Glycosaminoglycans modulate long-range mechanical communication between cells in collagen networks.

Cells can sense and respond to mechanical forces in fibrous extracellular matrices (ECMs) over distances much greater than their size. This phenomenon, termed long-range force transmission, is enabled by the realignment (buckling) of collagen fibers along directions where the forces are tensile (compressive). However, whether other key structural components of the ECM, in particular glycosaminoglycans (GAGs), can affect the efficiency of cellular force transmission remains unclear. Here we developed a theoretical model of force transmission in collagen networks with interpenetrating GAGs, capturing the competition between tension-driven collagen fiber alignment and the swelling pressure induced by GAGs. Using this model, we show that the swelling pressure provided by GAGs increases the stiffness of the collagen network by stretching the fibers in an isotropic manner. We found that the GAG-induced swelling pressure can help collagen fibers resist buckling as the cells exert contractile forces. This mechanism impedes the alignment of collagen fibers and decreases long-range cellular mechanical communication. We experimentally validated the theoretical predictions by comparing the intensity of collagen fiber alignment between cellular spheroids cultured on collagen gels versus collagen­GAG cogels. We found significantly lower intensities of aligned collagen in collagen­GAG cogels, consistent with the prediction that GAGs can prevent collagen fiber alignment. The role of GAGs in modulating force transmission uncovered in this work can be extended to understand pathological processes such as the formation of fibrotic scars and cancer metastasis, where cells communicate in the presence of abnormally high concentrations of GAGs.

Strong triaxial coupling and anomalous Poisson effect in collagen networks.

While cells within tissues generate and sense 3D states of strain, the current understanding of the mechanics of fibrous extracellular matrices (ECMs) stems mainly from uniaxial, biaxial, and shear tests. Here, we demonstrate that the multiaxial deformations of fiber networks in 3D cannot be inferred solely based on these tests. The interdependence of the three principal strains gives rise to anomalous ratios of biaxial to uniaxial stiffness between 8 and 9 and apparent Poisson's ratios larger than 1. These observations are explained using a microstructural network model and a coarse-grained constitutive framework that predicts the network Poisson effect and stress-strain responses in uniaxial, biaxial, and triaxial modes of deformation as a function of the microstructural properties of the network, including fiber mechanics and pore size of the network. Using this theoretical approach, we found that accounting for the Poisson effect leads to a 100-fold increase in the perceived elastic stiffness of thin collagen samples in extension tests, reconciling the seemingly disparate measurements of the stiffness of collagen networks using different methods. We applied our framework to study the formation of fiber tracts induced by cellular forces. In vitro experiments with low-density networks showed that the anomalous Poisson effect facilitates higher densification of fibrous tracts, associated with the invasion of cancerous acinar cells. The approach developed here can be used to model the evolving mechanics of ECM during cancer invasion and fibrosis.

Multiscale model predicts increasing focal adhesion size with decreasing stiffness in fibrous matrices.

We describe a multiscale model that incorporates force-dependent mechanical plasticity induced by interfiber cross-link breakage and stiffness-dependent cellular contractility to predict focal adhesion (FA) growth and mechanosensing in fibrous extracellular matrices (ECMs). The model predicts that FA size depends on both the stiffness of ECM and the density of ligands available to form adhesions. Although these two quantities are independent in commonly used hydrogels, contractile cells break cross-links in soft fibrous matrices leading to recruitment of fibers, which increases the ligand density in the vicinity of cells. Consequently, although the size of focal adhesions increases with ECM stiffness in nonfibrous and elastic hydrogels, plasticity of fibrous networks leads to a departure from the well-described positive correlation between stiffness and FA size. We predict a phase diagram that describes nonmonotonic behavior of FA in the space spanned by ECM stiffness and recruitment index, which describes the ability of cells to break cross-links and recruit fibers. The predicted decrease in FA size with increasing ECM stiffness is in excellent agreement with recent observations of cell spreading on electrospun fiber networks with tunable cross-link strengths and mechanics. Our model provides a framework to analyze cell mechanosensing in nonlinear and inelastic ECMs.

