Ehsan Ban

Fibrous nonlinear elasticity enables positive mechanical feedback between cells and ECMs

Significance Mechanical interactions between cells and the ECM critically regulate cell function, including growth and migration. By measuring forces exerted by breast tumor cells embedded within collagen matrices, we reveal a positive mechanical cross-talk between the cell and ECM: cells pulling onto collagen fibers align and stiffen the matrices, and stiffer collagen matrices promote greater cell force generation. Our work highlights the importance of strain-induced fiber alignment in mediating cell–ECM interaction within a 3D architecture. The basic force regulation principle uncovered here can be extended to understand the tissue-stiffening processes occurring in many diseases, such as tumor progression and fibrosis, and better design biomaterial scaffolds to control cell behavior in tissue engineering applications. 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.

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

Significance Focal adhesions play crucial roles in mechanotransduction and regulate processes such as spreading, proliferation, differentiation, and motility. It is well known that cells develop larger adhesions when cultured on stiffer elastic hydrogels, but the native extracellular matrix (ECM) is fibrous, nonlinear, and dissipative. We developed a multiscale model showing that adhesion size decreases with increasing stiffness in fibrous matrices, in excellent agreement with our experiments on engineered fibrous matrices. Our model shows that this is due to the feedback between cell contractility and the physical remodeling of ECM, which does not exist in elastic substrates. The basic stiffness–adhesion size principle uncovered can be applied to understand tumor progression fundamentally or to better design biomaterial scaffolds to control cell behavior. 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.

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 FCLs microstructure has limited the current understanding of its structure-function relationships. Here, the collagen organization was characterized using spatial correlation analysis of the FCLs 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.

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.

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.

Stiffness and strength of oxygen-functionalized graphene with vacancies

The 2D elastic modulus (E2D) and strength (σ2D) of defective graphene sheets containing vacancies, epoxide, and hydroxyl functional groups are evaluated at 300 K by atomistic simulations. The fraction of vacancies is controlled in the range 0% to 5%, while the density of functional groups corresponds to O:C ratios in the range 0% to 25%. In-plane modulus and strength diagrams as functions of vacancy and functional group densities are generated using models with a single type of defect and with combinations of two types of defects (vacancies and functional groups). It is observed that in models containing only vacancies, the rate at which strength decreases with increasing the concentration of defects is largest, followed by models containing only epoxide groups and those with only hydroxyl groups. The effect on modulus of vacancies and epoxides present alone in the model is similar, and much stronger than that of hydroxyl groups. When the concentration of defects is large, the combined effect of the funct...

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.

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.