Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.     

Orientations of Cells on Compliant Substrates under Biaxial Stretches: A Theoretical Study

Mechanical cues from the microenvironments play a regulating role in many physiological and pathological processes, such as stem cell differentiation and cancer cell metastasis. Experiments showed that cells adhered on a compliant substrate may change orientation with an externally applied strain in the substrate. By accounting for actin polymerization, actin retrograde flow, and integrin binding dynamics, here we develop a mechanism-based tensegrity model to study the orientations of polarized cells on a compliant substrate under biaxial stretches. We show that the cell can actively regulate its mechanical state by generating different traction force levels along its polarized direction. Under static or ultralow-frequency cyclic stretches, stretching a softer substrate leads to a higher increase in the traction force and induces a narrower distribution of cell alignment. Compared to static loadings, high-frequency cyclic loadings have a more significant influence on cell reorientation on a stiff substrate. In addition, the width of the cellular angular distribution scales inversely with the stretch amplitude under both static and cyclic stretches. Our results are in agreement with a wide range of experimental observations, and provide fundamental insights into the functioning of cellular mechanosensing systems.     

Eigenstrain as a mechanical set-point of cells

Cell contraction regulates how cells sense their mechanical environment. We sought to identify the set-point of cell contraction, also referred to as tensional homeostasis. In this work, bovine aortic endothelial cells (BAECs), cultured on substrates with different stiffness, were characterized using traction force microscopy (TFM). Numerical models were developed to provide insights into the mechanics of cell–substrate interactions. Cell contraction was modeled as eigenstrain which could induce isometric cell contraction without external forces. The predicted traction stresses matched well with TFM measurements. Furthermore, our numerical model provided cell stress and displacement maps for inspecting the fundamental regulating mechanism of cell mechanosensing. We showed that cell spread area, traction force on a substrate, as well as the average stress of a cell were increased in response to a stiffer substrate. However, the cell average strain, which is cell type-specific, was kept at the same level regardless of the substrate stiffness. This indicated that the cell average strain is the tensional homeostasis that each type of cell tries to maintain. Furthermore, cell contraction in terms of eigenstrain was found to be the same for both BAECs and fibroblast cells in different mechanical environments. This implied a potential mechanical set-point across different cell types. Our results suggest that additional measurements of contractility might be useful for monitoring cell mechanosensing as well as dynamic remodeling of the extracellular matrix (ECM). This work could help to advance the understanding of the cell-ECM relationship, leading to better regenerative strategies.     

Fibroblast polarization is a matrix-rigidity-dependent process controlled by focal adhesion mechanosensing

Cell elongation and polarization are basic morphogenetic responses to extracellular matrix adhesion. We demonstrate here that human cultured fibroblasts readily polarize when plated on rigid, but not on compliant, substrates. On rigid surfaces, large and uniformly oriented focal adhesions are formed, whereas cells plated on compliant substrates form numerous small and radially oriented adhesions. Live-cell monitoring showed that focal adhesion alignment precedes the overall elongation of the cell, indicating that focal adhesion orientation may direct cell polarization. siRNA-mediated knockdown of 85 human protein tyrosine kinases (PTKs) induced distinct alterations in the cell polarization response, as well as diverse changes in cell traction force generation and focal adhesion formation. Remarkably, changes in rigidity-dependent traction force development, or focal adhesion mechanosensing, were consistently accompanied by abnormalities in the cell polarization response. We propose that the different stages of cell polarization are regulated by multiple, PTK-dependent molecular checkpoints that jointly control cell contractility and focal-adhesion-mediated mechanosensing.     

Cell spread area and traction forces determine myosin-II-based cortex thickness regulation

Actomyosin network under the plasma membrane of cells forms a cortical layer that regulates cellular deformations during different processes. What regulates the cortex? Characterized by its thickness, it is believed to be regulated by actin dynamics, filament-length regulators and myosin motor proteins. However, its regulation by cellular morphology (e.g. cell spread area) or mechanical microenvironment (e.g. substrate stiffness) has remained largely unexplored. In this study, super- and high-resolution imaging of actin in CHO cells demonstrates that at high spread areas (>450 μm²), the cortex is thinner, better separated as layers, and sensitive to deactivation of myosin II motors or reduction of substrate stiffness (and traction forces). In less spread cells (<400 μm²) such perturbations do not elicit a response. Myosin IIA's mechanosensing is limited here due to its lowered actin-bound fraction and higher turnover rate. Cofilin, in line with its competitive inhibitory role, is found to be overexpressed in these cells. To establish the causal relation, we initiate a spread area drop by de-adhesion and find enhanced actin dynamics and fragmentation along with oscillations and increase in thickness. This is more correlated to the reduction of traction forces than the endocytosis-based reduction in cell volume. Cortex thickness control by spread area is also found be true during differentiation of THP-1 monocytes to macrophages. Thus, we propose that spread area regulates cortex and its thickness by traction-based mechanosensing of myosin II.     

