Actin cytoskeleton stiffness grades metastatic potential of ovarian carcinoma Hey A8 cells via nanoindentation mapping

Recent studies have indicated that the nanoindentation measured stiffness of carcinoma adherent cells is in general lower than normal cells, thus suggesting that cell stiffness may serve as a bio-marker for carcinoma. However, the proper establishment of such a conclusion would require biophysical understanding of the underlying mechanism of the cell stiffness. In this work, we compared the elastic moduli of the actin cytoskeletons of Hey A8 ovarian carcinoma cells with and without metastasis (HM and NM), as measured by 2D atomic force microscopy (AFM) with low-depth nanoindentation via a rate-jump method. The results indicate clearly that HM cells showed lower actin cytoskeleton stiffness atop of their nucleus position and higher actin cytoskeleton stiffness at their rims, compared to NM cells, suggesting that the local stiffness on the cytoskeleton can reflect actin filament distribution. Immunofluorescence staining and scanning electron microscopy (SEM) also indicated that the difference in stiffness in Hey A8 cells with different metastasis is associated with their F-actin rearrangement. Finite-element modelling (FEM) shows that a migrating cell would have its actin filaments bundled together to form stress fibers, which would exhibit lower indentation stiffness than the less aligned arrangement of filaments in a non-migrating cell. The results here indicate that the actin cytoskeleton stiffness can serve as a reliable marker for grading the metastasis of adherent carcinoma cells due to their cytoskeleton change and potentially predicting the migration direction of the cells.     

On atomic force microscopy and the constitutive behavior of living cells

Atomic force microscopy (AFM) is one of many new technologies available to study the mechanical properties and mechanobiological responses of living cells. Despite the widespread usage of this technology, there has been little attempt to develop new theoretical frameworks to interpret the associated data. Rather, most analyses rely on the classical Hertz solution for the indentation of an elastic half-space within the context of linearized elasticity. In contrast, we propose a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the three primary structural constituents of the cytoskeleton. Moreover, we extend a prior solution for a small indentation superimposed on a finite equibiaxial extension by incorporating in this mixture model for the special case of an initially random distribution of constituents (actin, intermediate filaments, and microtubules). We submit that this theoretical framework will allow an improved interpretation of indentation force-depth data from a sub-class of atomic force microscopy tests and will serve as an important analytical check for future finite element models. The latter will be necessary to exploit further the capabilities of both atomic force microscopy and nonlinear mixture theories for cell behavior.     

Probing the biophysical properties of tumor cells during mitosis by atomic force microscopy

Mitosis is an important physiological event accompanying with dramatic changes of cellar biophysical properties. Failure of mitosis results in cell death or chromosome aneuploidy. In this study, we used atomic force microscopy to probe and compare the biophysical properties of tumor cells at different stages during mitosis. The rounding forces of MCF-7 cells oscillated during mitosis. At anaphase, the average elasticity of cells was higher than that at other phases. Cholesterol depletion with M\(\upbeta \)CD led to an increase in the average elasticity, whereas the average roughness of membrane surface decreased at the absence of cholesterol. Our study indicated that the distribution of actin filaments could affect the biophysical properties of tumor cells and cellular morphology during mitosis. Furthermore, the biophysical properties of tumor cells were also regulated by membrane cholesterol during mitosis. This work provides a new detection approach for monitoring tumor cell development at single cell level.     

Force Production by a Bundle of Growing Actin Filaments Is Limited by Its Mechanical Properties

Bundles of actin filaments are central to a large variety of cellular structures such as filopodia, stress fibers, cytokinetic rings, and focal adhesions. The mechanical properties of these bundles are critical for proper force transmission and force bearing. Previous mathematical modeling efforts have focused on bundles’ rigidity and shape. However, it remains unknown how bundle length and buckling are controlled by external physical factors. In this work, we present a biophysical model for dynamic bundles of actin filaments submitted to an external load. In combination with in vitro motility assays of beads coated with formins, our model allowed us to characterize conditions for bead movement and bundle buckling. From the deformation profiles, we determined key biophysical properties of tethered actin bundles such as their rigidity and filament density.     

