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This work quantified how cell velocity and effective power output are influenced by the rate of actin depolymerization, which is affected by myosin contraction. Model analysis shows that the cell migration velocity displays a biphasic dependence on the rate of actin depolymerization and myosin contraction.

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.

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.

Migration of meiosis-I (MI) spindle from the cell center to a sub-cortical location is a critical step for mouse oocytes to undergo asymmetric meiotic cell division. In this study, we investigate the mechanism by which formin-2 (FMN2) orchestrates the initial movement of MI spindle. By defining protein domains responsible for targeting FMN2, we show that spindle-periphery localized FMN2 is required for spindle migration. The spindle-peripheral FMN2 nucleates short actin bundles from vesicles derived likely from the endoplasmic reticulum (ER) and concentrated in a layer outside the spindle. This layer is in turn surrounded by mitochondria. A model based on polymerizing actin filaments pushing against mitochondria, thus generating a counter force on the spindle, demonstrated an inherent ability of this system to break symmetry and evolve directional spindle motion. The model is further supported through experiments involving spatially biasing actin nucleation via optogenetics and disruption of mitochondrial distribution and dynamics., Mammalian oocytes divide asymmetrically during meiotic maturation. Here, the authors show that spindle movement away from oocyte center depends on actin filaments nucleated from the spindle periphery pushing against surrounding mitochondria, which polarizes spontaneously to produce directional spindle motion.

The nucleus is a significant obstacle that impedes migration of cells through confining microenvironments. Mistriotis et al. propose a conceptual model in which confinement-induced RhoA/myosin-II activation promotes nuclear volume expansion, nuclear envelope blebbing, and rupture by triggering passive nuclear influx from the cell posterior, ultimately leading to reduced cell motility., 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.

Skeletal muscles can regenerate throughout life time from resident Pax7-expressing (Pax7+) muscle stem cells (MuSCs)1–3. Pax7+ MuSCs are normally quiescent and localized at a niche in which they are attached to the extracellular matrix basally and compressed against the myofiber apically3–5. Upon muscle injury, MuSCs lose apical contact with the myofiber and re-enter cell cycle to initiate regeneration. Prior studies on the physical niche of MuSCs focused on basal elasticity6,7, and significance of the apical force exerted on MuSCs remains unaddressed. Here we simulate MuSCs’ mechanical environment in vivo by applying physical compression to MuSCs’ apical surface. We demonstrate that compression drives activated MuSCs back to a quiescent stem cell state, even when seeded on different basal elasticities. By mathematical modeling and manipulating cell tension, we conclude that low overall tension combined with high edge tension generated by compression lead to MuSC quiescence. We further show that apical compression results in up-regulation of Notch downstream genes, accompanied by increased levels of nuclear Notch. The compression-induced nuclear Notch is ligand-independent, as it does not require the canonical S2-cleavage of Notch by ADAM10/17. Our results fill the knowledge gap on the role of apical tension for MuSC fate. Implications to how stem cell fate and activity are interlocked with the mechanical integrity of its resident tissue are discussed.

Using a microfluidic method, it was found that YAP and TAZ are novel regulators of single-cell size and act independently of mTOR. YAP also influences cell cytoplasmic pressure and acts together with cytoskeletal tension to influence cell cycle progression., 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.

Aneuploidy, which refers to unbalanced chromosome numbers, represents a class of genetic variation that is associated with cancer, birth defects and eukaryotic micro-organisms1–4. Whereas it is known that each aneuploid chromosome stoichiometry can give rise to a distinct pattern of gene expression and phenotypic profile4,5, it remains a fundamental question as to whether there are common cellular defects that are associated with aneuploidy. Here we show the existence in budding yeast of a common aneuploidy gene-expression signature that is suggestive of hypo-osmotic stress, using a strategy that enables the observation of common transcriptome changes of aneuploidy by averaging out karyotype-specific dosage effects in aneuploid yeast-cell populations with random and diverse chromosome stoichiometry. Consistently, aneuploid yeast exhibited increased plasma-membrane stress that led to impaired endocytosis, and this defect was also observed in aneuploid human cells. Thermodynamic modelling showed that hypo-osmotic-like stress is a general outcome of the proteome imbalance that is caused by aneuploidy, and also predicted a relationship between ploidy and cell size that was observed in yeast and aneuploid cancer cells. A genome-wide screen uncovered a general dependency of aneuploid cells on a pathway of ubiquitin-mediated endocytic recycling of nutrient transporters. Loss of this pathway, coupled with the endocytic defect inherent to aneuploidy, leads to a marked alteration of intracellular nutrient homeostasis. A common aneuploidy gene-expression signature is identified in yeast that is suggestive of hypo-osmotic stress, and which leads to cells that exhibit increased plasma-membrane stress and impaired endocytosis.

