Cell nucleus as a microrheological probe to study the rheology of the cytoskeleton

Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies has enabled measuring the cell’s mechanical properties at high throughput so that mechanical phenotyping can be applied to large samples in reasonable timescales. These studies typically measure the stiffness of the cell as the only mechanical biomarker and do not disentangle the rheological contributions of different structural components of the cell, including the cell cortex, the interior cytoplasm and its immersed cytoskeletal structures, and the nucleus. Recent advancements in high-speed fluorescent imaging have enabled probing the deformations of the cell cortex while also tracking different intracellular components in rates applicable to microfluidic platforms. We present a, to our knowledge, novel method to decouple the mechanics of the cell cortex and the cytoplasm by analyzing the correlation between the cortical deformations that are induced by external microfluidic flows and the nucleus displacements, induced by those cortical deformations, i.e., we use the nucleus as a high-throughput microrheological probe to study the rheology of the cytoplasm, independent of the cell cortex mechanics. To demonstrate the applicability of this method, we consider a proof-of-concept model consisting of a rigid spherical nucleus centered in a spherical cell. We obtain analytical expressions for the time-dependent nucleus velocity as a function of the cell deformations when the interior cytoplasm is modeled as a viscous, viscoelastic, porous, and poroelastic material and demonstrate how the nucleus velocity can be used to characterize the linear rheology of the cytoplasm over a wide range of forces and timescales/frequencies.     

Transmission of Mechanical Stresses within the Cytoskeleton of Adherent Cells: A Theoretical Analysis Based on a Multi-Component Cell Model

How environmental mechanical forces affect cellular functions is a central problem in cell biology. Theoretical models of cellular biomechanics provide relevant tools for understanding how the contributions of deformable intracellular components and specific adhesion conditions at the cell interface are integrated for determining the overall balance of mechanical forces within the cell. We investigate here the spatial distributions of intracellular stresses when adherent cells are probed by magnetic twisting cytometry. The influence of the cell nucleus stiffness on the simulated nonlinear torque-bead rotation response is analyzed by considering a finite element multi-component cell model in which the cell and its nucleus are considered as different hyperelastic materials. We additionally take into account the mechanical properties of the basal cell cortex, which can be affected by the interaction of the basal cell membrane with the extracellular substrate. In agreement with data obtained on epithelial cells, the simulated behaviour of the cell model relates the hyperelastic response observed at the entire cell scale to the distribution of stresses and strains within the nucleus and the cytoskeleton, up to cell adhesion areas. These results, which indicate how mechanical forces are transmitted at distant points through the cytoskeleton, are compared to recent data imaging the highly localized distribution of intracellular stresses.     

Evaluating the nucleus effect on the dynamic indentation behavior of cells

The effect of the nucleus on the cell mechanical behavior was investigated based on the dynamic indentation response of cells under a spherical tip. A “two-component” cell model (including cytoplasm and nucleus) is used, and the dynamic indentation behavior is studied by a semiempirical method, which is established based on fitting the numerical simulation results of the quasi-static indentation response of cells. We found that the “routine analysis” (based on the Hertz’s contact solution of homogeneous model) significantly overestimated the nucleus effect on the overall cell indentation response due to the effects of the Hertz contact radius and the substrate stiffening. These effects are significantly stronger in the “two-component” cell model than in the homogeneous model. The inaccuracy created by the “routine analysis” slightly increases with the modulus ratio of nucleus to cytoplasm and the volume fraction of nucleus. Finally, the error sensitivity to the geometrical parameters used in the model is discussed, which shows the indentation analysis is not very sensitive to these parameters, and the reasonable assumptions for these parameters are effective. This systematic analysis can provide a useful guideline to understanding the mechanical behavior of cells and nuclei.     

