Active Biochemical Regulation of Cell Volume and a Simple Model of Cell Tension Response

Roles of membrane mechanics-mediated feedback in membrane traffic

Synthesizing the recent progresses, we present our perspectives on how local modulations of membrane curvature, tension, and bending energy define the feedback controls over membrane traffic processes. We speculate the potential mechanisms of, and the control logic behind, the different membrane mechanics-mediated feedback in endocytosis and exo-endocytosis coupling. We elaborate the path forward with the open questions for theoretical considerations and the grand challenges for experimental validations.

Dynamic nanomechanical characterization of cells in exosome therapy

Exosomes derived from mesenchymal stem cells (MSCs) have been confirmed to enhance cell proliferation and improve tissue repair. Exosomes release their contents into the cytoplasmic solution of the recipient cell to mediate cell expression, which is the main pathway through which exosomes exert therapeutic effects. The corresponding process of exosome internalization mainly occurs in the early stage of treatment. However, the therapeutic effect of exosomes in the early stage remains to be further studied. We report that the three-dimensional cell traction force can intuitively reflect the ability of exosomes to enhance the cytoskeleton and cell contractility of recipient cells, serving as an effective method to characterize the therapeutic effect of exosomes. Compared with traditional biochemical methods, we can visualize the early therapeutic effect of exosomes in real time without damage by quantifying the cell traction force. Through quantitative analysis of traction forces, we found that endometrial stromal cells exhibit short-term cell roundness accompanied by greater traction force during the early stage of exosome therapy. Further experiments revealed that exosomes enhance the traction force and cytoskeleton by regulating the Rac1/RhoA signaling pathway, thereby promoting cell proliferation. This work provides an effective method for rapidly quantifying the therapeutic effects of exosomes and studying the underlying mechanisms involved.

Unveiling the Intricate Connection: Cell Volume as a Key Regulator of Mechanotransduction

The volumes of living cells undergo dynamic changes to maintain the cells' structural and functional integrity in many physiological processes. Minor fluctuations in cell volume can serve as intrinsic signals that play a crucial role in cell fate determination during mechanotransduction. In this review, we discuss the variability of cell volume and its role in vivo, along with an overview of the mechanisms governing cell volume regulation. Additionally, we provide insights into the current approaches used to control cell volume in vitro. Furthermore, we summarize the biological implications of cell volume regulation and discuss recent advances in understanding the fundamental relationship between cell volume and mechanotransduction. Finally, we delve into the potential underlying mechanisms, including intracellular macromolecular crowding and cellular mechanics, that govern the global regulation of cell fate in response to changes in cell volume. By exploring the intricate interplay between cell volume and mechanotransduction, we underscore the importance of considering cell volume as a fundamental signaling cue to unravel the basic principles of mechanotransduction. Additionally, we propose future research directions that can extend our current understanding of cell volume in mechanotransduction. Overall, this review highlights the significance of considering cell volume as a fundamental signal in understanding the basic principles in mechanotransduction and points out the possibility of controlling cell volume to control cell fate, mitigate disease-related damage, and facilitate the healing of damaged tissues.

Cytoskeletal activation of NHE1 regulates mechanosensitive cell volume adaptation and proliferation

Mammalian cells can rapidly respond to osmotic and hydrostatic pressure imbalances during an environmental change, generating large fluxes of water and ions that alter cell volume within minutes. While the role of ion pump and leak in cell volume regulation has been well-established, the potential contribution of the actomyosin cytoskeleton and its interplay with ion transporters is unclear. We discovered a cell volume regulation system that is controlled by cytoskeletal activation of ion transporters. After a hypotonic shock, normal-like cells (NIH-3T3, MCF-10A, and others) display a slow secondary volume increase (SVI) following the immediate regulatory volume decrease. We show that SVI is initiated by hypotonic stress induced Ca 2+ influx through stretch activated channel Piezo1, which subsequently triggers actomyosin remodeling. The actomyosin network further activates NHE1 through their synergistic linker ezrin, inducing SVI after the initial volume recovery. We find that SVI is absent in cancer cell lines such as HT1080 and MDA-MB-231, where volume regulation is dominated by intrinsic response of ion transporters. A similar cytoskeletal activation of NHE1 can also be achieved by mechanical stretching. On compliant substrates where cytoskeletal contractility is attenuated, SVI generation is abolished. Moreover, cytoskeletal activation of NHE1 during SVI triggers nuclear deformation, leading to a significant, immediate transcriptomic change in 3T3 cells, a phenomenon that is again absent in HT1080 cells. While hypotonic shock hinders ERK-dependent cell growth, cells deficient in SVI are unresponsive to such inhibitory effects. Overall, our findings reveal the critical role of Ca 2+ and actomyosin-mediated mechanosensation in the regulation of ion transport, cell volume, transcriptomics, and cell proliferation.