Hydraulic resistance induces cell phenotype oscillations in confinement via the coupled dynamics of actin, myosin, and calcium., 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.

Cells lacking a stiff cell wall, e.g., mammalian cells, must actively regulate their volume to maintain proper cell function. On the time scale that protein production is negligible, water flow in and out of the cell determines the cell volume variation. Water flux follows hydraulic and osmotic gradients; the latter is generated by various ion channels, transporters, and pumps in the cell membrane. Compared to the widely studied roles of sodium, potassium, and chloride in cell volume regulation, the effects of proton and bicarbonate are less understood. In this work, we use mathematical models to analyze how proton and bicarbonate, combined with sodium, potassium, chloride, and buffer species, regulate cell volume upon inhibition of ion channels, transporters, and pumps. The model includes several common, widely expressed ion transporters and focuses on obtaining generic outcomes. Results show that the intracellular osmolarity remains almost constant before and after cell volume change. The steady-state cell volume does not depend on water permeability. In addition, to ensure the stability of cell volume and ion concentrations, cells need to develop redundant mechanisms to maintain homeostasis, i.e., multiple ion channels or transporters are involved in the flux of the same ion species. These results provide insights for molecular mechanisms of cell volume regulation with additional implications for water-driven cell migration.

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.

Cells are remarkable machines capable of performing an exquisite range of functions, many of which depend crucially on the activity of molecular motors that generate forces. Recent experiments have shown that intracellular random movements are not solely thermal in nature but also arise from stochasticity in the forces from these molecular motors. Here we consider the effects of these nonthermal random forces. We show that stochastic motor force not only enhances diffusion but also leads to size-dependent transport of objects that depends on the local density of the cytoskeletal filaments on which motors operate. As a consequence, we find that objects that are larger than the mesh size of the cytoskeleton should be attracted to regions of high cytoskeletal density, while objects that are smaller than the mesh size will preferentially avoid these regions. These results suggest a mechanism for size-based organelle positioning and also suggest that motor-driven random forces can additionally enhance motor-driven transport.

Actin cytoskeletal asymmetry produces unbalanced hydrodynamic forces to drive spindle rotation during mouse meiotic division., 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.

Cell density organizes collective migration within an epithelium. Computational models predict the regulation of collective migration in an in vivo epithelium and demonstrate how commonly altered cellular properties can prime groups of cells to adopt migration patterns that may be harnessed in health or exploited in disease., The mechanisms underlying collective migration are important for understanding development, wound healing, and tumor invasion. Here we focus on cell density to determine its role in collective migration. Our findings show that increasing cell density, as might be seen in cancer, transforms groups from broad collectives to small, narrow streams. Conversely, diminishing cell density, as might occur at a wound front, leads to large, broad collectives with a distinct leader–follower structure. Simulations identify force-sensitive contractility as a mediator of how density affects collectives, and guided by this prediction, we find that the baseline state of contractility can enhance or reduce organization. Finally, we test predictions from these data in an in vivo epithelium by using genetic manipulations to drive collective motion between predicted migratory phases. This work demonstrates how commonly altered cellular properties can prime groups of cells to adopt migration patterns that may be harnessed in health or exploited in disease.

Measuring the physical size of the cell is valuable in understanding cell growth control. Current single-cell volume measurement methods for mammalian cells are labor-intensive, inflexible, and can cause cell damage. We introduce CTRL: Cell Topography Reconstruction Learner, a label-free technique incorporating Deep Learning and Fluorescence Exclusion for reconstructing cell topography and estimating mammalian cell volume from DIC microscopy images alone. The method achieves quantitative accuracy, requires minimal sample preparation, and applies to extensive biological and experimental conditions. Using this method, we observe a noticeable reduction in cell size fluctuations during cell cycle, which is consistent with the presence of a cell size checkpoint. (https://GitHub.com/sxslabjhu/CTRL)

How mammalian cells regulate their physical size is currently poorly understood, in part due to the difficulty of 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 novel regulators of single cell volume. We report that the role of YAP/TAZ in cell volume regulation must go beyond its influence on total cell cycle duration or the 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 YAP/TAZ directly impacts the cell division volume. Based on the idea that YAP/TAZ is a mechanosensor, we find that inhibiting the assembly of myosin and cell tension slows cell cycle progression from G1 to S. These results suggest that YAP/TAZ and the Hippo pathway may be modulating cell volume in combination with cytoskeletal tension during cell cycle progression.

