Effects of extracellular matrix viscoelasticity on cellular behaviour.

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

Lipid droplets are intracellular mechanical stressors that impair hepatocyte function.

Matrix stiffening and external mechanical stress have been linked to disease and cancer development in multiple tissues, including the liver, where cirrhosis (which increases stiffness markedly) is the major risk factor for hepatocellular carcinoma. Patients with nonalcoholic fatty liver disease and lipid droplet-filled hepatocytes, however, can develop cancer in noncirrhotic, relatively soft tissue. Here, by treating primary human hepatocytes with the monounsaturated fatty acid oleate, we show that lipid droplets are intracellular mechanical stressors with similar effects to tissue stiffening, including nuclear deformation, chromatin condensation, and impaired hepatocyte function. Mathematical modeling of lipid droplets as inclusions that have only mechanical interactions with other cellular components generated results consistent with our experiments. These data show that lipid droplets are intracellular sources of mechanical stress and suggest that nuclear membrane tension integrates cell responses to combined internal and external stresses.

Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells.

The viscoelasticity of the crosslinked semiflexible polymer networks-such as the internal cytoskeleton and the extracellular matrix-that provide shape and mechanical resistance against deformation is assumed to dominate tissue mechanics. However, the mechanical responses of soft tissues and semiflexible polymer gels differ in many respects. Tissues stiffen in compression but not in extension1-5, whereas semiflexible polymer networks soften in compression and stiffen in extension6,7. In shear deformation, semiflexible polymer gels stiffen with increasing strain, but tissues do not1-8. Here we use multiple experimental systems and a theoretical model to show that a combination of nonlinear polymer network elasticity and particle (cell) inclusions is essential to mimic tissue mechanics that cannot be reproduced by either biopolymer networks or colloidal particle systems alone. Tissue rheology emerges from an interplay between strain-stiffening polymer networks and volume-conserving cells within them. Polymer networks that soften in compression but stiffen in extension can be converted to materials that stiffen in compression but not in extension by including within the network either cells or inert particles to restrict the relaxation modes of the fibrous networks that surround them. Particle inclusions also suppress stiffening in shear deformation; when the particle volume fraction is low, they have little effect on the elasticity of the polymer networks. However, as the particles become more closely packed, the material switches from compression softening to compression stiffening. The emergence of an elastic response in these composite materials has implications for how tissue stiffness is altered in disease and can lead to cellular dysfunction9-11. Additionally, the findings could be used in the design of biomaterials with physiologically relevant mechanical properties.

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.

Modeling links softening of myelin and spectrin scaffolds of axons after a concussion to increased vulnerability to repeated injuries.

Damage to the microtubule lattice, which serves as a rigid cytoskeletal backbone for the axon, is a hallmark mechanical initiator of pathophysiology after concussion. Understanding the mechanical stress transfer from the brain tissue to the axonal cytoskeleton is essential to determine the microtubule lattice's vulnerability to mechanical injury. Here, we develop an ultrastructural model of the axon's cytoskeletal architecture to identify the components involved in the dynamic load transfer during injury. Corroborative in vivo studies were performed using a gyrencephalic swine model of concussion via single and repetitive head rotational acceleration. Computational analysis of the load transfer mechanism demonstrates that the myelin sheath and the actin/spectrin cortex play a significant role in effectively shielding the microtubules from tissue stress. We derive failure maps in the space spanned by tissue stress and stress rate to identify physiological conditions in which the microtubule lattice can rupture. We establish that a softer axonal cortex leads to a higher susceptibility of the microtubules to failure. Immunohistochemical examination of tissue from the swine model of single and repetitive concussion confirms the presence of postinjury spectrin degradation, with more extensive pathology observed following repetitive injury. Because the degradation of myelin and spectrin occurs over weeks following the first injury, we show that softening of the myelin layer and axonal cortex exposes the microtubules to higher stress during repeated incidences of traumatic brain injuries. Our predictions explain how mechanical injury predisposes axons to exacerbated responses to repeated injuries, as observed in vitro and in vivo.

Collagen microarchitecture mechanically controls myofibroblast differentiation.

