Model of T-Cell Nuclear Deformation by the Cortical Actin Layer

Deformations of cell nuclei accompany a number of essential intracellular processes. Although evidence is being accumulated on the primary role actin structures play in controlling the shape of the nucleus, the mechanisms behind this phenomenon remain unknown. Here, we consider theoretically a specific paradigm of nuclear deformation, and a related actin rearrangement, in T cells stimulated by contact with a bead covered by surrogate antigens. We suggest that the nucleus is deformed by the elastic forces developed within a cylindrical layer of polymerized actin, which is generated as a result of the receptor-mediated T-cell activation. We substantiate this proposal with a theoretical analysis of mutual deformations in the actin layer and the nucleus, which recovers the experimentally observed nuclear shapes. Furthermore, we evaluate the forces developed by the actin polymerization that drives the nuclear deformation. The model predicts the mode of actin polymerization generated by the surrogate antigens covering a bead and the values of the elastic moduli of the nuclear shell. We provide a qualitative experimental support for the model assumptions by visualizing the stages of nuclear shape change and the corresponding evolution of the cortical actin.     

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.     

Role of Actin Dependent Nuclear Deformation in Regulating Early Gene Expression

The nucleus of a living cell is constantly undergoing changes in shape and size as a result of various mechanical forces in physiology. These changes correlate with alterations in gene expression, however it is unclear whether nuclear deformation alone is sufficient to elicit these alterations. We used T-cell activation as a model system to test the coupling between nuclear deformation (elongation) and gene expression. Naïve T-cell activation with surrogate antigens resulted in actin dependent nuclear elongation. This was accompanied with Erk and NF-κB signaling to the nucleus to induce CD69 expression. Importantly, inhibiting actin polymerization abolished both nuclear elongation and CD69 expression, while inhibiting Erk, NF-κB or microtubule depolymerization only abolished expression but not elongation. Immobilization of antigen-coated beads, under conditions where actin polymerization was inhibited, rescued both nuclear elongation and CD69 expression. In addition, fibroblast cells plated on fibronectin micropatterns of different sizes showed correlation between nuclear shape index and tenascin C expression. Upon inhibiting the signaling intermediate Erk, tenascin C expression was down regulated although the nuclear shape index remained unaltered. Our results highlight the importance of specific signaling intermediates accompanied with nuclear deformation in the modulation of cellular genomic programs.     

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.     

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.     

Force Generation by Endocytic Actin Patches in Budding Yeast

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel. The deformation of the gel is treated using a finite-element approach. We explore the effects and interplay of three different types of force driving invagination: 1), forces perpendicular to the membrane, generated by differences between actin polymerization rates at the edge of the patch and those at the center; 2), the inherent curvature of the coat-protein layer; and 3), forces parallel to the membrane that buckle the coat protein layer, generated by an actomyosin contractile ring. We find that with optimistic estimates for the stall stress of actin gel growth and the shear modulus of the actin gel, actin polymerization can generate almost enough force to overcome the turgor pressure. In combination with the other mechanisms, actin polymerization can the force over the critical value.     

Two nondimensional parameters for characterizing the nuclear morphology

Nuclear morphology is an important indicator of cell function. It is regulated by a variety of factors such as the osmotic pressure difference between the nucleoplasm and cytoplasm, cytoskeletal forces, elasticity of the nuclear envelope and chromosomes. Nucleus shape and size are typically quantified using multiple geometrical quantities that are not necessarily independent of one another. This interdependence makes it difficult to decipher the implications of changes in nuclear morphology. We resolved this by analyzing nucleus shapes of populations for multiple cell lines using a mechanics-based model. We deduced two independent nondimensional parameters, namely, flatness index and isometric scale factor. We show that nuclei in a cell population have similar flatness but variable scale factor. Furthermore, nuclei of different cell lines segregate according to flatness. Cellular perturbations using biochemical and biomechanical techniques suggest that the flatness index correlates with actin tension and the scale factor anticorrelates with elastic modulus of nuclear envelope. We argue that nuclear morphology measures such as volume, projected area, height etc., are subsumed by flatness and scale factor, which can unambiguously characterize nuclear morphology.     

Attachment conditions control actin filament buckling and the production of forces

Actin polymerization is the driving force for a large number of cellular processes. Formation of lamellipodia and filopodia at the leading edge of motile cells requires actin polymerization induced mechanical deformation of the plasma membrane. To generate different types of membrane protrusions, the mechanical properties of actin filaments can be constrained by interacting proteins. A striking example of such constraint is the buckling of actin filaments generated in vitro by the cooperative effect of a processive actin nucleating factor (formin) and a molecular motor (myosin II). We developed a physical model based on equations for an elastic rod that accounts for actin filament buckling. Both ends of the rod were maintained in a fixed position in space and we considered three sets of boundary conditions. The model qualitatively and quantitatively reproduces the shape distribution of actin filaments. We found that actin polymerization counterpoises a force in the range 0.4-1.6 pN for moderate end-to-end distance (approximately 1 microm) and could be as large as 10 pN for shorter distances. If the actin rod attachment includes a spring, we discovered that the stiffness must be in the range 0.1-1.2 pN/nm to account for the observed buckling.     

