A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration

Anisotropic power-law viscoelasticity of living cells is dominated by cytoskeletal network structure

During physiological and pathological processes, cells experience significant morphological alterations with the re-arrangement of cytoskeletal filaments, resulting in anisotropic viscoelasticity. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. We investigate how cell shape affects its creep responses in longitudinal and perpendicular directions. It is shown that cells exhibit power-law rheological behavior in both longitudinal and perpendicular directions under step stress, with a more solid-like behavior along the longitudinal direction. We reveal that the cell volume and cytoskeletal filament orientation, which have been neglected in most existing models, play a critical role in regulating cellular anisotropic viscoelasticity. The stiffness of the cell in both directions increases linearly with increasing its aspect ratio, due to the decrease of cell volume. Moreover, the increase in the cell's aspect ratio produces the aggregation of cytoskeletal filaments along the longitudinal direction, resulting in higher stiffness in this direction. It is also shown that the increase in cell's aspect ratio corresponds to a process of cellular ordering, which can be quantitatively characterized by the orientational entropy of cytoskeletal filaments. In addition, we present a simple yet robust method to establish the relationship between cell's aspect ratio and cell volume, thus providing a theoretical framework to capture the anisotropic viscoelastic behavior of cells. This study suggests that the structure-based cell models may be further developed to investigate cellular rheological responses to external mechanical stimuli and may be extended to the tissue scale. STATEMENT OF SIGNIFICANCE: The viscoelastic behaviors of cells hold significant importance in comprehending the roles of mechanical forces in embryo development, invasion, and metastasis of cancer cells. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. Our study highlights the crucial role of previously neglected factors, such as cell volume and cytoskeletal filament orientation, in regulating cellular anisotropic viscoelasticity. We further propose an orientational entropy of cytoskeletal filaments to quantitatively characterize the ordering process of cells with increasing aspect ratios. Moreover, we derived the analytical interrelationships between cell aspect ratio, cell stiffness, cell volume, and cytoskeletal fiber orientation. This study provides a theoretical framework to describe the anisotropic viscoelastic mechanical behavior of cells.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Nuclear blebs are associated with destabilized chromatin packing domains

Disrupted nuclear shape is associated with multiple pathological processes including premature aging disorders, cancer-relevant chromosomal rearrangements, and DNA damage. Nuclear blebs (i.e., herniations of the nuclear envelope) have been induced by (1) nuclear compression, (2) nuclear migration (e.g., cancer metastasis), (3) actin contraction, (4) lamin mutation or depletion, and (5) heterochromatin enzyme inhibition. Recent work has shown that chromatin transformation is a hallmark of bleb formation, but the transformation of higher-order structures in blebs is not well understood. As higher-order chromatin has been shown to assemble into nanoscopic packing domains, we investigated if (1) packing domain organization is altered within nuclear blebs and (2) if alteration in packing domain structure contributed to bleb formation. Using Dual-Partial Wave Spectroscopic microscopy, we show that chromatin packing domains within blebs are transformed both by B-type lamin depletion and the inhibition of heterochromatin enzymes compared to the nuclear body. Pairing these results with single-molecule localization microscopy of constitutive heterochromatin, we show fragmentation of nanoscopic heterochromatin domains within bleb domains. Overall, these findings indicate that translocation into blebs results in a fragmented higher-order chromatin structure.

SUMMARY STATEMENT

Nuclear blebs are linked to various pathologies, including cancer and premature aging disorders. We investigate alterations in higher-order chromatin structure within blebs, revealing fragmentation of nanoscopic heterochromatin domains.

Simulation and experimental study on the influence of lamina on nanoneedle penetration into the cell nucleus

We have developed a finite element model to simulate the penetration of nanoneedles into the cellular nucleus. It is found that the nuclear lamina, the primary supporting structure of the nuclear membrane, plays a crucial role in maintaining the integrity of the nuclear envelope and enhancing stress concentration in the nuclear membrane. Notably, nuclear lamina A exhibits a more pronounced effect compared to nuclear lamina B. Subsequently, we further conducted experiments by controlling the time of osteopontin (OPN) treatment to modify the nuclear lamina density, and the results showed that an increase in nuclear lamina density enhances the probability of nanoneedle penetration into the nuclear membrane. Through employing both simulation and experimental techniques, we have gathered compelling evidence indicating that an augmented density of nuclear lamina A can enhance the penetration of nanoneedles into the nuclear membrane.

Mechanobiology in oncology: basic concepts and clinical prospects

The interplay between genetic transformations, biochemical communications, and physical interactions is crucial in cancer progression. Metastasis, a leading cause of cancer-related deaths, involves a series of steps, including invasion, intravasation, circulation survival, and extravasation. Mechanical alterations, such as changes in stiffness and morphology, play a significant role in all stages of cancer initiation and dissemination. Accordingly, a better understanding of cancer mechanobiology can help in the development of novel therapeutic strategies. Targeting the physical properties of tumours and their microenvironment presents opportunities for intervention. Advancements in imaging techniques and lab-on-a-chip systems enable personalized investigations of tumor biomechanics and drug screening. Investigation of the interplay between genetic, biochemical, and mechanical factors, which is of crucial importance in cancer progression, offers insights for personalized medicine and innovative treatment strategies.

Magnetic nanoparticle swarm with upstream motility and peritumor blood vessel crossing ability

Micro-nano-robots show great potential and value for applications in targeted drug delivery; however, very few current studies have enabled micro-nano-robots to move against blood flow, and in addition, how micro-nano-robots can penetrate endothelial cells and enter tissues via vascular permeation remains unclear. Inspired by the bionics of dynamic aggregation in wild herring schools and transvascular permeation of leukocytes, we propose a novel drug delivery strategy where thousands of magnetic nanoparticles (MNPs) can be assembled into swarms under the guidance of a specially designed electromagnetic field. The vortex-like swarms of magnetic nanoparticles exhibit excellent stability, allowing them to withstand the impact of high-speed flow and move upstream along the vessel wall, stopping at the target location. When the vortex-like swarms encounter a tumor periphery without a continuous vessel wall, their rheological properties actively adhere them to the edges of the vascular endothelial gap, using their deformability to crawl through narrow intercellular gaps, enabling large-scale targeted drug delivery. This cluster of miniature nanorobots can be reshaped and reconfigured to perform a variety of tasks according to the environmental demands of the circulatory system, providing new solutions for a variety of biomedical field applications.

