Geometry of the nuclear envelope determines its flexural stiffness

Electromechanical interactions between cell membrane and nuclear envelope: Beyond the standard Schwan's model of biological cells

We investigate little-appreciated features of the hierarchical core-shell (CS) models of the electrical, mechanical, and electromechanical interactions between the cell membrane (CM) and nuclear envelope (NE). We first consider a simple model of an individual cell based on a coupled resistor-capacitor (Schwan model (SM)) network and show that the CM, when exposed to ac electric fields, acts as a low pass filter while the NE acts as a wide and asymmetric bandpass filter. We provide a simplified calculation for characteristic time associated with the capacitive charging of the NE and parameterize its range of behavior. We furthermore observe several new features dealing with mechanical analogs of the SM based on elementary spring-damper combinations. The chief merit of these models is that they can predict creep compliance responses of an individual cell under static stress and their effective retardation time constants. Next, we use an alternative and a more accurate CS physical model solved by finite element simulations for which geometrical cell reshaping under electromechanical stress (electrodeformation (ED)) is included in a continuum approach with spatial resolution. We show that under an electric field excitation, the elongated nucleus scales differently compared to the electrodeformed cell.

Investigating Uncertainties in Single-Molecule Localization Microscopy Using Experimentally Informed Monte Carlo Simulation

Single-molecule localization microscopy (SMLM) enables the visualization of cellular nanostructures in vitro with sub-20 nm resolution. While substructures can generally be imaged with SMLM, the structural understanding of the images remains elusive. To better understand the link between SMLM images and the underlying structure, we developed a Monte Carlo (MC) simulation based on experimental imaging parameters and geometric information to generate synthetic SMLM images. We chose the nuclear pore complex (NPC), a nanosized channel on the nuclear membrane which gates nucleo-cytoplasmic transport of biomolecules, as a test geometry for testing our MC model. Using the MC model to simulate SMLM images, we first optimized our clustering algorithm to separate >106 molecular localizations of fluorescently labeled NPC proteins into hundreds of individual NPCs in each cell. We then illustrated using our MC model to generate cellular substructures with different angles of labeling to inform our structural understanding through the SMLM images obtained.

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.

A Review of Continuum Mechanics for Mechanical Deformation of Lipid Membranes

Mechanical deformation of lipid membranes plays important roles in various cellular tasks. Curvature deformation and lateral stretching are two major energy contributions to the mechanical deformation of lipid membranes. In this paper, continuum theories for these two major membrane deformation events were reviewed. Theories based on curvature elasticity and lateral surface tension were introduced. Numerical methods as well as biological applications of the theories were discussed.

Nuclear lamin isoforms differentially contribute to LINC complex-dependent nucleocytoskeletal coupling and whole-cell mechanics

Interactions between the cell nucleus and cytoskeleton regulate cell mechanics and are facilitated by the interplay between the nuclear lamina and linker of nucleoskeleton and cytoskeleton (LINC) complexes. To date, the specific contribution of the four lamin isoforms to nucleocytoskeletal connectivity and whole-cell mechanics remains unknown. We discover that A- and B-type lamins distinctively interact with LINC complexes that bind F-actin and vimentin filaments to differentially modulate cortical stiffness, cytoplasmic stiffness, and contractility of mouse embryonic fibroblasts (MEFs). We propose and experimentally verify an integrated lamin–LINC complex–cytoskeleton model that explains cellular mechanical phenotypes in lamin-deficient MEFs. Our findings uncover potential mechanisms for cellular defects in human laminopathies and many cancers associated with mutations or modifications in lamin isoforms.

The ability of a cell to regulate its mechanical properties is central to its function. Emerging evidence suggests that interactions between the cell nucleus and cytoskeleton influence cell mechanics through poorly understood mechanisms. Here we conduct quantitative confocal imaging to show that the loss of A-type lamins tends to increase nuclear and cellular volume while the loss of B-type lamins behaves in the opposite manner. We use fluorescence recovery after photobleaching, atomic force microscopy, optical tweezer microrheology, and traction force microscopy to demonstrate that A-type lamins engage with both F-actin and vimentin intermediate filaments (VIFs) through the linker of nucleoskeleton and cytoskeleton (LINC) complexes to modulate cortical and cytoplasmic stiffness as well as cellular contractility in mouse embryonic fibroblasts (MEFs). In contrast, we show that B-type lamins predominantly interact with VIFs through LINC complexes to regulate cytoplasmic stiffness and contractility. We then propose a physical model mediated by the lamin–LINC complex that explains these distinct mechanical phenotypes (mechanophenotypes). To verify this model, we use dominant negative constructs and RNA interference to disrupt the LINC complexes that facilitate the interaction of the nucleus with the F-actin and VIF cytoskeletons and show that the loss of these elements results in mechanophenotypes like those observed in MEFs that lack A- or B-type lamin isoforms. Finally, we demonstrate that the loss of each lamin isoform softens the cell nucleus and enhances constricted cell migration but in turn increases migration-induced DNA damage. Together, our findings uncover distinctive roles for each of the four major lamin isoforms in maintaining nucleocytoskeletal interactions and cellular mechanics.

High Temporal Resolution 3D Live-Cell Imaging of Budding Yeast Meiosis Defines Discontinuous Actin/Telomere-Mediated Chromosome Motion, Correlated Nuclear Envelope Deformation and Actin Filament Dynamics

Chromosome movement is prominent at mid-meiotic prophase and is proposed to enhance the efficiency and/or stringency of homolog pairing and/or to help prevent or resolve topological entanglements. Here, we combine fluorescent repressor operator system (FROS) labeling with three-dimensional (3D) live-cell imaging at high spatio-temporal resolution to define the detailed kinetics of mid-meiotic prophase motion for a single telomere-proximal locus in budding yeast. Telomere motions can be grouped into three general categories: (i) pauses, in which the telomere “jiggles in place”; (ii) rapid, straight/curvilinear motion which reflects Myo2/actin-mediated transport of the monitored telomere; and (iii) slower directional motions, most of which likely reflect indirectly promoted motion of the monitored telomere in coordination with actin-mediated motion of an unmarked telomere. These and other findings highlight the importance of dynamic assembly/disassembly of telomere/LINC/actin ensembles and also suggest important roles for nuclear envelope deformations promoted by actin-mediated telomere/LINC movement. The presented low-SNR (signal-to-noise ratio) imaging methodology provides opportunities for future exploration of homolog pairing and related phenomena.

Nuclear pores dilate and constrict in cellulo

[Figure: see text].