How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

In order to move in a three-dimensional extracellular matrix, the nucleus of a cell must squeeze through the narrow spacing among the fibers and, by adhering to them, the cell needs to exert sufficiently strong traction forces. If the nucleus is too stiff, the spacing too narrow, or traction forces too weak, the cell is not able to penetrate the network. In this article, we formulate a mathematical model based on an energetic approach, for cells entering cylindrical channels composed of extracellular matrix fibers. Treating the nucleus as an elastic body covered by an elastic membrane, the energetic balance leads to the definition of a necessary criterion for cells to pass through the regular network of fibers, depending on the traction forces exerted by the cells (or possibly passive stresses), the stretchability of the nuclear membrane, the stiffness of the nucleus, and the ratio of the pore size within the extracellular matrix with respect to the nucleus diameter. The results obtained highlight the importance of the interplay between mechanical properties of the cell and microscopic geometric characteristics of the extracellular matrix and give an estimate for a critical value of the pore size that represents the physical limit of migration and can be used in tumor growth models to predict their invasive potential in thick regions of ECM.     

Contribution of the nucleus to the mechanical properties of endothelial cells.

The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force-deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force-deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500N/m(2) for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000N/m(2) for nuclei in the cell and on the order of 8000N/m(2) for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.     

Direct observations of the mechanical behaviors of the cytoskeleton in living fibroblasts

Cytoskeletal proteins tagged with green fluorescent protein were used to directly visualize the mechanical role of the cytoskeleton in determining cell shape. Rat embryo (REF 52) fibroblasts were deformed using glass needles either uncoated for purely physical manipulations, or coated with laminin to induce attachment to the cell surface. Cells responded to uncoated probes in accordance with a three-layer model in which a highly elastic nucleus is surrounded by cytoplasmic microtubules that behave as a jelly-like viscoelastic fluid. The third, outermost cortical layer is an elastic shell under sustained tension. Adhesive, laminin-coated needles caused focal recruitment of actin filaments to the contacted surface region and increased the cortical layer stiffness. This direct visualization of actin recruitment confirms a widely postulated model for mechanical connections between extracellular matrix proteins and the actin cytoskeleton. Cells tethered to laminin-treated needles strongly resisted elongation by actively contracting. Whether using uncoated probes to apply simple deformations or laminin-coated probes to induce surface-to-cytoskeleton interaction we observed that experimentally applied forces produced exclusively local responses by both the actin and microtubule cytoskeleton. This local accomodation and dissipation of force is inconsistent with the proposal that cellular tensegrity determines cell shape.     

Influence of fibril taper on the function of collagen to reinforce extracellular matrix

Collagen fibrils provide tensile reinforcement for extracellular matrix. In at least some tissues, the fibrils have a paraboloidal taper at their ends. The purpose of this paper is to determine the implications of this taper for the function of collagen fibrils. When a tissue is subjected to low mechanical forces, stress will be transferred to the fibrils elastically. This process was modelled using finite element analysis because there is no analytical theory for elastic stress transfer to a non-cylindrical fibril. When the tissue is subjected to higher mechanical forces, stress will be transferred plastically. This process was modelled analytically. For both elastic and plastic stress transfer, a paraboloidal taper leads to a more uniform distribution of axial tensile stress along the fibril than would be generated if it were cylindrical. The tapered fibril requires half the volume of collagen than a cylindrical fibril of the same length and the stress is shared more evenly along its length. It is also less likely to fracture than a cylindrical fibril of the same length in a tissue subjected to the same mechanical force.     

Viscoelastic properties of the cell nucleus

Mechanical factors play an important role in the regulation of cell physiology. One pathway by which mechanical stress may influence gene expression is through a direct physical connection from the extracellular matrix across the plasma membrane and to the nucleus. However, little is known of the mechanical properties or deformation behavior of the nucleus. The goal of this study was to quantify the viscoelastic properties of mechanically and chemically isolated nuclei of articular chondrocytes using micropipet aspiration in conjunction theoretical viscoelastic model. Isolated nuclei behaved as viscoelastic solid materials similar to the cytoplasm, but were 3-4 times stiffer and nearly twice as viscous as the cytoplasm. Quantitative information of the biophysical properties and deformation behavior of the nucleus may provide further insight on the relationships between the stress-strain state of the nucleus and that of the extracellular matrix, as well as potential mechanisms of mechanical signal transduction.     

