Nuclear shapes are geometrically determined by the excess surface area of the nuclear lamina.

Introduction: Nuclei have characteristic shapes dependent on cell type, which are critical for proper cell function, and nuclei lose their distinct shapes in multiple diseases including cancer, laminopathies, and progeria. Nuclear shapes result from deformations of the sub-nuclear components-nuclear lamina and chromatin. How these structures respond to cytoskeletal forces to form the nuclear shape remains unresolved. Although the mechanisms regulating nuclear shape in human tissues are not fully understood, it is known that different nuclear shapes arise from cumulative nuclear deformations post-mitosis, ranging from the rounded morphologies that develop immediately after mitosis to the various nuclear shapes that roughly correspond to cell shape (e.g., elongated nuclei in elongated cells, flat nuclei in flat cells). Methods: We formulated a mathematical model to predict nuclear shapes of cells in various contexts under the geometric constraints of fixed cell volume, nuclear volume and lamina surface area. Nuclear shapes were predicted and compared to experiments for cells in various geometries, including isolated on a flat surface, on patterned rectangles and lines, within a monolayer, isolated in a well, or when the nucleus is impinging against a slender obstacle. Results and Discussion: The close agreement between predicted and experimental shapes demonstrates a simple geometric principle of nuclear shaping: the excess surface area of the nuclear lamina (relative to that of a sphere of the same volume) permits a wide range of highly deformed nuclear shapes under the constraints of constant surface area and constant volume. When the lamina is smooth (tensed), the nuclear shape can be predicted entirely from these geometric constraints alone for a given cell shape. This principle explains why flattened nuclear shapes in fully spread cells are insensitive to the magnitude of the cytoskeletal forces. Also, the surface tension in the nuclear lamina and nuclear pressure can be estimated from the predicted cell and nuclear shapes when the cell cortical tension is known, and the predictions are consistent with measured forces. These results show that excess surface area of the nuclear lamina is the key determinant of nuclear shapes. When the lamina is smooth (tensed), the nuclear shape can be determined purely by the geometric constraints of constant (but excess) nuclear surface area, nuclear volume, and cell volume, for a given cell adhesion footprint, independent of the magnitude of the cytoskeletal forces involved.

Rho activation drives luminal collapse and eversion in epithelial acini.

Epithelial cells lining a gland and cells grown in a soft extracellular matrix polarize with apical proteins exposed to the lumen and basal proteins in contact with the extracellular matrix. Alterations to polarity, including an apical-out polarity, occur in human cancers. Although some aberrant polarity states may result from altered protein trafficking, recent observations of an extraordinary tissue-level inside-out unfolding suggest an alternative pathway for altered polarity. Because mechanical alterations are common in human cancer, including an upregulation of RhoA-mediated actomyosin tension in acinar epithelia, we explored whether perturbing mechanical homeostasis could cause apical-out eversion. Acinar eversion was robustly induced by direct activation of RhoA in normal and tumor epithelial acini, or indirect activation of RhoA through blockage of ß1-integrins, disruption of the LINC complex, oncogenic Ras activation, or Rac1 inhibition. Furthermore, laser ablation of a portion of the untreated acinus was sufficient to induce eversion. Analyses of acini revealed high curvature and low phosphorylated myosin in the apical cell surfaces relative to the basal surfaces. A vertex-based mathematical model that balances tension at cell-cell interfaces revealed a fivefold greater basal cell surface tension relative to the apical cell surface tension. The model suggests that the difference in surface energy between the apical and basal surfaces is the driving force for acinar eversion. Our findings raise the possibility that a loss of mechanical homeostasis may cause apical-out polarity states in human cancers.

A new function for nuclear lamins: providing surface tension to the nuclear drop.