The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments

Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045-4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513-537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.

The crucial role of adhesion in the transmigration of active droplets through interstitial orifices

Active fluid droplets are a class of soft materials exhibiting autonomous motion sustained by an energy supply. Such systems have been shown to capture motility regimes typical of biological cells and are ideal candidates as building-block for the fabrication of soft biomimetic materials of interest in pharmacology, tissue engineering and lab on chip devices. While their behavior is well established in unconstrained environments, much less is known about their dynamics under strong confinement. Here, we numerically study the physics of a droplet of active polar fluid migrating within a microchannel hosting a constriction with adhesive properties, and report evidence of a striking variety of dynamic regimes and morphological features, whose properties crucially depend upon droplet speed and elasticity, degree of confinement within the constriction and adhesiveness to the pore. Our results suggest that non-uniform adhesion forces are instrumental in enabling the crossing through narrow orifices, in contrast to larger gaps where a careful balance between speed and elasticity is sufficient to guarantee the transition. These observations may be useful for improving the design of artificial micro-swimmers, of interest in material science and pharmaceutics, and potentially for cell sorting in microfluidic devices.

Feedback between mechanosensitive signaling and active forces governs endothelial junction integrity

The formation and recovery of gaps in the vascular endothelium governs a wide range of physiological and pathological phenomena, from angiogenesis to tumor cell extravasation. However, the interplay between the mechanical and signaling processes that drive dynamic behavior in vascular endothelial cells is not well understood. In this study, we propose a chemo-mechanical model to investigate the regulation of endothelial junctions as dependent on the feedback between actomyosin contractility, VE-cadherin bond turnover, and actin polymerization, which mediate the forces exerted on the cell-cell interface. Simulations reveal that active cell tension can stabilize cadherin bonds, but excessive RhoA signaling can drive bond dissociation and junction failure. While actin polymerization aids gap closure, high levels of Rac1 can induce junction weakening. Combining the modeling framework with experiments, our model predicts the influence of pharmacological treatments on the junction state and identifies that a critical balance between RhoA and Rac1 expression is required to maintain junction stability. Our proposed framework can help guide the development of therapeutics that target the Rho family of GTPases and downstream active mechanical processes.

Magnetic torque–driven living microrobots for increased tumor infiltration

Biohybrid bacteria–based microrobots are increasingly recognized as promising externally controllable vehicles for targeted cancer therapy. Magnetic fields in particular have been used as a safe means to transfer energy and direct their motion. Thus far, the magnetic control strategies used in this context rely on poorly scalable magnetic field gradients, require active position feedback, or are ill-suited to diffuse distributions within the body. Here, we present a magnetic torque–driven control scheme for enhanced transport through biological barriers that complements the innate taxis toward tumor cores exhibited by a range of bacteria, shown for Magnetospirillum magneticum as a magnetically responsive model organism. This hybrid control strategy is readily scalable, independent of position feedback, and applicable to bacterial microrobots dispersed by the circulatory system. We observed a fourfold increase in translocation of magnetically responsive bacteria across a model of the vascular endothelium and found that the primary mechanism driving increased transport is torque-driven surface exploration at the cell interface. Using spheroids as a three-dimensional tumor model, fluorescently labeled bacteria colonized their core regions with up to 21-fold higher signal in samples exposed to rotating magnetic fields. In addition to enhanced transport, we demonstrated that our control scheme offers further advantages, including the possibility for closed-loop optimization based on inductive detection, as well as spatially selective actuation to reduce off-target effects. Last, after systemic intravenous injection in mice, we showed significantly increased bacterial tumor accumulation, supporting the feasibility of deploying this control scheme clinically for magnetically responsive biohybrid microrobots.

Mechanics and functional consequences of nuclear deformations

As the home of cellular genetic information, the nucleus has a critical role in determining cell fate and function in response to various signals and stimuli. In addition to biochemical inputs, the nucleus is constantly exposed to intrinsic and extrinsic mechanical forces that trigger dynamic changes in nuclear structure and morphology. Emerging data suggest that the physical deformation of the nucleus modulates many cellular and nuclear functions. These functions have long been considered to be downstream of cytoplasmic signalling pathways and dictated by gene expression. In this Review, we discuss an emerging perspective on the mechanoregulation of the nucleus that considers the physical connections from chromatin to nuclear lamina and cytoskeletal filaments as a single mechanical unit. We describe key mechanisms of nuclear deformations in time and space and provide a critical review of the structural and functional adaptive responses of the nucleus to deformations. We then consider the contribution of nuclear deformations to the regulation of important cellular functions, including muscle contraction, cell migration and human disease pathogenesis. Collectively, these emerging insights shed new light on the dynamics of nuclear deformations and their roles in cellular mechanobiology.

Microfluidic Lab-on-a-Chip for Studies of Cell Migration under Spatial Confinement

Understanding cell migration is a key step in unraveling many physiological phenomena and predicting several pathologies, such as cancer metastasis. In particular, confinement has been proven to be a key factor in the cellular migration strategy choice. As our insight in the field improves, new tools are needed in order to empower biologists’ analysis capabilities. In this framework, microfluidic devices have been used to engineer the mechanical and spatial stimuli and to investigate cellular migration response in a more controlled way. In this work, we will review the existing technologies employed in the realization of microfluidic cellular migration assays, namely the soft lithography of PDMS and hydrogels and femtosecond laser micromachining. We will give an overview of the state of the art of these devices, focusing on the different geometrical configurations that have been exploited to study specific aspects of cellular migration. Our scope is to highlight the advantages and possibilities given by each approach and to envisage the future developments in in vitro migration studies under spatial confinement in microfluidic devices.

Molecular sensors for detection of tumor-stroma crosstalk

In most solid tumors, malignant cells coexist with non-cancerous host tissue comprised of a variety of extracellular matrix components and cell types, notably fibroblasts, immune cells, and endothelial cells. It is becoming increasingly evident that the non-cancerous host tissue, often referred to as the tumor stroma or the tumor microenvironment, wields tremendous influence in the proliferation, survival, and metastatic ability of cancer cells. The tumor stroma has an active biological role in the transmission of signals, such as growth factors and chemokines that activate oncogenic signaling pathways by autocrine and paracrine mechanisms. Moreover, the constituents of the stroma define the mechanical properties and the physical features of solid tumors, which influence cancer progression and response to therapy. Inspired by the emerging importance of tumor-stroma crosstalk and oncogenic physical forces, numerous biosensors, or advanced imaging and analysis techniques have been developed and applied to investigate complex and challenging questions in cancer research. These techniques facilitate measurements and biological readouts at scales ranging from subcellular to tissue-level with unprecedented level of spatial and temporal precision. Here we examine the application of biosensor technology for studying the complex and dynamic multiscale interactions of the tumor-host system.

Rapid Plastic Deformation of Cancer Cells Correlates with High Metastatic Potential

Metastasis plays a crucial role in tumor development, however, lack of quantitative methods to characterize the capability of cells to undergo plastic deformations has hindered the understanding of this important process. Here, a microfluidic system capable of imposing precisely controlled cyclic deformation on cells and therefore probing their viscoelastic and plastic characteristics is developed. Interestingly, it is found that significant plastic strain can accumulate rapidly in highly invasive cancer cell lines and circulating tumor cells (CTCs) from late-stage lung cancer patients with a characteristic time of a few seconds. In constrast, very little irreversible deformation is observed in the less invasive cell lines and CTCs from early-stage lung cancer patients, highlighting the potential of using the plastic response of cells as a novel marker in future cancer study. Furthermore, author showed that the observed irreversible deformation should originate mainly from cytoskeleton damage, rather than plasticity of the cell nucleus.

The biophysics of cancer: emerging insights from micro- and nanoscale tools

Cancer is a complex and dynamic disease that is aberrant both biologically and physically. There is growing appreciation that physical abnormalities with both cancer cells and their microenvironment that span multiple length scales are important drivers for cancer growth and metastasis. The scope of this review is to highlight the key advancements in micro- and nano-scale tools for delineating the cause and consequences of the aberrant physical properties of tumors. We focus our review on three important physical aspects of cancer: 1) solid mechanical properties, 2) fluid mechanical properties, and 3) mechanical alterations to cancer cells. Beyond posing physical barriers to the delivery of cancer therapeutics, these properties are also known to influence numerous biological processes, including cancer cell invasion and migration leading to metastasis, and response and resistance to therapy. We comment on how micro- and nanoscale tools have transformed our fundamental understanding of the physical dynamics of cancer progression and their potential for bridging towards future applications at the interface of oncology and physical sciences.

Push or pull: how cytoskeletal crosstalk facilitates nuclear movement through 3D environments

As cells move from two-dimensional (2D) surfaces into complex 3D environments, the nucleus becomes a barrier to movement due to its size and rigidity. Therefore, moving the nucleus is a key step in 3D cell migration. In this review, we discuss how coordination between cytoskeletal and nucleoskeletal networks is required to pull the nucleus forward through complex 3D spaces. We summarize recent migration models which utilize unique molecular crosstalk to drive nuclear migration through different 3D environments. In addition, we speculate about the role of proteins that indirectly crosslink cytoskeletal networks and the role of 3D focal adhesions and how these protein complexes may drive 3D nuclear migration.

A survey of physical methods for studying nuclear mechanics and mechanobiology

It is increasingly appreciated that the cell nucleus is not only a home for DNA but also a complex material that resists physical deformations and dynamically responds to external mechanical cues. The molecules that confer mechanical properties to nuclei certainly contribute to laminopathies and possibly contribute to cellular mechanotransduction and physical processes in cancer such as metastasis. Studying nuclear mechanics and the downstream biochemical consequences or their modulation requires a suite of complex assays for applying, measuring, and visualizing mechanical forces across diverse length, time, and force scales. Here, we review the current methods in nuclear mechanics and mechanobiology, placing specific emphasis on each of their unique advantages and limitations. Furthermore, we explore important considerations in selecting a new methodology as are demonstrated by recent examples from the literature. We conclude by providing an outlook on the development of new methods and the judicious use of the current techniques for continued exploration into the role of nuclear mechanobiology.

Two nondimensional parameters for characterizing the nuclear morphology

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

Modelling Nuclear Morphology and Shape Transformation: A Review

As one of the most important cellular compartments, the nucleus contains genetic materials and separates them from the cytoplasm with the nuclear envelope (NE), a thin membrane that is susceptible to deformations caused by intracellular forces. Interestingly, accumulating evidence has also indicated that the morphology change of NE is tightly related to nuclear mechanotransduction and the pathogenesis of diseases such as cancer and Hutchinson–Gilford Progeria Syndrome. Theoretically, with the help of well-designed experiments, significant progress has been made in understanding the physical mechanisms behind nuclear shape transformation in different cellular processes as well as its biological implications. Here, we review different continuum-level (i.e., energy minimization, boundary integral and finite element-based) approaches that have been developed to predict the morphology and shape change of the cell nucleus. Essential gradients, relative advantages and limitations of each model will be discussed in detail, with the hope of sparking a greater research interest in this important topic in the future.

A mechanical test of the tenertaxis hypothesis for leukocyte diapedesis

As part of the immune response, leukocytes can directly transmigrate through the body of endothelial cells or through the gap between adjacent endothelial cells. These are known, respectively, as the transcellular and paracellular route of diapedesis. What determines the usage of one route over the other is unclear. A recently proposed tenertaxis hypothesis claims that leukocytes choose the path with less mechanical resistance against leukocyte protrusions. We examined this hypothesis using numerical simulation of the mechanical resistance during paracellular and transcellular protrusions. By using parameters based on human lung endothelium, our results show that the required force to breach the endothelium through the transcellular route is greater than paracellular route, in agreement with experiments. Moreover, experiments have demonstrated that manipulation of the relative strength between the two routes can make the transcellular route preferable. Our simulations have demonstrated this reversal and thus tentatively confirmed the hypothesis of tenertaxis.

Tumor cell nuclei soften during transendothelial migration

During cancer metastasis, tumor cells undergo significant deformation in order to traverse through endothelial cell junctions in the walls of blood vessels. As cells pass through narrow gaps, smaller than the nuclear diameter, the spatial configuration of chromatin must change along with the distribution of nuclear enzymes. Nuclear stiffness is an important determinant of the ability of cells to undergo transendothelial migration, yet no studies have been conducted to assess whether tumor cell cytoskeletal or nuclear stiffness changes during this critical process in order to facilitate passage. To address this question, we employed two non-contact methods, Brillouin confocal microscopy (BCM) and confocal reflectance quantitative phase microscopy (QPM), to track the changes in mechanical properties of live, transmigrating tumor cells in an in vitro collagen gel platform. Using these two imaging modalities to study transmigrating MDA-MB-231, A549, and A375 cells, we found that both the cells and their nuclei soften upon extravasation and that the nuclear membranes remain soft for at least 24 h. These new data suggest that tumor cells adjust their mechanical properties in order to facilitate extravasation.

Calculation of the force field required for nucleus deformation during cell migration through constrictions

During cell migration in confinement, the nucleus has to deform for a cell to pass through small constrictions. Such nuclear deformations require significant forces. A direct experimental measure of the deformation force field is extremely challenging. However, experimental images of nuclear shape are relatively easy to obtain. Therefore, here we present a method to calculate predictions of the deformation force field based purely on analysis of experimental images of nuclei before and after deformation. Such an inverse calculation is technically non-trivial and relies on a mechanical model for the nucleus. Here we compare two simple continuum elastic models of a cell nucleus undergoing deformation. In the first, we treat the nucleus as a homogeneous elastic solid and, in the second, as an elastic shell. For each of these models we calculate the force field required to produce the deformation given by experimental images of nuclei in dendritic cells migrating in microchannels with constrictions of controlled dimensions. These microfabricated channels provide a simplified confined environment mimicking that experienced by cells in tissues. Our calculations predict the forces felt by a deforming nucleus as a migrating cell encounters a constriction. Since a direct experimental measure of the deformation force field is very challenging and has not yet been achieved, our numerical approaches can make important predictions motivating further experiments, even though all the parameters are not yet available. We demonstrate the power of our method by showing how it predicts lateral forces corresponding to actin polymerisation around the nucleus, providing evidence for actin generated forces squeezing the sides of the nucleus as it enters a constriction. In addition, the algorithm we have developed could be adapted to analyse experimental images of deformation in other situations.

Many cell types are able to migrate and squeeze through constrictions that are narrower than the cell’s resting radius. For example, both immune cells and metastatic cancer cells change their shape to migrate through small holes in the complex tissue media they move in. During migration the cell nucleus is more difficult to deform than the cell cytoplasm and therefore significant forces are required for a cell to pass through spaces that are smaller than the resting size of the nucleus. Experimental measurements of these forces are extremely challenging but experimental images of nuclear deformation are regularly obtained in many labs. Therefore we present a computational method to analyse experimental images of nuclear deformation to deduce the forces required to produce such deformations. A mechanical model of the nucleus is necessary for this analysis and here we present two different models. Our computational tool enables us to obtain detailed information about forces causing deformation from microscopy images and consequently provide evidence for actin generated forces squeezing the sides of the nucleus as it enters a constriction.

Reduced Lamin A/C Does Not Facilitate Cancer Cell Transendothelial Migration but Compromises Lung Metastasis

The mechanisms by which the nuclear lamina of tumor cells influences tumor growth and migration are highly disputed. Lamin A and its variant lamin C are key lamina proteins that control nucleus stiffness and chromatin conformation. Downregulation of lamin A/C in two prototypic metastatic lines, B16F10 melanoma and E0771 breast carcinoma, facilitated cell squeezing through rigid pores, and reduced heterochromatin content. Surprisingly, both lamin A/C knockdown cells grew poorly in 3D spheroids within soft agar, and lamin A/C deficient cells derived from spheroids transcribed lower levels of the growth regulator Yap1. Unexpectedly, the transendothelial migration of both cancer cells in vitro and in vivo, through lung capillaries, was not elevated by lamin A/C knockdown and their metastasis in lungs was even dramatically reduced. Our results are the first indication that reduced lamin A/C content in distinct types of highly metastatic cancer cells does not elevate their transendothelial migration (TEM) capacity and diapedesis through lung vessels but can compromise lung metastasis at a post extravasation level.

Image-derived modeling of nucleus strain amplification associated with chromatin heterogeneity

Beyond the critical role of cell nuclei in gene expression and DNA replication, they also have a significant influence on cell mechanosensation and migration. Nuclear stiffness can impact force transmission and, furthermore, act as a physical barrier to translocation across tight spaces. As such, it is of wide interest to accurately characterize nucleus mechanical behavior. In this study, we present a computational investigation of the in situ deformation of a heterogeneous chondrocyte nucleus. A methodology is developed to accurately reconstruct a three-dimensional finite-element model of a cell nucleus from confocal microscopy. By incorporating the reconstructed nucleus into a chondrocyte model embedded in pericellular and extracellular matrix, we explore the relationship between spatially heterogeneous nuclear DNA content, shear stiffness, and resultant shear strain. We simulate an externally applied extracellular matrix shear deformation and compute intranuclear strain distributions, which are directly compared with corresponding experimentally measured distributions. Simulations suggest that the mechanical behavior of the nucleus is highly heterogeneous, with a nonlinear relationship between experimentally measured grayscale values and corresponding local shear moduli (μn). Three distinct phases are identified within the nucleus: a low-stiffness mRNA-rich interchromatin phase (0.17 kPa ≤ μn ≤ 0.63 kPa), an intermediate-stiffness euchromatin phase (1.48 kPa ≤ μn ≤ 2.7 kPa), and a high-stiffness heterochromatin phase (3.58 kPa ≤ μn ≤ 4.0 kPa). Our simulations also indicate that disruption of the nuclear envelope associated with lamin A/C depletion significantly increases nuclear strain in regions of low DNA concentration. We further investigate a phenotypic shift of chondrocytes to fibroblast-like cells, a signature for osteoarthritic cartilage, by increasing the contractility of the actin cytoskeleton to a level associated with fibroblasts. Peak nucleus strains increase by 35% compared to control, with the nucleus becoming more ellipsoidal. Our findings may have broad implications for current understanding of how local DNA concentrations and associated strain amplification can impact cell mechanotransduction and drive cell behavior in development, migration, and tumorigenesis.

A Cellular Potts Model for Analyzing Cell Migration across Constraining Pillar Arrays

Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in turn relies on their deformation capacity. In this respect, the nucleus, which occupies a large fraction of the cell volume and is substantially stiffer than the surrounding cytoplasm, imposes a major obstacle. This aspect has also been investigated with the use of microfluidic devices formed by dozens of arrays of aligned polymeric pillars that limit the available space for cell movement. Such experimental systems, in particular, in the designs developed by the groups of Denais and of Davidson, were here reproduced with a tailored version of the Cellular Potts model, a grid-based stochastic approach where cell dynamics are established by a Metropolis algorithm for energy minimization. The proposed model allowed quantitatively analyzing selected cell migratory determinants (e.g., the cell and nuclear speed and deformation, and forces acting at the nuclear membrane) in the case of different experimental setups. Most of the numerical results show a remarkable agreement with the corresponding empirical data.

A constriction channel analysis of astrocytoma stiffness and disease progression

Studies have demonstrated that cancer cells tend to have reduced stiffness (Young's modulus) compared to their healthy counterparts. The mechanical properties of primary brain cancer cells, however, have remained largely unstudied. To investigate whether the stiffness of primary brain cancer cells decreases as malignancy increases, we used a microfluidic constriction channel device to deform healthy astrocytes and astrocytoma cells of grade II, III, and IV and measured the entry time, transit time, and elongation. Calculating cell stiffness directly from the experimental measurements is not possible. To overcome this challenge, finite element simulations of the cell entry into the constriction channel were used to train a neural network to calculate the stiffness of the analyzed cells based on their experimentally measured diameter, entry time, and elongation in the channel. Our study provides the first calculation of stiffness for grades II and III astrocytoma and is the first to apply a neural network analysis to determine cell mechanical properties from a constriction channel device. Our results suggest that the stiffness of astrocytoma cells is not well-correlated with the cell grade. Furthermore, while other non-central-nervous-system cell types typically show reduced stiffness of malignant cells, we found that most astrocytoma cell lines had increased stiffness compared to healthy astrocytes, with lower-grade astrocytoma having higher stiffness values than grade IV glioblastoma. Differences in nucleus-to-cytoplasm ratio only partly explain differences in stiffness values. Although our study does have limitations, our results do not show a strong correlation of stiffness with cell grade, suggesting that other factors may play important roles in determining the invasive capability of astrocytoma. Future studies are warranted to further elucidate the mechanical properties of astrocytoma across various pathological grades.

Nuclear fragility, blaming the blebs

Although textbook pictures depict the cell nucleus as a simple ovoid object, it is now clear that it adopts a large variety of shapes in tissues. When cells deform, because of cell crowding or migration through dense matrices, the nucleus is subjected to large constraints that alter its shape. In this review, we discuss recent studies related to nuclear fragility, focusing on the surprising finding that the nuclear envelope can form blebs. Contrary to the better-known plasma membrane blebs, nuclear blebs are unstable and almost systematically lead to nuclear envelope opening and uncontrolled nucleocytoplasmic mixing. They expand, burst, and repair repeatedly when the nucleus is strongly deformed. Although blebs are a major source of nuclear instability, they are poorly understood so far, which calls for more in-depth studies of these structures.

Mechanical Adaptability of Tumor Cells in Metastasis

The most dangerous aspect of cancer lies in metastatic progression. Tumor cells will successfully form life-threatening metastases when they undergo sequential steps along a journey from the primary tumor to distant organs. From a biomechanics standpoint, growth, invasion, intravasation, circulation, arrest/adhesion, and extravasation of tumor cells demand particular cell-mechanical properties in order to survive and complete the metastatic cascade. With metastatic cells usually being softer than their non-malignant counterparts, high deformability for both the cell and its nucleus is thought to offer a significant advantage for metastatic potential. However, it is still unclear whether there is a finely tuned but fixed mechanical state that accommodates all mechanical features required for survival throughout the cascade or whether tumor cells need to dynamically refine their properties and intracellular components at each new step encountered. Here, we review the various mechanical requirements successful cancer cells might need to fulfill along their journey and speculate on the possibility that they dynamically adapt their properties accordingly. The mechanical signature of a successful cancer cell might actually be its ability to adapt to the successive microenvironmental constraints along the different steps of the journey.

Nuclear plasticity increases susceptibility to damage during confined migration

Large nuclear deformations during migration through confined spaces have been associated with nuclear membrane rupture and DNA damage. However, the stresses associated with nuclear damage remain unclear. Here, using a quasi-static plane strain finite element model, we map evolution of nuclear shape and stresses during confined migration of a cell through a deformable matrix. Plastic deformation of the nucleus observed for a cell with stiff nucleus transiting through a stiffer matrix lowered nuclear stresses, but also led to kinking of the nuclear membrane. In line with model predictions, transwell migration experiments with fibrosarcoma cells showed that while nuclear softening increased invasiveness, nuclear stiffening led to plastic deformation and higher levels of DNA damage. In addition to highlighting the advantage of nuclear softening during confined migration, our results suggest that plastic deformations of the nucleus during transit through stiff tissues may lead to bending-induced nuclear membrane disruption and subsequent DNA damage.

Stiffness of the nucleus is known to impede migration of cells through dense matrices. Nuclear translocation through small pores is achieved by active deformation of the nucleus by the cytoskeleton. However, stresses on the nucleus during confined migration may lead to nuclear damage, as observed experimentally. However, the factors contributing to nuclear damage remain incompletely understood. Here we show that plastic or permanent nuclear deformation which is necessary for successful migration through small pores in stiff matrices, also leads to bending of the nuclear membrane. We propose that this bending precedes nuclear blebs which are experimentally observed.

Computational estimates of mechanical constraints on cell migration through the extracellular matrix

Cell migration through a three-dimensional (3D) extracellular matrix (ECM) underlies important physiological phenomena and is based on a variety of mechanical strategies depending on the cell type and the properties of the ECM. By using computer simulations of the cell’s mid-plane, we investigate two such migration mechanisms—‘push-pull’ (forming a finger-like protrusion, adhering to an ECM node, and pulling the cell body forward) and ‘rear-squeezing’ (pushing the cell body through the ECM by contracting the cell cortex and ECM at the cell rear). We present a computational model that accounts for both elastic deformation and forces of the ECM, an active cell cortex and nucleus, and for hydrodynamic forces and flow of the extracellular fluid, cytoplasm, and nucleoplasm. We find that relations between three mechanical parameters—the cortex’s contractile force, nuclear elasticity, and ECM rigidity—determine the effectiveness of cell migration through the dense ECM. The cell can migrate persistently even if its cortical contraction cannot deform a near-rigid ECM, but then the contraction of the cortex has to be able to sufficiently deform the nucleus. The cell can also migrate even if it fails to deform a stiff nucleus, but then it has to be able to sufficiently deform the ECM. Simulation results show that nuclear stiffness limits the cell migration more than the ECM rigidity. Simulations show the rear-squeezing mechanism of motility results in more robust migration with larger cell displacements than those with the push-pull mechanism over a range of parameter values. Additionally, results show that the rear-squeezing mechanism is aided by hydrodynamics through a pressure gradient.

Computational simulations of two different mechanisms of 3D cell migration in an extracellular matrix are presented. One mechanism represents a mesenchymal mode, characterized by finger-like actin protrusions, while the second mode is more amoeboid in that rear contraction of the cortex propels the cell forward. In both mechanisms, the cell generates a thin actin protrusion on the cortex that attaches to an ECM node. The cell is then either pulled (mesenchymal) or pushed (amoeboid) forward. Results show both mechanisms result in successful migration over a range of simulated parameter values as long as the contractile tension of the cortex exceeds either the nuclear stiffness or ECM stiffness, but not necessarily both. However, the distance traveled by the amoeboid migration mode is more robust to changes in parameter values, and is larger than in simulations of the mesenchymal mode. Additionally, cells experience a favorable fluid pressure gradient when migrating in the amoeboid mode, and an adverse fluid pressure gradient in the mesenchymal mode.

Chromosomal Repositioning and Gene Regulation of Cells on a Micropillar Array

While various cell responses on material surfaces have been examined, relatively few reports are focused on significant self-deformation of cell nuclei and corresponding chromosomal repositioning. Herein, we prepared a micropillar array of poly(lactide-co-glycolide) (PLGA) and observed significant nuclear deformation of HeLa cells on the polymeric micropillars. In particular, we detected the territory positioning of chromosomes 18 and 19 and gene expression profiles of HeLa cells on the micropillar array using fluorescence in situ hybridization and a DNA microarray. Chromosome 18 was found to be translocated closer to the nuclear periphery than chromosome 19 on the micropillar array. With the repositioning of chromosomal territories, HeLa cells changed their gene expressions on the micropillar array with 180 genes upregulated and 255 genes downregulated for all of the 23 pairs of chromosomes under the experimental conditions and the employed Bioinformatics criteria. Hence, this work deepens the understanding on cell-material interactions by revealing that material surface topography can probably influence chromosomal repositioning in the nuclei and gene expressions of cells.

Nuclear mechanosensing: mechanism and consequences of a nuclear rupture

The physical connections between the cytoskeletal system and the nucleus provide a route for the nucleus to sense the mechanical stress both inside and outside of the cell. Failure to withstand such stress leads to nuclear rupture, which is observed in human diseases. In this review, we will go through the recent findings and our current understandings of nuclear rupture. Starting with the triggers of nuclear rupture, including the aberrant nuclear lamina composition and the elevated actomyosin contractility. We will also discuss the role of ESCRT-III in nuclear rupture repair and the biological consequences of nuclear rupture, including the negative impacts on cellular compartmentalization, DNA damage, and cellular differentiation. Recent studies on nuclear rupture provide further insights into the direct mechanistic link between nuclear rupture and several pathological conditions. Such knowledge can guide us in developing potential therapeutic solutions for the patients.

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.

Nuclear softening expedites interstitial cell migration in fibrous networks and dense connective tissues

Dense matrices impede interstitial cell migration and subsequent repair. We hypothesized that nuclear stiffness is a limiting factor in migration and posited that repair could be expedited by transiently decreasing nuclear stiffness. To test this, we interrogated the interstitial migratory capacity of adult meniscal cells through dense fibrous networks and adult tissue before and after nuclear softening via the application of a histone deacetylase inhibitor, Trichostatin A (TSA) or knockdown of the filamentous nuclear protein Lamin A/C. Our results show that transient softening of the nucleus improves migration through microporous membranes, electrospun fibrous matrices, and tissue sections and that nuclear properties and cell function recover after treatment. We also showed that biomaterial delivery of TSA promoted in vivo cellularization of scaffolds by endogenous cells. By addressing the inherent limitations to repair imposed by nuclear stiffness, this work defines a new strategy to promote the repair of damaged dense connective tissues.

Effect of Nuclear Stiffness on Cell Mechanics and Migration of Human Breast Cancer Cells

The migration and invasion of cancer cells through 3D confined extracellular matrices is coupled to cell mechanics and the mechanics of the extracellular matrix. Cell mechanics is mainly determined by both the mechanics of the largest organelle in the cell, the nucleus, and the cytoskeletal architecture of the cell. Hence, cytoskeletal and nuclear mechanics are the major contributors to cell mechanics. Among other factors, steric hindrances of the extracellular matrix confinement are supposed to affect nuclear mechanics and thus also influence cell mechanics. Therefore, we propose that the percentage of invasive cells and their invasion depths into loose and dense 3D extracellular matrices is regulated by both nuclear and cytoskeletal mechanics. In order to investigate the effect of both nuclear and cytoskeletal mechanics on the overall cell mechanics, we firstly altered nuclear mechanics by the chromatin de-condensing reagent Trichostatin A (TSA) and secondly altered cytoskeletal mechanics by addition of actin polymerization inhibitor Latrunculin A and the myosin inhibitor Blebbistatin. In fact, we found that TSA-treated MDA-MB-231 human breast cancer cells increased their invasion depth in dense 3D extracellular matrices, whereas the invasion depths in loose matrices were decreased. Similarly, the invasion depths of TSA-treated MCF-7 human breast cancer cells in dense matrices were significantly increased compared to loose matrices, where the invasion depths were decreased. These results are also valid in the presence of a matrix-metalloproteinase inhibitor GM6001. Using atomic force microscopy (AFM), we found that the nuclear stiffnesses of both MDA-MB-231 and MCF-7 breast cancer cells were pronouncedly higher than their cytoskeletal stiffness, whereas the stiffness of the nucleus of human mammary epithelial cells was decreased compared to their cytoskeleton. TSA treatment reduced cytoskeletal and nuclear stiffness of MCF-7 cells, as expected. However, a softening of the nucleus by TSA treatment may induce a stiffening of the cytoskeleton of MDA-MB-231 cells and subsequently an apparent stiffening of the nucleus. Inhibiting actin polymerization using Latrunculin A revealed a softer nucleus of MDA-MB-231 cells under TSA treatment. This indicates that the actin-dependent cytoskeletal stiffness seems to be influenced by the TSA-induced nuclear stiffness changes. Finally, the combined treatment with TSA and Latrunculin A further justifies the hypothesis of apparent nuclear stiffening, indicating that cytoskeletal mechanics seem to be regulated by nuclear mechanics.

Nesprin-2 accumulates at the front of the nucleus during confined cell migration

The mechanisms by which cells exert forces on their nuclei to migrate through openings smaller than the nuclear diameter remain unclear. We use CRISPR/Cas9 to fluorescently label nesprin-2 giant, which links the cytoskeleton to the nuclear interior. We demonstrate that nesprin-2 accumulates at the front of the nucleus during nuclear deformation through narrow constrictions, independently of the nuclear lamina. We find that nesprins are mobile at time scales similar to the accumulation. Using artificial constructs, we show that the actin-binding domain of nesprin-2 is necessary and sufficient for this accumulation. Actin filaments are organized in a barrel structure around the nucleus in the direction of movement. Using two-photon ablation and cytoskeleton-inhibiting drugs, we demonstrate an actomyosin-dependent pulling force on the nucleus from the front of the cell. The elastic recoil upon ablation is dampened when nesprins are reduced at the nuclear envelope. We thus show that actin redistributes nesprin-2 giant toward the front of the nucleus and contributes to pulling the nucleus through narrow constrictions, in concert with myosin.

Nuclear Mechanics within Intact Cells Is Regulated by Cytoskeletal Network and Internal Nanostructures

The mechanical properties of the cellular nucleus are extensively studied as they play a critical role in important processes, such as cell migration, gene transcription, and stem cell differentiation. While the mechanical properties of the isolated nucleus have been tested, there is a lack of measurements about the mechanical behavior of the nucleus within intact cells and specifically about the interplay of internal nuclear components with the intracellular microenvironment, because current testing methods are based on contact and only allow studying the nucleus after isolation from a cell or disruption of cytoskeleton. Here, all-optical Brillouin microscopy and 3D chemomechanical modeling are used to investigate the regulation of nuclear mechanics in physiological conditions. It is observed that the nuclear modulus can be modulated by epigenetic regulation targeting internal nuclear nanostructures such as lamin A/C and chromatin. It is also found that nuclear modulus is strongly regulated by cytoskeletal behavior through a robust mechanism conserved in different culturing conditions. Given the active role of cytoskeletal modulation in nearly all cell functions, this work will enable to reveal highly relevant mechanisms of nuclear mechanical regulations in physiological and pathological conditions.

Mechanosensing of Mechanical Confinement by Mesenchymal-Like Cells

Mesenchymal stem cells (MSCs) and tumor cells have the unique capability to migrate out of their native environment and either home or metastasize, respectively, through extremely heterogeneous environments to a distant location. Once there, they can either aid in tissue regrowth or impart an immunomodulatory effect in the case of MSCs, or form secondary tumors in the case of tumor cells. During these journeys, cells experience physically confining forces that impinge on the cell body and the nucleus, ultimately causing a multitude of cellular changes. Most drastically, confining individual MSCs within hydrogels or confining monolayers of MSCs within agarose wells can sway MSC lineage commitment, while applying a confining compressive stress to metastatic tumor cells can increase their invasiveness. In this review, we seek to understand the signaling cascades that occur as cells sense confining forces and how that translates to behavioral changes, including elongated and multinucleated cell morphologies, novel migrational mechanisms, and altered gene expression, leading to a unique MSC secretome that could hold great promise for anti-inflammatory treatments. Through comparison of these altered behaviors, we aim to discern how MSCs alter their lineage selection, while tumor cells may become more aggressive and invasive. Synthesizing this information can be useful for employing MSCs for therapeutic approaches through systemic injections or tissue engineered grafts, and developing improved strategies for metastatic cancer therapies.

Fluid shear stress coupled with narrow constrictions induce cell type-dependent morphological and molecular changes in SK-BR-3 and MDA-MB-231 cells

Cancer mortality mainly arises from metastases, due to cells that escape from a primary tumor, circulate in the blood as circulating tumor cells (CTCs), permeate across blood vessels and nest in distant organs. It is still unclear how CTCs overcome the harsh conditions of fluid shear stress and mechanical constraints within the microcirculation. Here, a minimal model of the blood microcirculation was established through the fabrication of microfluidic channels comprising constrictions. Metastatic breast cancer cells of epithelial-like and mesenchymal-like phenotypes were flowed into the microfluidic device. These cells were visualized during circulation and analyzed for their dynamical behavior, revealing long-lived plastic deformations and significant differences in biomechanics between cell types. γ-H2AX staining of cells retrieved post-circulation showed significant increase of DNA damage response in epithelial-like SK-BR-3 cells, while gene expression analysis of key regulators of epithelial-to-mesenchymal transition revealed significant changes upon circulation. This work thus documents first results of the changes at the cellular, subcellular and molecular scales induced by the two main mechanical stimuli arising from circulatory conditions, and suggest a significant role of this still elusive step of the metastatic cascade in cancer cells heterogeneity and aggressiveness.

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.

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.

A biomechanical model for the transendothelial migration of cancer cells

We propose a biomechanical model for the extravasation of a tumor cell (TC) through the endothelium of a blood vessel. Based on prior in vitro observations, we assume that the TC extends a protrusion between adjacent endothelial cells (ECs) that adheres to the basement membrane via focal adhesions (FAs). As the protrusion grows in size and branches out, the actomyosin contraction along the stress fibers (SFs) inside the protrusion pulls the relatively rigid nucleus through the endothelial opening. We model the chemo-mechanics of the SFs and the FAs by following the kinetics of the active myosin motors and high-affinity integrins, subject to mechanical feedback. This is incorporated into a finite-element simulation of the extravasation process, with the contractile force pulling the nucleus of the TC against elastic resistance of the ECs. To account for the interaction between the TC nucleus and the endothelium, we consider two scenarios: solid-solid contact and lubrication by cytosol. The former gives a lower bound for the required contractile force to realize transmigration, while the latter provides a more realistic representation of the process. Using physiologically reasonable parameters, our model shows that the SF and FA ensemble can produce a contractile force on the order of 70 nN, which is sufficient to deform the ECs and enable transmigration. Furthermore, we use an atomic force microscope to measure the resistant force on a human bladder cancer cell that is pushed through an endothelium cultured in vitro. The magnitude of the required force turns out to be in the range of 70-100 nN, comparable to the model predictions.

Confinement hinders motility by inducing RhoA-mediated nuclear influx, volume expansion, and blebbing

Cells migrate in vivo through complex confining microenvironments, which induce significant nuclear deformation that may lead to nuclear blebbing and nuclear envelope rupture. While actomyosin contractility has been implicated in regulating nuclear envelope integrity, the exact mechanism remains unknown. Here, we argue that confinement-induced activation of RhoA/myosin-II contractility, coupled with LINC complex-dependent nuclear anchoring at the cell posterior, locally increases cytoplasmic pressure and promotes passive influx of cytoplasmic constituents into the nucleus without altering nuclear efflux. Elevated nuclear influx is accompanied by nuclear volume expansion, blebbing, and rupture, ultimately resulting in reduced cell motility. Moreover, inhibition of nuclear efflux is sufficient to increase nuclear volume and blebbing on two-dimensional surfaces, and acts synergistically with RhoA/myosin-II contractility to further augment blebbing in confinement. Cumulatively, confinement regulates nuclear size, nuclear integrity, and cell motility by perturbing nuclear flux homeostasis via a RhoA-dependent pathway.

Systems Biology of Cancer Metastasis

Cancer metastasis is no longer viewed as a linear cascade of events but rather as a series of concurrent, partially overlapping processes, as successfully metastasizing cells assume new phenotypes while jettisoning older behaviors. The lack of a systemic understanding of this complex phenomenon has limited progress in developing treatments for metastatic disease. Because metastasis has traditionally been investigated in distinct physiological compartments, the integration of these complex and interlinked aspects remains a challenge for both systems-level experimental and computational modeling of metastasis. Here, we present some of the current perspectives on the complexity of cancer metastasis, the multiscale nature of its progression, and a systems-level view of the processes underlying the invasive spread of cancer cells. We also highlight the gaps in our current understanding of cancer metastasis as well as insights emerging from interdisciplinary systems biology approaches to understand this complex phenomenon.

Modeling Cell Migration Mechanics

Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.

Mechanics of nuclear membranes

Cellular nuclei are bound by two uniformly separated lipid membranes that are fused with each other at numerous donut-shaped pores. These membranes are structurally supported by an array of distinct proteins with distinct mechanical functions. As a result, the nuclear envelope possesses unique mechanical properties, which enables it to resist cytoskeletal forces. Here, we review studies that are beginning to provide quantitative insights into nuclear membrane mechanics. We discuss how the mechanical properties of the fused nuclear membranes mediate their response to mechanical forces exerted on the nucleus and how structural reinforcement by different nuclear proteins protects the nuclear membranes against rupture. We also highlight some open questions in nuclear envelope mechanics, and discuss their relevance in the context of health and disease.

Engineering approaches to studying cancer cell migration in three-dimensional environments

Cancer is one of the most devastating diseases of our time, with 17 million new cancer cases and 9.5 million cancer deaths in 2018 worldwide. The mortality associated with cancer results primarily from metastasis, i.e. the spreading of cancer cells from the primary tumour to other organs. The invasion and migration of cells through basement membranes, tight interstitial spaces and endothelial cell layers are key steps in the metastatic cascade. Recent studies demonstrated that cell migration through three-dimensional environments that mimic the in vivo conditions significantly differs from their migration on two-dimensional surfaces. Here, we review recent technological advances made in the field of cancer research that provide more 'true to the source' experimental platforms and measurements for the study of cancer cell invasion and migration in three-dimensional environments. These include microfabrication, three-dimensional bioprinting and intravital imaging tools, along with force and stiffness measurements of cells and their environments. These techniques will enable new studies that better reflect the physiological environment found in vivo, thereby producing more robust results. The knowledge achieved through these studies will aid in the development of new treatment options with the potential to ultimately lighten the devastating cost cancer inflicts on patients and their families. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.