Mechanics and Buckling of Biopolymeric Shells and Cell Nuclei

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus

Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a "wetting"-like interaction. In contrast, fluctuations are insensitive to heterochromatin's internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.

Rethinking nuclear shaping: insights from the nuclear drop model

Changes in the nuclear shape caused by cellular shape changes are generally assumed to reflect an elastic deformation from a spherical nuclear shape. Recent evidence, however, suggests that the nuclear lamina, which forms the outer nuclear surface together with the nuclear envelope, possesses more area than that of a sphere of the same volume. This excess area manifests as folds/wrinkles in the nuclear surface in rounded cells and allows facile nuclear flattening during cell spreading without any changes in nuclear volume or surface area. When the lamina becomes smooth and taut, it is inextensible, and supports a surface tension. At this point, it is possible to mathematically calculate the limiting nuclear shape purely based on geometric considerations. In this paper, we provide a commentary on the "nuclear drop model" which seeks to integrate the above features. We outline its testable physical properties and explore its biological implications.

CTCF is essential for proper mitotic spindle structure and anaphase segregation

Mitosis is an essential process in which the duplicated genome is segregated equally into two daughter cells. CTCF has been reported to be present in mitosis and has a role in localizing CENP-E, but its importance for mitotic fidelity remains to be determined. To evaluate the importance of CTCF in mitosis, we tracked mitotic behaviors in wild-type and two different CTCF CRISPR-based genetic knockdowns. We find that knockdown of CTCF results in prolonged mitoses and failed anaphase segregation via time-lapse imaging of SiR-DNA. CTCF knockdown did not alter cell cycling or the mitotic checkpoint, which was activated upon nocodazole treatment. Immunofluorescence imaging of the mitotic spindle in CTCF knockdowns revealed disorganization via tri/tetrapolar spindles and chromosomes behind the spindle pole. Imaging of interphase nuclei showed that nuclear size increased drastically, consistent with failure to divide the duplicated genome in anaphase. Long-term inhibition of CNEP-E via GSK923295 recapitulates CTCF knockdown abnormal mitotic spindles with polar chromosomes and increased nuclear sizes. Population measurements of nuclear shape in CTCF knockdowns do not display decreased circularity or increased nuclear blebbing relative to wild-type. However, failed mitoses do display abnormal nuclear morphologies relative to successful mitoses, suggesting that population images do not capture individual behaviors. Thus, CTCF is important for both proper metaphase organization and anaphase segregation which impacts the size and shape of the interphase nucleus likely through its known role in recruiting CENP-E.

A Computational Model of Mechanical Stretching of Cultured Cells on a Flexible Membrane

Mechanical forces applied to cells are known to regulate a wide variety of biological processes. Recent studies have supported that mechanical forces can cause nuclear deformation, leading to significant alterations in the gene expression and chromatin landscape of the cell. While the stresses and strains applied to cells is it is often known or controlled experimentally on a macroscopic length scale, it is often unclear what the actual forces and displacements are at the microscopic level of the cell. In this work, we created a model of cell deformation during application of mechanical stretch to cultured cells growth on a flexible membrane. This configuration is commonly used is in experimental studies as a means to apply controlled mechanical strains to adherent cultured cells. The parameters used in the study were used for application of strain to a mesenchymal stem cell stretched on a membrane. computational model was created to simulate the stresses and strains within the cell under a variety of stain amplitudes, waveforms and frequencies of mechanical loading with the range of commonly used experimental systems. The results demonstrate the connection between mechanical loading parameters applied through the flexible membrane and the resulting stresses and strains within the cell and nucleus. Using a viscoelastic model of chromatin, we connected the results provide to a rough model of resulting deformation within chromatin from the forces applied to the nucleus. Overall, the model is useful in providing insight between experimentally applied mechanical forces and the actual forces within the cell to better interpret the results of experimental studies.

Statement of Significance

In this work, we created a computational model of the mechanical stretching of cell on a flexible membrane under cyclic mechanical loading. This model provides insight into the forces and displacements inside of cell that result from that application of stretch. As many experiments use this set up, our work is relevant to interpreting many studies that use mechanical stretch to stimulate mechanotransduction.

Buckling kinetics of graphene membranes under uniaxial compression

Despite past investigations of the buckling instability, the kinetics of the buckling process is not well understood. We develop a generic framework for determining the buckling kinetics of membranes under compressive stress (σ_{b}) via molecular dynamics simulations. The buckling time (t_{b}) is modeled by an extended Boltzmann-Arrhenius-Zhurkov equation accounting for temperature (T) and scale-dependent bending rigidity. We discern three regimes: (I) t_{b} decreases with T; (II) t_{b} increases with T; (III) t_{b} is T independent. Regime II coheres with the predictions of the theory of fluctuating sheets (TFS). Regime I is seen at small scales due to fluctuations about equilibrium and is not predicted by the TFS.