Morphogenesis during human development relies on the interplay between physiochemical cues that are mediated in part by cellular density and cytoskeletal tension. Here, we interrogated these factors on vascular lineage specification during human-induced pluripotent stem-cell (hiPSC) fate decision. We found that independent of chemical cues, spatially presented physical cues induce the self-organization of Brachyury-positive mesodermal cells, in a RhoA/Rho-associated kinase (ROCK)-dependent manner. Using unbiased support vector machine (SVM) learning, we found that density alone is sufficient to predict mesodermal fate. Furthermore, the long-withstanding presentation of spatial confinement during hiPSC differentiation led to an organized vascular tissue, reminiscent of native blood vessels, a process dependent on cell density as found by SVM analysis. Collectively, these results show how tension and density relate to vascular identity mirroring early morphogenesis. We propose that such a system can be applied to study other aspects of the stem-cell niche and its role in embryonic patterning.

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.

In the epithelium of Drosophila during tissue elongation, contractile forces in follicle cells can oscillate. These oscillations correlate with increasing tension in the epithelium from egg chamber growth. A mathematical model is proposed to explain the observed oscillations, together with a mechanism of active regulation of cellular contractile forces., During tissue elongation from stage 9 to stage 10 in Drosophila oogenesis, the egg chamber increases in length by ∼1.7-fold while increasing in volume by eightfold. During these stages, spontaneous oscillations in the contraction of cell basal surfaces develop in a subset of follicle cells. This patterned activity is required for elongation of the egg chamber; however, the mechanisms generating the spatiotemporal pattern have been unclear. Here we use a combination of quantitative modeling and experimental perturbation to show that mechanochemical interactions are sufficient to generate oscillations of myosin contractile activity in the observed spatiotemporal pattern. We propose that follicle cells in the epithelial layer contract against pressure in the expanding egg chamber. As tension in the epithelial layer increases, Rho kinase signaling activates myosin assembly and contraction. The activation process is cooperative, leading to a limit cycle in the myosin dynamics. Our model produces asynchronous oscillations in follicle cell area and myosin content, consistent with experimental observations. In addition, we test the prediction that removal of the basal lamina will increase the average oscillation period. The model demonstrates that in principle, mechanochemical interactions are sufficient to drive patterning and morphogenesis, independent of patterned gene expression.

Eukaryotic cells are sensitive to mechanical forces that 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, or mechanotransduction. While the involvement of the cytoskeleton in mechanosensation is known, processes upstream to cytoskeletal changes is unclear. In this paper, using a microfluidic device that mechanically compresses live cells, we demonstrate that calcium currents and membrane tension-sensitive ion channels directly signals to the Rho GTPase and myosin contraction. In response to membrane tension changes, cell actively regulates 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 translocates from the nucleus to the cytoplasm in response to mechanical compression.

Cell migration is a fundamental process underlying diverse (patho)physiological phenomena. The classical understanding of the molecular mechanisms of cell migration has been based on in vitro studies on two-dimensional substrates. More recently, mounting evidence from intravital studies has shown that during metastasis, tumor cells must navigate complex microenvironments in vivo, including narrow, pre-existing microtracks created by anatomical structures. It is becoming apparent that unraveling the mechanisms of confined cell migration in this context requires a multi-disciplinary approach through integration of in vivo and in vitro studies, along with sophisticated bioengineering techniques and mathematical modeling. Here, we highlight such an approach that has led to discovery of a new model for cell migration in confined microenvironments (i.e., the Osmotic Engine Model).

Heterogeneity of cellular phenotypes in asynchronous cell populations placed in the same biochemical and biophysical environment may depend on cell cycle and chromatin modifications; however, no current method can measure these properties at single-cell resolution simultaneously and in situ. Here, we develop, test, and validate a new microscopy assay that rapidly quantifies global acetylation on histone H3 and measures a wide range of cell and nuclear properties, including cell and nuclear morphology descriptors, cell-cycle phase, and F-actin content of thousands of cells simultaneously, without cell detachment from their substrate, at single-cell resolution. These measurements show that isogenic, isotypic cells of identical DNA content and the same cell-cycle phase can still display large variations in H3 acetylation and that these variations predict specific phenotypic variations, in particular, nuclear size and actin cytoskeleton content, but not cell shape. The dependence of cell and nuclear properties on cell-cycle phase is assessed without artifact-prone cell synchronization. To further demonstrate its versatility, this assay is used to quantify the complex interplay among cell cycle, epigenetic modifications, and phenotypic variations following pharmacological treatments affecting DNA integrity, cell cycle, and inhibiting chromatin-modifying enzymes.—Chambliss, A. B., Wu, P.-H., Chen, W.-C., Sun, S. X., Wirtz, D. Simultaneously defining cell phenotypes, cell cycle, and chromatin modifications at single-cell resolution.

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.