CDK2 differentially controls normal cell senescence and cancer cell proliferation upon exposure to reactive oxygen species

The linker of nucleus and cytoskeleton (LINC) complex, including nesprin-1, has been suggested to be crucial for many biological processes. Previous studies have shown that mutations in nesprin-1 cause abnormal cellular functions and diseases, possibly because of insufficient force transmission to the nucleus through actin filaments (F-actin) bound to nesprin-1. However, little is known regarding the mechanical interaction between the nucleus and F-actin through nesprin-1. In this study, we examined nuclear deformation behavior in nesprin-1 knocked-down endothelial cells (ECs) subjected to uniaxial stretching by evaluating nuclear strain from lateral cross-sectional images. The widths of nuclei in nesprin-1 knocked-down ECs were smaller than those in wild-type cells. In addition, nuclear strain in nesprin-1 knocked-down cells, which is considered to be compressed by the actin cortical layer, increased compared with that in wild-type cells under stretching condition. These results indicate that nesprin-1 knockdown releases the nucleus from the tension of F-actin bound to the nucleus, thereby increasing allowance for deformation before stretching, and that F-actin bound to the nucleus through nesprin-1 causes sustainable force transmission to the nucleus.     

Three-dimensional study of the cytoskeleton in macrophages and multinucleate giant cells by quick-freezing and deep-etching method

The three-dimensional ultrastructure of multinucleate giant cells in subcutaneous granulomas was compared with those of peritoneal macrophages using a quick-freezing and deep-etching method. Subcutaneous granulomas were induced by implanting plastic coverslips in the dorsal subcutaneous tissue of rats. The quick-freezing and deep-etching replicas were prepared from the cells attached to the coverslips. Dense networks of actin filaments were distributed along all peripheral aspects (beneath the plasma membrane, and on free and coverslip-attached surfaces) of the multinucleate giant cells. On the coverslip-attached surface, numerous clathrin-coated pits and vesicles occurred between the actin filaments. In these cells, intermediate filaments, but not actin filaments, were the predominant cytoskeletal components in perinuclear regions and were attached to the cell nucleus, mitochondria and other vesicular cell organelles. A similar distribution of cytoskeletal components was observed in the mononuclear macrophages of the granulomas and the peritoneal macrophages. These results show that the cytoskeletal organization varies in different regions of the cytoplasm of multinucleate giant cells, while the characteristic cytoskeletal arrangement, resembling that of mononuclear macrophages, is maintained.     

Superficial and deep changes of cellular mechanical properties following cytoskeleton disassembly

The cytoskeleton, composed of actin filaments, intermediate filaments, and microtubules, is a highly dynamic supramolecular network actively involved in many essential biological mechanisms such as cellular structure, transport, movements, differentiation, and signaling. As a first step to characterize the biophysical changes associated with cytoskeleton functions, we have developed finite elements models of the organization of the cell that has allowed us to interpret atomic force microscopy (AFM) data at a higher resolution than that in previous work. Thus, by assuming that living cells behave mechanically as multilayered structures, we have been able to identify superficial and deep effects that could be related to actin and microtubule disassembly, respectively. In Cos-7 cells, actin destabilization with Cytochalasin D induced a decrease of the visco-elasticity close to the membrane surface, while destabilizing microtubules with Nocodazole produced a stiffness decrease only in deeper parts of the cell. In both cases, these effects were reversible. Cell softening was measurable with AFM at concentrations of the destabilizing agents that did not induce detectable effects on the cytoskeleton network when viewing the cells with fluorescent confocal microscopy. All experimental results could be simulated by our models. This technology opens the door to the study of the biophysical properties of signaling domains extending from the cell surface to deeper parts of the cell.     