Unexpected softening of a fibrous matrix by contracting inclusions

Cells respond to the stiffness of their surrounding environment, but quantifying the stiffness of a fibrous matrix at the scale of a cell is complicated, due to the effects of nonlinearity and complex force transmission pathways resulting from randomness in fiber density and connections. While it is known that forces produced by individual contractile cells can stiffen the matrix, it remains unclear how simultaneous contraction of multiple cells in a fibrous matrix alters the stiffness at the scale of a cell. Here, we used computational modeling and experiments to quantify the stiffness of a random fibrous matrix embedded with multiple contracting inclusions, which mimicked the contractile forces of a cell. The results showed that when the matrix was free to contract as a result of the forces produced by the inclusions, the matrix softened rather than stiffened, which was surprising given that the contracting inclusions applied tensile forces to the matrix. Using the computational model, we identified that the underlying cause of the softening was that the majority of the fibers were under a local state of axial compression, causing buckling. We verified that this buckling-induced matrix softening was sufficient for cells to sense and respond by altering their morphology and force generation. Our findings reveal that the localized forces induced by cells do not always stiffen the matrix; rather, softening can occur in instances wherein the matrix can contract in response to the cell-generated forces. This study opens up new possibilities to investigate whether cell-induced softening contributes to maintenance of homeostatic conditions or progression of disease. STATEMENT OF SIGNIFICANCE: Mechanical interactions between cells and the surrounding matrix strongly influence cellular functions. Cell-induced forces can alter matrix properties, and much prior literature in this area focused on the influence of individual contracting cells. Cells in tissues are rarely solitary; rather, they are interspersed with neighboring cells throughout the matrix. As a result, the mechanics are complicated, leaving it unclear how the multiple contracting cells affect matrix stiffness. Here, we show that multiple contracting inclusions within a fibrous matrix can cause softening that in turn affects cell sensing and response. Our findings provide new directions to determine impacts of cell-induced softening on maintenance of tissue or progression of disease.

Coordinated in confined migration: crosstalk between the nucleus and ion channel-mediated mechanosensation

Cell surface and intracellular mechanosensors enable cells to perceive different geometric, topographical, and physical cues. Mechanosensitive ion channels (MICs) localized at the cell surface and on the nuclear envelope (NE) are among the first to sense and transduce these signals. Beyond compartmentalizing the genome of the cell and its transcription, the nucleus also serves as a mechanical gauge of different physical and topographical features of the tissue microenvironment. In this review, we delve into the intricate mechanisms by which the nucleus and different ion channels regulate cell migration in confinement. We review evidence suggesting an interplay between macromolecular nuclear-cytoplasmic transport (NCT) and ionic transport across the cell membrane during confined migration. We also discuss the roles of the nucleus and ion channel-mediated mechanosensation, whether acting independently or in tandem, in orchestrating migratory mechanoresponses. Understanding nuclear and ion channel sensing, and their crosstalk, is critical to advancing our knowledge of cell migration in health and disease.

SPAK-dependent cotransporter activity mediates capillary adhesion and pressure during glioblastoma migration in confined spaces

The invasive potential of glioblastoma cells is attributed to large changes in pressure and volume, driven by diverse elements, including the cytoskeleton and ion cotransporters.  However, how the cell actuates changes in pressure and volume in confinement, and how these changes contribute to invasive motion is unclear. Here, we inhibited SPAK activity, with known impacts on the cytoskeleton and cotransporter activity and explored its role on the migration of glioblastoma cells in confining microchannels to model invasive spread through brain tissue. First, we found that confinement altered cell shape, inducing a transition in morphology that resembled droplet interactions with a capillary vessel, from "wetting" (more adherent) at low confinement, to "nonwetting" (less adherent) at high confinement. This transition was marked by a change from negative to positive pressure by the cells to the confining walls, and an increase in migration speed. Second, we found that the SPAK pathway impacted the migration speed in different ways dependent upon the extent of wetting. For nonwetting cells, SPAK inhibition increased cell-surface tension and cotransporter activity. By contrast, for wetting cells, it also reduced myosin II and YAP phosphorylation. In both cases, membrane-to-cortex attachment is dramatically reduced. Thus, our results suggest that SPAK inhibition differentially coordinates cotransporter and cytoskeleton-induced forces, to impact glioblastoma migration depending on the extent of confinement.

Dynamic response of the cell traction force to osmotic shock

Osmotic pressure is vital to many physiological activities, such as cell proliferation, wound healing and disease treatment. However, how cells interact with the extracellular matrix (ECM) when subjected to osmotic shock remains unclear. Here, we visualize the mechanical interactions between cells and the ECM during osmotic shock by quantifying the dynamic evolution of the cell traction force. We show that both hypertonic and hypotonic shocks induce continuous and large changes in cell traction force. Moreover, the traction force varies with cell volume: the traction force increases as cells shrink and decreases as cells swell. However, the direction of the traction force is independent of cell volume changes and is always toward the center of the cell-substrate interface. Furthermore, we reveal a mechanical mechanism in which the change in cortical tension caused by osmotic shock leads to the variation in traction force, which suggests a simple method for measuring changes in cell cortical tension. These findings provide new insights into the mechanical force response of cells to the external environment and may provide a deeper understanding of how the ECM regulates cell structure and function. Traction force exerted by cells under hypertonic and hypotonic shocks. Scale bar, 200 Pa. Color bar, Pa. The black arrows represent the tangential traction forces.

Mechanics of cell-cell junctions

Tissue cells in epithelial or endothelial monolayers are connected through cell-cell junctions, which are stabilized by transmembrane E-cadherin bonds and intracellular actin filaments. These bonds and junctions play a crucial role in maintaining the barrier function of epithelia and endothelia and are believed to transmit forces between cells. Additionally, E-cadherin bonds can impact the shape of cell-cell junctions. In this study, we develop a continuum mechanical model of the cell-cell junction by explicitly incorporating the cell membrane, distributions of E-cadherin bonds, cytoplasmic fluid pressure, and F-actin dynamics. The static force-balanced version of the model is able to analyze the influences of cell cortical tension, actin dynamics, and cytoplasmic pressure on the junction shape and E-cadherin bonds. Furthermore, an extended model that incorporates fluid flow, across the cell boundary as well as around the cell, is also examined. This model can couple cell-shape changes with cell cortical tension and fluid flow, and predicts the additional effect of fluid motion on cell-cell junction mechanics. Taken together, our models serve as an intermediate link between molecular-scale models of cell-junction molecules and cell-scale models of tissue and epithelia.