Specification of germline and somatic cell lineages in C. elegans originates in the polarized single-cell zygote. Several cell-fate determinants are partitioned unequally along the anterior-posterior axis of the zygote, ensuring the daughter cells a unique inheritance upon asymmetric cell division. Recent studies have revealed that partitioning of the germline determinant PIE-1 and the somatic determinant MEX-5 involve protein redistribution accompanied by spatiotemporal changes in protein diffusion rates. Here, we characterize the dynamics of MEX-5 in the zygote and propose a novel reaction/diffusion model to explain both its anterior enrichment and its remarkable intracellular dynamics without requiring asymmetrically distributed binding sites. We propose that asymmetric cortically localized PAR proteins mediate the anterior enrichment of MEX-5 by reversibly changing its diffusion rate at spatially distinct points in the embryo, thus generating a stable concentration gradient along the anterior-posterior axis of the cell. This work extends the scope of reaction/diffusion models to include not only germline morphogens, but also somatic determinants.

Eukaryotic and prokaryotic cells use cytoskeletal proteins to regulate and modify cell shape. During cytokinesis or eukaryotic cell crawling, contractile forces are generated inside the cell to constrict the division site or to haul the rear of the cell forward, respectively. In many cases, these forces have been attributed to the activity of molecular motors, such as myosin II, which, by pulling on actin filaments, can produce contraction of the actin cytoskeleton. However, prokaryotic division is driven by the tubulin-like protein FtsZ and does not seem to require additional molecular motors to constrict the division site. Likewise, Dictyostelium discoideum and Saccharomyces cerevisiae can perform cytokinesis under motor-free conditions. In addition, many crawling cells can translocate when myosin is inhibited or absent. In this review, we point out another force-generation mechanism that can play a significant role in driving these processes in eukaryotes and prokaryotes. This mechanism is mediated by cross-linking and bundling proteins that form effective interactions between cytoskeletal filaments. Some recent studies in this area are reviewed and the physical underpinnings of this force-generation mechanism are explained.

alpha-Catenin is essential in cadherin-mediated epithelium development and maintenance of tissues and in cancer progression and metastasis. However, recent studies question the conventional wisdom that alpha-catenin directly bridges the cadherin adhesion complex to the actin cytoskeleton. Therefore, whether alpha-catenin plays a direct role in cadherin-dependent cell adhesion is unknown. Here, single-molecule force spectroscopy measurements in cells depleted of alpha-catenin or expressing the hereditary diffuse gastric cancer associated V832M E-cadherin germ-line missense mutation show that alpha-catenin plays a critical role in cadherin-mediated intercellular recognition and subsequent multibond formation within the first 300 ms of cell contact. At short contact times, alpha-catenin mediates a 30% stronger interaction between apposing E-cadherin molecules than when it cannot bind the E-cadherin-beta-catenin complex. As contact time between cells increases, alpha-catenin is essential for the strengthening of the first intercellular cadherin bond and for the ensuing formation of additional bonds between the cells, all without the intervention of actin. These results suggest that a critical decision to form an adhesion complex between 2 cells occurs within an extremely short time span and at a single-molecule level and identify a previously unappreciated role for alpha-catenin in these processes.

Summary Background Cytokinesis in bacteria is mediated by a cytokinetic ring, termed the Z ring, which forms a scaffold for recruitment of other cell-division proteins. The Z ring is composed of FtsZ filaments, but their organization in the Z ring is poorly understood. In Escherichia coli , the Min system contributes to the spatial regulation of cytokinesis by preventing the assembly of the Z ring away from midcell. The effector of the Min system, MinC, inhibits Z ring assembly by a mechanism that is not clear. Results Here, we report that MinC controls the scaffolding function of FtsZ by antagonizing the mechanical integrity of FtsZ structures. Specifically, MinC antagonizes the ability of FtsZ filaments to be in a solid-like gel state. MinC is a modular protein whose two domains (MinC C and MinC N ) synergize to inhibit FtsZ function. MinC C interacts directly with FtsZ polymers to target MinC to Z rings. MinC C also prevents lateral interactions between FtsZ filaments, an activity that seems to be unique among cytoskeletal proteins. Because MinC C is inhibitory in vivo, it suggests that lateral interactions between FtsZ filaments are important for the structural integrity of the Z ring. MinC N contributes to MinC activity by weakening the longitudinal bonds between FtsZ molecules in a filament leading to a loss of polymer rigidity and consequent polymer shortening. On the basis of our results, we develop the first computational model of the Z ring and study the effects of MinC. Conclusions Control over the scaffolding activity of FtsZ probably represents a universal regulatory mechanism of bacterial cytokinesis.

The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli ) is sufficient to accomplish division.