Computational model for the cell-mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures

The mechanism by which mechanical stimulation on osteocytes results in biochemical signals that initiate the remodeling process inside living bone tissue is largely unknown. Even the type of stimulation acting on these cells is not yet clearly identified. However, the cytoskeleton of osteocytes is suggested to play a major role in the mechanosensory process due to the direct connection to the nucleus. In this paper, a computational approach to model and simulate the cell structure of osteocytes based on self-stabilizing tensegrity structures is suggested. The computational model of the cell consists of the major components with respect to mechanical aspects: the integrins that connect the cell with the extracellular bone matrix, and different types of protein fibers (microtubules and intermediate filaments) that form the cytoskeleton, the membrane-cytoskeleton (microfilaments), the nucleus and the centrosome. The proposed geometrical cell models represent the cell in its physiological environment which is necessary in order to give a statement on the cell behavior in vivo. Studies on the mechanical response of osteocytes after physiological loading and in particular the mechanical response of the nucleus show that the load acting on the nucleus is rising with increasing deformation applied to the integrins.     

The extracellular matrix viscoelasticity as a regulator of cell and tissue dynamics

The extracellular matrix mechanical properties regulate processes in development, cancer, and fibrosis. Among the distinct mechanical properties, the vast majority of research has focused on the extracellular matrix's elasticity as the primary determinant of cell and tissue behavior. However, both cells and the extracellular matrix are not only elastic but also viscous. Despite viscoelasticity being a universal feature of living tissues, our knowledge of the influence of the extracellular matrix's viscoelasticity in cell behavior is limited. This mini-review describes some of the recent findings that have highlighted the role of the extracellular matrix's viscoelasticity in cell and tissue dynamics.     

Calculation of the force field required for nucleus deformation during cell migration through constrictions

During cell migration in confinement, the nucleus has to deform for a cell to pass through small constrictions. Such nuclear deformations require significant forces. A direct experimental measure of the deformation force field is extremely challenging. However, experimental images of nuclear shape are relatively easy to obtain. Therefore, here we present a method to calculate predictions of the deformation force field based purely on analysis of experimental images of nuclei before and after deformation. Such an inverse calculation is technically non-trivial and relies on a mechanical model for the nucleus. Here we compare two simple continuum elastic models of a cell nucleus undergoing deformation. In the first, we treat the nucleus as a homogeneous elastic solid and, in the second, as an elastic shell. For each of these models we calculate the force field required to produce the deformation given by experimental images of nuclei in dendritic cells migrating in microchannels with constrictions of controlled dimensions. These microfabricated channels provide a simplified confined environment mimicking that experienced by cells in tissues. Our calculations predict the forces felt by a deforming nucleus as a migrating cell encounters a constriction. Since a direct experimental measure of the deformation force field is very challenging and has not yet been achieved, our numerical approaches can make important predictions motivating further experiments, even though all the parameters are not yet available. We demonstrate the power of our method by showing how it predicts lateral forces corresponding to actin polymerisation around the nucleus, providing evidence for actin generated forces squeezing the sides of the nucleus as it enters a constriction. In addition, the algorithm we have developed could be adapted to analyse experimental images of deformation in other situations.     

Contractile equilibration of single cells to step changes in extracellular stiffness

Extracellular stiffness has been shown to alter long timescale cell behaviors such as growth and differentiation, but the cellular response to changes in stiffness on short timescales is poorly understood. By studying the contractile response of cells to dynamic stiffness conditions using an atomic force microscope, we observe a seconds-timescale response to a step change in extracellular stiffness. Specifically, we observe acceleration in contraction velocity (μm/min) and force rate (nN/min) upon a step decrease in stiffness and deceleration upon a step increase in stiffness. Interestingly, this seconds-timescale response to a change in extracellular stiffness is not altered by inhibiting focal adhesion signaling or stretch-activated ion channels and is independent of cell height and contraction force. Rather, the response timescale is altered only by disrupting cytoskeletal mechanics and is well described by a simple mechanical model of a constant velocity actuator pulling against an internal cellular viscoelastic network. Consistent with the predictions of this model, we find that an osmotically expanding hydrogel responds to step changes in extracellular stiffness in a similar manner to cells. We therefore propose that an initial event in stiffness sensing is establishment of a mechanical equilibrium that balances contraction of the viscoelastic cytoskeleton with deformation of the extracellular matrix.     

