Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.     

The asymmetric self-assembly mechanism of adherens junctions: a cellular push-pull unit

To form adherens junctions (AJ), cells first establish contact by sending out lamellipodia onto neighboring cells. We investigated the role of contacting cells in AJ assembly by studying an asymmetric AJ motif: finger-like AJ extending across the cell-cell interface. Using a cytoskeleton replica and immunofluorescence, we observed that actin bundles embedded in the lamellipodia are co-localized with stress fibers in the neighboring cell at the AJ. This suggests that donor lamellipodia present actin fingers, which are stabilized by acceptor lamellae via acto-myosin contractility. Indeed, we show that changes in actin network geometry promoted by Rac overexpression lead to corresponding changes in AJ morphology. Moreover, contractility inhibition and enhancement (via drugs or local traction) lead respectively to the disappearance and further growth of AJ fingers. Thus, we propose that receiving lamellae exert a local pull on AJ, promoting further polymerization of the donor actin bundles. In spite of different compositions, AJ and focal contacts both act as cellular mechanosensors.     

Stress fibers are generated by two distinct actin assembly mechanisms in motile cells

Stress fibers play a central role in adhesion, motility, and morphogenesis of eukaryotic cells, but the mechanism of how these and other contractile actomyosin structures are generated is not known. By analyzing stress fiber assembly pathways using live cell microscopy, we revealed that these structures are generated by two distinct mechanisms. Dorsal stress fibers, which are connected to the substrate via a focal adhesion at one end, are assembled through formin (mDia1/DRF1)-driven actin polymerization at focal adhesions. In contrast, transverse arcs, which are not directly anchored to substrate, are generated by endwise annealing of myosin bundles and Arp2/3-nucleated actin bundles at the lamella. Remarkably, dorsal stress fibers and transverse arcs can be converted to ventral stress fibers anchored to focal adhesions at both ends. Fluorescence recovery after photobleaching analysis revealed that actin filament cross-linking in stress fibers is highly dynamic, suggesting that the rapid association-dissociation kinetics of cross-linkers may be essential for the formation and contractility of stress fibers. Based on these data, we propose a general model for assembly and maintenance of contractile actin structures in cells.     

Hysteresis in the Cell Response to Time-Dependent Substrate Stiffness

Mechanical cues like the rigidity of the substrate are main determinants for the decision-making of adherent cells. Here we use a mechano-chemical model to predict the cellular response to varying substrate stiffnesses. The model equations combine the mechanics of contractile actin filament bundles with a model for the Rho-signaling pathway triggered by forces at cell-matrix contacts. A bifurcation analysis of cellular contractility as a function of substrate stiffness reveals a bistable response, thus defining a lower threshold of stiffness, below which cells are not able to build up contractile forces, and an upper threshold of stiffness, above which cells are always in a strongly contracted state. Using the full dynamical model, we predict that rate-dependent hysteresis will occur in the cellular traction forces when cells are exposed to substrates of time-dependent stiffness.     

Mobility of filamentous actin in living cytoplasm

Filamentous actin in living cultured cells was labeled by microinjecting trace amounts of rhodamine-phalloidin (rh-pha) as a specific, high-affinity probe. The microinjection caused no detectable effect on cell morphology or cell division. The distribution of rh-pha- labeled filaments was then examined in dividing cells using image- intensified fluorescence microscopy, and the exchangeability of labeled filaments along stress fibers was studied during interphase using fluorescence recovery after photobleaching. rh-pha showed a rapid concentration at the contractile ring during cell division. In addition, recovery of fluorescence after photobleaching occurred along stress fibers with a halftime as short as 8 min. These observations suggest that at least some actin filaments undergo continuous movement and reorganization in living cells. This dynamic process may play an important role in various cellular functions.     

Ventral stress fibers induce plasma membrane deformation in human fibroblasts

Interactions between the actin cytoskeleton and the plasma membrane are important in many eukaryotic cellular processes. During these processes, actin structures deform the cell membrane outward by applying forces parallel to the fiber’s major axis (as in migration) or they deform the membrane inward by applying forces perpendicular to the fiber’s major axis (as in the contractile ring during cytokinesis). Here we describe a novel actin–membrane interaction in human dermal myofibroblasts. When labeled with a cytosolic fluorophore, the myofibroblasts displayed prominent fluorescent structures on the ventral side of the cell. These structures are present in the cell membrane and colocalize with ventral actin stress fibers, suggesting that the stress fibers bend the membrane to form a “cytosolic pocket” that the fluorophores diffuse into, creating the observed structures. The existence of this pocket was confirmed by transmission electron microscopy. While dissolving the stress fibers, inhibiting fiber protein binding, or inhibiting myosin II binding of actin removed the observed pockets, modulating cellular contractility did not remove them. Taken together, our results illustrate a novel actin–membrane bending topology where the membrane is deformed outward rather than being pinched inward, resembling the topological inverse of the contractile ring found in cytokinesis.     