Altered microarchitecture of collagen type I is a hallmark of wound healing and cancer that is commonly attributed to myofibroblasts. However, it remains unknown which effect collagen microarchitecture has on myofibroblast differentiation. Here, we combined experimental and computational approaches to investigate the hypothesis that the microarchitecture of fibrillar collagen networks mechanically regulates myofibroblast differentiation of adipose stromal cells (ASCs) independent of bulk stiffness. Collagen gels with controlled fiber thickness and pore size were microfabricated by adjusting the gelation temperature while keeping their concentration constant. Rheological characterization and simulation data indicated that networks with thicker fibers and larger pores exhibited increased strain-stiffening relative to networks with thinner fibers and smaller pores. Accordingly, ASCs cultured in scaffolds with thicker fibers were more contractile, expressed myofibroblast markers, and deposited more extended fibronectin fibers. Consistent with elevated myofibroblast differentiation, ASCs in scaffolds with thicker fibers exhibited a more proangiogenic phenotype that promoted endothelial sprouting in a contractility-dependent manner. Our findings suggest that changes of collagen microarchitecture regulate myofibroblast differentiation and fibrosis independent of collagen quantity and bulk stiffness by locally modulating cellular mechanosignaling. These findings have implications for regenerative medicine and anticancer treatments.

Enhanced substrate stress relaxation promotes filopodia-mediated cell migration.

Cell migration on two-dimensional substrates is typically characterized by lamellipodia at the leading edge, mature focal adhesions and spread morphologies. These observations result from adherent cell migration studies on stiff, elastic substrates, because most cells do not migrate on soft, elastic substrates. However, many biological tissues are soft and viscoelastic, exhibiting stress relaxation over time in response to a deformation. Here, we have systematically investigated the impact of substrate stress relaxation on cell migration on soft substrates. We observed that cells migrate minimally on substrates with an elastic modulus of 2 kPa that are elastic or exhibit slow stress relaxation, but migrate robustly on 2-kPa substrates that exhibit fast stress relaxation. Strikingly, migrating cells were not spread out and did not extend lamellipodial protrusions, but were instead rounded, with filopodia protrusions extending at the leading edge, and exhibited small nascent adhesions. Computational models of cell migration based on a motor-clutch framework predict the observed impact of substrate stress relaxation on cell migration and filopodia dynamics. Our findings establish substrate stress relaxation as a key requirement for robust cell migration on soft substrates and uncover a mode of two-dimensional cell migration marked by round morphologies, filopodia protrusions and weak adhesions.

Regulation of nuclear architecture, mechanics, and nucleocytoplasmic shuttling of epigenetic factors by cell geometric constraints.

Cells sense mechanical signals from their microenvironment and transduce them to the nucleus to regulate gene expression programs. To elucidate the physical mechanisms involved in this regulation, we developed an active 3D chemomechanical model to describe the three-way feedback between the adhesions, the cytoskeleton, and the nucleus. The model shows local tensile stresses generated at the interface of the cell and the extracellular matrix regulate the properties of the nucleus, including nuclear morphology, levels of lamin A,C, and histone deacetylation, as these tensile stresses 1) are transmitted to the nucleus through cytoskeletal physical links and 2) trigger an actomyosin-dependent shuttling of epigenetic factors. We then show how cell geometric constraints affect the local tensile stresses and subsequently the three-way feedback and induce cytoskeleton-mediated alterations in the properties of the nucleus such as nuclear lamina softening, chromatin stiffening, nuclear lamina invaginations, increase in nuclear height, and shrinkage of nuclear volume. We predict a phase diagram that describes how the disruption of cytoskeletal components impacts the feedback and subsequently induce contractility-dependent alterations in the properties of the nucleus. Our simulations show that these changes in contractility levels can be also used as predictors of nucleocytoplasmic shuttling of transcription factors and the level of chromatin condensation. The predictions are experimentally validated by studying the properties of nuclei of fibroblasts on micropatterned substrates with different shapes and areas.

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.

Dynamic self-reinforcement of gene expression determines acquisition of cellular mechanical memory.

Mechanotransduction describes activation of gene expression by changes in the cell's physical microenvironment. Recent experiments show that mechanotransduction can lead to long-term "mechanical memory," in which cells cultured on stiff substrates for sufficient time (priming phase) maintain altered phenotype after switching to soft substrates (dissipation phase) as compared to unprimed controls. The timescale of memory acquisition and retention is orders of magnitude larger than the timescale of mechanosensitive cellular signaling, and memory retention time changes continuously with priming time. We develop a model that captures these features by accounting for positive reinforcement in mechanical signaling. The sensitivity of reinforcement represents the dynamic transcriptional state of the cell composed of protein lifetimes and three-dimensional chromatin organization. Our model provides a single framework connecting microenvironment mechanical history to cellular outcomes ranging from no memory to terminal differentiation. Predicting cellular memory of environmental changes can help engineer cellular dynamics through changes in culture environments.