The nuclear lamina, a conserved structure in metazoans, provides mechanical rigidity to the nuclear envelope. A decrease in lamin levels and/or lamin mutations are associated with a host of human diseases. Despite being only about 15 nm thick, perturbation of components of the nuclear lamina dramatically impacts the deformation response of the entire nucleus through mechanisms that are not well understood. Here we discuss evidence for the recently proposed 'nuclear drop' model that explains the role of A-type lamins in nuclear deformation in migrating cells. In this model, the nuclear lamina acts as an inextensible surface, supporting a surface tension when fully unfolded, that balances nuclear interior pressure. Much like a liquid drop surface where the molecularly thin interface governs surface tension and drop shape under external forces, the thin nuclear lamina imparts a surface tension on the nuclear drop to resist nuclear deformation as well as to establish nuclear shape. We discuss implications of the nuclear drop model for the function of this crucially important eukaryotic organelle.

The Nucleus Bypasses Obstacles by Deforming Like a Drop with Surface Tension Mediated by Lamin A/C.

Migrating cells must deform their stiff cell nucleus to move through pores and fibers in tissue. Lamin A/C is known to hinder cell migration by limiting nuclear deformation and passage through confining channels, but its role in nuclear deformation and passage through fibrous environments is less clear. Cell and nuclear migration through discrete, closely spaced, slender obstacles which mimic the mechanical properties of collagen fibers are studied. Nuclei bypass slender obstacles while preserving their overall morphology by deforming around them with deep local invaginations of little resisting force. The obstacles do not impede the nuclear trajectory and do not cause rupture of the nuclear envelope. Nuclei likewise deform around single collagen fibers in cells migrating in 3D collagen gels. In contrast to its limiting role in nuclear passage through confining channels, lamin A/C facilitates nuclear deformation and passage through fibrous environments; nuclei in lamin-null (Lmna-/- ) cells lose their overall morphology and become entangled on the obstacles. Analogous to surface tension-mediated deformation of a liquid drop, lamin A/C imparts a surface tension on the nucleus that allows nuclear invaginations with little mechanical resistance, preventing nuclear entanglement and allowing nuclear passage through fibrous environments.

Viscous shaping of the compliant cell nucleus.

The cell nucleus is commonly considered to be a stiff organelle that mechanically resists changes in shape, and this resistance is thought to limit the ability of cells to migrate through pores or spread on surfaces. Generation of stresses on the cell nucleus during migration and nuclear response to these stresses is fundamental to cell migration and mechano-transduction. In this Perspective, we discuss our previous experimental and computational evidence that supports a dynamic model, in which the soft nucleus is irreversibly shaped by viscous stresses generated by the motion of cell boundaries and transmitted through the intervening cytoskeletal network. While the nucleus is commonly modeled as a stiff elastic body, we review how nuclear shape changes on the timescale of migration can be explained by simple geometric constraints of constant nuclear volume and constant surface area of the nuclear lamina. Because the lamina surface area is in excess of that of a sphere of the same volume, these constraints permit dynamic transitions between a wide range of shapes during spreading and migration. The excess surface area allows the nuclear shape changes to mirror those of the cell with little mechanical resistance. Thus, the nucleus can be easily shaped by the moving cell boundaries over a wide range of shape changes and only becomes stiff to more extreme deformations that would require the lamina to stretch or the volume to compress. This model explains how nuclei can easily flatten on surfaces during cell spreading or elongate as cells move through pores until the lamina smooths out and becomes tense.

Nuclear size changes caused by local motion of cell boundaries unfold the nuclear lamina and dilate chromatin and intranuclear bodies.

The mechanisms by which mammalian nuclear shape and size are established in cells, and become abnormal in disease states are not understood. Here, we tracked motile cells that underwent systematic changes in cell morphology as they moved from 1-D to 2-D micro-patterned adhesive domains. Motion of the cell boundaries during cell motility caused a dynamic and systematic change in nuclear volume. Short time scales (∼1 h) distinguished the dilation of the nucleus from the familiar increase that occurs during the cell cycle. Nuclear volume was systematically different between cells cultured in 3-D, 2-D and 1-D environments. Dilation of the nuclear volume was accompanied by dilation of chromatin, a decrease in the number of folds in the nuclear lamina, and an increase in nucleolar volume. Treatment of 2-D cells with non-muscle myosin-II inhibitors decreased cell volume, and proportionately caused a decrease in nuclear volume. These data suggest that nuclear size changes during cell migration may potentially impact gene expression through the modulation of intranuclear structure.