Traction Stresses and Translational Distortion of the Nucleus During Fibroblast Migration on a Physiologically Relevant ECM Mimic

Cellular traction forces, resulting in cell-substrate physical interactions, are generated by actin-myosin complexes and transmitted to the extracellular matrix through focal adhesions. These processes are highly dynamic under physiological conditions and modulate cell migration. To better understand the precise dynamics of cell migration, we measured the spatiotemporal redistribution of cellular traction stresses (force per area) during fibroblast migration at a submicron level and correlated it with nuclear translocation, an indicator of cell migration, on a physiologically relevant extracellular matrix mimic. We found that nuclear translocation occurred in pulses whose magnitude was larger on the low ligand density surfaces than on the high ligand density surfaces. Large nuclear translocations only occurred on low ligand density surfaces when the rear traction stresses completely relocated to a posterior nuclear location, whereas such relocation took much longer time on high ligand density surfaces, probably due to the greater magnitude of traction stresses. Nuclear distortion was also observed as the traction stresses redistributed. Our results suggest that the reinforcement of the traction stresses around the nucleus as well as the relaxation of nuclear deformation are critical steps during fibroblast migration, serving as a speed regulator, which must be considered in any dynamic molecular reconstruction model of tissue cell migration. A traction gradient foreshortening model was proposed to explain how the relocation of rear traction stresses leads to pulsed fibroblast migration.     

Mechanosensitive axon outgrowth mediated by L1-laminin clutch interface

Mechanical properties of the extracellular environment modulate axon outgrowth. Growth cones at the tip of extending axons generate traction force for axon outgrowth by transmitting the force of actin filament retrograde flow, produced by actomyosin contraction and F-actin polymerization, to adhesive substrates through clutch and cell adhesion molecules. A molecular clutch between the actin filament flow and substrate is proposed to contribute to cellular mechanosensing. However, the molecular identity of the clutch interface responsible for mechanosensitive growth cone advance is unknown. We previously reported that mechanical coupling between actin filament retrograde flow and adhesive substrates through the clutch molecule shootin1a and the cell adhesion molecule L1 generates traction force for axon outgrowth and guidance. Here, we show that cultured mouse hippocampal neurons extend longer axons on stiffer substrates under elastic conditions that correspond to the soft brain environments. We demonstrate that this stiffness-dependent axon outgrowth requires actin-adhesion coupling mediated by shootin1a, L1, and laminin on the substrate. Speckle imaging analyses showed that L1 at the growth cone membrane switches between two adhesive states: L1 that is immobilized and that undergoes retrograde movement on the substrate. The duration of the immobilized phase was longer on stiffer substrates; this was accompanied by increases in actin-adhesion coupling and in the traction force exerted on the substrate. These data suggest that the interaction between L1 and laminin is enhanced on stiffer substrates, thereby promoting force generation for axon outgrowth.     

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.     

A minimal mechanics model for mechanosensing of substrate rigidity gradient in durotaxis

Durotaxis refers to the phenomenon in which cells can sense the spatial gradient of the substrate rigidity in the process of cell migration. A conceptual two-part theory consisting of the focal adhesion force generation and mechanotransduction has been proposed previously by Lo et al. to explain the mechanism underlying durotaxis. In the present work, we are concerned with the first part of the theory: how exactly is the larger focal adhesion force generated in the part of the cell adhering to the stiffer region of the substrate? Using a simple elasticity model and by assuming the cell adheres to the substrate continuously underneath the whole cell body, we show that the mechanics principle of static equilibrium alone is sufficient to account for the generation of the larger traction stress on the stiffer region of the substrate. We believe that our model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering.     

Mechanical Checkpoint For Persistent Cell Polarization In Adhesion-Naive Fibroblasts

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.     

Mechanical Checkpoint For Persistent Cell Polarization In Adhesion-Naive Fibroblasts

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.     