Myosin and [Formula: see text]-actinin regulation of stress fiber contractility under tensile stress

Stress fibers are actomyosin bundles that regulate cellular mechanosensation and force transduction. Interacting with the extracellular matrix through focal adhesion complexes, stress fibers are highly dynamic structures regulated by myosin motors and crosslinking proteins. Under external mechanical stimuli such as tensile forces, the stress fiber remodels its architecture to adapt to external cues, displaying properties of viscoelastic materials. How the structural remodeling of stress fibers is related to the generation of contractile force is not well understood. In this work, we simulate mechanochemical dynamics and force generation of stress fibers using the molecular simulation platform MEDYAN. We model stress fiber as two connecting bipolar bundles attached at the ends to focal adhesion complexes. The simulated stress fibers generate contractile force that is regulated by myosin motors and [Formula: see text]-actinin crosslinkers. We find that stress fibers enhance contractility by reducing the distance between actin filaments to increase crosslinker binding, and this structural remodeling ability depends on the crosslinker turnover rate. Under tensile pulling force, the stress fiber shows an instantaneous increase of the contractile forces followed by a slow relaxation into a new steady state. While the new steady state contractility after pulling depends only on the overlap between actin bundles, the short-term contractility enhancement is sensitive to the tensile pulling distance. We further show that this mechanical response is also sensitive to the crosslinker turnover rate. Our results provide new insights into the stress fiber mechanics that have significant implications for understanding cellular adaptation to mechanical signaling.

Volume regulation in adhered cells: Roles of surface tension and cell swelling

The volume of adhered cells has been shown experimentally to decrease during spreading. This effect can be understood from the pump-leak model, which we have extended to include mechano-sensitive ion transporters. We identify a novel effect that has important consequences on cellular volume loss: cells that are swollen due to a modulation of ion transport rates are more susceptible to volume loss in response to a tension increase. This effect explains in a plausible manner the discrepancies between three recent, independent experiments on adhered cells, between which both the magnitude of the volume change and its dynamics varied substantially. We suggest that starved and synchronized cells in two of the experiments were in a swollen state and, consequently, exhibited a large volume loss at steady state. Nonswollen cells, for which there is a very small steady-state volume decrease, are still predicted to transiently lose volume during spreading due to a relaxing viscoelastic tension that is large compared with the steady-state tension. We elucidate the roles of cell swelling and surface tension in cellular volume regulation and discuss their possible microscopic origins.

Mechanical compression creates a quiescent muscle stem cell niche

Tissue stem cell niches are regulated by their mechanical environment, notably the extracellular matrix (ECM). Skeletal muscles consist of bundled myofibers for force transmission. Within this macroscopic architecture, quiescent Pax7-expressing (Pax7⁺) muscle stem cells (MuSCs) are compressed between ECM basally and myofiber apically. Muscle injury causes MuSCs to lose apical compression from the myofiber and re-enter the cell cycle for regeneration. While ECM elasticities have been shown to affect MuSC's renewal, the significance of apical compression remains unknown. To investigate the role of apical compression, we simulate the MuSCs' in vivo mechanical environment by applying physical compression to MuSCs' apical surface. We demonstrate that compression drives activated MuSCs back to a quiescent stem cell state, regardless of basal elasticities and chemistries. By mathematical modeling and cell tension manipulation, we conclude that low overall tension combined with high axial tension generated by compression leads to MuSCs' stemness and quiescence. Unexpectedly, we discovered that apical compression results in up-regulation of Notch downstream genes, accompanied by the increased levels of nuclear Notch1&3 in a Delta ligand (Dll) and ADAM10/17 independent manner. Our results fill a knowledge gap on the role of apical compression for MuSC fate and have implications to stem cells in other tissues.

Non-muscle myosin II and the plasticity of 3D cell migration

Confined cells migrating through 3D environments are also constrained by the laws of physics, meaning for every action there must be an equal and opposite reaction for cells to achieve motion. Fascinatingly, there are several distinct molecular mechanisms that cells can use to move, and this is reflected in the diverse ways non-muscle myosin II (NMII) can generate the mechanical forces necessary to sustain 3D cell migration. This review summarizes the unique modes of 3D migration, as well as how NMII activity is regulated and localized within each of these different modes. In addition, we highlight tropomyosins and septins as two protein families that likely have more secrets to reveal about how NMII activity is governed during 3D cell migration. Together, this information suggests that investigating the mechanisms controlling NMII activity will be helpful in understanding how a single cell transitions between distinct modes of 3D migration in response to the physical environment.

Trans-epithelial fluid flow and mechanics of epithelial morphogenesis

Active fluid transport across epithelial monolayers is emerging as a major driving force of tissue morphogenesis in a variety of healthy and diseased systems, as well as during embryonic development. Cells use directional transport of ions and osmotic gradients to drive fluid flow across the cell surface, in the process also building up fluid pressure. The basic physics of this process is described by the osmotic engine model, which also underlies actin-independent cell migration. Recently, the trans-epithelial fluid flux and the hydraulic pressure gradient have been explicitly measured for a variety of cellular and tissue model systems across various species. For the kidney, it was shown that tubular epithelial cells behave as active mechanical fluid pumps: the trans-epithelial fluid flux depends on the hydraulic pressure difference across the epithelial layer. When a stall pressure is reached, the fluid flux vanishes. Hydraulic forces generated from active fluid pumping are important in tissue morphogenesis and homeostasis, and could also underlie multiple morphogenic events seen in other developmental contexts. In this review, we highlight findings that examined the role of trans-epithelial fluid flux and hydraulic pressure gradient in driving tissue-scale morphogenesis. We also review organ pathophysiology due to impaired fluid pumping and the loss of hydraulic pressure sensing at the cellular scale. Finally, we draw an analogy between cellular fluidic pumps and a connected network of water pumps in a city. The dynamics of fluid transport in an active and adaptive network is determined globally at the systemic level, and transport in such a network is best when each pump is operating at its optimal efficiency.