In situ mechanical properties of the chondrocyte cytoplasm and nucleus

The way in which the nucleus experiences mechanical forces has important implications for understanding mechanotransduction. Knowledge of nuclear material properties and, specifically, their relationship to the properties of the bulk cell can help determine if the nucleus directly experiences mechanical loads, or if it is a signal transduction mechanism secondary to cell membrane deformation that leads to altered gene expression. Prior work measuring nuclear material properties using micropipette aspiration suggests that the nucleus is substantially stiffer than the bulk cell [Guilak, F., Tedrow, J.R., Burgkart, R., 2000. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269, 781–786], whereas recent work with unconfined compression of single chondrocytes showed a nearly one-to-one correlation between cellular and nuclear strains [Leipzig, N.D., Athanasiou, K.A., 2008. Static compression of single chondrocytes catabolically modifies single-cell gene expression. Biophys. J. 94, 2412–2422]. In this study, a linearly elastic finite element model of the cell with a nuclear inclusion was used to simulate the unconfined compression data. Cytoplasmic and nuclear stiffnesses were varied from 1 to 7 kPa for several combinations of cytoplasmic and nuclear Poisson's ratios. It was found that the experimental data were best fit when the ratio of cytoplasmic to nuclear stiffness was 1.4, and both cytoplasm and nucleus were modeled as incompressible. The cytoplasmic to nuclear stiffness ratio is significantly lower than prior reports for isolated nuclei. These results suggest that the nucleus may behave mechanically different in situ than when isolated.     

Measurement of intracellular strain on deformable substrates with texture correlation

Mechanical stimuli are important factors that regulate cell proliferation, survival, metabolism and motility in a variety of cell types. The relationship between mechanical deformation of the extracellular matrix and intracellular deformation of cellular sub-regions and organelles has not been fully elucidated, but may provide new insight into the mechanisms involved in transducing mechanical stimuli to biological responses. In this study, a novel fluorescence microscopy and image analysis method was applied to examine the hypothesis that mechanical strains are fully transferred from a planar, deformable substrate to cytoplasmic and intranuclear regions within attached cells. Intracellular strains were measured in cells derived from the anulus fibrosus of the intervertebral disc when attached to an elastic silicone membrane that was subjected to tensile stretch. Measurements indicated cytoplasmic strains were similar to those of the underlying substrate, with a strain transfer ratio (STR) of 0.79. In contrast, nuclear strains were much smaller than those of the substrate, with an STR of 0.17. These findings are consistent with previous studies indicating nuclear stiffness is significantly greater than cytoplasmic stiffness, as measured using other methods. This study provides a novel method for the study of cellular mechanics, including a new technique for measuring intranuclear deformations, with evidence of differential magnitudes and patterns of strain transferred from the substrate to cell cytoplasm and nucleus.     

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.     

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.     

In the middle of it all: Mutual mechanical regulation between the nucleus and the cytoskeleton

The nucleus is typically treated as the large phase-dense or easy-to-label structure at the center of the cell which is manipulated by the governing mechanical machinery inside the cytoplasm. However, recent evidence has suggested that the mechanical properties of the nucleus are important to cell fate. We will discuss many aspects of the structural and functional interconnections between nuclear mechanics and cellular mechanics in this review. There are numerous implications for the progression of many disease states associated with both nuclear structural proteins and cancers. The nucleus itself is a large organelle taking up significant volume within the cell, and most studies agree that nuclei are significantly stiffer than the surrounding cytoplasm. Thus when a cell is exposed to force, the nucleus is exposed to and helps resist that force. The nucleus and nucleoskeleton are interconnected with the cellular cytoskeleton, and these connections may aid in helping disperse forces within tissues and/or with mechanotransduction. During translocation and transmigration the nucleus can act as a resistive element. Understanding the role of mechanical regulation of the nucleus may aid in understanding cellular motility and crawling through confined geometries. Thus the nucleus plays a role in developing mechanical territories and niches, affecting rates of wound healing and allowing cells to transmigrate through tissues for developmental, repair or pathological means.     

Probing compressibility of the nuclear interior in wild-type and lamin deficient cells using microscopic imaging and computational modeling