Mechanical Stabilization of the Glandular Acinus by Linker of Nucleoskeleton and Cytoskeleton Complex.

The nucleoskeleton and cytoskeleton are important protein networks that govern cellular behavior and are connected together by the linker of nucleoskeleton and cytoskeleton (LINC) complex. Mutations in LINC complex components may be relevant to cancer, but how cell-level changes might translate into tissue-level malignancy is unclear. We used glandular epithelial cells in a three-dimensional culture model to investigate the effect of perturbations of the LINC complex on higher order cellular architecture. We show that inducible LINC complex disruption in human mammary epithelial MCF-10A cells and canine kidney epithelial MDCK II cells mechanically destabilizes the acinus. Lumenal collapse occurs because the acinus is unstable to increased mechanical tension that is caused by upregulation of Rho-kinase-dependent non-muscle myosin II motor activity. These findings provide a potential mechanistic explanation for how disruption of LINC complex may contribute to a loss of tissue structure in glandular epithelia.

Apical cell protrusions cause vertical deformation of the soft cancer nucleus.

Breast cancer nuclei have highly irregular shapes, which are diagnostic and prognostic markers of breast cancer progression. The mechanisms by which irregular cancer nuclear shapes develop are not well understood. Here we report the existence of vertical, apical cell protrusions in cultured MDA-MB-231 breast cancer cells. Once formed, these protrusions persist over time scales of hours and are associated with vertically upward nuclear deformations. They are absent in normal mammary epithelial cells (MCF-10A cells). Microtubule disruption enriched these protrusions preferentially in MDA-MB-231 cells compared with MCF-10A cells, whereas inhibition of nonmuscle myosin II (NMMII) abolished this enrichment. Dynamic confocal imaging of the vertical cell and nuclear shape revealed that the apical cell protrusions form first, and in response, the nucleus deforms and/or subsequently gets vertically extruded into the apical protrusion. Overexpression of lamin A/C in MDA-MB-231 cells reduced nuclear deformation in apical protrusions. These data highlight the role of mechanical stresses generated by moving boundaries, as well as abnormal nuclear mechanics in the development of abnormal nuclear shapes in breast cancer cells.

Local, transient tensile stress on the nuclear membrane causes membrane rupture.

Cancer cell migration through narrow constrictions generates compressive stresses on the nucleus that deform it and cause rupture of nuclear membranes. Nuclear membrane rupture allows uncontrolled exchange between nuclear and cytoplasmic contents. Local tensile stresses can also cause nuclear deformations, but whether such deformations are accompanied by nuclear membrane rupture is unknown. Here we used a direct force probe to locally deform the nucleus by applying a transient tensile stress to the nuclear membrane. We found that a transient (∼0.2 s) deformation (∼1% projected area strain) in normal mammary epithelial cells (MCF-10A cells) was sufficient to cause rupture of the nuclear membrane. Nuclear membrane rupture scaled with the magnitude of nuclear deformation and the magnitude of applied tensile stress. Comparison of diffusive fluxes of nuclear probes between wild-type and lamin-depleted MCF-10A cells revealed that lamin A/C, but not lamin B2, protects the nuclear membranes against rupture from tensile stress. Our results suggest that transient nuclear deformations typically caused by local tensile stresses are sufficient to cause nuclear membrane rupture.

Mechanical principles of nuclear shaping and positioning.

Positioning and shaping the nucleus represents a mechanical challenge for the migrating cell because of its large size and resistance to deformation. Cells shape and position the nucleus by transmitting forces from the cytoskeleton onto the nuclear surface. This force transfer can occur through specialized linkages between the nuclear envelope and the cytoskeleton. In response, the nucleus can deform and/or it can move. Nuclear movement will occur when there is a net differential in mechanical force across the nucleus, while nuclear deformation will occur when mechanical forces overcome the mechanical resistance of the various structures that comprise the nucleus. In this perspective, we review current literature on the sources and magnitude of cellular forces exerted on the nucleus, the nuclear envelope proteins involved in transferring cellular forces, and the contribution of different nuclear structural components to the mechanical response of the nucleus to these forces.