A combination of physical and chemical processes is involved in determining the bacterial cell shape. In standard medium, Escherichia coli cells are rod-shaped and maintain a constant diameter during exponential growth. Here, we demonstrate that by applying compressive forces to growing E. coli, cells no longer retain their rod-like shapes but grow and divide with a flat pancake-like geometry. The deformation is reversible: deformed cells can recover back to rod-like shapes in several generations after compressive forces are removed. During compression, the cell elongation rate, proliferation rate, DNA replication rate and protein synthesis are not significantly altered from those of the normal rod-shaped cells. Quantifying the rate of cell wall growth under compression reveals that the cell wall growth rate depends on the local cell curvature. MreB not only influences the rate of cell wall growth, but also influences how the growth rate scales with cell geometry. The result is consistent with predictions of a mechanochemical model and suggests an active mechanical role for MreB during cell wall growth. The developed compressive device is also useful for studying a variety of cells in unique geometries.

Alterations in nuclear morphology are closely associated with essential cell functions, such as cell motility and polarization, and correlate with a wide range of human diseases, including cancer, muscular dystrophy, dilated cardiomyopathy, and progeria. However, the mechanics and forces that shape the nucleus are not well understood. Here, we demonstrate that when an adherent cell is detached from its substratum, the nucleus undergoes a large volumetric reduction accompanied by a morphological transition from an almost smooth to a heavily folded surface. We develop a mathematical model that systematically analyzes the evolution of nuclear shape and volume. The analysis suggests that the pressure difference across the nuclear envelope, which is influenced by changes in cell volume and regulated by microtubules and actin filaments, is a major factor determining nuclear morphology. Our results show that physical and chemical properties of the extracellular microenvironment directly influence nuclear morphology and suggest a direct link between the environment and gene regulation.

Stem cell differentiation underlies many fundamental processes such as development, tissue growth and regeneration, as well as disease progression. Understanding how stem cell differentiation is controlled in mixed cell populations is an important step in developing quantitative models of cell population dynamics. Here we focus on quantifying the role of cell-cell interactions in determining stem cell fate. Toward this, we monitor stem cell differentiation in adherent cultures on micropatterns and collect statistical cell fate data. Results show high cell fate variability and a bimodal probability distribution of stem cell fraction on small (80–140 μm diameter) micropatterns. On larger (225–500 μm diameter) micropatterns, the variability is also high but the distribution of the stem cell fraction becomes unimodal. Using a stochastic model, we analyze the differentiation dynamics and quantitatively determine the differentiation probability as a function of stem cell fraction. Results indicate that stem cells can interact and sense cellular composition in their immediate neighborhood and adjust their differentiation probability accordingly. Blocking epithelial cadherin (E-cadherin) can diminish this cell-cell contact mediated sensing. For larger micropatterns, cell motility adds a spatial dimension to the picture. Taken together, we find stochasticity and cell-cell interactions are important factors in determining cell fate in mixed cell populations.

Cells under external electric field will migrate along electrical potential differences. The direction of migration depends on the cell type. Although cell motility on 2-D substrates is facilitated by actin and myosin, polarized cells can also migrate under confined conditions when actin polymerization is inhibited. This actin-independent migration is driven by water permeation through the cell membrane. In this work, we study flow-driven cell migration under electric fields. Our mathematical model considers 1-D cells in a confined microenvironment. The fluid flux through the membrane is governed by the difference of chemical potential across the membrane. The osmotic pressure is obtained from the ion diffusion and flux and the hydrostatic pressure is obtained from the fluid dynamics inside the cell. The flux of cations and anions across the cell membrane is determined by the properties of the ion channels as well as the external electric field. Results show that without the contribution from actin network and myosin contraction, water permeation can also drive non-polarized cells with the presence of an external electric field. The direction of migration is affected by the properties of ion channels which are cell-type dependent. The results suggest that external voltages can be used to sort cells.

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.

Cell cycle distribution of adherent cells is typically assessed using flow cytometry, which precludes the measurements of many cell properties and their cycle phase in the same environment. Here we develop and validate a microscopy system to quantitatively analyze the cell-cycle phase of thousands of adherent cells and their associated cell properties simultaneously. This assay demonstrates that population-averaged cell phenotypes can be written as a linear combination of cell-cycle fractions and phase-dependent phenotypes. By perturbing the cell cycle through inhibition of cell-cycle regulators or changing nuclear morphology by depletion of structural proteins, our results reveal that cell cycle regulators and structural proteins can significantly interfere with each other's prima facie functions. This study introduces a high-throughput method to simultaneously measure the cell cycle and phenotypes at single-cell resolution, which reveals a complex functional interplay between the cell cycle and cell phenotypes.