Fibrous nonlinear elasticity enables positive mechanical feedback between cells and ECMs.

In native states, animal cells of many types are supported by a fibrous network that forms the main structural component of the ECM. Mechanical interactions between cells and the 3D ECM critically regulate cell function, including growth and migration. However, the physical mechanism that governs the cell interaction with fibrous 3D ECM is still not known. In this article, we present single-cell traction force measurements using breast tumor cells embedded within 3D collagen matrices. We recreate the breast tumor mechanical environment by controlling the microstructure and density of type I collagen matrices. Our results reveal a positive mechanical feedback loop: cells pulling on collagen locally align and stiffen the matrix, and stiffer matrices, in return, promote greater cell force generation and a stiffer cell body. Furthermore, cell force transmission distance increases with the degree of strain-induced fiber alignment and stiffening of the collagen matrices. These findings highlight the importance of the nonlinear elasticity of fibrous matrices in regulating cell-ECM interactions within a 3D context, and the cell force regulation principle that we uncover may contribute to the rapid mechanical tissue stiffening occurring in many diseases, including cancer and fibrosis.

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.

Collagen Organization in Facet Capsular Ligaments Varies With Spinal Region and With Ligament Deformation.

The spinal facet capsular ligament (FCL) is primarily comprised of heterogeneous arrangements of collagen fibers. This complex fibrous structure and its evolution under loading play a critical role in determining the mechanical behavior of the FCL. A lack of analytical tools to characterize the spatial anisotropy and heterogeneity of the FCL's microstructure has limited the current understanding of its structure-function relationships. Here, the collagen organization was characterized using spatial correlation analysis of the FCL's optically obtained fiber orientation field. FCLs from the cervical and lumbar spinal regions were characterized in terms of their structure, as was the reorganization of collagen in stretched cervical FCLs. Higher degrees of intra- and intersample heterogeneity were found in cervical FCLs than in lumbar specimens. In the cervical FCLs, heterogeneity was manifested in the form of curvy patterns formed by collections of collagen fibers or fiber bundles. Tensile stretch, a common injury mechanism for the cervical FCL, significantly increased the spatial correlation length in the stretch direction, indicating an elongation of the observed structural features. Finally, an affine estimation for the change of correlation length under loading was performed which gave predictions very similar to the actual values. These findings provide structural insights for multiscale mechanical analyses of the FCLs from various spinal regions and also suggest methods for quantitative characterization of complex tissue patterns.

Softening in Random Networks of Non-Identical Beams.

Random fiber networks are assemblies of elastic elements connected in random configurations. They are used as models for a broad range of fibrous materials including biopolymer gels and synthetic nonwovens. Although the mechanics of networks made from the same type of fibers has been studied extensively, the behavior of composite systems of fibers with different properties has received less attention. In this work we numerically and theoretically study random networks of beams and springs of different mechanical properties. We observe that the overall network stiffness decreases on average as the variability of fiber stiffness increases, at constant mean fiber stiffness. Numerical results and analytical arguments show that for small variabilities in fiber stiffness the amount of network softening scales linearly with the variance of the fiber stiffness distribution. This result holds for any beam structure and is expected to apply to a broad range of materials including cellular solids.

Effect of Fiber Crimp on the Elasticity of Random Fiber Networks With and Without Embedding Matrices.

Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.

Strength of DNA sticky end links.