Integrin diversity brings specificity in mechanotransduction

Cells sense and respond to the biochemical and physical properties of the extracellular matrix (ECM) through adhesive structures that bridge the cell cytoskeleton and the surrounding environment. Integrin‐mediated adhesions interact with specific ECM proteins and sense the rigidity of the substrate to trigger signalling pathways that, in turn, regulate cellular processes such as adhesion, motility, proliferation and differentiation. This process, called mechanotransduction, influenced by the involvement of different integrin subtypes and their high ECM–ligand binding specificity, contributes to the cell‐type‐specific mechanical responses. In this review, we describe how the expression of particular integrin subtypes affects cellular adaptation to substrate rigidity. We then explain the role of integrins and associated proteins in mechanotransduction, focusing on their specificity in mechanosensing and force transmission.     

Guidance of Cell Migration by Substrate Dimension

There is increasing evidence to suggest that physical parameters, including substrate rigidity, topography, and cell geometry, play an important role in cell migration. As there are significant differences in cell behavior when cultured in 1D, 2D, or 3D environments, we hypothesize that migrating cells are also able to sense the dimension of the environment as a guidance cue. NIH 3T3 fibroblasts were cultured on micropatterned substrates where the path of migration alternates between 1D lines and 2D rectangles. We found that 3T3 cells had a clear preference to stay on 2D rather than 1D substrates. Cells on 2D surfaces generated stronger traction stress than did those on 1D surfaces, but inhibition of myosin II caused cells to lose their sensitivity to substrate dimension, suggesting that myosin-II-dependent traction forces are the determining factor for dimension sensing. Furthermore, oncogene-transformed fibroblasts are defective in mechanosensing while generating similar traction forces on 1D and 2D surfaces. Dimension sensing may be involved in guiding cell migration for both physiological functions and tissue engineering, and for maintaining normal cells in their home tissue.     

Integrin-based mechanosensing through conformational deformation

Conversion of integrins from low to high affinity states, termed activation, is important in biological processes, including immunity, hemostasis, angiogenesis, and embryonic development. Integrin activation is regulated by large-scale conformational transitions from closed, low affinity states to open, high affinity states. Although it has been suggested that substrate stiffness shifts the conformational equilibrium of integrin and governs its unbinding, here, we address the role of integrin conformational activation in cellular mechanosensing. Comparison of wild-type versus activating mutants of integrin αVβ3 show that activating mutants shift cell spreading, focal adhesion kinase activation, traction stress, and force on talin toward high stiffness values at lower stiffness. Although all activated integrin mutants showed equivalent binding affinity for soluble ligands, the β3 S243E mutant showed the strongest shift in mechanical responses. To understand this behavior, we used coarse-grained computational models derived from molecular level information. The models predicted that wild-type integrin αVβ3 displaces under force and that activating mutations shift the required force toward lower values, with S243E showing the strongest effect. Cellular stiffness sensing thus correlates with computed effects of force on integrin conformation. Together, these data identify a role for force-induced integrin conformational deformation in cellular mechanosensing.     

Distinct Roles of Frontal and Rear Cell-Substrate Adhesions in Fibroblast Migration

Cell migration involves complex physical and chemical interactions with the substrate. To probe the mechanical interactions under different regions of migrating 3T3 fibroblasts, we have disrupted cell-substrate adhesions by local application of the GRGDTP peptide, while imaging stress distribution on the substrate with traction force microscopy. Both spontaneous and GRGDTP-induced detachment of the trailing edge caused extensive cell shortening, without changing the overall level of traction forces or the direction of migration. In contrast, disruption of frontal adhesions caused dramatic, global loss of traction forces before any significant shortening of the cell. Although traction forces and cell migration recovered within 10-20 min of transient frontal treatment, persistent treatment with GRGDTP caused the cell to develop traction forces elsewhere and reorient toward a new direction. We conclude that contractile forces of a fibroblast are transmitted to the substrate through two distinct types of adhesions. Leading edge adhesions are unique in their ability to transmit active propulsive forces. Their functions cannot be transferred directly to existing adhesions upon detachment. Trailing end adhesions create passive resistance during cell migration and readily redistribute their loads upon detachment. Our results indicate the distinct nature of mechanical interactions at the leading versus trailing edges, which together generate the mechanical interactions for fibroblast migration.     

Filamin structure,function and mechanics: are altered filamin-mediated force responses associated with human disease?

The cytoskeleton framework is essential not only for cell structure and stability but also for dynamic processes such as cell migration, division and differentiation. The F-actin cytoskeleton is mechanically stabilised and regulated by various actin-binding proteins, one family of which are the filamins that cross-link F-actin into networks that greatly alter the elastic properties of the cytoskeleton. Filamins also interact with cell membrane-associated extracellular matrix receptors and intracellular signalling proteins providing a potential mechanism for cells to sense their external environment by linking these signalling systems. The stiffness of the external matrix to which cells are attached is an important environmental variable for cellular behaviour. In order for a cell to probe matrix stiffness, a mechanosensing mechanism functioning via alteration of protein structure and/or binding events in response to external tension is required. Current structural, mechanical, biochemical and human disease-associated evidence suggests filamins are good candidates for a role in mechanosensing.     