Multiple experimental results have shown eukaryotic cells are able to respond to its mechanical environment. Such responds are not only crucial during cell migration, polarization and tissue formation, but also determining cellular volume and shape.In this study, we show a simple mechanical force balance, coupled with previously-purposed chemical model on Rho GTPase activation, is able to predict the cellular shape when cells spreading on substrates with different sizes and/or stiffness, indicating the importance of mechanical forces that regulates different cell activities, including myosin activities, cellular volume, as well as traction stresses between cell and substrate. Moreover, if cell is placed in the growth medium, such mechanical signal may trigger cell division.With previously developed FRET pair, we are also able to observe RhoA activity during cell spreading experimentally, which is a crucial prove to our purposed model.

Cells often migrate in vivo in an extracellular matrix that is intrinsically three-dimensional (3D) and the role of actin filament architecture in 3D cell migration is less well understood. Here we show that, while recently identified linkers of nucleoskeleton to cytoskeleton (LINC) complexes play a minimal role in conventional 2D migration, they play a critical role in regulating the organization of a subset of actin filament bundles – the perinuclear actin cap - connected to the nucleus through Nesprin2giant and Nesprin3 in cells in 3D collagen I matrix. Actin cap fibers prolong the nucleus and mediate the formation of pseudopodial protrusions, which drive matrix traction and 3D cell migration. Disruption of LINC complexes disorganizes the actin cap, which impairs 3D cell migration. A simple mechanical model explains why LINC complexes and the perinuclear actin cap are essential in 3D migration by providing mechanical support to the formation of pseudopodial protrusions.

The ability for cells to sense and adapt to different physical microenvironments plays a critical role in development, immune responses, and cancer metastasis. Here we identify a small subset of focal adhesions that terminate fibers in the actin cap, a highly ordered filamentous actin structure that is anchored to the top of the nucleus by the LINC complexes; these differ from conventional focal adhesions in morphology, subcellular organization, movements, turnover dynamics, and response to biochemical stimuli. Actin cap associated focal adhesions (ACAFAs) dominate cell mechanosensing over a wide range of matrix stiffness, an ACAFA-specific function regulated by actomyosin contractility in the actin cap, while conventional focal adhesions are restrictively involved in mechanosensing for extremely soft substrates. These results establish the perinuclear actin cap and associated ACAFAs as major mediators of cellular mechanosensing and a critical element of the physical pathway that transduce mechanical cues all the way to the nucleus.

Actin filaments play many important roles in the cellular processes including motility, morphogenesis, and mechanosensing of the environment. One of the keys to better understanding of how actin filaments perform those roles lies in understanding the mechanical properties of actin filament, such as persistence length. There have been intensive studies on the mechanical properties of actin filament and its network. The measurements so far show the diversity of persistence length, ranging from several to a few tens of microns, also dependent upon the chemical states of actin molecules. Another interesting issue is the description of actin filament breaking. In order to understand these, we built up a simple model where each actin monomer is treated as a spherical particle connected by a set of springs. These spring stiffness parameters are determined from the known information on the chemical bonds in the actin filament and stretching deformation of the actin filament as an elastic rod. Our results show the length dependency of the persistence length, especially in a shorter length range which is relevant to the physiological conditions. They also show that the diversity of persistence length measurements is closely related to the breaking of the bonds in the actin filament, as well as the chemical states of actin monomers in the filament. Finally the mechanism of actin filament breaking is discussed.

Background Crescentin, the recently discovered bacterial intermediate filament protein, organizes into an extended filamentous structure that spans the length of the bacterium Caulobacter crescentus and plays a critical role in defining its curvature. The mechanism by which crescentin mediates cell curvature and whether crescentin filamentous structures are dynamic and/or polar are not fully understood. Methodology/Principal Findings Using light microscopy, electron microscopy and quantitative rheology, we investigated the mechanics and dynamics of crescentin structures. Live-cell microscopy reveals that crescentin forms structures in vivo that undergo slow remodeling. The exchange of subunits between these structures and a pool of unassembled subunits is slow during the life cycle of the cell however; in vitro assembly and gelation of C. crescentus crescentin structures are rapid. Moreover, crescentin forms filamentous structures that are elastic, solid-like, and, like other intermediate filaments, can recover a significant portion of their network elasticity after shear. The assembly efficiency of crescentin is largely unaffected by monovalent cations (K+, Na+), but is enhanced by divalent cations (Mg2+, Ca2+), suggesting that the assembly kinetics and micromechanics of crescentin depend on the valence of the ions present in solution. Conclusions/Significance These results indicate that crescentin forms filamentous structures that are elastic, labile, and stiff, and that their low dissociation rate from established structures controls the slow remodeling of crescentin in C. crescentus.

