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.

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.

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.

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.

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.

Direct force probe reveals the mechanics of nuclear homeostasis in the mammalian cell.

How cells maintain nuclear shape and position against various intracellular and extracellular forces is not well understood, although defects in nuclear mechanical homeostasis are associated with a variety of human diseases. We estimated the force required to displace and deform the nucleus in adherent living cells with a technique to locally pull the nuclear surface. A minimum pulling force of a few nanonewtons--far greater than typical intracellular motor forces--was required to significantly displace and deform the nucleus. Upon force removal, the original shape and position were restored quickly within a few seconds. This stiff, elastic response required the presence of vimentin, lamin A/C, and SUN (Sad1p, UNC-84)-domain protein linkages, but not F-actin or microtubules. Although F-actin and microtubules are known to exert mechanical forces on the nuclear surface through molecular motor activity, we conclude that the intermediate filament networks maintain nuclear mechanical homeostasis against localized forces.

Investigation of in vivo microtubule and stress fiber mechanics with laser ablation.

Laser ablation has emerged as a useful technique to study the mechanical properties of the cytoskeleton in living cells. Laser ablation perturbs the force balance in the cytoskeleton, resulting in a dynamic response which can be imaged. Quantitative measurement of the dynamic response allows the testing of mechanical theories of the cytoskeleton in living cells. This review discusses recent work in applying laser ablation to study stress fiber and microtubule mechanics in living endothelial cells. These studies reveal that molecular motors are major determinants of the mechanical properties of the cytoskeleton in cells.

Effects of dynein on microtubule mechanics and centrosome positioning.

To determine forces on intracellular microtubules, we measured shape changes of individual microtubules following laser severing in bovine capillary endothelial cells. Surprisingly, regions near newly created minus ends increased in curvature following severing, whereas regions near new microtubule plus ends depolymerized without any observable change in shape. With dynein inhibited, regions near severed minus ends straightened rapidly following severing. These observations suggest that dynein exerts a pulling force on the microtubule that buckles the newly created minus end. Moreover, the lack of any observable straightening suggests that dynein prevents lateral motion of microtubules. To explain these results, we developed a model for intracellular microtubule mechanics that predicts the enhanced buckling at the minus end of a severed microtubule. Our results show that microtubule shapes reflect a dynamic force balance in which dynein motor and friction forces dominate elastic forces arising from bending moments. A centrosomal array of microtubules subjected to dynein pulling forces and resisted by dynein friction is predicted to center on the experimentally observed time scale, with or without the pushing forces derived from microtubule buckling at the cell periphery.

Molecular mechanism of Ena/VASP-mediated actin-filament elongation.

Ena/VASP proteins are implicated in a variety of fundamental cellular processes including axon guidance and cell migration. In vitro, they enhance elongation of actin filaments, but at rates differing in nearly an order of magnitude according to species, raising questions about the molecular determinants of rate control. Chimeras from fast and slow elongating VASP proteins were generated and their ability to promote actin polymerization and to bind G-actin was assessed. By in vitro TIRF microscopy as well as thermodynamic and kinetic analyses, we show that the velocity of VASP-mediated filament elongation depends on G-actin recruitment by the WASP homology 2 motif. Comparison of the experimentally observed elongation rates with a quantitative mathematical model moreover revealed that Ena/VASP-mediated filament elongation displays a saturation dependence on the actin monomer concentration, implying that Ena/VASP proteins, independent of species, are fully saturated with actin in vivo and generally act as potent filament elongators. Moreover, our data showed that spontaneous addition of monomers does not occur during processive VASP-mediated filament elongation on surfaces, suggesting that most filament formation in cells is actively controlled.

Mechanics of Vorticella contraction.

