. The resulting fiber displacements propagate over a long range with radial displacements u scaling as r^-n with n ≈ 1. By contrast, we find linear homogeneous materials have n ≈ 2, in agreement with classical linear elastic theory. Our experimental data supports the notion that the long range displacements result from buckling of fibers in compression and local straightening of fibers in tension, in agreement with previous studies. Surprisingly, global network anisotropy appears to have only a modest effect on the displacement propagation. These insights into the microscale mechanics demonstrate that the decay power n provides a useful metric to quantify the mechanics of fibrous materials. We therefore suggest it is a means to compare new theories with experimental data.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

General theory of skin reinforcement

Macroscopic mechanical properties of human skin in vivo cannot be considered independent of adjacent subcutaneous white adipose tissue (sWAT). The layered system skin/sWAT appears as the hierarchical structural composite in which single layers behave as fiber-reinforced structures. Effective macroscopic mechanical properties of such composites are mainly determined either by the properties of the skin or by those of the sWAT, dependent on the conditions of mechanical loading. Mechanical interactions between the skin and the adjacent sWAT associated with a mismatch in the mechanical moduli of these two layers can lead to production of the skin wrinkles. Reinforcement of the composite skin/sWAT can take place in different ways. It can be provided through reorientation of collagen fibers under applied loading, through production of new bonds between existing collagen fibers and through induction of additional collagen structures. Effectiveness of this type of reinforcement is strongly dependent on the type of mechanical loading. Different physical interventions induce the reinforcement of at least one of these two layers, thus increasing the effective macroscopic stiffness of the total composite. At the same time, the standalone reinforcement of the skin appears to be less effective to achieve a delay or a reduction of the apparent signs of skin aging relative to the reinforcement of the sWAT.

Strain Stiffening Hydrogels through Self-Assembly and Covalent Fixation of Semi-Flexible Fibers

Biomimetic, strain-stiffening materials are reported, made through self-assembly and covalent fixation of small building blocks to form fibrous hydrogels that are able to stiffen by an order of magnitude in response to applied stress. The gels consist of semi-flexible rodlike micelles of bisurea bolaamphiphiles with oligo(ethylene oxide) (EO) outer blocks and a polydiacetylene (PDA) backbone. The micelles are fibers, composed of 9-10 ribbons. A gelation method based on Cu-catalyzed azide-alkyne cycloaddition (CuAAC), was developed and shown to lead to strain-stiffening hydrogels with unusual, yet universal, linear and nonlinear stress-strain response. Upon gelation, the X-ray scattering profile is unchanged, suggesting that crosslinks are formed at random positions along the fiber contour without fiber bundling. The work expands current knowledge about the design principles and chemistries needed to achieve fully synthetic, biomimetic soft matter with on-demand, targeted mechanical properties.

Spatial distributions of pericellular stiffness in natural extracellular matrices are dependent on cell-mediated proteolysis and contractility

Bulk tissue stiffness has been correlated with regulation of cellular processes and conversely cells have been shown to remodel their pericellular tissue according to a complex feedback mechanism critical to development, homeostasis, and disease. However, bulk rheological methods mask the dynamics within a heterogeneous fibrous extracellular matrix (ECM) in the region proximal to a cell (pericellular region). Here, we use optical tweezers active microrheology (AMR) to probe the distribution of the complex material response function (α=α'+α″, in units of µm/nN) within a type I collagen ECM, a biomaterial commonly used in tissue engineering. We discovered cells both elastically and plastically deformed the pericellular material. α' is wildly heterogeneous, with 1/α' values spanning three orders of magnitude around a single cell. This was observed in gels having a cell-free 1/α' of approximately 0.5nN/µm. We also found that inhibition of cell contractility instantaneously softens the pericellular space and reduces stiffness heterogeneity, suggesting the system was strain hardened and not only plastically remodeled. The remaining regions of high stiffness suggest cellular remodeling of the surrounding matrix. To test this hypothesis, cells were incubated within the type I collagen gel for 24-h in a media containing a broad-spectrum matrix metalloproteinase (MMP) inhibitor. While pericellular material maintained stiffness asymmetry, stiffness magnitudes were reduced. Dual inhibition demonstrates that the combination of MMP activity and contractility is necessary to establish the pericellular stiffness landscape. This heterogeneity in stiffness suggests the distribution of pericellular stiffness, and not bulk stiffness alone, must be considered in the study of cell-ECM interactions and design of complex biomaterial scaffolds.