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus

Abnormalities in the shapes of mammalian cell nuclei are hallmarks of a variety of diseases, including progeria, muscular dystrophy, and various cancers. Experiments have shown that there is a causal relationship between chromatin organization and nuclear morphology. Decreases in heterochromatin levels, perturbations to heterochromatin organization, and increases in euchromatin levels all lead to misshapen nuclei, which exhibit deformations, such as nuclear blebs and nuclear ruptures. However, the polymer physical mechanisms of how chromatin governs nuclear shape and integrity are poorly understood. To investigate how heterochromatin and euchromatin, which are thought to microphase separate in vivo , govern nuclear morphology, we implemented a composite coarse-grained polymer and elastic shell model. By varying chromatin volume fraction (density), heterochromatin levels and structure, and heterochromatin-lamina interactions, we show how the spatial organization of chromatin polymer phases within the nucleus could perturb nuclear shape in some scenarios. Increasing the volume fraction of chromatin in the cell nucleus stabilizes the nuclear lamina against large fluctuations. However, surprisingly, we find that increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations in our simulations by a "wetting"-like interaction. In contrast, shape fluctuations are largely insensitive to the internal structure of the heterochromatin, such as the presence or absence of chromatin-chromatin crosslinks. Therefore, our simulations suggest that heterochromatin accumulation at the nuclear periphery could perturb nuclear morphology in a nucleus or nuclear region that is sufficiently soft, while stabilization of the nucleus via heterochromatin likely occurs through mechanisms other than chromatin microphase organization.

Nuclear growth and import can be uncoupled

What drives nuclear growth? Studying nuclei assembled in Xenopus egg extract and focusing on importin α/β-mediated nuclear import, we show that, while import is required for nuclear growth, nuclear growth and import can be uncoupled when chromatin structure is manipulated. Nuclei treated with micrococcal nuclease to fragment DNA grew slowly despite exhibiting little to no change in import rates. Nuclei assembled around axolotl chromatin with 20-fold more DNA than Xenopus grew larger but imported more slowly. Treating nuclei with reagents known to alter histone methylation or acetylation caused nuclei to grow less while still importing to a similar extent or to grow larger without significantly increasing import. Nuclear growth but not import was increased in live sea urchin embryos treated with the DNA methylator N-nitrosodimethylamine. These data suggest that nuclear import is not the primary driving force for nuclear growth. Instead, we observed that nuclear blebs expanded preferentially at sites of high chromatin density and lamin addition, whereas small Benzonase-treated nuclei lacking DNA exhibited reduced lamin incorporation into the nuclear envelope. In summary, we report experimental conditions where nuclear import is not sufficient to drive nuclear growth, hypothesizing that this uncoupling is a result of altered chromatin structure.

Transcription inhibition suppresses nuclear blebbing and rupture independently of nuclear rigidity

Chromatin plays an essential role in the nuclear mechanical response and determining nuclear shape, which maintain nuclear compartmentalization and function. However, major genomic functions, such as transcription activity, might also impact cell nuclear shape via blebbing and rupture through their effects on chromatin structure and dynamics. To test this idea, we inhibited transcription with several RNA polymerase II inhibitors in wild-type cells and perturbed cells that presented increased nuclear blebbing. Transcription inhibition suppressed nuclear blebbing for several cell types, nuclear perturbations and transcription inhibitors. Furthermore, transcription inhibition suppressed nuclear bleb formation, bleb stabilization and bleb-based nuclear ruptures. Interestingly, transcription inhibition did not alter the histone H3 lysine 9 (H3K9) modification state, nuclear rigidity, and actin compression and contraction, which typically control nuclear blebbing. Polymer simulations suggested that RNA polymerase II motor activity within chromatin could drive chromatin motions that deform the nuclear periphery. Our data provide evidence that transcription inhibition suppresses nuclear blebbing and rupture, in a manner separate and distinct from chromatin rigidity.

Biophysical ordering transitions underlie genome 3D re-organization during cricket spermiogenesis

Spermiogenesis is a radical process of differentiation whereby sperm cells acquire a compact and specialized morphology to cope with the constraints of sexual reproduction while preserving their main cargo, an intact copy of the paternal genome. In animals, this often involves the replacement of most histones by sperm-specific nuclear basic proteins (SNBPs). Yet, how the SNBP-structured genome achieves compaction and accommodates shaping remain largely unknown. Here, we exploit confocal, electron and super-resolution microscopy, coupled with polymer modeling to identify the higher-order architecture of sperm chromatin in the needle-shaped nucleus of the emerging model cricket Gryllus bimaculatus. Accompanying spermatid differentiation, the SNBP-based genome is strikingly reorganized as ~25nm-thick fibers orderly coiled along the elongated nucleus axis. This chromatin spool is further found to achieve large-scale helical twisting in the final stages of spermiogenesis, favoring its ultracompaction. We reveal that these dramatic transitions may be recapitulated by a surprisingly simple biophysical principle based on a nucleated rigidification of chromatin linked to the histone-to-SNBP transition within a confined nuclear space. Our work highlights a unique, liquid crystal-like mode of higher-order genome organization in ultracompact cricket sperm, and establishes a multidisciplinary methodological framework to explore the diversity of non-canonical modes of DNA organization.