Correction: Long-range mechanical signaling in biological systems.

Correction for 'Long-range mechanical signaling in biological systems' by Farid Alisafaei et al., Soft Matter, 2020, DOI: 10.1039/d0sm01442g.

Long-range mechanical signaling in biological systems.

Cells can respond to signals generated by other cells that are remarkably far away. Studies from at least the 1920's showed that cells move toward each other when the distance between them is on the order of a millimeter, which is many times the cell diameter. Chemical signals generated by molecules diffusing from the cell surface would move too slowly and dissipate too fast to account for these effects, suggesting that they might be physical rather than biochemical. The non-linear elastic responses of sparsely connected networks of stiff or semiflexible filament such as those that form the extracellular matrix (ECM) and the cytoskeleton have unusual properties that suggest multiple mechanisms for long-range signaling in biological tissues. These include not only direct force transmission, but also highly non-uniform local deformations, and force-generated changes in fiber alignment and density. Defining how fibrous networks respond to cell-generated forces can help design new methods to characterize abnormal tissues and can guide development of improved biomimetic materials.

Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates.

Recent evidence has shown that, in addition to rigidity, the viscous response of the extracellular matrix (ECM) significantly affects the behavior and function of cells. However, the mechanism behind such mechanosensitivity toward viscoelasticity remains unclear. In this study, we systematically examined the dynamics of motor clutches (i.e., focal adhesions) formed between the cell and a viscoelastic substrate using analytical methods and direct Monte Carlo simulation. Interestingly, we observe that, for low ECM rigidity, maximum cell spreading is achieved at an optimal level of viscosity in which the substrate relaxation time falls between the timescale for clutch binding and its characteristic binding lifetime. That is, viscosity serves to stiffen soft substrates on a timescale faster than the clutch off-rate, which enhances cell-ECM adhesion and cell spreading. On the other hand, for substrates that are stiff, our model predicts that viscosity will not influence cell spreading, since the bound clutches are saturated by the elevated stiffness. The model was tested and validated using experimental measurements on three different material systems and explained the different observed effects of viscosity on each substrate. By capturing the mechanism by which substrate viscoelasticity affects cell spreading across a wide range of material parameters, our analytical model provides a useful tool for designing biomaterials that optimize cellular adhesion and mechanosensing.

Mechanisms of Local Stress Amplification in Axons near the Gray-White Matter Interface.

Diffuse axonal injury is a primary neuropathological feature of concussion and is thought to greatly contribute to the classical symptoms of decreased processing speed and memory dysfunction. Although previous studies have investigated the injury biomechanics at the micro- and mesoscale of concussion, few have addressed the multiscale transmission of mechanical loading at thresholds that can induce diffuse axonal injury. Because it has been recognized that axonal pathology is commonly found at anatomic interfaces across all severities of traumatic brain injury, we combined computational, analytical, and experimental approaches to investigate the potential mechanical vulnerability of axons that span the gray-white tissue interface. Our computational models predict that material heterogeneities at the gray-white interface lead to a highly nonuniform distribution of stress in axons, which was most amplified in axonal regions near the interface. This mechanism was confirmed using an analytical model of an individual fiber in a strained bimaterial interface. Comparisons of these collective data with histopathological evaluation of a swine model of concussion demonstrated a notably similar pattern of axonal damage adjacent to the gray-white interface. The results suggest that the tissue property mismatch at the gray-white matter interface places axons crossing this region at greater risk of mechanical damage during brain tissue deformation from traumatic brain injury.

Tailoring Electronic and Optical Properties of MXenes through Forming Solid Solutions.

Alloying is a long-established strategy to tailor properties of metals for specific applications, thus retaining or enhancing the principal elemental characteristics while offering additional functionality from the added elements. We propose a similar approach to the control of properties of two-dimensional transition metal carbides known as MXenes. MXenes (Mn+1Xn) have two sites for compositional variation: elemental substitution on both the metal (M) and carbon/nitrogen (X) sites presents promising routes for tailoring the chemical, optical, electronic, or mechanical properties of MXenes. Herein, we systematically investigated three interrelated binary solid-solution MXene systems based on Ti, Nb, and/or V at the M-site in a M2XTx structure (Ti2-yNbyCTx, Ti2-yVyCTx, and V2-yNbyCTx, where Tx stands for surface terminations) showing the evolution of electronic and optical properties as a function of composition. All three MXene systems show unlimited solubility and random distribution of metal elements in the metal sublattice. Optically, the MXene systems are tailorable in a nonlinear fashion, with absorption peaks from ultraviolet to near-infrared wavelength. The macroscopic electrical conductivity of solid solution MXenes can be controllably varied over 3 orders of magnitude at room temperature and 6 orders of magnitude from 10 to 300 K. This work greatly increases the number of nonstoichiometric MXenes reported to date and opens avenues for controlling physical properties of different MXenes with a limitless number of compositions possible through M-site solid solutions.