Macrophage adhesion on fibronectin evokes an increase in the elastic property of the cell membrane and cytoskeleton: an atomic force microscopy study

Interactions between cells and microenvironments are essential to cellular functions such as survival, exocytosis and differentiation. Cell adhesion to the extracellular matrix (ECM) evokes a variety of biophysical changes in cellular organization, including modification of the cytoskeleton and plasma membrane. In fact, the cytoskeleton and plasma membrane are structures that mediate adherent contacts with the ECM; therefore, they are closely correlated. Considering that the mechanical properties of the cell could be affected by cell adhesion-induced changes in the cytoskeleton, the purpose of this study was to investigate the influence of the ECM on the elastic properties of fixed macrophage cells using atomic force microscopy. The results showed that there was an increase (~50 %) in the Young’s modulus of macrophages adhered to an ECM-coated substrate as compared with an uncoated glass substrate. In addition, cytochalasin D-treated cells had a 1.8-fold reduction of the Young’s modulus of the cells, indicating the contribution of the actin cytoskeleton to the elastic properties of the cell. Our findings show that cell adhesion influences the mechanical properties of the plasma membrane, providing new information toward understanding the influence of the ECM on elastic alterations of macrophage cell membranes.     

Biophysical regulation of histone acetylation in mesenchymal stem cells

Histone deacetylation and acetylation are catalyzed by histone deacetylase (HDAC) and histone acetyltransferase, respectively, which play important roles in the regulation of chromatin remodeling, gene expression, and cell functions. However, whether and how biophysical cues modulate HDAC activity and histone acetylation is not well understood. Here, we tested the hypothesis that microtopographic patterning and mechanical strain on the substrate regulate nuclear shape, HDAC activity, and histone acetylation. Bone marrow mesenchymal stem cells (MSCs) were cultured on elastic membranes patterned with parallel microgrooves 10 μm wide that kept MSCs aligned along the axis of the grooves. Compared with MSCs on an unpatterned substrate, MSCs on microgrooves had elongated nuclear shape, a decrease in HDAC activity, and an increase of histone acetylation. To investigate anisotropic mechanical sensing by MSCs, cells on the elastic micropatterned membranes were subjected to static uniaxial mechanical compression or stretch in the direction parallel or perpendicular to the microgrooves. Among the four types of loads, compression or stretch perpendicular to the microgrooves caused a decrease in HDAC activity, accompanied by the increase in histone acetylation and slight changes of nuclear shape. Knocking down nuclear matrix protein lamin A/C abolished mechanical strain-induced changes in HDAC activity. These results demonstrate that micropattern and mechanical strain on the substrate can modulate nuclear shape, HDAC activity, and histone acetylation in an anisotropic manner and that nuclear matrix mediates mechanotransduction. These findings reveal a new mechanism, to our knowledge, by which extracellular biophysical signals are translated into biochemical signaling events in the nucleus, and they will have significant impact in the area of mechanobiology and mechanotransduction.     

The Role of Vinculin in the Regulation of the Mechanical Properties of Cells

Vinculin couples as a focal adhesion protein the extracellular matrix (ECM) through integrins to the actomyosin cytoskeleton. During the last years vinculin has become the focus of cell mechanical measurements and a key protein regulating the transmission of contractile forces. In earlier reports vinculin has been described as an inhibitor of cell migration on planar substrates, because knock-out of vinculin in F9 mouse embryonic carcinoma cells and mouse embryonic fibroblasts showed increased cell motility on 2D substrates. The role of vinculin in cell invasion through a 3D extracellular matrix is still fragmentarily investigated. This review presents vinculin in its role as a regulator of cellular mechanical functions. Contractile force generation is reduced when vinculin is absent, or enhanced when vinculin is present. Moreover, the generation of contractile forces is a prerequisite for cell invasion through a dense 3D ECM, where the pore-size is smaller than the diameter of the cell nucleus (<2 μm). Measurements of cell’s biophysical properties will be presented. In summary, vinculin’s leading role among focal adhesion proteins in regulating the mechanical properties of cells will be discussed.     

Measurements of mechanical properties of the blastula wall reveal which hypothesized mechanisms of primary invagination are physically plausible in the sea urchin Strongylocentrotus purpuratus.