Sticky ends are unpaired nucleotides at the ends of DNA molecules that can associate to link DNA segments. Self-assembly of DNA molecules via sticky ends is currently used to grow DNA structures with desired architectures. The sticky end links are the weakest parts of such structures. In this work, the strength of sticky end links is studied by computational means. The number of basepairs in the sticky end and the sequence are varied, and the response to tension along the axis of the molecule is evaluated using a full atomistic model. It is observed that, generally, increasing the number of basepairs in the sticky end increases the strength, but the central factor controlling this parameter is the basepair sequence. The sticky ends are divided into two classes of low and high strength. The second class has strength comparable with that of a double stranded molecule with one nick in one of the strands. The strength of the first class is roughly half that of the strong sticky ends. For all strong sticky ends tested, the enhanced stability is associated with the formation of an unusually stable complex composed from two basepairs and two flanking bases of certain sequence. This complex rotates and aligns with the direction of the force allowing significant deformation and providing enhanced strength. This is similar to a mechanism recently suggested to enhance the mechanical stability of an RNA kissing loop from the Moloney murine leukemia virus. The model is tested against experimental structural data for sticky ends and against published simulation results for the stretch of double stranded DNA. The results provide guidance for the design of DNA self-assembled structures and indicate the types of sticky ends desirable if maximizing the strength and stability of these structures is targeted.

Extended law of laplace for measurement of the cloverleaf anatomy of the aortic root.

The cross-sectional shape of the aortic root is cloverleaf, not circular, raising controversy regarding how best to measure its radiographic "diameter" for aortic event prediction. We mathematically extended the law of Laplace to estimate aortic wall stress within this cloverleaf region, simultaneously identifying a new metric of aortic root dimension that can be applied to clinical measurement of the aortic root and sinuses of Valsalva on clinical computerized tomographic scans. Enforcing equilibrium between blood pressure and wall stress, finite element computations were performed to evaluate the mathematical derivation. The resulting Laplace diameter was compared with existing methods of aortic root measurement across four patient groups: non-syndromic aneurysm, bicuspid aortic valve, Marfan syndrome, and non-dilated root patients (total 106 patients, 62 M, 44 F). (1) Wall stress: Mean wall stress at the depth of the sinuses followed this equation: Wall stress = BP × Circumscribing circle diameter/(2 × Aortic wall thickness). Therefore, the diameter of the circle enclosing the root cloverleaf, that is, twice the distance between the center, where the sinus-to-commissure lines coincide, and the depth of the sinuses, may replace diameter in the Laplace relation for a cloverleaf cross-section (or any shaped cross-section with two or more planes of symmetry). This mathematically derived result was verified by computational finite element analyses. (2) Diameters: CT scan measurements showed a significant difference between this new metric, the Laplace diameter, and the sinus-to-commissure, mid-sinus-to-mid-sinus, and coronal measurements in all four groups (p-value < 0.05). The average Laplace diameter measurements differed significantly from the other measurements in all patient groups. Among the various possible measurements within the aortic root, the diameter of the circumscribing circle, enclosing the cloverleaf, represents the diameter most closely related to wall stress. This diameter is larger than the other measurements, indicating an underestimation of wall stress by prior measurements, and otherwise provides an unbiased, convenient, consistent, physics-based measurement for clinical use. "Diameter" applies to circles. Our mathematical derivation of an extension of the law of Laplace, from circular to cloverleaf cross-sectional geometries of the aortic root, has implications for measurement of aortic root "diameter." The suggested method is as follows: (1) the "center" of the aortic root is identified by drawing three sinus-to-commissure lines. The intersection of these three lines identifies the "center" of the cloverleaf. (2) The largest radius from this center point to any of the sinuses is identified as the "radius" of the aortic root. (3) This radius is doubled to give the "diameter" of the aortic root. We find that this diameter best corresponds to maximal wall stress in the aortic root. Please note that this diameter defines the smallest circle that completely encloses the cloverleaf shape, touching the depths of all three sinuses.

Critical Pressure of Intramural Delamination in Aortic Dissection.