Mechanical Heterogeneity Favors Fragmentation of Strained Actin Filaments

We present a general model of actin filament deformation and fragmentation in response to compressive forces. The elastic free energy density along filaments is determined by their shape and mechanical properties, which were modeled in terms of bending, twisting, and twist-bend coupling elasticities. The elastic energy stored in filament deformation (i.e., strain) tilts the fragmentation-annealing reaction free-energy profile to favor fragmentation. The energy gradient introduces a local shear force that accelerates filament intersubunit bond rupture. The severing protein, cofilin, renders filaments more compliant in bending and twisting. As a result, filaments that are partially decorated with cofilin are mechanically heterogeneous (i.e., nonuniform) and display asymmetric shape deformations and energy profiles distinct from mechanically homogenous (i.e., uniform), bare actin, or saturated cofilactin filaments. The local buckling strain depends on the relative size of the compliant segment as well as the bending and twisting rigidities of flanking regions. Filaments with a single bare/cofilin-decorated boundary localize energy and force adjacent to the boundary, within the compliant cofilactin segment. Filaments with small cofilin clusters were predicted to fragment within the compliant cofilactin rather than at boundaries. Neglecting contributions from twist-bend coupling elasticity underestimates the energy density and gradients along filaments, and thus the net effects of filament strain to fragmentation. Spatial confinement causes compliant cofilactin segments and filaments to adopt higher deformation modes and store more elastic energy, thereby promoting fragmentation. The theory and simulations presented here establish a quantitative relationship between actin filament fragmentation thermodynamics and elasticity, and reveal how local discontinuities in filament mechanical properties introduced by regulatory proteins can modulate both the severing efficiency and location along filaments. The emergent behavior of mechanically heterogeneous filaments, particularly under confinement, emphasizes that severing in cells is likely to be influenced by multiple physical and chemical factors.     

Strain field in actin filament network in lamellipodia of migrating cells: Implication for network reorganization

Cell motility is spatiotemporally regulated by interactions among mechanical and biochemical factors involved in the regulation of cytoskeletal actin structure reorganization. Although the molecular mechanisms underlying cell motility have been well investigated, the contributions of mechanical factors such as strain in the network reorganization remain unclear. In this study, we have quantitatively evaluated the strain field in the actin filament network forming the lamellipodia of migrating fish keratocytes to elucidate the mechanism by which actin filament network reorganization is regulated by biomechanical factors. The results highlight the existence of a negative (compressive) strain in the lamellipodia whose direction is parallel to that of cell movement. A close correlation was found between the distributions of the strain and the actin filament density in the lamellipodia, suggesting that negative strain may be involved in filament depolymerization. Based on this result, we propose a selective depolymerization model which suggests that negative strain may couple with biomechanical factors such as ADF/cofilin to promote selective depolymerization of filaments oriented in the direction of the deformation because such filaments experience relatively higher levels of the deformation. This model, in conjunction with others, may explain the observed reduction in filament density and the reorganization of actin filament network at the back of the lamellipodia of migrating fish keratocytes. Thus, we suggest that by coupling with biochemical factors, mechanical factors are involved in the regulation of actin filament depolymerization, thereby contributing to the regulation of cell motility.     

Substrate deformation determines actin cytoskeleton reorganization: A mathematical modeling and experimental study

A mathematical model has been developed to define the relationship between the actin cytoskeleton reorganization of a cell and substrate deformation acting on the cell. The model is based on the following major assumptions: (a) normal substrate strain, not the shear substrate strain, determines the actin cytoskeleton reorganization; (b) the normal substrate strain is transmitted to individual actin filaments; (c) each actin filament has a basal strain energy (BSE) when the cell adheres to the substrate without stretching; and (d) the actin filaments undergo disassembly when their strain energies are decreased to zero or increased to twice their BSEs. The resulting model predicts that the actin filaments are formed in the direction where their BSEs are minimally altered. This direction is therefore the one without normal substrate strain. The prediction was confirmed by experiments conducted on both fibroblasts and endothelial cells. The present model may be relevant for understanding better the effects of mechanical stimuli on the cells.     

Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling

Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drug-treated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement.     

Osmo-sensitive and stretch-activated calcium-permeable channels in Vicia faba guard cells are regulated by actin dynamics

In responses to a number of environmental stimuli, changes of cytoplasmic [Ca(2+)](cyt) in stomatal guard cells play important roles in regulation of stomatal movements. In this study, the osmo-sensitive and stretch-activated (SA) Ca(2+) channels in the plasma membrane of Vicia faba guard cells are identified, and their regulation by osmotic changes and actin dynamics are characterized. The identified Ca(2+) channels were activated under hypotonic conditions at both whole-cell and single-channel levels. The channels were also activated by a stretch force directly applied to the membrane patches. The channel-mediated inward currents observed under hypotonic conditions or in the presence of a stretch force were blocked by the Ca(2+) channel inhibitor Gd(3+). Disruption of actin filaments activated SA Ca(2+) channels, whereas stabilization of actin filaments blocked the channel activation induced by stretch or hypotonic treatment, indicating that actin dynamics may mediate the stretch activation of these channels. In addition, [Ca(2+)](cyt) imaging demonstrated that both the hypotonic treatment and disruption of actin filaments induced significant Ca(2+) elevation in guard cell protoplasts, which is consistent with our electrophysiological results. It is concluded that stomatal guard cells may utilize SA Ca(2+) channels as osmo sensors, by which swelling of guard cells causes elevation of [Ca(2+)](cyt) and consequently inhibits overswelling of guard cells. This SA Ca(2+) channel-mediated negative feedback mechanism may coordinate with previously hypothesized positive feedback mechanisms and regulate stomatal movement in response to environmental changes.     

A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts

In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibroblasts. Beyond the simulation (from a quantitative, parametrized model) of the experimentally observed oscillatory cell deformations, a final goal of this work is to underline that a set of common assumptions regarding intracellular actin dynamics and associated cell membrane local motion allows us to describe a wide variety of cell morphologies and protrusive activity. The model proposed describes cell membrane deformations as a consequence of the endogenous cortical actin dynamics where the driving force for large-amplitude cell protrusion is provided by the coupling between F-actin polymerization and contractility of the cortical actomyosin network. Cell membrane movements then result of two competing forces acting on the membrane, namely an intracellular hydrostatic protrusive force counterbalanced by a retraction force exerted by the actin filaments of the cell cortex. Protrusion and retraction forces are moreover modulated by an additional membrane curvature stress. As a first approximation, we start by considering a heterogeneous but stationary distribution of actin along the cell periphery in order to evaluate the possible morphologies that an individual cell might adopt. Then non-stationary actin distributions are considered. The simulated dynamic behaviour of this cytomechanical model not only reproduces the small amplitude rotating waves of deformations of round-shaped cells such as keratinocytes [as proposed in the original model of Alt and Tranquillo (1995, J. Biol. Syst. 3, 905–916)] but is furthermore in very good agreement with the protrusive activity of cells such as fibroblasts, where large amplitude contracting/retracting pseudopods are more or less periodically extended in opposite directions. In addition, the biophysical and biochemical processes taken into account by the cytomechanical model are characterized by well-defined parameters which (for the majority) can be discussed with regard to experimental data obtained in various experimental situations.     