The uniformity and stability of cellular mass density in mammalian cell culture

Cell dry mass is principally determined by the sum of biosynthesis and degradation. Measurable change in dry mass occurs on a time scale of hours. By contrast, cell volume can change in minutes by altering the osmotic conditions. How changes in dry mass and volume are coupled is a fundamental question in cell size control. If cell volume were proportional to cell dry mass during growth, the cell would always maintain the same cellular mass density, defined as cell dry mass dividing by cell volume. The accuracy and stability against perturbation of this proportionality has never been stringently tested. Normalized Raman Imaging (NoRI), can measure both protein and lipid dry mass density directly. Using this new technique, we have been able to investigate the stability of mass density in response to pharmaceutical and physiological perturbations in three cultured mammalian cell lines. We find a remarkably narrow mass density distribution within cells, that is, significantly tighter than the variability of mass or volume distribution. The measured mass density is independent of the cell cycle. We find that mass density can be modulated directly by extracellular osmolytes or by disruptions of the cytoskeleton. Yet, mass density is surprisingly resistant to pharmacological perturbations of protein synthesis or protein degradation, suggesting there must be some form of feedback control to maintain the homeostasis of mass density when mass is altered. By contrast, physiological perturbations such as starvation or senescence induce significant shifts in mass density. We have begun to shed light on how and why cell mass density remains fixed against some perturbations and yet is sensitive during transitions in physiological state.

The interplay between physical cues and mechanosensitive ion channels in cancer metastasis

Physical cues have emerged as critical influencers of cell function during physiological processes, like development and organogenesis, and throughout pathological abnormalities, including cancer progression and fibrosis. While ion channels have been implicated in maintaining cellular homeostasis, their cell surface localization often places them among the first few molecules to sense external cues. Mechanosensitive ion channels (MICs) are especially important transducers of physical stimuli into biochemical signals. In this review, we describe how physical cues in the tumor microenvironment are sensed by MICs and contribute to cancer metastasis. First, we highlight mechanical perturbations, by both solid and fluid surroundings typically found in the tumor microenvironment and during critical stages of cancer cell dissemination from the primary tumor. Next, we describe how Piezo1/2 and transient receptor potential (TRP) channels respond to these physical cues to regulate cancer cell behavior during different stages of metastasis. We conclude by proposing alternative mechanisms of MIC activation that work in tandem with cytoskeletal components and other ion channels to bestow cells with the capacity to sense, respond and navigate through the surrounding microenvironment. Collectively, this review provides a perspective for devising treatment strategies against cancer by targeting MICs that sense aberrant physical characteristics during metastasis, the most lethal aspect of cancer.

Intrinsic cell rheology drives junction maturation

A fundamental property of higher eukaryotes that underpins their evolutionary success is stable cell-cell cohesion. Yet, how intrinsic cell rheology and stiffness contributes to junction stabilization and maturation is poorly understood. We demonstrate that localized modulation of cell rheology governs the transition of a slack, undulated cell-cell contact (weak adhesion) to a mature, straight junction (optimal adhesion). Cell pairs confined on different geometries have heterogeneous elasticity maps and control their own intrinsic rheology co-ordinately. More compliant cell pairs grown on circles have slack contacts, while stiffer triangular cell pairs favour straight junctions with flanking contractile thin bundles. Counter-intuitively, straighter cell-cell contacts have reduced receptor density and less dynamic junctional actin, suggesting an unusual adaptive mechano-response to stabilize cell-cell adhesion. Our modelling informs that slack junctions arise from failure of circular cell pairs to increase their own intrinsic stiffness and resist the pressures from the neighbouring cell. The inability to form a straight junction can be reversed by increasing mechanical stress artificially on stiffer substrates. Our data inform on the minimal intrinsic rheology to generate a mature junction and provide a springboard towards understanding elements governing tissue-level mechanics.

A mechano-osmotic feedback couples cell volume to the rate of cell deformation

Mechanics has been a central focus of physical biology in the past decade. In comparison, how cells manage their size is less understood. Here we show that a parameter central to both the physics and the physiology of the cell, its volume, depends on a mechano-osmotic coupling. We found that cells change their volume depending on the rate at which they change shape, when they spontaneously spread are externally deformed. Cells undergo slow deformation at constant volume, while fast deformation leads to volume loss. We propose a mechano-sensitive pump and leak model to explain this phenomenon. Our model and experiments suggest that volume modulation depends on the state of the actin cortex and the coupling of ion fluxes to membrane tension. This mechano-osmotic coupling defines a membrane tension homeostasis module constantly at work in cells, causing volume fluctuations associated with fast cell shape changes, with potential consequences on cellular physiology.

Intercellular water exchanges trigger soliton-like waves in multicellular systems

Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatio-temporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The travelling wave propagates along intercellular osmotic pressure gradient and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the travelling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

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

The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.

Active Regulation of Pressure and Volume Defines an Energetic Constraint on the Size of Cell Aggregates

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the F-actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.

Compression enhances invasive phenotype and matrix degradation of breast Cancer cells via Piezo1 activation

Background

Uncontrolled growth in solid breast cancer generates mechanical compression that may drive the cancer cells into a more invasive phenotype, but little is known about how such compression affects the key events and corresponding regulatory mechanisms associated with invasion of breast cancer cells including cellular behaviors and matrix degradation.

Results

Here we show that compression enhanced invasion and matrix degradation of breast cancer cells. We also identified Piezo1 as the putative mechanosensitive cellular component that transmitted compression to not only enhance the invasive phenotype, but also induce calcium influx and downstream Src signaling. Furthermore, we demonstrated that Piezo1 was mainly localized in caveolae, and both Piezo1 expression and compression-enhanced invasive phenotype of the breast cancer cells were reduced when caveolar integrity was compromised by either knocking down caveolin1 expression or depleting cholesterol content.