Computational models of aortic dissection can examine mechanisms by which this potentially lethal condition develops and propagates. We present results from phase-field finite element simulations that are motivated by a classical but seldom repeated experiment. Initial simulations agreed qualitatively and quantitatively with data, yet because of the complexity of the problem it was difficult to discern trends. Simplified analytical models were used to gain further insight. Together, simplified and phase-field models reveal power-law-based relationships between the pressure that initiates an intramural tear and key geometric and mechanical factors-insult surface area, wall stiffness, and tearing energy. The degree of axial stretch and luminal pressure similarly influence the pressure of tearing, which was ~88 kPa for healthy and diseased human aortas having sub-millimeter-sized initial insults, but lower for larger tear sizes. Finally, simulations show that the direction a tear propagates is influenced by focal regions of weakening or strengthening, which can drive the tear towards the lumen (dissection) or adventitia (rupture). Additional data on human aortas having different predisposing disease conditions will be needed to extend these results further, but the present findings show that physiologic pressures can propagate initial medial defects into delaminations that can serve as precursors to dissection.

Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network.

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. This surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

Differential propensity of dissection along the aorta.

Aortic dissections progress, in part, by delamination of the wall. Previous experiments on cut-open segments of aorta demonstrated that fluid injected within the wall delaminates the aorta in two distinct modes: stepwise progressive tearing in the abdominal aorta and a more prevalent sudden mode of tearing in the thoracic aorta that can also manifest in other regions. A microstructural understanding that delineates these two modes of tearing has remained wanting. We implemented a phase-field finite-element model of the aortic wall, motivated in part by two-photon imaging, and found correlative relations for the maximum pressure prior to tearing as a function of local geometry and material properties. Specifically, the square of the pressure of tearing relates directly to both tissue stiffness and the critical energy of tearing and inversely to the square root of the torn area; this correlation explains the sudden mode of tearing and, with the microscopy, suggests a mechanism for progressive tearing. Microscopy also confirmed that thick interlamellar radial struts are more abundant in the abdominal region of the aorta, where progressive tearing was observed previously. The computational results suggest that structurally significant radial struts increase tearing pressure by two mechanisms: confining the fluid by acting as barriers to flow and increasing tissue stiffness by holding the adjacent lamellae together. Collectively, these two phase-field models provide new insights into the mechanical factors that can influence intramural delaminations that promote aortic dissection.

Soft robotic constrictor for in vitro modeling of dynamic tissue compression.

Here we present a microengineered soft-robotic in vitro platform developed by integrating a pneumatically regulated novel elastomeric actuator with primary culture of human cells. This system is capable of generating dynamic bending motion akin to the constriction of tubular organs that can exert controlled compressive forces on cultured living cells. Using this platform, we demonstrate cyclic compression of primary human endothelial cells, fibroblasts, and smooth muscle cells to show physiological changes in their morphology due to applied forces. Moreover, we present mechanically actuatable organotypic models to examine the effects of compressive forces on three-dimensional multicellular constructs designed to emulate complex tissues such as solid tumors and vascular networks. Our work provides a preliminary demonstration of how soft-robotics technology can be leveraged for in vitro modeling of complex physiological tissue microenvironment, and may enable the development of new research tools for mechanobiology and related areas.

Programmable and contractile materials through cell encapsulation in fibrous hydrogel assemblies.

The natural extracellular matrix (ECM) within tissues is physically contracted and remodeled by cells, allowing the collective shaping of functional tissue architectures. Synthetic materials that facilitate self-assembly similar to natural ECM are needed for cell culture, tissue engineering, and in vitro models of development and disease. To address this need, we develop fibrous hydrogel assemblies that are stabilized with photocrosslinking and display fiber density­dependent strain-responsive properties (strain stiffening and alignment). Encapsulated mesenchymal stromal cells locally contract low fiber density assemblies, resulting in macroscopic volumetric changes with increased cell densities and moduli. Because of properties such as shear-thinning and self-healing, assemblies can be processed into microtissues with aligned ECM deposition or through extrusion bioprinting and photopatterning to fabricate constructs with programmed shape changes due to cell contraction. These materials provide a synthetic approach to mimic features of natural ECM, which can now be processed for applications in biofabrication and tissue engineering.

