Water permeation drives tumor cell migration in confined microenvironments.

Cell migration is a critical process for diverse (patho)physiological phenomena. Intriguingly, cell migration through physically confined spaces can persist even when typical hallmarks of 2D planar migration, such as actin polymerization and myosin II-mediated contractility, are inhibited. Here, we present an integrated experimental and theoretical approach ("Osmotic Engine Model") and demonstrate that directed water permeation is a major mechanism of cell migration in confined microenvironments. Using microfluidic and imaging techniques along with mathematical modeling, we show that tumor cells confined in a narrow channel establish a polarized distribution of Na+/H+ pumps and aquaporins in the cell membrane, which creates a net inflow of water and ions at the cell leading edge and a net outflow of water and ions at the trailing edge, leading to net cell displacement. Collectively, this study presents an alternate mechanism of cell migration in confinement that depends on cell-volume regulation via water permeation.

Extracellular fluid viscosity enhances cell migration and cancer dissemination.

Cells respond to physical stimuli, such as stiffness1, fluid shear stress2 and hydraulic pressure3,4. Extracellular fluid viscosity is a key physical cue that varies under physiological and pathological conditions, such as cancer5. However, its influence on cancer biology and the mechanism by which cells sense and respond to changes in viscosity are unknown. Here we demonstrate that elevated viscosity counterintuitively increases the motility of various cell types on two-dimensional surfaces and in confinement, and increases cell dissemination from three-dimensional tumour spheroids. Increased mechanical loading imposed by elevated viscosity induces an actin-related protein 2/3 (ARP2/3)-complex-dependent dense actin network, which enhances Na+/H+ exchanger 1 (NHE1) polarization through its actin-binding partner ezrin. NHE1 promotes cell swelling and increased membrane tension, which, in turn, activates transient receptor potential cation vanilloid 4 (TRPV4) and mediates calcium influx, leading to increased RHOA-dependent cell contractility. The coordinated action of actin remodelling/dynamics, NHE1-mediated swelling and RHOA-based contractility facilitates enhanced motility at elevated viscosities. Breast cancer cells pre-exposed to elevated viscosity acquire TRPV4-dependent mechanical memory through transcriptional control of the Hippo pathway, leading to increased migration in zebrafish, extravasation in chick embryos and lung colonization in mice. Cumulatively, extracellular viscosity is a physical cue that regulates both short- and long-term cellular processes with pathophysiological relevance to cancer biology.

Hypo-osmotic-like stress underlies general cellular defects of aneuploidy.

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.

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.

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.

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.

CTRL - a label-free artificial intelligence method for dynamic measurement of single-cell volume.

Measuring the physical size of a 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 the deep learning algorithm and the fluorescence exclusion method for reconstructing cell topography and estimating mammalian cell volume from differential interference contrast (DIC) microscopy images alone. The method achieves quantitative accuracy, requires minimal sample preparation, and applies to a wide range of biological and experimental conditions. The method can be used to track single-cell volume dynamics over arbitrarily long time periods. For HT1080 fibrosarcoma cells, we observe that the cell size at division is positively correlated with the cell size at birth (sizer), and there is a noticeable reduction in cell size fluctuations at 25% completion of the cell cycle in HT1080 fibrosarcoma cells.

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.

On the energy efficiency of cell migration in diverse physical environments.

In this work, we explore fundamental energy requirements during mammalian cell movement. Starting with the conservation of mass and momentum for the cell cytosol and the actin-network phase, we develop useful identities that compute dissipated energies during extensions of the cell boundary. We analyze 2 complementary mechanisms of cell movement: actin-driven and water-driven. The former mechanism occurs on 2-dimensional cell-culture substrate without appreciable external hydraulic resistance, while the latter mechanism is prominent in confined channels where external hydraulic resistance is high. By considering various forms of energy input and dissipation, we find that the water-driven cell-migration mechanism is inefficient and requires more energy. However, in environments with sufficiently high hydraulic resistance, the efficiency of actin-polymerization-driven cell migration decreases considerably, and the water-based mechanism becomes more efficient. Hence, the most efficient way for cells to move depends on the physical environment. This work can be extended to higher dimensions and has implication for understanding energetics of morphogenesis in early embryonic development and cancer-cell metastasis and provides a physical basis for understanding changing metabolic requirements for cell movement in different conditions.

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.

Response of collagen matrices under pressure and hydraulic resistance in hydrogels.

Extracellular matrices in animal tissue are hydrogels mostly made of collagen. In these matrices, collagen fibers are hierarchically assembled and cross-linked to form a porous and elastic material, through which migrating cells can move by either pushing through open matrix pores, or by actively digesting collagen fibers. The influence of matrix mechanical properties on cell behavior is well studied. Less attention has been focused on hydraulic properties of extracellular matrices, and how hydrodynamic flows in these porous hydrogels are influenced by matrix composition and architecture. Here we study the response of collagen hydrogels using rapid changes in the hydraulic pressure within a microfluidic device, and analyze the data using a poroelastic theory. Major poroelastic parameters can be obtained in a single experiment. Results show that depending on the density, porosity, and the degree of geometric confinement, moving micron-sized objects such as cells can experience substantially increased hydraulic resistance (by as much as 106 times) when compared to 2D environments. Therefore, in addition to properties such as mechanical stiffness, the fluidic environment of the cell is also likely to impact cell behavior.