Direct Force Probe for Nuclear Mechanics.

We describe a recently reported method for directly applying a known, nanonewton-scale force to the nucleus in a living, intact cell. First, a suction seal is applied on the nuclear surface using a micropipette. Then, the micropipette is translated away from the nucleus. The nucleus deforms and translates with the moving micropipette and then eventually detaches from the micropipette and recovers (roughly) its original shape and position. At the point of detachment, the resisting force (from the deformed nucleus and connected cytoskeleton) balances the suction force. Because the suction force is precisely known and reproducibly applied, this method therefore allows comparisons of nuclear response across disruptions to the cytoskeleton, nucleus, or cell. This method is useful for quantifying nuclear elastic properties in its native, integrated environment.

The nucleus is irreversibly shaped by motion of cell boundaries in cancer and non-cancer cells.

Actomyosin stress fibers impinge on the nucleus and can exert compressive forces on it. These compressive forces have been proposed to elongate nuclei in fibroblasts, and lead to abnormally shaped nuclei in cancer cells. In these models, the elongated or flattened nuclear shape is proposed to store elastic energy. However, we found that deformed shapes of nuclei are unchanged even after removal of the cell with micro-dissection, both for smooth, elongated nuclei in fibroblasts and abnormally shaped nuclei in breast cancer cells. The lack of shape relaxation implies that the nuclear shape in spread cells does not store any elastic energy, and the cellular stresses that deform the nucleus are dissipative, not static. During cell spreading, the deviation of the nucleus from a convex shape increased in MDA-MB-231 cancer cells, but decreased in MCF-10A cells. Tracking changes of nuclear and cellular shape on micropatterned substrata revealed that fibroblast nuclei deform only during deformations in cell shape and only in the direction of nearby moving cell boundaries. We propose that motion of cell boundaries exert a stress on the nucleus, which allows the nucleus to mimic cell shape. The lack of elastic energy in the nuclear shape suggests that nuclear shape changes in cells occur at constant surface area and volume.

Distinct VASP tetramers synergize in the processive elongation of individual actin filaments from clustered arrays.

Ena/VASP proteins act as actin polymerases that drive the processive elongation of filament barbed ends in membrane protrusions or at the surface of bacterial pathogens. Based on previous analyses of fast and slow elongating VASP proteins by in vitro total internal reflection fluorescence microscopy (TIRFM) and kinetic and thermodynamic measurements, we established a kinetic model of Ena/VASP-mediated actin filament elongation. At steady state, it entails that tetrameric VASP uses one of its arms to processively track growing filament barbed ends while three G-actin-binding sites (GABs) on other arms are available to recruit and deliver monomers to the filament tip, suggesting that VASP operates as a single tetramer in solution or when clustered on a surface, albeit processivity and resistance toward capping protein (CP) differ dramatically between both conditions. Here, we tested the model by variation of the oligomerization state and by increase of the number of GABs on individual polypeptide chains. In excellent agreement with model predictions, we show that in solution the rates of filament elongation directly correlate with the number of free GABs. Strikingly, however, irrespective of the oligomerization state or presence of additional GABs, filament elongation on a surface invariably proceeded with the same rate as with the VASP tetramer, demonstrating that adjacent VASP molecules synergize in the elongation of a single filament. Additionally, we reveal that actin ATP hydrolysis is not required for VASP-mediated filament assembly. Finally, we show evidence for the requirement of VASP to form tetramers and provide an amended model of processive VASP-mediated actin assembly in clustered arrays.

Transient Pinning and Pulling: A Mechanism for Bending Microtubules.