Mechanical properties of the cell nucleus play an important role in maintaining the integrity of the genome and controlling the cellular force balance. Irregularities in these properties have been related to disruption of a variety of force-dependent processes in the cell, such as migration, division, growth or differentiation. Characterizing mechanical properties of the cell nucleus in situ and relating these parameters to cellular phenotypes remain challenging tasks, as conventional micromanipulation techniques do not allow direct probing of intracellular structures. Here, we present a framework based on light microscopic imaging and automated mechanical modeling that enables characterization of the compressibility of the nuclear interior in situ. Based entirely on optical methods, our approach does not require application of destructive or contacting techniques and it enables measurements of a significantly larger number of cells. Compressibility, in this paper represented by Poisson's ratio ν, is determined by fitting a numerical model to experimentally observed time series of microscopic images of fluorescent cell nuclei in which bleached patterns are introduced. In a proof-of-principle study, this framework was applied to estimate ν in wild type cells and cells lacking important structural proteins of the nuclear envelope (LMNA(-/-)). Based on measurements of a large number of cells, our study revealed distinctive changes in compressibility of the nuclear interior between these two cell types. Our method allows an automated, contact-free estimation of mechanical properties of intracellular structures. Combined with knockdown and overexpression screens, it paves the way towards a high-throughput measurement of intracellular mechanical properties in functional phenotyping screens.     

Cellular mechanobiology and cancer metastasis

The primary cause of cancer treatment failure is invasion and metastasis, and invading tumor cells utilize many of the motility patterns that have been documented for normal morphogenesis. Recently, the role of mechanical forces in guiding various tissue and cell movements in embryonic development has been systematically analyzed with new experimental and computational methods. The tissue and cellular mechanobiology approach also holds promise for increasing the understanding of tumor invasion. In fact, the mechanical stiffness of tumors has correlated with invasiveness, and manipulation of extracellular matrix (ECM) stiffness in vitro has suppressed the cancer phenotype. Several important signaling molecules reside on the cytoskeleton, which is affected by external stress imparted by the ECM, and deformation of the nucleus can trigger the activation of certain genes. All these observations suggest that a synthesis of the biology of cancer cell invasion and cellular mechanobiology may offer new targets for the treatment of malignant disease. Accordingly, sensitive and relevant in vivo models and methods to study cancer mechanobiology are needed.     

Towards an integrated understanding of the structure and mechanics of the cell nucleus

Changes in the shape and structural organization of the cell nucleus occur during many fundamental processes including development, differentiation and aging. In many of these processes, the cell responds to physical forces by altering gene expression within the nucleus. How the nucleus itself senses and responds to such mechanical cues is not well understood. In addition to these external forces, epigenetic modifications of chromatin structure inside the nucleus could also alter its physical properties. To achieve a better understanding, we need to elucidate the relationship between nuclear structure and material properties. Recently, new approaches have been developed to systematically investigate nuclear mechanical properties. These experiments provide important new insights into the disease mechanism of a growing class of tissue-specific disorders termed 'nuclear envelopathies'. Here we review our current understanding of what determines the shape and mechanical properties of the cell nucleus.     

Cell and tissue mechanics in cell migration

Migrating cells generate traction forces to counteract the movement-resisting forces arising from cell-internal stresses and matrix adhesions. In the case of collective migration in a cell colony, or in the case of 3-dimensional migration through connective tissue, movement-resisting forces arise also from external stresses. Although the deformation of a stiffer cell or matrix causes larger movement-resisting forces, at the same time a larger stiffness can also promote cell migration due to a feedback between forces, deformations, and deformation speed that is mediated by the acto-myosin contractile machinery of cells. This mechanical feedback is also important for stiffness sensing, durotaxis, plithotaxis, and collective migration in cell colonies.     

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.     

A Nondimensional Model Reveals Alterations in Nuclear Mechanics upon Hepatitis C Virus Replication

Morphology of the nucleus is an important regulator of gene expression. Nuclear morphology is in turn a function of the forces acting on it and the mechanical properties of the nuclear envelope. Here, we present a two-parameter, nondimensional mechanical model of the nucleus that reveals a relationship among nuclear shape parameters, such as projected area, surface area, and volume. Our model fits the morphology of individual nuclei and predicts the ratio between forces and modulus in each nucleus. We analyzed the changes in nuclear morphology of liver cells due to hepatitis C virus (HCV) infection using this model. The model predicted a decrease in the elastic modulus of the nuclear envelope and an increase in the pre-tension in cortical actin as the causes for the change in nuclear morphology. These predictions were validated biomechanically by showing that liver cells expressing HCV proteins possessed enhanced cellular stiffness and reduced nuclear stiffness. Concomitantly, cells expressing HCV proteins showed downregulation of lamin-A,C and upregulation of β-actin, corroborating the predictions of the model. Our modeling assumptions are broadly applicable to adherent, monolayer cell cultures, making the model amenable to investigate changes in nuclear mechanics due to other stimuli by merely measuring nuclear morphology. Toward this, we present two techniques, graphical and numerical, to use our model for predicting physical changes in the nucleus.     