To generate cellular diversity in developing organisms while simultaneously maintaining the developmental potential of the germline, germ cells must be able to preferentially endow germline daughter cells with a cytoplasmic portion containing specialized cell fate determinants not inherited by somatic cells. In Caenorhabditis elegans, germline inheritance of the protein PIE-1 is accomplished by first asymmetrically localizing the protein to the germplasm before cleavage and subsequently degrading residual levels of the protein in the somatic cytoplasm after cleavage. Despite its critical involvement in cell fate determination, the enrichment of germline determinants remains poorly understood. Here, combining live-cell fluorescence methods and kinetic modeling, we demonstrate that the enrichment process does not involve protein immobilization, intracellular compartmentalization, or localized protein degradation. Instead, our results support a heterogeneous reaction/diffusion model for PIE-1 enrichment in which the diffusion coefficient of PIE-1 is reversibly reduced in the posterior, resulting in a stable protein gradient across the zygote at steady state.

Forces are important in biological systems for accomplishing key cell functions, such as motility, organelle transport, and cell division. Currently, known force generation mechanisms typically involve motor proteins. In bacterial cells, no known motor proteins are involved in cell division. Instead, a division ring (Z-ring) consists of mostly FtsZ, FtsA, and ZipA is used to exerting a contractile force. The mechanism of force generation in bacterial cell division is unknown. Using computational modeling, we show that Z-ring formation results from the colocalization of FtsZ and FtsA mediated by the favorable alignment of FtsZ polymers. The model predicts that the Z-ring undergoes a condensation transition from a low-density state to a high-density state and generates a sufficient contractile force to achieve division. FtsZ GTP hydrolysis facilitates monomer turnover during the condensation transition, but does not directly generate forces. In vivo fluorescence measurements show that FtsZ density increases during division, in accord with model results. The mechanism is akin to van der Waals picture of gas-liquid condensation, and shows that organisms can exploit microphase transitions to generate mechanical forces.

Mechanical properties of the living cell are important in cell movement, cell division, cancer development and cell signaling. There is considerable interest in measuring local mechanical properties of living materials and the living cytoskeleton using micromechanical techniques. However, living materials are constantly undergoing internal dynamics such as growth and remodeling. A modeling framework that combines mechanical deformations with cytoskeletal growth dynamics is necessary to describe cellular shape changes. The present paper develops a general finite deformation modeling approach that can treat the viscoelastic cytoskeleton. Given the growth dynamics in the cytoskeletal network and the relationship between deformation and stress, the shape of the network is computed in an incremental fashion. The growth dynamics of the cytoskeleton can be modeled as stress dependent. The result is a consistent treatment of overall cell deformation. The framework is applied to a growing 1-d bundle of actin filaments against an elastic cantilever, and a 2-d cell undergoing wave-like protrusion dynamics. In the latter example, mechanical forces on the cell adhesion are examined as a function of the protrusion dynamics.

Lamellipodium extension, incorporating actin filament dynamics and the cell membrane, is simulated in three dimensions. The actin filament network topology and the role of actin-associated proteins such as Arp2/3 are examined. We find that the orientational pattern of the filaments is in accord with the experimental data only if the spatial orientation of the Arp2/3 complex is restricted during each branching event. We hypothesize that branching occurs when Arp2/3 is bound to Wiskott-Aldrich syndrome protein (WASP), which is in turn bound to Cdc42 signaling complex; Arp2/3 binding geometry is restricted by the membrane-bound complex. Using mechanical and energetic arguments, we show that any membrane protein that is conical or trapezoidal in shape preferentially resides at the curved regions of the plasma membrane. We hypothesize that the transmembrane receptors involved in the recruitment of Cdc42/WASP complex has this property and concentrate at the leading edge. These features, combined with the mechanical properties of the cell membrane, explain why lamellipodium is a flat organelle.

Homeostasis in skin epidermis, the first line of defense against potential damage due to environmental exposures and external stress, is the key element of epithelial tissue maintenance. It is known that cell proliferation in the basal layer of skin epidermis is balanced with cell loss of terminally differentiated cells in the outermost surface. It is fundamentally important to understand the dynamic characteristics of the epidermal homeostasis, because understanding the epidermal homeostasis is the first step toward unraveling the mechanisms on skin diseases and cancer. In this work, we develop a computational model to investigate how skin epidermal homeostasis is achieved through cell proliferation, differentiation, and cell loss. As a recent study showed, cell division, as well as cell loss events, is described as stochastic in our model. Important factors such as cell size changes during the differentiation are included in the model. Our results reveal that coupling effects are crucial in maintaining skin epidermal structure. In particular, coupling effects both on cell division and cell loss are required to maintain the epidermis. Our model also predicts that mechano-biological coupling in basal progenitor cell division has a dominant role in the epidermal homeostasis, as shown in a recent study where, upon disruption of cell-cell junctions in skin tissue, proliferation and apoptotic rates of epithelial cells are dramatically changed, leading to possible disease states. Strong coupling effect on cell division leads to stable epidermal structure with wider ranges of other parameters including cell loss rate and coupling parameters in this study. Our model also predicts aberrant situations that mimic skin diseases such as palmoplantar keratodermas (PPK) by varying model parameters, which in turn confirms the existence and importance of coupling effects. Hence consideration of mechano-biological coupling in the tissue would also have high clinical relevance.