Nuclear growth and import can be uncoupled

What drives nuclear growth? Studying nuclei assembled in Xenopus egg extract and focusing on importin α/β-mediated nuclear import, we show that, while nuclear growth depends on nuclear import, nuclear growth and import can be uncoupled. Nuclei containing fragmented DNA grew slowly despite exhibiting normal import rates, suggesting nuclear import itself is insufficient to drive nuclear growth. Nuclei containing more DNA grew larger but imported more slowly. Altering chromatin modifications caused nuclei to grow less while still importing to the same extent or to grow larger without increasing nuclear import. Increasing heterochromatin in vivo in sea urchin embryos increased nuclear growth but not import. These data suggest that nuclear import is not the primary driving force for nuclear growth. Instead, live imaging showed that nuclear growth preferentially occurred at sites of high chromatin density and lamin addition, whereas small nuclei lacking DNA exhibited less lamin incorporation. Our hypothesized model is that lamin incorporation and nuclear growth are driven by chromatin mechanical properties, which depend on and can be tuned by nuclear import.

CTCF is essential for proper mitotic spindle structure and anaphase segregation

Mitosis is an essential process in which the duplicated genome is segregated equally into two daughter cells. CTCF has been reported to be present in mitosis but its importance for mitotic fidelity remains to be determined. To evaluate the importance of CTCF in mitosis, we tracked mitotic behaviors in wild type and two different CTCF CRISPR-based genetic knockdowns. We find that knockdown of CTCF results in prolonged mitoses and failed anaphase segregation via time lapse imaging of SiR-DNA. CTCF knockdown did not alter cell cycling or the mitotic checkpoint, which was activated upon nocodazole treatment. Immunofluorescence imaging of the mitotic spindle in CTCF knockdowns revealed disorganization via tri/tetrapolar spindles and chromosomes behind the spindle pole. Imaging of interphase nuclei showed that nuclear size increased drastically, consistent with failure to divide the duplicated genome in anaphase. Population measurements of nuclear shape in CTCF knockdowns do not display decreased circularity or increased nuclear blebbing relative to wild type. However, failed mitoses do display abnormal nuclear morphologies relative to successful mitoses, suggesting population images do not capture individual behaviors. Thus, CTCF is important for both proper metaphase organization and anaphase segregation which impacts the size and shape of the interphase nucleus.

A Versatile Micromanipulation Apparatus for Biophysical Assays of the Cell Nucleus

Intro

Force measurements of the nucleus, the strongest organelle, have propelled the field of mechanobiology to understand the basic mechanical components of the nucleus and how these components properly support nuclear morphology and function. Micromanipulation force measurement provides separation of the relative roles of nuclear mechanical components chromatin and lamin A.

Methods

To provide access to this technique, we have developed a universal micromanipulation apparatus for inverted microscopes. We outline how to engineer and utilize this apparatus through dual micromanipulators, fashion and calibrate micropipettes, and flow systems to isolate a nucleus and provide force vs. extensions measurements. This force measurement approach provides the unique ability to measure the separate contributions of chromatin at short extensions and lamin A strain stiffening at long extensions. We then investigated the apparatus’ controllable and programmable micromanipulators through compression, isolation, and extension in conjunction with fluorescence to develop new assays for nuclear mechanobiology.

Results

Using this methodology, we provide the first rebuilding of the micromanipulation setup outside of its lab of origin and recapitulate many key findings including spring constant of the nucleus and strain stiffening across many cell types. Furthermore, we have developed new micromanipulation-based techniques to compress nuclei inducing nuclear deformation and/or rupture, track nuclear shape post-isolation, and fluorescence imaging during micromanipulation force measurements.

Conclusion

We provide the workflow to build and use a micromanipulation apparatus with any inverted microscope to perform nucleus isolation, force measurements, and various other biophysical techniques.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-022-00734-y.