Conclusions

Taken together, our data indicate that mechanical compression activates Piezo1 channels to mediate enhanced breast cancer cell invasion, which involves both cellular events and matrix degradation. This may be a critical mechanotransduction pathway during breast cancer metastasis, and thus potentially a novel therapeutic target for the disease.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12860-021-00401-6.

Effect of extracellular volume on the energy stored in transmembrane concentration gradients

The amount of energy that can be retrieved from a concentration gradient across a membrane separating two compartments depends on the relative size of the compartments. Having a larger low-concentration compartment is in general beneficial. It is shown here analytically that the retrieved energy further increases when the high-concentration compartment shrinks during the mixing process, and a general formula is derived for the energy when the ratio of transported solvent to solute varies. These calculations are then applied to the interstitial compartment of the brain, which is rich in Na^{+} and Cl^{-} ions and poor in K^{+}. The reported shrinkage of this compartment, and swelling of the neurons, during oxygen deprivation is shown to enhance the energy recovered from NaCl entering the neurons. The slight loss of energy on the part of K^{+} can be compensated for by the uptake of K^{+} ions by glial cells. In conclusion, the present study proposes that the reported fluctuations in the size of the interstitial compartment of the brain (expansion during sleep and contraction during oxygen deprivation) optimize the amount of energy that neurons can store in, and retrieve from, their ionic concentration gradients.

Spatiotemporal model of cellular mechanotransduction via Rho and YAP

How cells sense and respond to mechanical stimuli remains an open question. Recent advances have identified the translocation of Yes-associated protein (YAP) between nucleus and cytoplasm as a central mechanism for sensing mechanical forces and regulating mechanotransduction. We formulate a spatiotemporal model of the mechanotransduction signalling pathway that includes coupling of YAP with the cell force-generation machinery through the Rho family of GTPases. Considering the active and inactive forms of a single Rho protein (GTP/GDP-bound) and of YAP (non-phosphorylated/phosphorylated), we study the cross-talk between cell polarization due to active Rho and YAP activation through its nuclear localization. For fixed mechanical stimuli, our model predicts stationary nuclear-to-cytoplasmic YAP ratios consistent with experimental data at varying adhesive cell area. We further predict damped and even sustained oscillations in the YAP nuclear-to-cytoplasmic ratio by accounting for recently reported positive and negative YAP-Rho feedback. Extending the framework to time-varying mechanical stimuli that simulate cyclic stretching and compression, we show that the YAP nuclear-to-cytoplasmic ratio's time dependence follows that of the cyclic mechanical stimulus. The model presents one of the first frameworks for understanding spatiotemporal YAP mechanotransduction, providing several predictions of possible YAP localization dynamics, and suggesting new directions for experimental and theoretical studies.

Hydraulic resistance induces cell phenotypic transition in confinement

Cells penetrating into confinement undergo mesenchymal-to-amoeboid transition. The topographical features of the microenvironment expose cells to different hydraulic resistance levels. How cells respond to hydraulic resistance is unknown. We show that the cell phenotype shifts from amoeboid to mesenchymal upon increasing resistance. By combining automated morphological tracking and wavelet analysis along with fluorescence recovery after photobleaching (FRAP), we found an oscillatory phenotypic transition that cycles from blebbing to short, medium, and long actin network formation, and back to blebbing. Elevated hydraulic resistance promotes focal adhesion maturation and long actin filaments, thereby reducing the period required for amoeboid-to-mesenchymal transition. The period becomes independent of resistance upon blocking the mechanosensor TRPM7. Mathematical modeling links intracellular calcium oscillations with actomyosin turnover and force generation and recapitulates experimental data. We identify hydraulic resistance as a critical physical cue controlling cell phenotype and present an approach for connecting fluorescent signal fluctuations to morphological oscillations.

Insights into the model of non-perfect osmometer cells for cryopreservation: A parametric sweep analysis

Recently, a mathematical model able to describe the non-perfect osmotic behavior of cells during cryopreservation was proposed. The model improves the two-parameter formalism typically adopted in cryopreservation literature by allowing the transmembrane permeation of ions/salt, through the temporary opening of mechanosensitive channels whenever membrane stretching occurs: cells can reach an equilibrium volume different from the initial one, when isotonic conditions are re-established after contacting with impermeant or permeant solutes, such as sucrose or a cryoprotectant agent like dimethyl sulfoxide, respectively. Although the model was conceived as a conservative development of the two-parameter formalism to avoid over-parameterization, a complex picture of the system emerges. To describe this, first an appropriate non-dimensional version of the model equations is derived. Then, a parametric sweep analysis is performed and discussed to highlight the features of the novel model in comparison with the two-parameter formalism: the conditions by which the first reduces to the second are identified. Only equilibrium equations with impermeant sucrose may be analytically derived from the model: their validity is here extended much more than originally assumed. When permeant dimethyl sulfoxide comes into play, the temporary opening of mechanosensitive channels is difficult to predict and prevents the derivation of the equilibrium equations: in this case, a numerical integration of system dynamics up to steady state is required to determine the cell volume at equilibrium. In conclusion, cell volume at equilibrium depends on the position of the temporal window of mechanosensitive channels opening, which, in general, is a complex function of model parameters and operating conditions.