High Resolution,Large Deformation 3D Traction Force Microscopy

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients.     

Reinforcement versus Fluidization in Cytoskeletal Mechanoresponsiveness

Every adherent eukaryotic cell exerts appreciable traction forces upon its substrate. Moreover, every resident cell within the heart, great vessels, bladder, gut or lung routinely experiences large periodic stretches. As an acute response to such stretches the cytoskeleton can stiffen, increase traction forces and reinforce, as reported by some, or can soften and fluidize, as reported more recently by our laboratory, but in any given circumstance it remains unknown which response might prevail or why. Using a novel nanotechnology, we show here that in loading conditions expected in most physiological circumstances the localized reinforcement response fails to scale up to the level of homogeneous cell stretch; fluidization trumps reinforcement. Whereas the reinforcement response is known to be mediated by upstream mechanosensing and downstream signaling, results presented here show the fluidization response to be altogether novel: it is a direct physical effect of mechanical force acting upon a structural lattice that is soft and fragile. Cytoskeletal softness and fragility, we argue, is consistent with early evolutionary adaptations of the eukaryotic cell to material properties of a soft inert microenvironment.     

A Novel Cell Traction Force Microscopy to Study Multi-Cellular System

Traction forces exerted by adherent cells on their microenvironment can mediate many critical cellular functions. Accurate quantification of these forces is essential for mechanistic understanding of mechanotransduction. However, most existing methods of quantifying cellular forces are limited to single cells in isolation, whereas most physiological processes are inherently multi-cellular in nature where cell-cell and cell-microenvironment interactions determine the emergent properties of cell clusters. In the present study, a robust finite-element-method-based cell traction force microscopy technique is developed to estimate the traction forces produced by multiple isolated cells as well as cell clusters on soft substrates. The method accounts for the finite thickness of the substrate. Hence, cell cluster size can be larger than substrate thickness. The method allows computing the traction field from the substrate displacements within the cells'' and clusters'' boundaries. The displacement data outside these boundaries are not necessary. The utility of the method is demonstrated by computing the traction generated by multiple monkey kidney fibroblasts (MKF) and human colon cancerous (HCT-8) cells in close proximity, as well as by large clusters. It is found that cells act as individual contractile groups within clusters for generating traction. There may be multiple of such groups in the cluster, or the entire cluster may behave a single group. Individual cells do not form dipoles, but serve as a conduit of force (transmission lines) over long distances in the cluster. The cell-cell force can be either tensile or compressive depending on the cell-microenvironment interactions.     

The Effect of Substrate Elasticity and Actomyosin Contractility on Different Forms of Endocytosis

Substrate mechanical properties have emerged as potent determinants of cell functions and fate. We here tested the hypothesis that different forms of endocytosis are regulated by the elasticity of the synthetic hydrogels cells are cultured on. Towards this objective, we quantified cell-associated fluorescence of the established endocytosis markers transferrin (Tf) and cholera toxin subunit B (CTb) using a flow-cytometry based protocol, and imaged marker internalization using microscopy techniques. Our results demonstrated that clathrin-mediated endocytosis of Tf following a 10-minute incubation with a fibroblast cell line was lower on the softer substrates studied (5 kPa) compared to those with elasticities of 40 and 85 kPa. This effect was cancelled after 1-hour incubation revealing that intracellular accumulation of Tf at this time point did not depend on substrate elasticity. Lipid-raft mediated endocytosis of CTb, on the other hand, was not affected by substrate elasticity in the studied range of time and substrate elasticity. The use of pharmacologic contractility inhibitors revealed inhibition of endocytosis for both Tf and CTb after a 10-minute incubation and a dissimilar effect after 1 hour depending on the inhibitor type. Further, the internalization of fluorescent NPs, used as model drug delivery systems, showed a dependence on substrate elasticity, while transfection efficiency was unaffected by it. Finally, an independence on substrate elasticity of Tf and CTb association with HeLa cells indicated that there are cell-type differences in this respect. Overall, our results suggest that clathrin-mediated but not lipid-raft mediated endocytosis is potentially influenced by substrate mechanics at the cellular level, while intracellular trafficking and accumulation show a more complex dependence. Our findings are discussed in the context of previous work on how substrate mechanics affect the fundamental process of endocytosis and highlight important considerations for future studies.