Microtubules have a persistence length of the order of millimeters in vitro, but inside cells they bend over length scales of microns. It has been proposed that polymerization forces bend microtubules in the vicinity of the cell boundary or other obstacles, yet bends develop even when microtubules are polymerizing freely, unaffected by obstacles and cell boundaries. How these bends are formed remains unclear. By tracking the motions of microtubules marked by photobleaching, we found that in LLC-PK1 epithelial cells local bends develop primarily by plus-end directed transport of portions of the microtubule contour towards stationary locations (termed pinning points) along the length of the microtubule. The pinning points were transient in nature, and their eventual release allowed the bends to relax. The directionality of the transport as well as the overall incidence of local bends decreased when dynein was inhibited, while myosin inhibition had no observable effect. This suggests that dynein generates a tangential force that bends microtubules against stationary pinning points. Simulations of microtubule motion and polymerization accounting for filament mechanics and dynein forces predict the development of bends of size and shape similar to those observed in cells. Furthermore, simulations show that dynein-generated bends at a pinning point near the plus end can cause a persistent rotation of the tip consistent with the observation that bend formation near the tip can change the direction of microtubule growth. Collectively, these results suggest a simple physical mechanism for the bending of growing microtubules by dynein forces accumulating at pinning points.

Concentration Sensing by the Moving Nucleus in Cell Fate Determination: A Computational Analysis.

During development of the vertebrate neuroepithelium, the nucleus in neural progenitor cells (NPCs) moves from the apex toward the base and returns to the apex (called interkinetic nuclear migration) at which point the cell divides. The fate of the resulting daughter cells is thought to depend on the sampling by the moving nucleus of a spatial concentration profile of the cytoplasmic Notch intracellular domain (NICD). However, the nucleus executes complex stochastic motions including random waiting and back and forth motions, which can expose the nucleus to randomly varying levels of cytoplasmic NICD. How nuclear position can determine daughter cell fate despite the stochastic nature of nuclear migration is not clear. Here we derived a mathematical model for reaction, diffusion, and nuclear accumulation of NICD in NPCs during interkinetic nuclear migration (INM). Using experimentally measured trajectory-dependent probabilities of nuclear turning, nuclear waiting times and average nuclear speeds in NPCs in the developing zebrafish retina, we performed stochastic simulations to compute the nuclear trajectory-dependent probabilities of NPC differentiation. Comparison with experimentally measured nuclear NICD concentrations and trajectory-dependent probabilities of differentiation allowed estimation of the NICD cytoplasmic gradient. Spatially polarized production of NICD, rapid NICD cytoplasmic consumption and the time-averaging effect of nuclear import/export kinetics are sufficient to explain the experimentally observed differentiation probabilities. Our computational studies lend quantitative support to the feasibility of the nuclear concentration-sensing mechanism for NPC fate determination in zebrafish retina.

Vertical uniformity of cells and nuclei in epithelial monolayers.

Morphological variability in cytoskeletal organization, organelle position and cell boundaries is a common feature of cultured cells. Remarkable uniformity and reproducibility in structure can be accomplished by providing cells with defined geometric cues. Cells in tissues can also self-organize in the absence of directing extracellular cues; however the mechanical principles for such self-organization are not understood. We report that unlike horizontal shapes, the vertical shapes of the cell and nucleus in the z-dimension are uniform in cells in cultured monolayers compared to isolated cells. Apical surfaces of cells and their nuclei in monolayers were flat and heights were uniform. In contrast, isolated cells, or cells with disrupted cell-cell adhesions had nuclei with curved apical surfaces and variable heights. Isolated cells cultured within micron-sized square wells displayed flat cell and nuclear shapes similar to cells in monolayers. Local disruption of nuclear-cytoskeletal linkages resulted in spatial variation in vertical uniformity. These results suggest that competition between cell-cell pulling forces that expand and shorten the vertical cell cross-section, thereby widening and flattening the nucleus, and the resistance of the nucleus to further flattening results in uniform cell and nuclear cross-sections. Our results reveal the mechanical principles of self-organized vertical uniformity in cell monolayers.

Coordinated Dynamics of RNA Splicing Speckles in the Nucleus.