Early spindle assembly in Drosophila embryos: role of a force balance involving cytoskeletal dynamics and nuclear mechanics

Mitotic spindle morphogenesis depends upon the action of microtubules (MTs), motors and the cell cortex. Previously, we proposed that cortical- and MT-based motors acting alone can coordinate early spindle assembly in Drosophila embryos. Here, we tested this model using microscopy of living embryos to analyze spindle pole separation, cortical reorganization, and nuclear dynamics in interphase-prophase of cycles 11-13. We observe that actin caps remain flat as they expand and that furrows do not ingress. As centrosomes separate, they follow a linear trajectory, maintaining a constant pole-to-furrow distance while the nucleus progressively deforms along the elongating pole-pole axis. These observations are incorporated into a model in which outward forces generated by zones of active cortical dynein are balanced by inward forces produced by nuclear elasticity and during cycle 13, by Ncd, which localizes to interpolar MTs. Thus, the force-balance driving early spindle morphogenesis depends upon MT-based motors acting in concert with the cortex and nucleus.     

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.     

Perinuclear cytoskeleton of acrosome-less spermatids in the blind sterile mutant mouse.

The perinuclear cytoskeleton of mammalian spermatids is thought to play a major role in nucleus-acrosome association and in shape changes of the head during spermiogenesis. To test these hypotheses acrosome-less spermatids in blind-sterile mutant mice were investigated for the development of the subacrosomal layer. Immunogold procedures were used for the detection of actin and calmodulin. In addition to various other abnormalities many acrosome-less round and elongating spermatids developed a subacrosomal layer with an actin and calmodulin distribution similar to that observed in normal spermatids. However, in mutant elongating spermatids the apical part of the nucleus was truncated and/or folded. The expected elongation and shaping of the nucleus only occurred in its caudal part associated with an hypertrophied and somewhat ectopic manchette. These abnormalities and those previously observed in mutant and experimental models indicated that the subacrosomal layer may form independently of the acrosome. It is suggested that the subacrosomal filamentous actin is a transitory scaffolding which might be involved in the assemblage of other proteins of the perinuclear cytoskeleton. However, by itself, this layer is not sufficient to ensure a normal shaping of the nucleus. Acrosome-nucleus interactions mediated by the subacrosomal layer seem necessary to shape the cranial spermatid head. The manchette appears to be involved only in the caudal nuclear shaping.     

Cell Visco-Elasticity Measured with AFM and Optical Trapping at Sub-Micrometer Deformations

The measurement of the elastic properties of cells is widely used as an indicator for cellular changes during differentiation, upon drug treatment, or resulting from the interaction with the supporting matrix. Elasticity is routinely quantified by indenting the cell with a probe of an AFM while applying nano-Newton forces. Because the resulting deformations are in the micrometer range, the measurements will be affected by the finite thickness of the cell, viscous effects and even cell damage induced by the experiment itself. Here, we have analyzed the response of single 3T3 fibroblasts that were indented with a micrometer-sized bead attached to an AFM cantilever at forces from 30–600 pN, resulting in indentations ranging from 0.2 to 1.2 micrometer. To investigate the cellular response at lower forces up to 10 pN, we developed an optical trap to indent the cell in vertical direction, normal to the plane of the coverslip. Deformations of up to two hundred nanometers achieved at forces of up to 30 pN showed a reversible, thus truly elastic response that was independent on the rate of deformation. We found that at such small deformations, the elastic modulus of 100 Pa is largely determined by the presence of the actin cortex. At higher indentations, viscous effects led to an increase of the apparent elastic modulus. This viscous contribution that followed a weak power law, increased at larger cell indentations. Both AFM and optical trapping indentation experiments give consistent results for the cell elasticity. Optical trapping has the benefit of a lower force noise, which allows a more accurate determination of the absolute indentation. The combination of both techniques allows the investigation of single cells at small and large indentations and enables the separation of their viscous and elastic components.     

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.     

High resolution detection of mechanical forces exerted by locomoting fibroblasts on the substrate

We have developed a new approach to detect mechanical forces exerted by locomoting fibroblasts on the substrate. Cells were cultured on elastic, collagen-coated polyacrylamide sheets embedded with 0. 2-micrometer fluorescent beads. Forces exerted by the cell cause deformation of the substrate and displacement of the beads. By recording the position of beads during cell locomotion and after cell removal, we discovered that most forces were radially distributed, switching direction in the anterior region. Deformations near the leading edge were strong, transient, and variable in magnitude, consistent with active local contractions, whereas those in the posterior region were weaker, more stable, and more uniform, consistent with passive resistance. Treatment of cells with cytochalasin D or myosin II inhibitors caused relaxation of the forces, suggesting that they are generated primarily via actin-myosin II interactions; treatment with nocodazole caused no immediate effect on forces. Immunofluorescence indicated that the frontal region of strong deformation contained many vinculin plaques but no apparent concentration of actin or myosin II filaments. Strong mechanical forces in the anterior region, generated by locally activated myosin II and transmitted through vinculin-rich structures, likely play a major role in cell locomotion and in mechanical signaling with the surrounding environment.     