Nuclear Mechanics within Intact Cells Is Regulated by Cytoskeletal Network and Internal Nanostructures.

The mechanical properties of the cellular nucleus are extensively studied as they play a critical role in important processes, such as cell migration, gene transcription, and stem cell differentiation. While the mechanical properties of the isolated nucleus have been tested, there is a lack of measurements about the mechanical behavior of the nucleus within intact cells and specifically about the interplay of internal nuclear components with the intracellular microenvironment, because current testing methods are based on contact and only allow studying the nucleus after isolation from a cell or disruption of cytoskeleton. Here, all-optical Brillouin microscopy and 3D chemomechanical modeling are used to investigate the regulation of nuclear mechanics in physiological conditions. It is observed that the nuclear modulus can be modulated by epigenetic regulation targeting internal nuclear nanostructures such as lamin A/C and chromatin. It is also found that nuclear modulus is strongly regulated by cytoskeletal behavior through a robust mechanism conserved in different culturing conditions. Given the active role of cytoskeletal modulation in nearly all cell functions, this work will enable to reveal highly relevant mechanisms of nuclear mechanical regulations in physiological and pathological conditions.

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.

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.

Engineering Magnetic Phases in Two-Dimensional Non-van der Waals Transition-Metal Oxides.

The family of 2D magnetic materials is continuously expanding because of the rapid discovery of exfoliable van der Waals magnetic systems. Recently, the synthesis of non-van der Waals magnetic "hematene" from common iron ore has opened an unconventional route to 2D material discovery. These non-van der Waals 2D systems are chemically stable and easily available and may have different or enhanced properties compared to their van der Waals counterparts. In this work, we have investigated and explained the nature of magnetic ordering in non-van der Waals 2D metal oxides. Two-dimensional hematene is found to be fully oxygen-passivated and stable under ambient conditions. It exhibits a striped ferrimagnetic ground state with a small net magnetic moment. Superexchange interactions are predicted to control the magnetic ground state of hematene, where pressure-induced spin crossover results in an observable net magnetic moment. Modulating the superexchange by alloying hematenes alters the magnetic ordering, tuning the system to a ferromagnetic ground state. Extending this strategy to the design of a new 2D material, we propose 2D chromia (α-Cr2O3) or "chromene", which, because of larger inter-transition metal distances and suppressed AFM superexchange, has a ferromagnetic ground state. We also show that tuning the magnetic ordering in these materials controls the transport properties by modulating the band gap, which may be of use in spintronic or catalytic applications.

Tension- and Adhesion-Regulated Retraction of Injured Axons.

Damage-induced retraction of axons during traumatic brain injury is believed to play a key role in the disintegration of the neural network and to eventually lead to severe symptoms such as permanent memory loss and emotional disturbances. However, fundamental questions such as how axon retraction progresses and what physical factors govern this process still remain unclear. Here, we report a combined experimental and modeling study to address these questions. Specifically, a sharp atomic force microscope probe was used to transect axons and trigger their retraction in a precisely controlled manner. Interestingly, we showed that the retracting motion of a well-developed axon can be arrested by strong cell-substrate attachment. However, axon retraction was found to be retriggered if a second transection was conducted, albeit with a lower shrinking amplitude. Furthermore, disruption of the actin cytoskeleton or cell-substrate adhesion significantly altered the retracting dynamics of injured axons. Finally, a mathematical model was developed to explain the observed injury response of neural cells in which the retracting motion was assumed to be driven by the pre-tension in the axon and progress against neuron-substrate adhesion as well as the viscous resistance of the cell. Using realistic parameters, model predictions were found to be in good agreement with our observations under a variety of experimental conditions. By revealing the essential physics behind traumatic axon retraction, findings here could provide insights on the development of treatment strategies for axonal injury as well as its possible interplay with other neurodegenerative diseases.