Interactions between myosin and actin crosslinkers control cytokinesis contractility dynamics and mechanics

INTRODUCTION: Contractile networks are fundamental to many cellular functions, particularly cytokinesis and cell motility. Contractile networks depend on myosin-II mechanochemistry to generate sliding force on the actin polymers. However, to be contractile, the networks must also be crosslinked by crosslinking proteins, and to change the shape of the cell, the network must be linked to the plasma membrane. Discerning how this integrated network operates is essential for understanding cytokinesis contractility and shape control. Here, we analyzed the cytoskeletal network that drives furrow ingression in Dictyostelium. RESULTS: We establish that the actin polymers are assembled into a meshwork and that myosin-II does not assemble into a discrete ring in the Dictyostelium cleavage furrow of adherent cells. We show that myosin-II generates regional mechanics by increasing cleavage furrow stiffness and slows furrow ingression during late cytokinesis as compared to myoII nulls. Actin crosslinkers dynacortin and fimbrin similarly slow furrow ingression and contribute to cell mechanics in a myosin-II-dependent manner. By using FRAP, we show that the actin crosslinkers have slower kinetics in the cleavage furrow cortex than in the pole, that their kinetics differ between wild-type and myoII null cells, and that the protein dynamics of each crosslinker correlate with its impact on cortical mechanics. CONCLUSIONS: These observations suggest that myosin-II along with actin crosslinkers establish local cortical tension and elasticity, allowing for contractility independent of a circumferential cytoskeletal array. Furthermore, myosin-II and actin crosslinkers may influence each other as they modulate the dynamics and mechanics of cell-shape change.     

Dynamic and structural signatures of lamellar actomyosin force generation

The regulation of cellular traction forces on the extracellular matrix is critical to cell adhesion, migration, proliferation, and differentiation. Diverse lamellar actin organizations ranging from contractile lamellar networks to stress fibers are observed in adherent cells. Although lamellar organization is thought to reflect the extent of cellular force generation, understanding of the physical behaviors of the lamellar actin cytoskeleton is lacking. To elucidate these properties, we visualized the actomyosin dynamics and organization in U2OS cells over a broad range of forces. At low forces, contractile lamellar networks predominate and force generation is strongly correlated to actomyosin retrograde flow dynamics with nominal change in organization. Lamellar networks build ～60% of cellular tension over rapid time scales. At high forces, reorganization of the lamellar network into stress fibers results in moderate changes in cellular tension over slower time scales. As stress fibers build and tension increases, myosin band spacing decreases and α-actinin bands form. On soft matrices, force generation by lamellar networks is unaffected, whereas tension-dependent stress fiber assembly is abrogated. These data elucidate the dynamic and structural signatures of the actomyosin cytoskeleton at different levels of tension and set a foundation for quantitative models of cell and tissue mechanics.     

Pluripotency of embryonic stem cells lacking clathrin-mediated endocytosis cannot be rescued by restoring cellular stiffness

Mouse embryonic stem cells (mESCs) display unique mechanical properties, including low cellular stiffness in contrast to differentiated cells, which are stiffer. We have previously shown that mESCs lacking the clathrin heavy chain (Cltc), an essential component for clathrin-mediated endocytosis (CME), display a loss of pluripotency and an enhanced expression of differentiation markers. However, it is not known whether physical properties such as cellular stiffness also change upon loss of Cltc, similar to what is seen in differentiated cells, and if so, how these altered properties specifically impact pluripotency. Using atomic force microscopy (AFM), we demonstrate that mESCs lacking Cltc display higher Young''s modulus, indicative of greater cellular stiffness, compared with WT mESCs. The increase in stiffness was accompanied by the presence of actin stress fibers and accumulation of the inactive, phosphorylated, actin-binding protein cofilin. Treatment of Cltc knockdown mESCs with actin polymerization inhibitors resulted in a decrease in the Young''s modulus to values similar to those obtained with WT mESCs. However, a rescue in the expression profile of pluripotency factors was not obtained. Additionally, whereas WT mouse embryonic fibroblasts could be reprogrammed to a state of pluripotency, this was inhibited in the absence of Cltc. This indicates that the presence of active CME is essential for the pluripotency of embryonic stem cells. Additionally, whereas physical properties may serve as a simple readout of the cellular state, they may not always faithfully recapitulate the underlying molecular fate.     