STATEMENT OF SIGNIFICANCE

Collagen is a fibrous extracellular matrix (ECM) protein widely used to study cell-ECM interactions. Stiffness of ECM has been shown to instruct cells, which can in turn modify their ECM, as has been shown in the study of cancer and regenerative medicine. Here we measure the stiffness of the collagen microenvironment surrounding cells and quantitatively measure the dependence of pericellular stiffness on MMP activity and cytoskeletal contractility. Competent cell-mediated stiffening results in a wildly heterogeneous micromechanical topography, with values spanning orders of magnitude around a single cell. We speculate studies must consider this notable heterogeneity generated by cells when testing theories regarding the role of ECM mechanics in health and disease.

Compression-induced structural and mechanical changes of fibrin-collagen composites

Fibrin and collagen as well as their combinations play an important biological role in tissue regeneration and are widely employed in surgery as fleeces or sealants and in bioengineering as tissue scaffolds. Earlier studies demonstrated that fibrin-collagen composite networks displayed improved tensile mechanical properties compared to the isolated protein matrices. Unlike previous studies, here unconfined compression was applied to a fibrin-collagen filamentous polymer composite matrix to study its structural and mechanical responses to compressive deformation. Combining collagen with fibrin resulted in formation of a composite hydrogel exhibiting synergistic mechanical properties compared to the isolated fibrin and collagen matrices. Specifically, the composite matrix revealed a one order of magnitude increase in the shear storage modulus at compressive strains>0.8 in response to compression compared to the mechanical features of individual components. These material enhancements were attributed to the observed structural alterations, such as network density changes, an increase in connectivity along with criss-crossing, and bundling of fibers. In addition, the compressed composite collagen/fibrin networks revealed a non-linear transformation of their viscoelastic properties with softening and stiffening regimes. These transitions were shown to depend on protein concentrations. Namely, a decrease in protein content drastically affected the mechanical response of the networks to compression by shifting the onset of stiffening to higher degrees of compression. Since both natural and artificially composed extracellular matrices experience compression in various (patho)physiological conditions, our results provide new insights into the structural biomechanics of the polymeric composite matrix that can help to create fibrin-collagen sealants, sponges, and tissue scaffolds with tunable and predictable mechanical properties.

Imaging Extracellular Matrix Remodeling In Vitro by Diffusion-Sensitive Optical Coherence Tomography