Nuclear lamins: Structure and function in mechanobiology

Nuclear lamins are type V intermediate filament proteins that polymerize into complex filamentous meshworks at the nuclear periphery and in less structured forms throughout the nucleoplasm. Lamins interact with a wide range of nuclear proteins and are involved in numerous nuclear and cellular functions. Within the nucleus, they play roles in chromatin organization and gene regulation, nuclear shape, size, and mechanics, and the organization and anchorage of nuclear pore complexes. At the whole cell level, they are involved in the organization of the cytoskeleton, cell motility, and mechanotransduction. The expression of different lamin isoforms has been associated with developmental progression, differentiation, and tissue-specific functions. Mutations in lamins and their binding proteins result in over 15 distinct human diseases, referred to as laminopathies. The laminopathies include muscular (e.g., Emery-Dreifuss muscular dystrophy and dilated cardiomyopathy), neurological (e.g., microcephaly), and metabolic (e.g., familial partial lipodystrophy) disorders as well as premature aging diseases (e.g., Hutchinson-Gilford Progeria and Werner syndromes). How lamins contribute to the etiology of laminopathies is still unknown. In this review article, we summarize major recent findings on the structure, organization, and multiple functions of lamins in nuclear and more global cellular processes.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

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.

A Liquid State Perspective on Dynamics of Chromatin Compartments

The interior of the eukaryotic cell nucleus has a crowded and heterogeneous environment packed with chromatin polymers, regulatory proteins, and RNA molecules. Chromatin polymer, assisted by epigenetic modifications, protein and RNA binders, forms multi-scale compartments which help regulate genes in response to cellular signals. Furthermore, chromatin compartments are dynamic and tend to evolve in size and composition in ways that are not fully understood. The latest super-resolution imaging experiments have revealed a much more dynamic and stochastic nature of chromatin compartments than was appreciated before. An emerging mechanism explaining chromatin compartmentalization dynamics is the phase separation of protein and nucleic acids into membraneless liquid condensates. Consequently, concepts and ideas from soft matter and polymer systems have been rapidly entering the lexicon of cell biology. In this respect, the role of computational models is crucial for establishing a rigorous and quantitative foundation for the new concepts and disentangling the complex interplay of forces that contribute to the emergent patterns of chromatin dynamics and organization. Several multi-scale models have emerged to address various aspects of chromatin dynamics, ranging from equilibrium polymer simulations, hybrid non-equilibrium simulations coupling protein binding and chromatin folding, and mesoscopic field-theoretic models. Here, we review these emerging theoretical paradigms and computational models with a particular focus on chromatin’s phase separation and liquid-like properties as a basis for nuclear organization and dynamics.

Lamin A as a Determinant of Mechanical Properties of the Cell Nucleus in Health and Disease

One of the main factors associated with worse prognosis in oncology is metastasis, which is based on the ability of tumor cells to migrate from the primary source and to form secondary tumors. The search for new strategies to control migration of metastatic cells is one of the urgent issues in biomedicine. One of the strategies to stop spread of cancer cells could be regulation of the nuclear elasticity. Nucleus, as the biggest and stiffest cellular compartment, determines mechanical properties of the cell as a whole, and, hence, could prevent cell migration through the three-dimensional extracellular matrix. Nuclear rigidity is maintained by the nuclear lamina, two-dimensional network of intermediate filaments in the inner nuclear membrane (INM). Here we present the most significant factors defining nucleus rigidity, discuss the role of nuclear envelope composition in the cell migration, as well consider possible approaches to control lamina composition in order to change plasticity of the cell nucleus and ability of the tumor cells to metastasize.

HP1α is a chromatin crosslinker that controls nuclear and mitotic chromosome mechanics

Chromatin, which consists of DNA and associated proteins, contains genetic information and is a mechanical component of the nucleus. Heterochromatic histone methylation controls nucleus and chromosome stiffness, but the contribution of heterochromatin protein HP1α (CBX5) is unknown. We used a novel HP1α auxin-inducible degron human cell line to rapidly degrade HP1α. Degradation did not alter transcription, local chromatin compaction, or histone methylation, but did decrease chromatin stiffness. Single-nucleus micromanipulation reveals that HP1α is essential to chromatin-based mechanics and maintains nuclear morphology, separate from histone methylation. Further experiments with dimerization-deficient HP1αI165E indicate that chromatin crosslinking via HP1α dimerization is critical, while polymer simulations demonstrate the importance of chromatin-chromatin crosslinkers in mechanics. In mitotic chromosomes, HP1α similarly bolsters stiffness while aiding in mitotic alignment and faithful segregation. HP1α is therefore a critical chromatin-crosslinking protein that provides mechanical strength to chromosomes and the nucleus throughout the cell cycle and supports cellular functions.