Transition from Actin-Driven to Water-Driven Cell Migration Depends on External Hydraulic Resistance.

Cells in vivo can reside in diverse physical and biochemical environments. For example, epithelial cells typically live in a two-dimensional (2D) environment, whereas metastatic cancer cells can move through dense three-dimensional matrices. These distinct environments impose different kinds of mechanical forces on cells and thus potentially can influence the mechanism of cell migration. For example, cell movement on 2D flat surfaces is mostly driven by forces from focal adhesion and actin polymerization, whereas in confined geometries, it can be driven by water permeation. In this work, we utilize a two-phase model of the cellular cytoplasm in which the mechanics of the cytosol and the F-actin network are treated on an equal footing. Using conservation laws and simple force balance considerations, we are able to describe the contributions of water flux, actin polymerization and flow, and focal adhesions to cell migration both on 2D surfaces and in confined spaces. The theory shows how cell migration can seamlessly transition from a focal adhesion- and actin-based mechanism on 2D surfaces to a water-based mechanism in confined geometries.

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.

Ergodicity, hidden bias and the growth rate gain.

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the 'von Foerster equation' for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, 'a single individual observed over many generations recapitulates the behavior of the entire ensemble' is implied by the other, 'the probability of observing any state is conserved across time and over all individuals' in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the 'growth rate gain'-the phenomenon that variations in the cell cycle duration leads to an improved population-level growth rate-in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

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.

Cell mechanics: a dialogue.

Under the microscope, eukaryotic animal cells can adopt a variety of different shapes and sizes. These cells also move and deform, and the physical mechanisms driving these movements and shape changes are important in fundamental cell biology, tissue mechanics, as well as disease biology. This article reviews some of the basic mechanical concepts in cells, emphasizing continuum mechanics description of cytoskeletal networks and hydrodynamic flows across the cell membrane. We discuss how cells can generate movement and shape changes by controlling mass fluxes at the cell boundary. These mass fluxes can come from polymerization/depolymerization of actin cytoskeleton, as well as osmotic and hydraulic pressure-driven flow of water across the cell membrane. By combining hydraulic pressure control with force balance conditions at the cell surface, we discuss a quantitative mechanism of cell shape and volume control. The broad consequences of this model on cell mechanosensation and tissue mechanics are outlined.

Volume regulation and shape bifurcation in the cell nucleus.

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 that there is a direct link between the environment and gene regulation.

Three-dimensional cell migration does not follow a random walk.

Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cell-to-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and self-correlation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.

The twisted tauopathies: surface interactions of helically patterned filaments seen in alzheimer's disease and elsewhere.

This paper broadly examines the dynamics of helically patterned filaments interacting with a surface and focuses on the surface interaction of amyloid fibrils formed by tau protein. Two structures are addressed in detail: cylindrical filaments with periodic thinning (CF-PT) and paired helical filaments (PHFs). PHFs are observed in neural tissue affected by Alzheimer's disease and may aggregate to form the pathological neurofibrillary tangles associated with the illness. Work using electron microscopy has demonstrated the conversion of CF-PT into PHFs in vitro, suggesting CF-PT to be a PHF precursor in vivo. Here we model CF-PT as a patterned elastic rod placed on a flat surface (characteristic of the environment during microscopy) and examine the conformational changes resulting in stable surface bonding. Analysis of this conformational space reveals structures resembling PHFs and thus provides a mechanistic explanation of the CF-PT to PHF transition. We develop a general phase diagram of the filament conformation as a function of filament twist and bend rigidity. Results of this work also suggest that we can obtain desired filament conformations by patterning interactions of elastic filaments with a substrate, and therefore can be used as a method in microfabrication.

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

Active contractile forces exerted by eukaryotic cells play significant roles during embryonic development, tissue formation, and cell motility. At the molecular level, small GTPases in signaling pathways can regulate active cell contraction. Here, starting with mechanical force balance at the cell cortex, and the recent discovery that tension-sensitive membrane channels can catalyze the conversion of the inactive form of Rho to the active form, we show mathematically that this active regulation of cellular contractility together with osmotic regulation can robustly control the cell size and membrane tension against external mechanical or osmotic shocks. We find that the magnitude of active contraction depends on the rate of mechanical pulling, but the cell tension can recover. The model also predicts that the cell exerts stronger contractile forces against a stiffer external environment, and therefore exhibits features of mechanosensation. These results suggest that a simple system for maintaining homeostatic values of cell volume and membrane tension could explain cell tension response and mechanosensation in different environments.