Mechanical properties of actin stress fibers in living cells

Actin stress fibers (SFs) play an important role in many cellular functions, including morphological stability, adhesion, and motility. Because of their central role in force transmission, it is important to characterize the mechanical properties of SFs. However, most of the existing studies focus on properties of whole cells or of actin filaments isolated outside cells. In this study, we explored the mechanical properties of individual SFs in living endothelial cells by nanoindentation using an atomic force microscope. Our results demonstrate the pivotal role of SF actomyosin contractile level on mechanical properties. In the same SF, decreasing contractile level with 10 μM blebbistatin decreased stiffness, whereas increasing contractile level with 2 nM calyculin A increased stiffness. Incrementally stretching and indenting SFs made it possible to determine stiffness as a function of strain level and demonstrated that SFs have nearly linear stress-stain properties in the baseline state but nonlinear properties at a lower contractile level. The stiffnesses of peripheral and central portions of the same SF, which were nearly the same in the baseline state, became markedly different after contractile level was increased with calyculin A. Because these results pertain to effects of interventions in the same SF in a living cell, they provide important new understanding about cell mechanics.     

A multi-modular tensegrity model of an actin stress fiber

Stress fibers are contractile bundles in the cytoskeleton that stabilize cell structure by exerting traction forces on the extracellular matrix. Individual stress fibers are molecular bundles composed of parallel actin and myosin filaments linked by various actin-binding proteins, which are organized end-on-end in a sarcomere-like pattern within an elongated three-dimensional network. While measurements of single stress fibers in living cells show that they behave like tensed viscoelastic fibers, precisely how this mechanical behavior arises from this complex supramolecular arrangement of protein components remains unclear. Here we show that computationally modeling a stress fiber as a multi-modular tensegrity network can predict several key behaviors of stress fibers measured in living cells, including viscoelastic retraction, fiber splaying after severing, non-uniform contraction, and elliptical strain of a puncture wound within the fiber. The tensegrity model can also explain how they simultaneously experience passive tension and generate active contraction forces; in contrast, a tensed cable net model predicts some, but not all, of these properties. Thus, tensegrity models may provide a useful link between molecular and cellular scale mechanical behaviors and represent a new handle on multi-scale modeling of living materials.     

Experimental and Computational Investigation of the Role of Stress Fiber Contractility in the Resistance of Osteoblasts to Compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell’s actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.     

The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

Abstract

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.     

Differential response of three types of actin filament bundles to depletion of cellular ATP levels

The effect of low levels of ATP on actin filament bundles in PtK2 cells was investigated by using 2-deoxyglucose, together with either sodium cyanide, sodium azide, or 2,4-dinitrophenol. Three actin filament systems were examined: stress fibers, cleavage rings, and dimethyl-sulfoxide (DMSO)-induced actin bundles in the nucleus. Of the three, only stress fibers disassembled when the ATP production was inhibited. The disassembly progressed slowly with the cells losing all stress fibers after about 90 min, but remaining in flat interconnected sheets. Mitotic cells that had progressed as far as metaphase when inhibitors were added, assembled cleavage rings. The process of cytokinesis took place in these cells but at a rate 5 to 10 times slower than normal, and disassembly of the cleavage ring was inhibited after the completion of cytokinesis. DMSO-induced nuclear actin bundles did not disassemble in cells depleted of ATP even when DMSO was eliminated from the medium. The peripheral aggregates of contractile proteins present in these cells became redistributed, however, and the cells flattened in the low ATP environment when DMSO was removed. Nuclear actin bundles did not form in DMSO-treated cells if the ATP inhibitors were present for as little as 5 min prior to DMSO exposure. Thus, the three types of actin filament bundles are affected in different ways by low intracellular levels of ATP. Stress fibers are most sensitive and cleavage rings, the least.     

Cellular stiffness response to external deformation: tensional homeostasis in a single fibroblast

Stiffness responses of fibroblasts were measured by scanning probe microscopy, following elongation or compression by deformation of an elastic substrate by 8%. The cellular stiffness, reflecting intracellular tension acting along stress fibers, decreased or increased instantly in response to the elongating or compressing stimuli, respectively. After this rapid change, the fibroblasts gradually recovered to their initial stiffness during the following 2 h, and then stabilized. The cells did not show conspicuous changes in shape after the 8% deformation during the SPM measurements. Fluorescence examination for GFP-actin demonstrated that the structure of the stress fibers was not altered noticeably by this small degree of deformation. Treatment with Y-27632, to inhibit myosin phosphorylation and abrogate cellular contractility, eliminated the change in stiffness after the mechanical elongation. These results indicate that fibroblasts possess a mechanism that regulates intracellular tension along stress fibers to maintain the cellular stiffness in a constant equilibrium state.     