Cytoskeletal prestress: The cellular hallmark in mechanobiology and mechanomedicine

Increasing evidence demonstrates that mechanical forces, in addition to soluble molecules, impact cell and tissue functions in physiology and diseases. How living cells integrate mechanical signals to perform appropriate biological functions is an area of intense investigation. Here, we review the evidence of the central role of cytoskeletal prestress in mechanotransduction and mechanobiology. Elevating cytoskeletal prestress increases cell stiffness and reinforces cell stiffening, facilitates long-range cytoplasmic mechanotransduction via integrins, enables direct chromatin stretching and rapid gene expression, spurs embryonic development and stem cell differentiation, and boosts immune cell activation and killing of tumor cells whereas lowering cytoskeletal prestress maintains embryonic stem cell pluripotency, promotes tumorigenesis and metastasis of stem cell-like malignant tumor-repopulating cells, and elevates drug delivery efficiency of soft-tumor-cell-derived microparticles. The overwhelming evidence suggests that the cytoskeletal prestress is the governing principle and the cellular hallmark in mechanobiology. The application of mechanobiology to medicine (mechanomedicine) is rapidly emerging and may help advance human health and improve diagnostics, treatment, and therapeutics of diseases.

Dynamic Nuclear Structure Emerges from Chromatin Cross-Links and Motors

The cell nucleus houses the chromosomes, which are linked to a soft shell of lamin protein filaments. Experiments indicate that correlated chromosome dynamics and nuclear shape fluctuations arise from motor activity. To identify the physical mechanisms, we develop a model of an active, cross-linked Rouse chain bound to a polymeric shell. System-sized correlated motions occur but require both motor activity and cross-links. Contractile motors, in particular, enhance chromosome dynamics by driving anomalous density fluctuations. Nuclear shape fluctuations depend on motor strength, cross-linking, and chromosome-lamina binding. Therefore, complex chromosome dynamics and nuclear shape emerge from a minimal, active chromosome-lamina system.

Liquid chromatin Hi-C characterizes compartment-dependent chromatin interaction dynamics

Nuclear compartmentalization of active and inactive chromatin is thought to occur through microphase separation mediated by interactions between loci of similar type. The nature and dynamics of these interactions are not known. We developed liquid chromatin Hi-C to map the stability of associations between loci. Before fixation and Hi-C, chromosomes are fragmented, which removes strong polymeric constraint, enabling detection of intrinsic locus-locus interaction stabilities. Compartmentalization is stable when fragments are larger than 10-25 kb. Fragmentation of chromatin into pieces smaller than 6 kb leads to gradual loss of genome organization. Lamin-associated domains are most stable, whereas interactions for speckle- and polycomb-associated loci are more dynamic. Cohesin-mediated loops dissolve after fragmentation. Liquid chromatin Hi-C provides a genome-wide view of chromosome interaction dynamics.

Nuclear envelope wrinkling predicts mesenchymal progenitor cell mechano-response in 2D and 3D microenvironments

Exogenous mechanical cues are transmitted from the extracellular matrix to the nuclear envelope (NE), where mechanical stress on the NE mediates shuttling of transcription factors and other signaling cascades that dictate downstream cellular behavior and fate decisions. To systematically study how nuclear morphology can change across various physiologic microenvironmental contexts, we cultured mesenchymal progenitor cells (MSCs) in engineered 2D and 3D hyaluronic acid hydrogel systems. Across multiple contexts we observed highly 'wrinkled' nuclear envelopes, and subsequently developed a quantitative single-cell imaging metric to better evaluate how wrinkles in the nuclear envelope relate to progenitor cell mechanotransduction. We determined that in soft 2D environments the NE is predominately wrinkled, and that increases in cellular mechanosensing (indicated by cellular spreading, adhesion complex growth, and nuclear localization of YAP/TAZ) occurred only in absence of nuclear envelope wrinkling. Conversely, in 3D hydrogel and tissue contexts, we found NE wrinkling occurred along with increased YAP/TAZ nuclear localization. We further determined that these NE wrinkles in 3D were largely generated by actin impingement, and compared to other nuclear morphometrics, the degree of nuclear wrinkling showed the greatest correlation with nuclear YAP/TAZ localization. These findings suggest that the degree of nuclear envelope wrinkling can predict mechanotransduction state in mesenchymal progenitor cells and highlights the differential mechanisms of NE stress generation operative in 2D and 3D microenvironmental contexts.

Advances in Chromatin and Chromosome Research: Perspectives from Multiple Fields

Nucleosomes package genomic DNA into chromatin. By regulating DNA access for transcription, replication, DNA repair, and epigenetic modification, chromatin forms the nexus of most nuclear processes. In addition, dynamic organization of chromatin underlies both regulation of gene expression and evolution of chromosomes into individualized sister objects, which can segregate cleanly to different daughter cells at anaphase. This collaborative review shines a spotlight on technologies that will be crucial to interrogate key questions in chromatin and chromosome biology including state-of-the-art microscopy techniques, tools to physically manipulate chromatin, single-cell methods to measure chromatin accessibility, computational imaging with neural networks and analytical tools to interpret chromatin structure and dynamics. In addition, this review provides perspectives on how these tools can be applied to specific research fields such as genome stability and developmental biology and to test concepts such as phase separation of chromatin.