Computer simulations showed that the elastic modulus of the cell layer relative to the elastic modulus of the extracellular layers predicted the effectiveness of different force-generating mechanisms for sea urchin primary invagination [L. A. Davidson, M. A. R. Koehl, R. Keller, and G. F. Oster (1995) Development 121, 2005-2018]. Here, we measured the composite elastic modulus of the cellular and extracellular matrix layers in the blastula wall of Strongylocentrotus purpuratus embryos at the mesenchyme blastula stage. Combined, these two layers exhibit a viscoelastic response with an initial stiffness ranging from 600 to 2300 Pa. To identify the cellular structures responsible for this stiffness we disrupted these structures and correlated the resulting lesions to changes in the elastic modulus. We treated embryos with cytochalasin D to disrupt the actin-based cytoskeleton, nocodazole to disrupt the microtubule-based cytoskeleton, and a gentle glycine extraction to disrupt the apical extracellular matrix (ECM). Embryos treated less than 60 min in cytochalasin D showed no change in their time-dependent elastic modulus even though F-actin was severely disrupted. Similarly, nocodazole had no effect on the elastic modulus even as the microtubules were severely disrupted. However, glycine extraction resulted in a 40 to 50% decrease in the elastic modulus along with a dramatic reduction in the hyalin protein at the apical ECM, thus implicating the apical ECM as a major mechanical component of the blastula wall. This finding bears on the mechanical plausibility of several models for primary invagination.     

Elastic Anisotropy Governs the Range of Cell-Induced Displacements

The unique nonlinear mechanics of the fibrous extracellular matrix (ECM) facilitates long-range cell-cell mechanical communications that would be impossible for linear elastic substrates. Past research has described the contribution of two separated effects on the range of force transmission, including ECM elastic nonlinearity and fiber alignment. However, the relation between these different effects is unclear, and how they combine to dictate force transmission range is still elusive. Here, we combine discrete fiber simulations with continuum modeling to study the decay of displacements induced by a contractile cell in fibrous networks. We demonstrate that fiber nonlinearity and fiber reorientation both contribute to the strain-induced elastic anisotropy of the cell’s local environment. This elastic anisotropy is a “lumped” parameter that governs the slow decay of displacements, and it depends on the magnitude of applied strain, either an external tension or an internal contraction, as a model of the cell. Furthermore, we show that accounting for artificially prescribed elastic anisotropy dictates the decay of displacements induced by a contracting cell. Our findings unify previous single effects into a mechanical theory that explains force transmission in fibrous networks. This work may provide insights into biological processes that involve communication of distant cells mediated by the ECM, such as those occurring in morphogenesis, wound healing, angiogenesis, and cancer metastasis. It may also provide design parameters for biomaterials to control force transmission between cells as a way to guide morphogenesis in tissue engineering.     

Stiffness of the extracellular matrix affects apoptosis of nucleus pulposus cells by regulating the cytoskeleton and activating the TRPV2 channel protein

It is known that nucleus pulposus cells (NPs) play an important role in intervertebral disc degeneration (IVDD), and a previous study indicated that the stiffness of NP tissue changes during the degeneration process. However, the mechanism underlying the cellular response to ECM stiffness is still unclear. To analyze the effects of extracellular matrix (ECM) with different degrees of stiffness on NPs, we prepared polyacrylamide (PA) gels with different elastic moduli, and cells grown under different stiffness conditions were obtained and analyzed. The results showed that the spreading morphology of NPs changed significantly under increased ECM elastic modulus conditions and that TRPV2 and the PI3K / AKT signaling pathway were activated by stiffer ECM. At the same time, mitochondria released cytochrome c (Cyt c) and activated caspase proteins to promote the apoptosis of NPs. After TRPV2 was specifically knocked out, the activation of the PI3K / AKT signaling pathway decreased, and the release of Cyt c and NP apoptosis were reduced. These results indicate that TRPV2 is closely linked to the detection of extracellular mechanical signals, and that conversion of mechanical and biological signals plays an important role in regulating the biological behavior of cells. This study offers a new perspective on the cellular and biochemical events underlying IVDD which could result in novel treatments.     

Loss of stability: a new look at the physics of cell wall behavior during plant cell growth

In this article we investigate aspects of turgor-driven plant cell growth within the framework of a model derived from the Eulerian concept of instability. In particular we explore the relationship between cell geometry and cell turgor pressure by extending loss of stability theory to encompass cylindrical cells. Beginning with an analysis of the three-dimensional stress and strain of a cylindrical pressure vessel, we demonstrate that loss of stability is the inevitable result of gradually increasing internal pressure in a cylindrical cell. The turgor pressure predictions based on this model differ from the more traditional viscoelastic or creep-based models in that they incorporate both cell geometry and wall mechanical properties in a single term. To confirm our predicted working turgor pressures, we obtained wall dimensions, elastic moduli, and turgor pressures of sequential internodal cells of intact Chara corallina plants by direct measurement. The results show that turgor pressure predictions based on loss of stability theory fall within the expected physiological range of turgor pressures for this plant. We also studied the effect of varying wall Poisson's ratio nu on extension growth in living cells, showing that while increasing elastic modulus has an understandably negative effect on wall expansion, increasing Poisson's ratio would be expected to accelerate wall expansion.     