The fusion of the human immunodeficiency virus type 1 (HIV-1) with its host cell is the target for new antiretroviral therapies. Viral particles interact with the flexible plasma membrane via viral surface protein gp120 which binds its primary cellular receptor CD4 and subsequently the coreceptor CCR5. However, whether and how these receptors become organized at the adhesive junction between cell and virion are unknown. Here, stochastic modeling predicts that, regarding binding to gp120, cellular receptors CD4 and CCR5 form an organized, ring-like, nanoscale structure beneath the virion, which locally deforms the plasma membrane. This organized adhesive junction between cell and virion, which we name the viral junction, is reminiscent of the well-characterized immunological synapse, albeit at much smaller length scales. The formation of an organized viral junction under multiple physiopathologically relevant conditions may represent a novel intermediate step in productive infection., Author Summary The entry of human immunodeficiency virus (HIV) into cells is the target for new therapies preventing HIV infection. While intermediate steps of viral entry have been characterized, the progression between these steps and how they result in productive infection are not well understood. By using stochastic modeling, we examine the initial interaction of a single viral particle with a flexible plasma membrane populated with viral receptors. The model predicts the formation of an organized receptor ultrastructure beneath the viral particle, which we name viral junction and which may contribute to productive viral infection. The organization of the viral junction depends on receptor density, CD4 bond stability, membrane mechanical flexibility, as well as viral protein organization and density.

Tissue cells sense and respond to the stiffness of the surface on which they adhere. Precisely how cells sense surface stiffness remains an open question, though various biochemical pathways are critical for a proper stiffness response. Here, based on a simple mechanochemical model of biological friction, we propose a model for cell mechanosensation as opposed to previous more biochemically based models. Our model of adhesion complexes predicts that these cell-surface interactions provide a viscous drag that increases with the elastic modulus of the surface. The force-velocity relation of myosin II implies that myosin generates greater force when the adhesion complexes slide slowly. Then, using a simple cytoskeleton model, we show that an external force applied to the cytoskeleton causes actin filaments to aggregate and orient parallel to the direction of force application. The greater the external force, the faster this aggregation occurs. As the steady-state probability of forming these bundles reflects a balance between the time scale of bundle formation and destruction (because of actin turnover), more bundles are formed when the cytoskeleton time-scale is small (i.e., on stiff surfaces), in agreement with experiment. As these large bundles of actin, called stress fibers, appear preferentially on stiff surfaces, our mechanical model provides a mechanism for stress fiber formation and stiffness sensing in cells adhered to a compliant surface.

A cell plated on a two-dimensional substrate forms adhesions with that surface. These adhesions, which consist of aggregates of various proteins, are thought to be important in mechanosensation, the process by which the cell senses and responds to the mechanical properties of the substrate (e.g., stiffness). On the basis of experimental measurements, we model these proteins as idealized molecules that can bind to the substrate in a strain-dependent manner and can undergo a force-dependent state transition. The model forms molecular aggregates that are similar to adhesions. Substrate stiffness affects whether a simulated adhesion is initially formed and how long it grows, but not how that adhesion grows or shrinks. Our own experimental tests support these predictions, suggesting that the mechanosensitivity of adhesions is an emergent property of a simple molecular-mechanical system.

Cytokinesis in bacteria is accomplished by a ring-shaped cell-division complex (the Z-ring). The primary component of the Z-ring is FtsZ, a filamentous tubulin homolog that serves as a scaffold for the recruitment of other cell-division-related proteins. FtsZ forms filaments and bundles. In the cell, it has been suggested that FtsZ filaments form the arcs of the ring and are aligned in the cell-circumferential direction. Using polarized fluorescence microscopy in live Escherichia coli cells, we measure the structural organization of FtsZ filaments in the Z-ring. The data suggest a disordered organization: a substantial portion of FtsZ filaments are aligned in the cell-axis direction. FtsZ organization in the Z-ring also appears to depend on the bacterial species. Taken together, the unique arrangement of FtsZ suggests novel unexplored mechanisms in bacterial cell division.