Correlating nuclear morphology and external force with combined atomic force microscopy and light sheet imaging separates roles of chromatin and lamin A/C in nuclear mechanics

Nuclei are often under external stress, be it during migration through tight constrictions or compressive pressure by the actin cap, and the mechanical properties of nuclei govern their subsequent deformations. Both altered mechanical properties of nuclei and abnormal nuclear morphologies are hallmarks of a variety of disease states. Little work, however, has been done to link specific changes in nuclear shape to external forces. Here, we utilize a combined atomic force microscope and light sheet microscope to show SKOV3 nuclei exhibit a two-regime force response that correlates with changes in nuclear volume and surface area, allowing us to develop an empirical model of nuclear deformation. Our technique further decouples the roles of chromatin and lamin A/C in compression, showing they separately resist changes in nuclear volume and surface area, respectively; this insight was not previously accessible by Hertzian analysis. A two-material finite element model supports our conclusions. We also observed that chromatin decompaction leads to lower nuclear curvature under compression, which is important for maintaining nuclear compartmentalization and function. The demonstrated link between specific types of nuclear morphological change and applied force will allow researchers to better understand the stress on nuclei throughout various biological processes.

Correlating nuclear morphology and external force with combined atomic force microscopy and light sheet imaging separates roles of chromatin and lamin A/C in nuclear mechanics

Nuclei are often under external stress, be it during migration through tight constrictions or compressive pressure by the actin cap, and the mechanical properties of nuclei govern their subsequent deformations. Both altered mechanical properties of nuclei and abnormal nuclear morphologies are hallmarks of a variety of disease states. Little work, however, has been done to link specific changes in nuclear shape to external forces. Here, we utilize a combined atomic force microscope and light sheet microscope to show SKOV3 nuclei exhibit a two-regime force response that correlates with changes in nuclear volume and surface area, allowing us to develop an empirical model of nuclear deformation. Our technique further decouples the roles of chromatin and lamin A/C in compression, showing they separately resist changes in nuclear volume and surface area, respectively; this insight was not previously accessible by Hertzian analysis. A two-material finite element model supports our conclusions. We also observed that chromatin decompaction leads to lower nuclear curvature under compression, which is important for maintaining nuclear compartmentalization and function. The demonstrated link between specific types of nuclear morphological change and applied force will allow researchers to better understand the stress on nuclei throughout various biological processes.

Modeling of Cell Nuclear Mechanics: Classes, Components, and Applications

Cell nuclei are paramount for both cellular function and mechanical stability. These two roles of nuclei are intertwined as altered mechanical properties of nuclei are associated with altered cell behavior and disease. To further understand the mechanical properties of cell nuclei and guide future experiments, many investigators have turned to mechanical modeling. Here, we provide a comprehensive review of mechanical modeling of cell nuclei with an emphasis on the role of the nuclear lamina in hopes of spurring future growth of this field. The goal of this review is to provide an introduction to mechanical modeling techniques, highlight current applications to nuclear mechanics, and give insight into future directions of mechanical modeling. There are three main classes of mechanical models-schematic, continuum mechanics, and molecular dynamics-which provide unique advantages and limitations. Current experimental understanding of the roles of the cytoskeleton, the nuclear lamina, and the chromatin in nuclear mechanics provide the basis for how each component is subsequently treated in mechanical models. Modeling allows us to interpret assay-specific experimental results for key parameters and quantitatively predict emergent behaviors. This is specifically powerful when emergent phenomena, such as lamin-based strain stiffening, can be deduced from complimentary experimental techniques. Modeling differences in force application, geometry, or composition can additionally clarify seemingly conflicting experimental results. Using these approaches, mechanical models have informed our understanding of relevant biological processes such as migration, nuclear blebbing, nuclear rupture, and cell spreading and detachment. There remain many aspects of nuclear mechanics for which additional mechanical modeling could provide immediate insight. Although mechanical modeling of cell nuclei has been employed for over a decade, there are still relatively few models for any given biological phenomenon. This implies that an influx of research into this realm of the field has the potential to dramatically shape both future experiments and our current understanding of nuclear mechanics, function, and disease.

Chromatin rigidity provides mechanical and genome protection

The nucleus is the organelle in the cell that contains the genome and its associate proteins which is collectively called chromatin. New work has shown that chromatin and its compaction level, dictated largely through histone modification state, provides rigidity to protect and stabilize the nucleus. Alterations in chromatin, its mechanics, and downstream loss of nuclear shape and stability are hallmarks of human disease. Weakened nuclear mechanics and abnormal morphology have been shown to cause rupturing of the nucleus which results in nuclear dysfunction including DNA damage. Thus, the rigidity provided by chromatin to maintain nuclear mechanical stability also provides its own protection from DNA damage via compartmentalization maintenance.

Chromatin and Cytoskeletal Tethering Determine Nuclear Morphology in Progerin-Expressing Cells

The nuclear morphology of eukaryotic cells is determined by the interplay between the lamina forming the nuclear skeleton, the chromatin inside the nucleus, and the coupling with the cytoskeleton. Nuclear alterations are often associated with pathological conditions as in Hutchinson-Gilford progeria syndrome, in which a mutation in the lamin A gene yields an altered form of the protein, named progerin, and an aberrant nuclear shape. Here, we introduce an inducible cellular model of Hutchinson-Gilford progeria syndrome in HeLa cells in which increased progerin expression leads to alterations in the coupling of the lamin shell with cytoskeletal or chromatin tethers as well as with polycomb group proteins. Furthermore, our experiments show that progerin expression leads to enhanced nuclear shape fluctuations in response to cytoskeletal activity. To interpret the experimental results, we introduce a computational model of the cell nucleus that explicitly includes chromatin fibers, the nuclear shell, and coupling with the cytoskeleton. The model allows us to investigate how the geometrical organization of the chromatin-lamin tether affects nuclear morphology and shape fluctuations. In sum, our findings highlight the crucial role played by lamin-chromatin and lamin-cytoskeletal alterations in determining nuclear shape morphology and in affecting cellular functions and gene regulation.

A Unified Linear Viscoelastic Model of the Cell Nucleus Defines the Mechanical Contributions of Lamins and Chromatin

The cell nucleus is constantly subjected to externally applied forces. During metazoan evolution, the nucleus has been optimized to allow physical deformability while protecting the genome under load. Aberrant nucleus mechanics can alter cell migration across narrow spaces in cancer metastasis and immune response and disrupt nucleus mechanosensitivity. Uncovering the mechanical roles of lamins and chromatin is imperative for understanding the implications of physiological forces on cells and nuclei. Lamin-knockout and -rescue fibroblasts and probed nucleus response to physiologically relevant stresses are generated. A minimal viscoelastic model is presented that captures dynamic resistance across different cell types, lamin composition, phosphorylation states, and chromatin condensation. The model is conserved at low and high loading and is validated by micropipette aspiration and nanoindentation rheology. A time scale emerges that separates between dominantly elastic and dominantly viscous regimes. While lamin-A and lamin-B1 contribute to nucleus stiffness, viscosity is specified mostly by lamin-A. Elastic and viscous association of lamin-B1 and lamin-A is supported by transcriptional and proteomic profiling analyses. Chromatin decondensation quantified by electron microscopy softens the nucleus unless lamin-A is expressed. A mechanical framework is provided for assessing nucleus response to applied forces in health and disease.

Chromosome Conformation Capture and Beyond: Toward an Integrative View of Chromosome Structure and Function

Rapidly developing technologies have recently fueled an exciting era of discovery in the field of chromosome structure and nuclear organization. In addition to chromosome conformation capture (3C) methods, new alternative techniques have emerged to study genome architecture and biological processes in the nucleus, often in single or living cells. This sets an unprecedented stage for exploring the mechanisms that link chromosome structure and biological function. Here we review popular as well as emerging approaches to study chromosome organization, focusing on the contribution of complementary methodologies to our understanding of structures revealed by 3C methods and their biological implications, and discuss the next technical and conceptual frontiers.

Crystalline membrane morphology beyond polyhedra

Elastic crystalline membranes exhibit a buckling transition from sphere to polyhedron. However, their morphologies are restricted to convex polyhedra and are difficult to externally control. Here we study morphological changes of closed crystalline membranes of superparamagnetic particles. The competition of magnetic dipole-dipole interactions with the elasticity of this magnetoelastic membrane leads to concave morphologies. Interestingly, as the magnetic field strength increases, the symmetry of the buckled membrane decreases from 5-fold to 3-fold, to 2-fold and, finally, to 1-fold rotational symmetry. This gives the ability to switch the membrane morphology between convex and concave shapes with specific symmetry and provides promising applications for membrane shape control in the design of actuatable microcontainers for targeted delivery systems.

Physicochemical mechanotransduction alters nuclear shape and mechanics via heterochromatin formation

The nucleus houses, organizes, and protects chromatin to ensure genome integrity and proper gene expression, but how the nucleus adapts mechanically to changes in the extracellular environment is poorly understood. Recent studies have revealed that extracellular physical stresses induce chromatin compaction via mechanotransductive processes. We report that increased extracellular multivalent cations lead to increased heterochromatin levels through activation of mechanosensitive ion channels (MSCs), without large-scale cell stretching. In cells with perturbed chromatin or lamins, this increase in heterochromatin suppresses nuclear blebbing associated with nuclear rupture and DNA damage. Through micromanipulation force measurements, we show that this increase in heterochromatin increases chromatin-based nuclear rigidity, which protects nuclear morphology and function. In addition, transduction of elevated extracellular cations rescues nuclear morphology in model and patient cells of human diseases, including progeria and the breast cancer model cell line MDA-MB-231. We conclude that nuclear mechanics, morphology, and function can be modulated by cell sensing of the extracellular environment through MSCs and consequent changes to histone modification state and chromatin-based nuclear rigidity.