The importance of water and hydraulic pressure in cell dynamics

All mammalian cells live in the aqueous medium, yet for many cell biologists, water is a passive arena in which proteins are the leading players that carry out essential biological functions. Recent studies, as well as decades of previous work, have accumulated evidence to show that this is not the complete picture. Active fluxes of water and solutes of water can play essential roles during cell shape changes, cell motility and tissue function, and can generate significant mechanical forces. Moreover, the extracellular resistance to water flow, known as the hydraulic resistance, and external hydraulic pressures are important mechanical modulators of cell polarization and motility. For the cell to maintain a consistent chemical environment in the cytoplasm, there must exist an intricate molecular system that actively controls the cell water content as well as the cytoplasmic ionic content. This system is difficult to study and poorly understood, but ramifications of which may impact all aspects of cell biology from growth to metabolism to development. In this Review, we describe how mammalian cells maintain the cytoplasmic water content and how water flows across the cell surface to drive cell movement. The roles of mechanical forces and hydraulic pressure during water movement are explored.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

Single Cell Volume Measurement Utilizing the Fluorescence Exclusion Method (FXm)

The measurement of single cell size remains an obstacle towards a deeper understanding of cell growth control, tissue homeostasis, organogenesis, and a wide range of pathologies. Recent advances have placed a spotlight on the importance of cell volume in the regulation of fundamental cell signaling pathways including those known to orchestrate progression through the cell cycle. Here we provide our protocol for the Fluorescence Exclusion Method (FXm); references to the development of FXm; and a brief outlook on future advances in image analysis which may expand the range of problems studied utilizing FXm as well as lower the barrier to entry for groups interested in adding cell volume measurements into their experimental repertoire.

Symmetry breaking in hydrodynamic forces drives meiotic spindle rotation in mammalian oocytes

Patterned cell divisions require a precisely oriented spindle that segregates chromosomes and determines the cytokinetic plane. In this study, we investigated how the meiotic spindle orients through an obligatory rotation during meiotic division in mouse oocytes. We show that spindle rotation occurs at the completion of chromosome segregation, whereby the separated chromosome clusters each define a cortical actomyosin domain that produces cytoplasmic streaming, resulting in hydrodynamic forces on the spindle. These forces are initially balanced but become unbalanced to drive spindle rotation. This force imbalance is associated with spontaneous symmetry breaking in the distribution of the Arp2/3 complex and myosin-II on the cortex, brought about by feedback loops comprising Ran guanosine triphosphatase signaling, Arp2/3 complex activity, and myosin-II contractility. The torque produced by the unbalanced hydrodynamic forces, coupled with a pivot point at the spindle midzone cortical contract, constitutes a unique mechanical system for meiotic spindle rotation.

Microscale pressure measurements based on an immiscible fluid/fluid interface

A method of microscale pressure measurement based on immiscible fluid/fluid interface is proposed. This method utilizes observed curvature changes in a fluid/fluid interface, and can accurately report hydraulic pressure in fluids at length scales of 10 microns. The method is especially suited for measuring fluid pressure in micro-scale biological samples. Using this method, we probe fluid pressure build up in epithelial domes, murine mammary gland organoids embedded in hydrogel, and lumen pressure in the developing mouse embryo. Results reveal that the pressure developed across epithelial barriers is on the order of 100~300 Pa, and is modulated by ion channel activity.

Stiffness Sensing by Cells

Physical stimuli are essential for the function of eukaryotic cells, and changes in physical signals are important elements in normal tissue development as well as in disease initiation and progression. The complexity of physical stimuli and the cellular signals they initiate are as complex as those triggered by chemical signals. One of the most important, and the focus of this review, is the effect of substrate mechanical properties on cell structure and function. The past decade has produced a nearly exponentially increasing number of mechanobiological studies to define how substrate stiffness alters cell biology using both purified systems and intact tissues. Here we attempt to identify common features of mechanosensing in different systems while also highlighting the numerous informative exceptions to what in early studies appeared to be simple rules by which cells respond to mechanical stresses.

YAP and TAZ regulate cell volume

How mammalian cells regulate their physical size is currently poorly understood, in part due to the difficulty in accurately quantifying cell volume in a high-throughput manner. Here, using the fluorescence exclusion method, we demonstrate that the mechanosensitive transcriptional regulators YAP (Yes-associated protein) and TAZ (transcriptional coactivator with PDZ-binding motif) are regulators of single-cell volume. The role of YAP/TAZ in volume regulation must go beyond its influence on total cell cycle duration or cell shape to explain the observed changes in volume. Moreover, for our experimental conditions, volume regulation by YAP/TAZ is independent of mTOR. Instead, we find that YAP/TAZ directly impacts the cell division volume, and YAP is involved in regulating intracellular cytoplasmic pressure. Based on the idea that YAP/TAZ is a mechanosensor, we find that inhibiting myosin assembly and cell tension slows cell cycle progression from G1 to S. These results suggest that YAP/TAZ may be modulating cell volume in combination with cytoskeletal tension during cell cycle progression.

Osmolyte homeostasis controls single-cell growth rate and maximum cell size of Saccharomyces cerevisiae

Cell growth is well described at the population level, but precisely how nutrient and water uptake and cell wall expansion drive the growth of single cells is poorly understood. Supported by measurements of single-cell growth trajectories and cell wall elasticity, we present a single-cell growth model for yeast. The model links the thermodynamic quantities, such as turgor pressure, osmolarity, cell wall elasto-plasticity, and cell size, applying concepts from rheology and thin shell theory. It reproduces cell size dynamics during single-cell growth, budding, and hyper-osmotic or hypo-osmotic stress. We find that single-cell growth rate and final size are primarily governed by osmolyte uptake and consumption, while bud expansion requires additionally different cell wall extensibilities between mother and bud. Based on first principles the model provides a more accurate description of size dynamics than previous attempts and its analytical simplification allows for easy combination with models for other cell processes.