Vorticella convallaria is one of a class of fast-moving organisms that can traverse its body size in less than a millisecond by rapidly coiling a slender stalk anchoring it to a nearby surface. The stalk houses a fiber called the spasmoneme, which winds helically within the stalk and rapidly contracts in response to calcium signaling. We have developed a coupled mechanical-chemical model of the coiling process, accounting for the coiling of the elastic stalk and the binding of calcium to the protein spasmin. Simulations of the model describe the contraction and recovery processes quantitatively. The stalk-spasmoneme system is shown to satisfy geometric constraints, which explains why the cell body sometimes rotates during contraction. The shape of the collapsing and recovering stalk bounds its effective bending stiffness. Simulations suggest that recovery from the contracted state is driven by the stalk at a rate controlled by dissociation of calcium from spasmin.

Sarcomere mechanics in capillary endothelial cells.

Tension generation in endothelial cells of the aorta, spleen, and eye occurs in actin stress fibers, and is necessary for normal cell function. Sarcomeres are the tension-generating units of actin stress fibers in endothelial cells. How sarcomeres generate and maintain tension in stress fibers is not well understood. Using femtosecond laser ablation, we severed living stress fibers and measured sarcomere contraction under zero tension. The length of the sarcomere decreased in two phases: an instantaneous initial response, followed by a slower change in length attributed to myosin activity. The latter phase ceased abruptly after a minimum sarcomere length was reached, suggesting a rigid resistance that prevents further contraction. Furthermore, severed, contracted stress fibers did not relax when treated with myosin inhibitors, indicating that contracted stress fibers do not store elastic potential energy. These novel measurements combined with modeling suggest that myosin-generated forces in adjacent sarcomeres are directly in balance, and argue against sarcomere models with springlike elements in parallel with myosin contractile elements. We propose a new model for tension generation in the sarcomere, which provides a mechanistic interpretation for our observations and previous observations of inhomogeneous sarcomere contraction and apparent stress fiber viscoelastic behavior.

Guidance of actin filament elongation on filament-binding tracks.

Biomolecular motors, which convert chemical energy into mechanical work in intracellular processes, have high potential in bionanotechnology in vitro as molecular shuttles or nanoscale actuators. In this context, guided elongation of actin filaments in vitro could be used to lay tracks for myosin motor-based shuttles or to direct nanoscale actuators based on actin filament end-tracking motors. To guide the direction of filament polymerization on surfaces, microcontact printing was used to create tracks of chemically modified myosin, which binds to, but cannot exert force on, filaments. These filament-binding tracks captured nascent filaments from solution and guided the direction of their subsequent elongation. The effect of track width and protein surface density on filament alignment and elongation rate was quantified. These results indicate that microcontact printing is a useful method for guiding actin filament polymerization in vitro for biomolecular motor-based applications.

Force generation by cytoskeletal filament end-tracking proteins.

Force generation in several types of cell motility is driven by rapidly elongating cytoskeletal filaments that are persistently tethered at their polymerizing ends to propelled objects. These properties are not easily explained by force-generation models that require free (i.e., untethered) filament ends to fluctuate away from the surface for addition of new monomers. In contrast, filament end-tracking proteins that processively advance on filament ends can facilitate rapid elongation and substantial force generation by persistently tethered filaments. Such processive end-tracking proteins, termed here filament end-tracking motors, maintain possession of filament ends and, like other biomolecular motors, advance by means of 5'-nucleoside triphosphate (NTP) hydrolysis-driven affinity-modulated interactions. On-filament NTP hydrolysis/phosphate release yields substantially more energy than that required for driving steady-state assembly/disassembly of free filament ends (i.e., filament treadmilling), as revealed by an energy inventory on the treadmilling cycle. The kinetic and thermodynamic properties of two simple end-tracking mechanisms (an end-tracking stepping motor and a direct-transfer end-tracking motor) are analyzed to illustrate the advantages of an end-tracking motor over free filament-end elongation, and over passive end-trackers that operate without the benefit of NTP hydrolysis, in terms of generating force, facilitating rapid monomer addition, and maintaining tight possession of the filament ends. We describe an additional cofactor-assisted end-tracking motor to account for suggested roles of cofactors in the affinity-modulated interactions, such as profilin in actin-filament end-tracking motors and EB1 in microtubule end-tracking motors.