Probing cytoskeletal pre-stress and nuclear mechanics in endothelial cells with spatiotemporally controlled (de-)adhesion kinetics on micropatterned substrates

The mechanical properties of living cells reflect their propensity to migrate and respond to external forces. Both cellular and nuclear stiffnesses are strongly influenced by the rigidity of the extracellular matrix (ECM) through reorganization of the cyto- and nucleoskeletal protein connections. Changes in this architectural continuum affect cell mechanics and underlie many pathological conditions. In this context, an accurate and combined quantification of the mechanical properties of both cells and nuclei can contribute to a better understanding of cellular (dys-)function. To address this challenge, we have established a robust method for probing cellular and nuclear deformation during spreading and detachment from micropatterned substrates. We show that (de-)adhesion kinetics of endothelial cells are modulated by substrate stiffness and rely on the actomyosin network. We combined this approach with measurements of cell stiffness by magnetic tweezers to show that relaxation dynamics can be considered as a reliable parameter of cellular pre-stress in adherent cells. During the adhesion stage, large cellular and nuclear deformations occur over a long time span (>60 min). Conversely, nuclear deformation and condensed chromatin are relaxed in a few seconds after detachment. Finally, our results show that accumulation of farnesylated prelamin leads to modifications of the nuclear viscoelastic properties, as reflected by increased nuclear relaxation times. Our method offers an original and non-intrusive way of simultaneously gauging cellular and nuclear mechanics, which can be extended to high-throughput screens of pathological conditions and potential countermeasures.     

Exogenous and endogenous force regulation of endothelial cell behavior

Endothelial cells live in a dynamic environment where they are constantly exposed to external hemodynamic forces and generate cytoskeletal-based endogenous forces. These exogenous and endogenous forces are critical regulators of endothelial cell health and blood vessel maintenance at all generations of the vascular system, from large arteries to capillary beds. The first part of this review highlights the role of the primary exogenous hemodynamic forces of shear, cyclic strain, and pressure forces in mediating endothelial cell response. We then discuss the emergent role of the mechanical properties of the extracellular matrix and of cellular endogenous force generation on endothelial cell function, implicating substrate stiffness and cellular traction stresses as important mediators of endothelial cell health. The intersection of exogenous and endogenous forces on endothelial cell function is discussed, suggesting some of the many remaining questions in the field of endothelial mechanobiology.     

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

     

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.     

Ultrasound induced strain cytoskeleton rearrangement: An experimental and simulation study

Cytoskeleton and specially actin filaments are responsible for mechanical modulation of cellular behavior. These structures could be fluidized in response to transient mechanical cues. Ultrasound devices have been widely used in medicine which their generated ultrasonic waves could disrupt/fluidize actin filaments in cytoskeleton and thus could affect cellular organization. Present research aims at revealing the mechanism of fluidization caused by ultrasound induced strains. First, a numerical simulation was performed to reveal the effect of oscillating ultrasonic pressure on induced deformation in the cell with respect to different cell geometries and exposure conditions. The model revealed that higher pressure and frequencies induce higher levels of strain in the cell. The results also showed that spread cells are more exposed to cytomechanical remodeling due to higher level of ultrasound induced deformations but also the effect of harmonic excitation decreases with spreading. Furthermore, strain values found to be less in the nucleus comparing the value in the cytoplasm, but still these strains can affect the behavior of the cell through mechanotransduction mechanisms. Then, different experimental ultrasound protocols were used to evaluate their effects on cell viability and actin cytoskeleton distribution. Results of Live/Dead assay indicated that high pressure and duration of the exposure had negative effects on the viability of C2C12 cells, while the viability ratio still remained above 85%. In addition, actin fluorescent staining showed that high levels of filament disruption could occur with increasing the pressure. The results of this study shed light on cellular response to mechanical stimuli applied by ultrasonic waves.