Depth-sensing analysis of cytoskeleton organization based on AFM data

Atomic force microscopy is a common technique used to determine the elastic properties of living cells. It furnishes the relative Young’s modulus, which is typically determined for indentation depths within the range 300–500 nm. Here, we present the results of depth-sensing analysis of the mechanical properties of living fibroblasts measured under physiological conditions. Distributions of the Young’s moduli were obtained for all studied cells and for every cell. The results show that for small indentation depths, histograms of the relative values of the Young’s modulus described the regions rich in the network of actin filaments. For large indentation depths, the overall stiffness of a whole cell was obtained, which was accompanied by a decrease of the modulus value. In conclusion, the results enable us to describe the non-homogeneity of the cell cytoskeleton, particularly, its contribution linked to actin filaments located beneath the cell membrane. Preliminary results showing a potential application to improve the detection of cancerous cells, have been presented for melanoma cell lines.     

Cellular motility driven by assembly and disassembly of actin filaments

Motile cells extend a leading edge by assembling a branched network of actin filaments that produces physical force as the polymers grow beneath the plasma membrane. A core set of proteins including actin, Arp2/3 complex, profilin, capping protein, and ADF/cofilin can reconstitute the process in vitro, and mathematical models of the constituent reactions predict the rate of motion. Signaling pathways converging on WASp/Scar proteins regulate the activity of Arp2/3 complex, which mediates the initiation of new filaments as branches on preexisting filaments. After a brief spurt of growth, capping protein terminates the elongation of the filaments. After filaments have aged by hydrolysis of their bound ATP and dissociation of the gamma phosphate, ADF/cofilin proteins promote debranching and depolymerization. Profilin catalyzes the exchange of ADP for ATP, refilling the pool of ATP-actin monomers bound to profilin, ready for elongation.     

Form-Finding Model Shows How Cytoskeleton Network Stiffness Is Realized

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.     

Distribution of actin microfilaments in frog skin epithelial granular cells

Summary— Microfilaments were localised by immunofluorescence and immunogold cytochemistry to examine their distribution in granular cells of the isolated frog skin epithelium. Strongly fluorescent bundles of actin were observed beneath the plasma membrane with little evidence for actin in the central regions. Higher resolution offered by cytochemistry revealed that bundles of actin filaments comprised a substantial portion of the cortical cytoskeleton. Quantitative analysis of the frequency of gold label revealed an extremely rich array of filaments beneath the apical membrane of granular cells, with markedly less babel along the basolateral membrane and in the central cytoplasm. Treating cells with cytochalasin B or arginine vasopressin caused an apparent disruption of the apical actin fibres, concurrent with a decrease in gold label density. Assumably these signs are indicative of depolymerization of the filaments. Although the significance of this distribution is unknown, the apical polarisation of actin is consistent with a role in regulating the Na⁺ permeability of the apical membrane. The data are discussed in relation to possible roles of the cytoskeleton in the regulation of transepithelial sodium transport by vasopressin.     

A mathematical approach to cytoskeletal assembly

The cytoskeleton is a fundamental and important part of cell's structure, and is known to play a large role in controlling the shape, function, division, and motility of the cell. In recent years, the traditional biological and biophysical experimental work on the cytoskeleton has been enhanced by a variety of theoretical, physical and mathematical approaches. Many of these approaches have been developed in the traditional frameworks of physico-chemical and statistical mechanics or equilibrium thermodynamic principles. An alternative is to use kinetic modelling and couch the analysis in terms of differential equations which describe mean field properties of cytoskeletal networks or assemblies. This paper describes two such recent efforts. In the first part of the paper, a summary of work on the kinetics of polymerization, fragmentation, and dynamics of actin and polymers in the presence of gelsolin (which nulceates, fragments, and caps the filaments) is given. In the second part, some of the kinetic models aimed at elucidating the spatio-angular density distribution of actin filaments interacting via crosslinks is described. This model given insight into effects that govern the formation of clusters and bundles of actin filaments, and their spatial distribution. Received: 7 January 1998 / Revised version: 4 March 1998 / Accepted: 7 March 1998     

An Experimental and Computational Study of the Effect of ActA Polarity on the Speed of Listeria monocytogenes Actin-based Motility

Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cell's dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation.