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

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.

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.

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'.

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.

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.

Cell Type and Nuclear Size Dependence of the Nuclear Deformation of Cells on a Micropillar Array

While various cellular responses to materials have been published, little concerns the deformation of cell nuclei. Herein we fabricated a polymeric micropillar array of appropriate dimensions to trigger the significant self-deformation of cell nuclei and examined six cell types, which could be classified into cancerous cells (Hela and HepG2) versus healthy cells (HCvEpC, MC3T3-E1, NIH3T3, and hMSC) or epithelial-like cells (Hela, HepG2, and HCvEpC) versus fibroblast-like cells (MC3T3-E1, NIH3T3, and hMSC). While all of the cell types exhibited severe nuclear deformation on the poly(lactide- co-glycolide) (PLGA) micropillar array, the difference between the epithelial-like and fibroblast-like cells was much more significant than that between the cancerous and healthy cells. We also examined the statistics of nuclear shape indexes of cells with an inevitable dispersity of nuclear sizes. It was found that larger nuclei favored more significant deformation on the micropillar array for each cell type. In the same region of nuclear size, the parts of the epithelial-like cells exhibited more significant nuclear deformation than those of the fibroblast-like cells. Hence, this article reports the nuclear size dependence of the self-deformation of cell nuclei on micropillar arrays for the first time and meanwhile strengthens the cell-type dependence.

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.

Balance of mechanical forces drives endothelial gap formation and may facilitate cancer and immune-cell extravasation

The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration.

The Physics of Cancer

While often described as a "disease of the genes," cancer is, in fact, a complex dynamic system in which evolving cells both affect and are affected by the physical properties of their environment. About 10 years ago, after a number of multidisciplinary workshops and meetings, the NCI leadership embarked on a bold program to systematically integrate physical sciences into cancer biology and treatment through formation of the Physical Sciences-Oncology Network (PS-ON). Here, we highlight key areas in which the two disciplines have been successfully integrated and lessons learned from the first decade of the PS-ON experiment.

Helical nanofiber yarn enabling highly stretchable engineered microtissue

Development of microtissues that possess mechanical properties mimicking those of native stretchable tissues, such as muscle and tendon, is in high demand for tissue engineering and regenerative medicine. However, regardless of the significant advances in synthetic biomaterials, it remains challenging to fabricate living microtissue with high stretchability because application of large strains to microtissues can damage the cells by rupturing their structures. Inspired by the hierarchical helical structure of native fibrous tissues and its behavior of nonaffine deformation, we develop a highly stretchable and tough microtissue fiber made up of a hierarchical helix yarn scaffold, scaling from nanometers to millimeters, that can overcome this limitation. This microtissue can be stretched up to 15 times its initial length and has a toughness of 57 GJ m^-3 More importantly, cells grown on this scaffold maintain high viability, even under severe cyclic strains (up to 600%) that can be attributed to the nonaffine deformation under large strains, mimicking native biopolymer scaffolds. Furthermore, as proof of principle, we demonstrate that the nanotopography of the helical nanofiber yarn is able to induce cytoskeletal alignment and nuclear elongation, which promote myogenic differentiation of mesenchymal stem cells by triggering nuclear translocation of transcriptional coactivator with PDZ-binding motif (TAZ). The highly stretchable microtissues we develop here will facilitate a variety of tissue engineering applications and the development of engineered living systems.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

A Nondimensional Model Reveals Alterations in Nuclear Mechanics upon Hepatitis C Virus Replication

Morphology of the nucleus is an important regulator of gene expression. Nuclear morphology is in turn a function of the forces acting on it and the mechanical properties of the nuclear envelope. Here, we present a two-parameter, nondimensional mechanical model of the nucleus that reveals a relationship among nuclear shape parameters, such as projected area, surface area, and volume. Our model fits the morphology of individual nuclei and predicts the ratio between forces and modulus in each nucleus. We analyzed the changes in nuclear morphology of liver cells due to hepatitis C virus (HCV) infection using this model. The model predicted a decrease in the elastic modulus of the nuclear envelope and an increase in the pre-tension in cortical actin as the causes for the change in nuclear morphology. These predictions were validated biomechanically by showing that liver cells expressing HCV proteins possessed enhanced cellular stiffness and reduced nuclear stiffness. Concomitantly, cells expressing HCV proteins showed downregulation of lamin-A,C and upregulation of β-actin, corroborating the predictions of the model. Our modeling assumptions are broadly applicable to adherent, monolayer cell cultures, making the model amenable to investigate changes in nuclear mechanics due to other stimuli by merely measuring nuclear morphology. Toward this, we present two techniques, graphical and numerical, to use our model for predicting physical changes in the nucleus.

Proliferation of Cells with Severe Nuclear Deformation on a Micropillar Array

Cellular responses on a topographic surface are fundamental topics about interfaces and biology. Herein, a poly(lactide- co-glycolide) (PLGA) micropillar array was prepared and found to trigger significant self-deformation of cell nuclei. The time-dependent cell viability and thus cell proliferation was investigated. Despite significant nuclear deformation, all of the examined cell types (Hela, HepG2, MC3T3-E1, and NIH3T3) could survive and proliferate on the micropillar array yet exhibited different proliferation abilities. Compared to the corresponding groups on the smooth surface, the cell proliferation abilities on the micropillar array were decreased for Hela and MC3T3-E1 cells and did not change significantly for HepG2 and NIH3T3 cells. We also found that whether the proliferation ability changed was related to whether the nuclear sizes decreased in the micropillar array, and thus the size deformation of cell nuclei should, besides shape deformation, be taken into consideration in studies of cells on topological surfaces.

Migration through a small pore disrupts inactive chromatin organization in neutrophil-like cells

BACKGROUND

Mammalian cells are flexible and can rapidly change shape when they contract, adhere, or migrate. The nucleus must be stiff enough to withstand cytoskeletal forces, but flexible enough to remodel as the cell changes shape. This is particularly important for cells migrating through confined spaces, where the nuclear shape must change in order to fit through a constriction. This occurs many times in the life cycle of a neutrophil, which must protect its chromatin from damage and disruption associated with migration. Here we characterized the effects of constricted migration in neutrophil-like cells.

RESULTS

Total RNA sequencing identified that migration of neutrophil-like cells through 5- or 14-μm pores was associated with changes in the transcript levels of inflammation and chemotaxis-related genes when compared to unmigrated cells. Differentially expressed transcripts specific to migration with constriction were enriched for groups of genes associated with cytoskeletal remodeling. Hi-C was used to capture the genome organization in control and migrated cells. Limited switching was observed between the active (A) and inactive (B) compartments after migration. However, global depletion of short-range contacts was observed following migration with constriction compared to migration without constriction. Regions with disrupted contacts, TADs, and compartments were enriched for inactive chromatin.

CONCLUSION

Short-range genome organization is preferentially altered in inactive chromatin, possibly protecting transcriptionally active contacts from the disruptive effects of migration with constriction. This is consistent with current hypotheses implicating heterochromatin as the mechanoresponsive form of chromatin. Further investigation concerning the contribution of heterochromatin to stiffness, flexibility, and protection of nuclear function will be important for understanding cell migration in relation to human health and disease.

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.

Intracellular mechanics: connecting rheology and mechanotransduction

Cell mechanics is crucial for a wide range of cell functions, including proliferation, polarity, migration and differentiation. Cells sense external physical cues and translate them into a cellular response. While force sensing occurs in the vicinity of the plasma membrane, forces can reach deep in the cell interior and to the nucleus. We review here the recent developments in the field of intracellular mechanics. We focus first on intracellular rheology, the study of the mechanical properties of the cell interior, and recapitulate the contribution of active mechanisms, the cytoskeleton and intracellular organelles to cell rheology. We then discuss how forces are transmitted inside the cell during mechanotransduction events, through direct force transmission and biochemical signaling, and how intracellular rheology and mechanotransduction are connected.

G9a Correlates with VLA-4 Integrin and Influences the Migration of Childhood Acute Lymphoblastic Leukemia Cells

Acute lymphoblastic leukemia (ALL) is the most common pediatric cancer. As ALL progresses, leukemic cells cross the endothelial barrier and infiltrate other tissues. Epigenetic enzymes represent novel therapeutic targets in hematological malignancies, and might contribute to cells' capacity to migrate across physical barriers. Although many molecules drive this process, the role of the nucleus and its components remain unclear. We report here, for the first time, that the expression of G9a (a histone methyltransferase related with gene silencing) correlates with the expression of the integrin subunit α4 in children with ALL. We have demonstrated that G9a depletion or its inhibition with BIX01294 abrogated the ability of ALL cells to migrate through an endothelial monolayer. Moreover, G9a-depleted and BIX01294-treated cells presented bigger nuclei and more adherent phenotype than control cells on endothelial monolayers. Blocking G9a did not affect the cell cytoskeleton or integrin expression of ALL cell lines, and only its depletion reduced slightly F-actin polymerization. Similarly to the transendothelial migration, G9a inhibition impaired the cell migration induced by the integrin VLA-4 (α4β1) of primary cells and ALL cell lines through narrow spaces in vitro. Our results suggest a cellular connection between G9a and VLA-4, which underlies novel functions of G9a during ALL cell migration.

Mechanical property characterization of hundreds of single nuclei based on microfluidic constriction channel

As label-free biomarkers, the mechanical properties of nuclei are widely treated as promising biomechanical markers for cell type classification and cellular status evaluation. However, previously reported mechanical parameters were derived from only around 10 nuclei, lacking statistical significances due to low sample numbers. To address this issue, nuclei were first isolated from SW620 and A549 cells, respectively, using a chemical treatment method. This was followed by aspirating them through two types of microfluidic constriction channels for mechanical property characterization. In this study, hundreds of nuclei were characterized, producing passage times of 0.5 ± 1.2 s for SW620 nuclei in type I constriction channel (n = 153), 0.045 ± 0.047 s for SW620 nuclei in type II constriction channel (n = 215) and 0.50 ± 0.86 s for A549 nuclei in type II constriction channel. In addition, neural network based pattern recognition was used to classify the nuclei isolated from SW620 and A549 cells, producing successful classification rates of 87.2% for diameters of nuclei, 85.5% for passage times of nuclei and 89.3% for both passage times and diameters of nuclei. These results indicate that the characterization of the mechanical properties of nuclei may contribute to the classification of different tumor cells.

Mechanical and Systems Biology of Cancer

Mechanics and biochemical signaling are both often deregulated in cancer, leading toincreased cell invasiveness, proliferation, and survival. The dynamics and interactions of cytoskeletal components control basic mechanical properties, such as cell tension, stiffness, and engagement with the extracellular environment, which can lead to extracellular matrix remodeling. Intracellular mechanics can alter signaling and transcription factors, impacting cell decision making. Additionally, signaling from soluble and mechanical factors in the extracellular environment, such as substrate stiffness and ligand density, can modulate cytoskeletal dynamics. Computational models closely integrated with experimental support, incorporating cancer-specific parameters, can provide quantitative assessments and serve as predictive tools toward dissecting the feedback between signaling and mechanics and across multiple scales and domains in tumor progression.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

A phenomenological model for cell and nucleus deformation during cancer metastasis

Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.

Role of the Nucleus as a Sensor of Cell Environment Topography

The proper integration of biophysical cues from the cell vicinity is crucial for cells to maintain homeostasis, cooperate with other cells within the tissues, and properly fulfill their biological function. It is therefore crucial to fully understand how cells integrate these extracellular signals for tissue engineering and regenerative medicine. Topography has emerged as a prominent component of the cellular microenvironment that has pleiotropic effects on cell behavior. This progress report focuses on the recent advances in the understanding of the topography sensing mechanism with a special emphasis on the role of the nucleus. Here, recent techniques developed for monitoring the nuclear mechanics are reviewed and the impact of various topographies and their consequences on nuclear organization, gene regulation, and stem cell fate is summarized. The role of the cell nucleus as a sensor of cell-scale topography is further discussed.

Maturation State and Matrix Microstructure Regulate Interstitial Cell Migration in Dense Connective Tissues

Few regenerative approaches exist for the treatment of injuries to adult dense connective tissues. Compared to fetal tissues, adult connective tissues are hypocellular and show limited healing after injury. We hypothesized that robust repair can occur in fetal tissues with an immature extracellular matrix (ECM) that is conducive to cell migration, and that this process fails in adults due to the biophysical barriers imposed by the mature ECM. Using the knee meniscus as a platform, we evaluated the evolving micromechanics and microstructure of fetal and adult tissues, and interrogated the interstitial migratory capacity of adult meniscal cells through fetal and adult tissue microenvironments with or without partial enzymatic digestion. To integrate our findings, a computational model was implemented to determine how changing biophysical parameters impact cell migration through these dense networks. Our results show that the micromechanics and microstructure of the adult meniscus ECM sterically hinder cell mobility, and that modulation of these ECM attributes via an exogenous matrix-degrading enzyme permits migration through this otherwise impenetrable network. By addressing the inherent limitations to repair imposed by the mature ECM, these studies may define new clinical strategies to promote repair of damaged dense connective tissues in adults.

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.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

A numerical model suggests the interplay between nuclear plasticity and stiffness during a perfusion assay

Cell deformability is a necessary condition for a cell to be able to migrate, an ability that is vital both for healthy and diseased organisms. The nucleus being the largest and stiffest organelle, it often is a barrier to cell migration. It is thus essential to characterize its mechanical behaviour. First, we numerically investigate the visco-elasto-plastic properties of the isolated nucleus during a compression test. This simulation highlights the impact of the mechanical behaviour of the nuclear lamina and the nucleoplasm on the overall plasticity. Second, a whole cell model is developed to simulate a perfusion experiment to study the possible interactions between the cytoplasm and the nucleus. We analyze and discuss the role of the lamina for a wild-type cell model, and a lamin-deficient one, in which the Young's modulus of the lamina is set to 1% of its nominal value. This simulation suggests an interplay between the cytoplasm and the nucleoplasm, especially in the lamin-deficient cell, showing the need of a stiffer nucleoplasm to maintain nuclear plasticity.

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

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

Inside the Cell: Integrins as New Governors of Nuclear Alterations?

Cancer cell migration is a complex process that requires coordinated structural changes and signals in multiple cellular compartments. The nucleus is the biggest and stiffest organelle of the cell and might alter its physical properties to allow cancer cell movement. Integrins are transmembrane receptors that mediate cell-cell and cell-extracellular matrix interactions, which regulate numerous intracellular signals and biological functions under physiological conditions. Moreover, integrins orchestrate changes in tumor cells and their microenvironment that lead to cancer growth, survival and invasiveness. Most of the research efforts have focused on targeting integrin-mediated adhesion and signaling. Recent exciting data suggest the crucial role of integrins in controlling internal cellular structures and nuclear alterations during cancer cell migration. Here we review the emerging role of integrins in nuclear biology. We highlight increasing evidence that integrins are critical for changes in multiple nuclear components, the positioning of the nucleus and its mechanical properties during cancer cell migration. Finally, we discuss how integrins are integral proteins linking the plasma membrane and the nucleus, and how they control cell migration to enable cancer invasion and infiltration. The functional connections between these cell receptors and the nucleus will serve to define new attractive therapeutic targets.

Role of the unfolded protein response in topography-induced osteogenic differentiation in rat bone marrow mesenchymal stem cells

The topography of biomaterials can significantly influence the osteogenic differentiation of cells. Understanding topographical signal transduction is critical for developing biofunctional surfaces, but the current knowledge is insufficient. Recently, numerous reports have suggested that the unfolded protein response (UPR) and osteogenic differentiation are inter-linked. Therefore, we hypothesize that the UPR pathway may be involved in the topography-induced osteogenesis. In the present study, different surface topographies were fabricated on pure titanium foils and the endoplasmic reticulum (ER) stress and UPR pathway were systematically investigated. We found that ER stress and the PERK-eIF2α-ATF4 pathway were activated in a time- and topography-dependent manner. Additionally, the activation of the PERK-eIF2α-ATF4 pathway by different topographies was in line with their osteogenic induction capability. More specifically, the osteogenic differentiation could be enhanced or weakened when the PERK-eIF2α-ATF4 pathway was promoted or inhibited, respectively. Furthermore, tuning of the degree of ER stress with different concentrations of thapsigargin revealed that mild ER stress promotes osteogenic differentiation, whereas excessive ER stress inhibits osteogenic differentiation and causes apoptosis. Taken together, our findings suggest that the UPR may play a critical role in topography-induced osteogenic differentiation, which may help to provide new insights into topographical signal transduction.

STATEMENT OF SIGNIFICANCE

Suitable implant surface topography can effectively improve bioactivity and eventual bone affinity. However, the mechanism of topographical signaling transduction is unclear and criteria for designation of an appropriate implant surface topography is lacking. This study shows that the ER stress and PERK-eIF2α-ATF4 pathway were activated by micro- and micro/nano-topographies, which is corresponding to the osteogenic induction abilities of these topographies. Furthermore, we have found that mild ER stress improves osteogenic differentiation, whereas excessive ER stress inhibits osteogenic differentiation and causes apoptosis. Our findings demonstrate that the UPR plays a critical role in the topography induced osteogenic differentiation, which may help to provide new insights into the topographical signaling transduction.

Consequences of a tight squeeze: Nuclear envelope rupture and repair

Cell migration through tight spaces can induce substantial deformations of the nucleus and cause nuclear envelope (NE) rupture, resulting in uncontrolled exchange of nuclear and cytosolic proteins. These events can cause DNA damage and, in severe cases, nuclear fragmentation, challenging the integrity of the genomic material. Cells overcome NE ruptures during interphase by repairing the NE using components of the endosomal sorting complexes required for transport (ESCRT) machinery. Paralleling the molecular mechanism used during NE reformation in late mitosis, ESCRT-III subunits and the associated AAA-ATPase VPS4B are recruited to NE rupture sites and help restore NE integrity. While these findings are common to many cell types, they are particularly relevant in the context of cancer metastasis, where nuclear deformation and rupture could drive genomic instability in invading cells and further promote cancer progression. At the same time, inhibiting NE repair may offer new therapeutic approaches to specifically target invasive cancer cells.

Bursting the Bubble - Nuclear Envelope Rupture as a Path to Genomic Instability?

The nuclear envelope safeguards the genetic material inside the nucleus by separating it from the cytoplasm. Until recently, it was assumed that nuclear envelope (NE) breakdown occurs only in a highly controlled fashion during mitosis when the chromatin is condensed and divided between the daughter cells. However, recent studies have demonstrated that adherent and migrating cells exhibit transient NE rupture during interphase caused by compression from cytoskeletal or external forces. NE rupture results in uncontrolled exchange between the nuclear interior and cytoplasm and leads to DNA damage. In this review, we discuss the causes and consequences of NE rupture, and how NE rupture could contribute to genomic instability.

Emerging roles of mechanical forces in chromatin regulation

Cells are constantly subjected to a spectrum of mechanical cues, such as shear stress, compression, differential tissue rigidity and strain, to which they adapt by engaging mechanisms of mechanotransduction. While the central role of cell adhesion receptors in this process is established, it has only recently been appreciated that mechanical cues reach far beyond the plasma membrane and the cytoskeleton, and are directly transmitted to the nucleus. Furthermore, changes in the mechanical properties of the perinuclear cytoskeleton, nuclear lamina and chromatin are critical for cellular responses and adaptation to external mechanical cues. In that respect, dynamic changes in the nuclear lamina and the surrounding cytoskeleton modify mechanical properties of the nucleus, thereby protecting genetic material from damage. The importance of this mechanism is highlighted by debilitating genetic diseases, termed laminopathies, that result from impaired mechanoresistance of the nuclear lamina. What has been less evident, and represents one of the exciting emerging concepts, is that chromatin itself is an active rheological element of the nucleus, which undergoes dynamic changes upon application of force, thereby facilitating cellular adaption to differential force environments. This Review aims to highlight these emerging concepts by discussing the latest literature in this area and by proposing an integrative model of cytoskeletal and chromatin-mediated responses to mechanical stress.