Mechanochemical Adhesion and Plasticity in Multifiber Hydrogel Networks.

The extracellular matrix (ECM) has force-responsive (i.e., mechanochemical) properties that enable adaptation to mechanical loading through changes in fibrous network structure and interfiber bonding. Imparting such properties into synthetic fibrous materials will allow reinforcement under mechanical load, the potential for material self-adhesion, and the general mimicking of ECM. Multifiber hydrogel networks are developed through the electrospinning of multiple fibrous hydrogel populations, where fibers contain complementary chemical moieties (e.g., aldehyde and hydrazide groups) that form covalent bonds within minutes when brought into contact under mechanical load. These fiber interactions lead to microscale anisotropy, as well as increased material stiffness and plastic deformation. Macroscale structures (e.g., tubes and layered scaffolds) are fabricated from these materials through interfiber bonding and adhesion when placed into contact while maintaining a microscale fibrous architecture. The design principles for engineering plasticity described can be applied to numerous material systems to introduce unique properties, from textiles to biomedical applications.

Remodeling of the Collagen Matrix in Aging Skin Promotes Melanoma Metastasis and Affects Immune Cell Motility.

Physical changes in skin are among the most visible signs of aging. We found that young dermal fibroblasts secrete high levels of extracellular matrix (ECM) constituents, including proteoglycans, glycoproteins, and cartilage-linking proteins. The most abundantly secreted was HAPLN1, a hyaluronic and proteoglycan link protein. HAPLN1 was lost in aged fibroblasts, resulting in a more aligned ECM that promoted metastasis of melanoma cells. Reconstituting HAPLN1 inhibited metastasis in an aged microenvironment, in 3-D skin reconstruction models, and in vivo. Intriguingly, aged fibroblast-derived matrices had the opposite effect on the migration of T cells, inhibiting their motility. HAPLN1 treatment of aged fibroblasts restored motility of mononuclear immune cells, while impeding that of polymorphonuclear immune cells, which in turn affected regulatory T-cell recruitment. These data suggest that although age-related physical changes in the ECM can promote tumor cell motility, they may adversely affect the motility of some immune cells, resulting in an overall change in the immune microenvironment. Understanding the physical changes in aging skin may provide avenues for more effective therapy for older patients with melanoma. SIGNIFICANCE: These data shed light on the mechanochemical interactions that occur between aged skin, tumor, and immune cell populations, which may affect tumor metastasis and immune cell infiltration, with implications for the efficacy of current therapies for melanoma.See related commentary by Marie and Merlino, p. 19.This article is highlighted in the In This Issue feature, p. 1.

Dynamic Loading and Tendon Healing Affect Multiscale Tendon Properties and ECM Stress Transmission.

The extracellular matrix (ECM) is the primary biomechanical environment that interacts with tendon cells (tenocytes). Stresses applied via muscle contraction during skeletal movement transfer across structural hierarchies to the tenocyte nucleus in native uninjured tendons. Alterations to ECM structural and mechanical properties due to mechanical loading and tissue healing may affect this multiscale strain transfer and stress transmission through the ECM. This study explores the interface between dynamic loading and tendon healing across multiple length scales using living tendon explants. Results show that macroscale mechanical and structural properties are inferior following high magnitude dynamic loading (fatigue) in uninjured living tendon and that these effects propagate to the microscale. Although similar macroscale mechanical effects of dynamic loading are present in healing tendon compared to uninjured tendon, the microscale properties differed greatly during early healing. Regression analysis identified several variables (collagen and nuclear disorganization, cellularity, and F-actin) that directly predict nuclear deformation under loading. Finite element modeling predicted deficits in ECM stress transmission following fatigue loading and during healing. Together, this work identifies the multiscale response of tendon to dynamic loading and healing, and provides new insight into microenvironmental features that tenocytes may experience following injury and after cell delivery therapies.