The mammary gland extracellular matrix (ECM) is comprised of biopolymers, primarily collagen I, that are created and maintained by stromal fibroblasts. ECM remodeling by fibroblasts results in changes in ECM fiber spacing (pores) that have been shown to play a critical role in the aggressiveness of breast cancer. However, minimally invasive methods to measure the spatial distribution of ECM pore areas within tissues and in vitro 3D culture models are currently lacking. We introduce diffusion-sensitive optical coherence tomography (DS-OCT) to image the nanoscale porosity of ECM by sensing weakly constrained diffusion of gold nanorods (GNRs). DS-OCT combines the principles of low-coherence interferometry and heterodyne dynamic light scattering. By collecting co- and cross-polarized light backscattered from GNRs within tissue culture, the ensemble-averaged translational self-diffusion rate, DT, of GNRs is resolved within ∼3 coherence volumes (10 × 5 μm, x × z). As GNRs are slowed by intermittent collisions with ECM fibers, DT is sensitive to ECM porosity on the size scale of their hydrodynamic diameter (∼46 nm). Here, we validate the utility of DS-OCT using pure collagen I gels and 3D mammary fibroblast cultures seeded in collagen/Matrigel, and associate differences in artificial ECM pore areas with gel concentration and cell seed density. Across all samples, DT was highly correlated with pore area obtained by scanning electron microscopy (R(2) = 0.968). We also demonstrate that DS-OCT can accurately map the spatial heterogeneity of layered samples. Importantly, DS-OCT of 3D mammary fibroblast cultures revealed the impact of fibroblast remodeling, where the spatial heterogeneity of matrix porosity was found to increase with cell density. This provides an unprecedented view into nanoscale changes in artificial ECM porosity over effective pore diameters ranging from ∼43 to 360 nm using a micron-scale optical imaging technique. In combination with the topical deposition of GNRs, the minimally invasive nature of DS-OCT makes this a promising technology for studying tissue remodeling processes.

Design and application of 'J-shaped' stress-strain behavior in stretchable electronics: a review

A variety of natural biological tissues (e.g., skin, ligaments, spider silk, blood vessel) exhibit 'J-shaped' stress-strain behavior, thereby combining soft, compliant mechanics and large levels of stretchability, with a natural 'strain-limiting' mechanism to prevent damage from excessive strain. Synthetic materials with similar stress-strain behaviors have potential utility in many promising applications, such as tissue engineering (to reproduce the nonlinear mechanical properties of real biological tissues) and biomedical devices (to enable natural, comfortable integration of stretchable electronics with biological tissues/organs). Recent advances in this field encompass developments of novel material/structure concepts, fabrication approaches, and unique device applications. This review highlights five representative strategies, including designs that involve open network, wavy and wrinkled morphologies, helical layouts, kirigami and origami constructs, and textile formats. Discussions focus on the underlying ideas, the fabrication/assembly routes, and the microstructure-property relationships that are essential for optimization of the desired 'J-shaped' stress-strain responses. Demonstration applications provide examples of the use of these designs in deformable electronics and biomedical devices that offer soft, compliant mechanics but with inherent robustness against damage from excessive deformation. We conclude with some perspectives on challenges and opportunities for future research.

Muscle and Limb Mechanics

Understanding of the musculoskeletal system has evolved from the collection of individual phenomena in highly selected experimental preparations under highly controlled and often unphysiological conditions. At the systems level, it is now possible to construct complete and reasonably accurate models of the kinetics and energetics of realistic muscles and to combine them to understand the dynamics of complete musculoskeletal systems performing natural behaviors. At the reductionist level, it is possible to relate most of the individual phenomena to the anatomical structures and biochemical processes that account for them. Two large challenges remain. At a systems level, neuroscience must now account for how the nervous system learns to exploit the many complex features that evolution has incorporated into muscle and limb mechanics. At a reductionist level, medicine must now account for the many forms of pathology and disability that arise from the many diseases and injuries to which this highly evolved system is inevitably prone. © 2017 American Physiological Society. Compr Physiol 7:429-462, 2017.

Structure-properties relation for random networks of fibers with noncircular cross section

The mechanical behavior of three-dimensional cross-linked random fiber networks composed from fibers of noncircular cross section characterized by two principal moments of inertia is studied in this work. Such fibers store energy in the axial deformation mode and two bending modes of unequal stiffness. We show that the torsional stiffness of fibers becomes important as it determines the relative contribution of the two bending modes to the overall deformation. The scaling of the small strain modulus with the network parameters is established. The large strain deformation of these structures is less sensitive to the shape of the cross section.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy-based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion.

Influence of high energy electron irradiation on the network structure of gelatin hydrogels as investigated by small-angle X-ray scattering (SAXS)

Small-angle X-ray scattering revealed ranging structural differences in physically entangled and irradiation-crosslinked gelatin hydrogels.