A Structurally and Functionally Biomimetic Biphasic Scaffold for Intervertebral Disc Tissue Engineering

Tissue engineering offers high hopes for the treatment of intervertebral disc (IVD) degeneration. Whereas scaffolds of the disc nucleus and annulus have been extensively studied, a truly biomimetic and mechanically functional biphasic scaffold using naturally occurring extracellular matrix is yet to be developed. Here, a biphasic scaffold was fabricated with collagen and glycosaminoglycans (GAGs), two of the most abundant extracellular matrix components in the IVD. Following fabrication, the scaffold was characterized and benchmarked against native disc. The biphasic scaffold was composed of a collagen-GAG co-precipitate making up the nucleus pulposus-like core, and this was encapsulated in multiple lamellae of photochemically crosslinked collagen membranes comprising the annulus fibrosus-like lamellae. On mechanical testing, the height of our engineered disc recovered by ~82-89% in an annulus-independent manner, when compared with the 99% recovery exhibited by native disc. The annulus-independent nature of disc height recovery suggests that the fluid replacement function of the engineered nucleus pulposus core might mimic this hitherto unique feature of native disc. Biphasic scaffolds comprised of 10 annulus fibrosus-like lamellae had the best overall mechanical performance among the various designs owing to their similarity to native disc in most aspects, including elastic compliance during creep and recovery, and viscous compliance during recovery. However, the dynamic mechanical performance (including dynamic stiffness and damping factor) of all the biphasic scaffolds was similar to that of the native discs. This study contributes to the rationalized design and development of a biomimetic and mechanically viable biphasic scaffold for IVD tissue engineering.     

The nanomechanics of polycystin-1 extracellular region

Recent evidence suggests that polycystin-1 (PC1) acts as a mechanosensor, receiving signals from the primary cilia, neighboring cells, and extracellular matrix and transduces them into cellular responses that regulate proliferation, adhesion, and differentiation that are essential for the control of renal tubules and kidney morphogenesis. PC1 has an unusually long extracellular region ( approximately 3000 amino acids) with a multimodular structure. Proteins with a similar architecture have structural and mechanical roles. Based on the structural similarities between PC1 and other modular proteins that have elastic properties we hypothesized that PC1 functions mechanically by providing a flexible and elastic linkage between cells. Here we directly tested this hypothesis by analyzing the mechanical properties of the entire PC1 extracellular region by using single molecule force spectroscopy. We show that the PC1 extracellular region is highly extensible and that this extensibility is mainly caused by the unfolding of its Ig-like domains. Stretching the native PC1 extracellular region results in a sawtooth pattern with equally spaced force peaks that have a wide range of unfolding forces (50-200 pN). By combining single-molecule force spectroscopy and protein engineering techniques, we demonstrate that the sawtooth pattern in native PC1 extracellular region corresponds to the sequential unfolding of individual Ig-like domains. We found that Ig-like domains refold after mechanical unfolding. Hence, the PC1 extracellular region displays a dynamic extensibility whereby the resting length might be regulated through unfolding/refolding of its Ig-like domains. These force-driven reactions may be important for cell elasticity and the regulation of cell signaling events mediated by PC1.     

Characterization of the nuclear deformation caused by changes in endothelial cell shape

We investigated the mechanotransduction pathway in endothelial cells between their nucleus and adhesions to the extracellular matrix. First, we measured nuclear deformations in response to alterations of cell shape as cells detach from a flat surface. We found that the nuclear deformation appeared to be in direct and immediate response to alterations of the cell adhesion area. The nucleus was then treated as a neo-Hookean compressible material, and we estimated the stress associated with the cytoskeleton and acting on the nucleus during cell rounding. With the obtained stress field, we estimated the magnitude of the forces deforming the nucleus. Considering the initial and final components of this adhesion-cytoskeleton-nucleus force transmission pathway, we found our estimate for the internal forces acting on the nucleus to be on the same order of magnitude as previously measured traction forces, suggesting a direct mechanical link between adhesions and the nucleus.