DNA Mechanics and Topology

We review the current understanding of the mechanics of DNA and DNA-protein complexes, from scales of base pairs up to whole chromosomes. Mechanics of the double helix as revealed by single-molecule experiments will be described, with an emphasis on the role of polymer statistical mechanics. We will then discuss how topological constraints- entanglement and supercoiling-impact physical and mechanical responses. Models for protein-DNA interactions, including effects on polymer properties of DNA of DNA-bending proteins will be described, relevant to behavior of protein-DNA complexes in vivo. We also discuss control of DNA entanglement topology by DNA-lengthwise-compaction machinery acting in concert with topoisomerases. Finally, the chapter will conclude with a discussion of relevance of several aspects of physical properties of DNA and chromatin to oncology.

Chromatin's physical properties shape the nucleus and its functions

The cell nucleus encloses, organizes, and protects the genome. Chromatin maintains nuclear mechanical stability and shape in coordination with lamins and the cytoskeleton. Abnormal nuclear shape is a diagnostic marker for human diseases, and it can cause nuclear dysfunction. Chromatin mechanics underlies this link, as alterations to chromatin and its physical properties can disrupt or rescue nuclear shape. The cell can regulate nuclear shape through mechanotransduction pathways that sense and respond to extracellular cues, thus modulating chromatin compaction and rigidity. These findings reveal how chromatin's physical properties can regulate cellular function and drive abnormal nuclear morphology and dysfunction in disease.

Effects of altering histone posttranslational modifications on mitotic chromosome structure and mechanics

During cell division, chromatin is compacted into mitotic chromosomes to aid faithful segregation of the genome between two daughter cells. Posttranslational modifications (PTMs) of histones alter compaction of interphase chromatin, but it remains poorly understood how these modifications affect mitotic chromosome stiffness and structure. Using micropipette-based force measurements and epigenetic drugs, we probed the influence of canonical histone PTMs that dictate interphase euchromatin (acetylation) and heterochromatin (methylation) on mitotic chromosome stiffness. By measuring chromosome doubling force (the force required to double chromosome length), we find that histone methylation, but not acetylation, contributes to mitotic structure and stiffness. We discuss our findings in the context of chromatin gel modeling of the large-scale organization of mitotic chromosomes.

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.

Chromatin histone modifications and rigidity affect nuclear morphology independent of lamins

Nuclear shape and architecture influence gene localization, mechanotransduction, transcription, and cell function. Abnormal nuclear morphology and protrusions termed "blebs" are diagnostic markers for many human afflictions including heart disease, aging, progeria, and cancer. Nuclear blebs are associated with both lamin and chromatin alterations. A number of prior studies suggest that lamins dictate nuclear morphology, but the contributions of altered chromatin compaction remain unclear. We show that chromatin histone modification state dictates nuclear rigidity, and modulating it is sufficient to both induce and suppress nuclear blebs. Treatment of mammalian cells with histone deacetylase inhibitors to increase euchromatin or histone methyltransferase inhibitors to decrease heterochromatin results in a softer nucleus and nuclear blebbing, without perturbing lamins. Conversely, treatment with histone demethylase inhibitors increases heterochromatin and chromatin nuclear rigidity, which results in reduced nuclear blebbing in lamin B1 null nuclei. Notably, increased heterochromatin also rescues nuclear morphology in a model cell line for the accelerated aging disease Hutchinson-Gilford progeria syndrome caused by mutant lamin A, as well as cells from patients with the disease. Thus, chromatin histone modification state is a major determinant of nuclear blebbing and morphology via its contribution to nuclear rigidity.

Separate roles for chromatin and lamins in nuclear mechanics

The cell nucleus houses, protects, and arranges the genome within the cell. Therefore, nuclear mechanics and morphology are important for dictating gene regulation, and these properties are perturbed in many human diseases, such as cancers and progerias. The field of nuclear mechanics has long been dominated by studies of the nuclear lamina, the intermediate filament shell residing just beneath the nuclear membrane. However, a growing body of work shows that chromatin and chromatin-related factors within the nucleus are an essential part of the mechanical response of the cell nucleus to forces. Recently, our group demonstrated that chromatin and the lamina provide distinct mechanical contributions to nuclear mechanical response. The lamina is indeed important for robust response to large, whole-nucleus stresses, but chromatin dominates the short-extension response. These findings offer a clarifying perspective on varied nuclear mechanics measurements and observations, and they suggest several new exciting possibilities for understanding nuclear morphology, organization, and mechanics.