Cooperative symmetry-breaking by actin polymerization in a model for cell motility

Polymerizing networks of actin filaments are capable of exerting significant mechanical forces, used by eukaryotic cells and their prokaryotic pathogens to change shape or to move. Here we show that small beads coated uniformly with a protein that catalyses actin polymerization are initially surrounded by symmetrical clouds of actin filaments. This symmetry is broken spontaneously, after which the beads undergo directional motion. We have developed a stochastic theory, in which each actin filament is modelled as an elastic brownian ratchet, that quantitatively accounts for the observed emergent symmetry-breaking behaviour. Symmetry-breaking can only occur for polymers that have a significant subunit off-rate, such as the biopolymers actin and tubulin.     

A three-dimensional random network model of the cytoskeleton and its role in mechanotransduction and nucleus deformation

We have developed a three-dimensional random network model of the intracellular actin cytoskeleton and have used it to study the role of the cytoskeleton in mechanotransduction and nucleus deformation. We use the model to predict the deformation of the nucleus when mechanical stresses applied on the plasma membrane are propagated through the random cytoskeletal network to the nucleus membrane. We found that our results agree with previous experiments utilizing micropipette pulling. Therefore, we propose that stress propagation through the random cytoskeletal network can be a mechanism to effect nucleus deformation, without invoking any biochemical signaling activity. Using our model, we also predict how nucleus strain and its relative displacement within the cytosol vary with varying concentrations of actin filaments and actin-binding proteins. We find that nucleus strain varies in a sigmoidal manner with actin filament concentration, while there exists an optimal concentration of actin-binding proteins that maximize nucleus displacement. We provide a theoretical analysis for these nonlinearities in terms of the connectivity of the random cytoskeletal network. Finally, we discuss laser ablation experiments that can be performed to validate these results in order to advance our understanding of the role of the cytoskeleton in mechanotransduction.     

Nuclear mechanics during cell migration

During cell migration, the movement of the nucleus must be coordinated with the cytoskeletal dynamics at the leading edge and trailing end, and, as a result, undergoes complex changes in position and shape, which in turn affects cell polarity, shape, and migration efficiency. We here describe the steps of nuclear positioning and deformation during cell polarization and migration, focusing on migration through three-dimensional matrices. We discuss molecular components that govern nuclear shape and stiffness, and review how nuclear dynamics are connected to and controlled by the actin, tubulin and intermediate cytoskeleton-based migration machinery and how this regulation is altered in pathological conditions. Understanding the regulation of nuclear biomechanics has important implications for cell migration during tissue regeneration, immune defence and cancer.     

Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model

Endothelial cells possess a mechanical network connecting adhesions on the basal surface, the cytoskeleton, and the nucleus. Transmission of force at adhesions via this pathway can deform the nucleus, ultimately resulting in an alteration of gene expression and other cellular changes (mechanotransduction). Previously, we measured cell adhesion area and apparent nuclear stretch during endothelial cell rounding. Here, we reconstruct the stress map of the nucleus from the observed strains using finite-element modeling. To simulate the disruption of adhesions, we prescribe displacement boundary conditions at the basal surface of the axisymmetric model cell. We consider different scenarios of the cytoskeletal arrangement, and represent the cytoskeleton as either discrete fibers or as an effective homogeneous layer When the nucleus is in the initial (spread) state, cytoskeletal tension holds the nucleus in an elongated, ellipsoidal configuration. Loss of cytoskeletal tension during cell rounding is represented by reactive forces acting on the nucleus in the model. In our simulations of cell rounding, we found that, for both representations of the cytoskeleton, the loss of cytoskeletal tension contributed more to the observed nuclear deformation than passive properties. Since the simulations make no assumption about the heterogeneity of the nucleus, the stress components both within and on the surface of the nucleus were calculated. The nuclear stress map showed that the nucleus experiences stress on the order of magnitude that can be significant for the function of DNA molecules and chromatin fibers. This study of endothelial cell mechanobiology suggests the possibility that mechanotransduction could result, in part, from nuclear deformation, and may be relevant to angiogenesis, wound healing, and endothelial barrier dysfunction.     

Role of Actin Filaments in Correlating Nuclear Shape and Cell Spreading

It is well known that substrate properties like stiffness and adhesivity influence stem cell morphology and differentiation. Recent experiments show that cell morphology influences nuclear geometry and hence gene expression profile. The mechanism by which surface properties regulate cell and nuclear properties is only beginning to be understood. Direct transmission of forces as well as chemical signalling are involved in this process. Here, we investigate the formal aspect by studying the correlation between cell spreading and nuclear deformation using Mesenchymal stem cells under a wide variety of conditions. It is observed that a robust quantitative relation holds between the cell and nuclear projected areas, irrespective of how the cell area is modified or when various cytoskeletal or nuclear components are perturbed. By studying the role of actin stress fibers in compressing the nucleus we propose that nuclear compression by stress fibers can lead to enhanced cell spreading due to an interplay between elastic and adhesion factors. The significance of myosin-II in regulating this process is also explored. We demonstrate this effect using a simple technique to apply external compressive loads on the nucleus.