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.     

Atomic force microscope-based single cell force spectroscopy of breast cancer cell lines: An approach for evaluating cellular invasion

The adhesiveness of cancerous cells to their neighboring cells significantly contributes to tumor progression and metastasis. The single-cell force spectroscopy (SCFS) approach was implemented to survey the cell–cell adhesion force between cancerous cells in three cancerous breast cell lines (MCF-7, T47D, and MDA-MB-231). The gene expression levels of two dominant cell adhesion markers (E-cadherin and N-cadherin) were quantified by real-time PCR. Additionally, the local stiffness of the cell bodies was measured by atomic force microscopy (AFM), and the actin cytoskeletal organization was examined by confocal microscopy. Results indicated that the adhesion force between cells was conversely correlated with their invasion potential. The highest adhesion force was observed in the MCF-7 cells. A reduction in cell–cell adhesion, which is required for the detachment of cells from the main tumor during metastasis, is partly due to the loss of E-cadherin expression and the enhanced expression of N-cadherins. The reduced adhesion was accompanied by the softening of cells, as described by the rearrangement of actin filaments through confocal microscopy observations. The softening of the cell body and the reduced cellular adhesiveness are two adaptive mechanisms through which malignant cells achieve the increased deformability, motility, and strong metastasis potential necessary for passage through endothelial junctions and positioning in host tissue. This study presented application of SCFS to survey cell phenotype transformation during cancer progression. The results can be implemented as a platform for further investigations that target the manipulation of cellular adhesiveness and stiffness as a therapeutic choice.     

The RhoGEF TEM4 Regulates Endothelial Cell Migration by Suppressing Actomyosin Contractility

Persistent cellular migration requires efficient protrusion of the front of the cell, the leading edge where the actin cytoskeleton and cell-substrate adhesions undergo constant rearrangement. Rho family GTPases are essential regulators of the actin cytoskeleton and cell adhesion dynamics. Here, we examined the role of the RhoGEF TEM4, an activator of Rho family GTPases, in regulating cellular migration of endothelial cells. We found that TEM4 promotes the persistence of cellular migration by regulating the architecture of actin stress fibers and cell-substrate adhesions in protruding membranes. Furthermore, we determined that TEM4 regulates cellular migration by signaling to RhoC as suppression of RhoC expression recapitulated the loss-of-TEM4 phenotypes, and RhoC activation was impaired in TEM4-depleted cells. Finally, we showed that TEM4 and RhoC antagonize myosin II-dependent cellular contractility and the suppression of myosin II activity rescued the persistence of cellular migration of TEM4-depleted cells. Our data implicate TEM4 as an essential regulator of the actin cytoskeleton that ensures proper membrane protrusion at the leading edge of migrating cells and efficient cellular migration via suppression of actomyosin contractility.     

The mechanochemistry of cytoskeletal force generation

In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the non-equilibrium thermodynamics, which is necessary to address the mechanics as well as the chemistry of dynamic cell contractility. In this setting, we are able to develop a framework that relates (a) the dynamics of force generation within the cell and (b) the cell’s response to external stimuli to the chemical processes occurring within the cell, as well as to the mechanics of linkage between the stress fibers, focal adhesions and extracellular matrix.     

The assembly and function of perinuclear actin cap in migrating cells

Stress fibers are actin bundles encompassing actin filaments, actin-crosslinking, and actin-associated proteins that represent the major contractile system in the cell. Different types of stress fibers assemble in adherent cells, and they are central to diverse cellular processes including establishment of the cell shape, morphogenesis, cell polarization, and migration. Stress fibers display specific cellular organization and localization, with ventral fibers present at the basal side, and dorsal fibers and transverse actin arcs rising at the cell front from the ventral to the dorsal side and toward the nucleus. Perinuclear actin cap fibers are a specific subtype of stress fibers that rise from the leading edge above the nucleus and terminate at the cell rear forming a dome-like structure. Perinuclear actin cap fibers are fixed at three points: both ends are anchored in focal adhesions, while the central part is physically attached to the nucleus and nuclear lamina through the linker of nucleoskeleton and cytoskeleton (LINC) complex. Here, we discuss recent work that provides new insights into the mechanism of assembly and the function of these actin stress fibers that directly link extracellular matrix and focal adhesions with the nuclear envelope.