Emerging themes and unifying concepts underlying cell behavior regulation by the pericellular space

Cells reside in a complex three-dimensional (3D) microenvironment where physical, chemical, and architectural features of the pericellular space regulate important cellular functions like migration, differentiation, and morphogenesis. A major goal of tissue engineering is to identify which properties of the pericellular space orchestrate these emergent cell behaviors and how. In this review, we highlight recent studies at the interface of biomaterials and single cell biophysics that are lending deeper insight towards this goal. Advanced methods have enabled the decoupling of architectural and mechanical features of the microenvironment, revealing multiple mechanisms of adhesion and mechanosensing modulation by biomaterials. Such studies are revealing important roles for pericellular space degradability, hydration, and adhesion competition in cell shape, volume, and differentiation regulation. STATEMENT OF SIGNIFICANCE: Cell fate and function are closely regulated by the local extracellular microenvironment. Advanced methods at the interface of single cell biophysics and biomaterials have shed new light on regulators of cell-pericellular space interactions by decoupling more features of the complex pericellular milieu than ever before. These findings lend deeper mechanistic insight into how biomaterials can be designed to fine-tune outcomes like differentiation, migration, and collective morphogenesis.

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 sensing and decision-making in confinement: The role of TRPM7 in a tug of war between hydraulic pressure and cross-sectional area

How cells sense hydraulic pressure and make directional choices in confinement remains elusive. Using trifurcating Ψ-like microchannels of different hydraulic resistances and cross-sectional areas, we discovered that the TRPM7 ion channel is the critical mechanosensor, which directs decision-making of blebbing cells toward channels of lower hydraulic resistance irrespective of their cross-sectional areas. Hydraulic pressure-mediated TRPM7 activation triggers calcium influx and supports a thicker cortical actin meshwork containing an elevated density of myosin-IIA. Cortical actomyosin shields cells against external forces and preferentially directs cell entrance in low resistance channels. Inhibition of TRPM7 function or actomyosin contractility renders cells unable to sense different resistances and alters the decision-making pattern to cross-sectional area-based partition. Cell distribution in microchannels is captured by a mathematical model based on the maximum entropy principle using cortical actin as a key variable. This study demonstrates the unique role of TRPM7 in controlling decision-making and navigating migration in complex microenvironments.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the "mechanism of adhesion-induced compression of cells," i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.

Cell tension and mechanical regulation of cell volume

Animal cells use an unknown mechanism to control their growth and physical size. Here, using the fluorescence exclusion method, we measure cell volume for adherent cells on substrates of varying stiffness. We discover that the cell volume has a complex dependence on substrate stiffness and is positively correlated with the size of the cell adhesion to the substrate. From a mechanical force–balance condition that determines the geometry of the cell surface, we find that the observed cell volume variation can be predicted quantitatively from the distribution of active myosin through the cell cortex. To connect cell mechanical tension with cell size homeostasis, we quantified the nuclear localization of YAP/TAZ, a transcription factor involved in cell growth and proliferation. We find that the level of nuclear YAP/TAZ is positively correlated with the average cell volume. Moreover, the level of nuclear YAP/TAZ is also connected to cell tension, as measured by the amount of phosphorylated myosin. Cells with greater apical tension tend to have higher levels of nuclear YAP/TAZ and a larger cell volume. These results point to a size-sensing mechanism based on mechanical tension: the cell tension increases as the cell grows, and increasing tension feeds back biochemically to growth and proliferation control.

Epithelial vertex models with active biochemical regulation of contractility can explain organized collective cell motility

Collective motions of groups of cells are observed in many biological settings such as embryo development, tissue formation, and cancer metastasis. To effectively model collective cell movement, it is important to incorporate cell specific features such as cell size, cell shape, and cell mechanics, as well as active behavior of cells such as protrusion and force generation, contractile forces, and active biochemical signaling mechanisms that regulate cell behavior. In this paper, we develop a comprehensive model of collective cell migration in confluent epithelia based on the vertex modeling approach. We develop a method to compute cell-cell viscous friction based on the vertex model and incorporate RhoGTPase regulation of cortical myosin contraction. Global features of collective cell migration are examined by computing the spatial velocity correlation function. As active cell force parameters are varied, we found rich dynamical behavior. Furthermore, we find that cells exhibit nonlinear phenomena such as contractile waves and vortex formation. Together our work highlights the importance of active behavior of cells in generating collective cell movement. The vertex modeling approach is an efficient and versatile approach to rigorously examine cell motion in the epithelium.

Electromechanics and Volume Dynamics in Nonexcitable Tissue Cells

Cell volume regulation is fundamentally important in phenomena such as cell growth, proliferation, tissue homeostasis, and embryogenesis. How the cell size is set, maintained, and changed over a cell's lifetime is not well understood. In this work we focus on how the volume of nonexcitable tissue cells is coupled to the cell membrane electrical potential and the concentrations of membrane-permeable ions in the cell environment. Specifically, we demonstrate that a sudden cell depolarization using the whole-cell patch clamp results in a 50% increase in cell volume, whereas hyperpolarization results in a slight volume decrease. We find that cell volume can be partially controlled by changing the chloride or the sodium/potassium concentrations in the extracellular environment while maintaining a constant external osmotic pressure. Depletion of external chloride leads to a volume decrease in suspended HN31 cells. Introducing cells to a high-potassium solution causes volume increase up to 50%. Cell volume is also influenced by cortical tension: actin depolymerization leads to cell volume increase. We present an electrophysiology model of water dynamics driven by changes in membrane potential and the concentrations of permeable ions in the cells surrounding. The model quantitatively predicts that the cell volume is directly proportional to the intracellular protein content.