Despite being densely packed with chromatin, nuclear bodies and a nucleoskeletal network, the nucleus is a remarkably dynamic organelle. Chromatin loops form and relax, RNA transcripts and transcription factors move diffusively, and nuclear bodies move. We show here that RNA splicing speckled domains (splicing speckles) fluctuate in constrained nuclear volumes and remodel their shapes. Small speckles move in a directed way toward larger speckles with which they fuse. This directed movement is reduced upon decreasing cellular ATP levels or inhibiting RNA polymerase II activity. The random movement of speckles is reduced upon decreasing cellular ATP levels, moderately reduced after inhibition of SWI/SNF chromatin remodeling and modestly increased upon inhibiting RNA polymerase II activity. To define the paths through which speckles can translocate in the nucleus, we generated a pressure gradient to create flows in the nucleus. In response to the pressure gradient, speckles moved along curvilinear paths in the nucleus. Collectively, our results demonstrate a new type of ATP-dependent motion in the nucleus. We present a model where recycling splicing factors return as part of small sub-speckles from distal sites of RNA processing to larger splicing speckles by a directed ATP-driven mechanism through interchromatin spaces.

New approaches for understanding the nuclear force balance in living, adherent cells.

Cytoskeletal forces are transmitted to the nucleus to position and shape it. Linkages mediated by the LINC (linker of nucleoskeleton and cytoskeleton) complex transfer these forces to the nuclear envelope. Nuclear position and shape can be thought to be determined by a balance of cytoskeletal forces generated by microtubule motors that shear the nuclear surface, actomyosin forces that can pull, push and shear the nucleus, and intermediate filaments that may passively resist nuclear decentering and deformation. Parsing contributions of these different forces to nuclear mechanics is a very challenging task. Here we review new approaches that can be used in living cells to probe and understand the nuclear force balance.

Dynamic, mechanical integration between nucleus and cell- where physics meets biology.

Nuclear motions like rotation, translation and deformation suggest that the nucleus is acted upon by mechanical forces. Molecular linkages with the cytoskeleton are thought to transfer forces to the nuclear surface. We developed an approach to apply reproducible, known mechanical forces to the nucleus in spread adherent cells and quantified the elastic response of the mechanically integrated nucleus-cell. The method is sensitive to molecular perturbations and revealed new insight into the function of the LINC complex. While these experiments revealed elastic behaviors, turnover of the cytoskeleton by assembly/disassembly and binding/unbinding of linkages are expected to dissipate any stored mechanical energy in the nucleus or the cytoskeleton. Experiments investigating nuclear forces over longer time scales demonstrated the mechanical principle that expansive/compressive stresses on the nuclear surface arise from the movement of the cell boundaries to shape and position the nucleus. Such forces can shape the nucleus to conform to cell shapes during cell movements with or without myosin activity.

Moving Cell Boundaries Drive Nuclear Shaping during Cell Spreading.

The nucleus has a smooth, regular appearance in normal cells, and its shape is greatly altered in human pathologies. Yet, how the cell establishes nuclear shape is not well understood. We imaged the dynamics of nuclear shaping in NIH3T3 fibroblasts. Nuclei translated toward the substratum and began flattening during the early stages of cell spreading. Initially, nuclear height and width correlated with the degree of cell spreading, but over time, reached steady-state values even as the cell continued to spread. Actomyosin activity, actomyosin bundles, microtubules, and intermediate filaments, as well as the LINC complex, were all dispensable for nuclear flattening as long as the cell could spread. Inhibition of actin polymerization as well as myosin light chain kinase with the drug ML7 limited both the initial spreading of cells and flattening of nuclei, and for well-spread cells, inhibition of myosin-II ATPase with the drug blebbistatin decreased cell spreading with associated nuclear rounding. Together, these results show that cell spreading is necessary and sufficient to drive nuclear flattening under a wide range of conditions, including in the presence or absence of myosin activity. To explain this observation, we propose a computational model for nuclear and cell mechanics that shows how frictional transmission of stress from the moving cell boundaries to the nuclear surface shapes the nucleus during early cell spreading. Our results point to a surprisingly simple mechanical system in cells for establishing nuclear shapes.