Role of membrane-tension gated Ca2+ flux in cell mechanosensation

Eukaryotic cells are sensitive to mechanical forces they experience from the environment. The process of mechanosensation is complex, and involves elements such as the cytoskeleton and active contraction from myosin motors. Ultimately, mechanosensation is connected to changes in gene expression in the cell, known as mechanotransduction. While the involvement of the cytoskeleton in mechanosensation is known, the processes upstream of cytoskeletal changes are unclear. In this paper, by using a microfluidic device that mechanically compresses live cells, we demonstrate that Ca2+ currents and membrane tension-sensitive ion channels directly signal to the Rho GTPase and myosin contraction. In response to membrane tension changes, cells actively regulate cortical myosin contraction to balance external forces. The process is captured by a mechanochemical model where membrane tension, myosin contraction and the osmotic pressure difference between the cytoplasm and extracellular environment are connected by mechanical force balance. Finally, to complete the picture of mechanotransduction, we find that the tension-sensitive transcription factor YAP family of proteins translocate from the nucleus to the cytoplasm in response to mechanical compression.

Going with the Flow: Water Flux and Cell Shape during Cytokinesis

Cell shape changes during cytokinesis in eukaryotic cells have been attributed to contractile forces from the actomyosin ring and the actomyosin cortex. Here we propose an additional mechanism where active pumping of ions and water at the cell poles and the division furrow can also achieve the same type of shape change during cytokinesis without myosin contraction. We develop a general mathematical model to examine shape changes in a permeable object subject to boundary fluxes. We find that hydrodynamic flows in the cytoplasm and the relative drag between the cytoskeleton network phase and the water phase also play a role in determining the cell shape during cytokinesis. Forces from the actomyosin contractile ring and cortex do contribute to the cell shape, and can work together with water permeation to facilitate cytokinesis. To influence water flow, we osmotically shock the cell during cell division, and find that the cell can actively adapt to osmotic changes and complete division. Depolymerizing the actin cytoskeleton during cytokinesis also does not affect the contraction speed. We also explore the role of membrane ion channels and pumps in setting up the spatially varying water flux.

Mechanical stress as a regulator of cell motility

The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can symmetrize and arrest moving cells. We show further that sufficiently strong squeezing can lead to the loss of cell integrity. The overall behavior of the system depends on the two dimensionless parameters characterizing internal driving (chemical activity) and external loading (applied stress). We construct a phase diagram in this parameter space distinguishing between static, motile, and collapsed states. The obtained results are relevant for the mechanical understanding of contact inhibition and the epithelial-to-mesenchymal transition.

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.

A Computational Model of YAP/TAZ Mechanosensing

In cell proliferation, stem cell differentiation, chemoresistance, and tissue organization, the ubiquitous role of YAP/TAZ continues to impact our fundamental understanding in numerous physiological and disease systems. YAP/TAZ is an important signaling nexus integrating diverse mechanical and biochemical signals, such as ECM stiffness, adhesion ligand density, or cell-cell contacts, and thus strongly influences cell fate. Recent studies show that YAP/TAZ mechanical sensing is dependent on RhoA-regulated stress fibers. However, current understanding of YAP/TAZ remains limited due to the unknown interaction between the canonical Hippo pathway and cell tension. Furthermore, the multiscale relationship connecting adhesion signaling to YAP/TAZ activity through cytoskeleton dynamics remains poorly understood. To identify the roles of key signaling molecules in mechanical signal sensing and transduction, we present a, to our knowledge, novel computational model of the YAP/TAZ signaling pathway. This model converts extracellular-matrix mechanical properties to biochemical signals via adhesion, and integrates intracellular signaling cascades associated with cytoskeleton dynamics. We perform perturbations of molecular levels and sensitivity analyses to predict how various signaling molecules affect YAP/TAZ activity. Adhesion molecules, such as FAK, are predicted to rescue YAP/TAZ activity in soft environments via the RhoA pathway. We also found that changes of molecule concentrations result in different patterns of YAP/TAZ stiffness response. We also investigate the sensitivity of YAP/TAZ activity to ECM stiffness, and compare with that of SRF/MAL, which is another important regulator of differentiation. In addition, the model shows that the unresolved synergistic effect of YAP/TAZ activity between the mechanosensing and the Hippo pathways can be explained by the interaction of LIM-kinase and LATS. Overall, our model provides a, to our knowledge, novel platform for studying YAP/TAZ activity in the context of integrating different signaling pathways. This platform can be used to gain, to our knowledge, new fundamental insights into roles of key molecular and mechanical regulators on development, tissue engineering, or tumor progression.

Probing cooperative force generation in collective cancer invasion

Collective cellular dynamics in the three-dimensional extracellular matrix (ECM) plays a crucial role in many physiological processes such as cancer invasion. Both chemical and mechanical signaling support cell-cell communications on a variety of length scales, leading to collective migratory behaviors. Here we conduct experiments using 3D in vitro tumor models and develop a phenomenological model in order to probe the cooperativity of force generation in the collective invasion of breast cancer cells. In our model, cell-cell communication is characterized by a single parameter that quantifies the correlation length of cellular migration cycles. We devise a stochastic reconstruction method to generate realizations of cell colonies with specific contraction phase correlation functions and correlation length a. We find that as a increases, the characteristic size of regions containing cells with similar contraction phases grows. For small a values, the large fluctuations in individual cell contraction phases smooth out the temporal fluctuations in the time-dependent deformation field in the ECM. For large a values, the periodicity of an individual cell contraction cycle is clearly manifested in the temporal variation of the overall deformation field in the ECM. Through quantitative comparisons of the simulated and experimentally measured deformation fields, we find that the correlation length for collective force generation in the breast cancer diskoid in geometrically micropatterned ECM (DIGME) system is [Formula: see text], which is roughly twice the linear size of a single cell. One possible mechanism for this intermediate cell correlation length is the fiber-mediated stress propagation in the 3D ECM network in the DIGME system.