Animal cell hydraulics

T cell migration requires ion and water influx to regulate actin polymerization

Migration of T cells is essential for their ability to mount immune responses. Chemokine-induced T cell migration requires WNK1, a kinase that regulates ion influx into the cell. However, it is not known why ion entry is necessary for T cell movement. Here we show that signaling from the chemokine receptor CCR7 leads to activation of WNK1 and its downstream pathway at the leading edge of migrating CD4+ T cells, resulting in ion influx and water entry by osmosis. We propose that WNK1-induced water entry is required to swell the membrane at the leading edge, generating space into which actin filaments can polymerize, thereby facilitating forward movement of the cell. Given the broad expression of WNK1 pathway proteins, our study suggests that ion and water influx are likely to be essential for migration in many cell types, including leukocytes and metastatic tumor cells.

Imaging the subcellular viscoelastic properties of mouse oocytes

In recent years, cellular biomechanical properties have been investigated as an alternative to morphological assessments for oocyte selection in reproductive science. Despite the high relevance of cell viscoelasticity characterization, the reconstruction of spatially distributed viscoelastic parameter images in such materials remains a major challenge. Here, a framework for mapping viscoelasticity at the subcellular scale is proposed and applied to live mouse oocytes. The strategy relies on the principles of optical microelastography for imaging in combination with the overlapping subzone nonlinear inversion technique for complex-valued shear modulus reconstruction. The three-dimensional nature of the viscoelasticity equations was accommodated by applying an oocyte geometry-based 3D mechanical motion model to the measured wave field. Five domains-nucleolus, nucleus, cytoplasm, perivitelline space, and zona pellucida-could be visually differentiated in both oocyte storage and loss modulus maps, and statistically significant differences were observed between most of these domains in either property reconstruction. The method proposed herein presents excellent potential for biomechanical-based monitoring of oocyte health and complex transformations across lifespan. It also shows appreciable latitude for generalization to cells of arbitrary shape using conventional microscopy equipment.

Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

The cytoplasm is a complex, crowded, actively driven environment whose biophysical characteristics modulate critical cellular processes such as cytoskeletal dynamics, phase separation, and stem cell fate. Little is known about the variance in these cytoplasmic properties. Here, we employed particle-tracking nanorheology on genetically encoded multimeric 40 nm nanoparticles (GEMs) to measure diffusion within the cytoplasm of individual fission yeast (Schizosaccharomyces pombe) cellscells. We found that the apparent diffusion coefficients of individual GEM particles varied over a 400-fold range, while the differences in average particle diffusivity among individual cells spanned a 10-fold range. To determine the origin of this heterogeneity, we developed a Doppelgänger simulation approach that uses stochastic simulations of GEM diffusion that replicate the experimental statistics on a particle-by-particle basis, such that each experimental track and cell had a one-to-one correspondence with their simulated counterpart. These simulations showed that the large intra- and inter-cellular variations in diffusivity could not be explained by experimental variability but could only be reproduced with stochastic models that assume a wide intra- and inter-cellular variation in cytoplasmic viscosity. The simulation combining intra- and inter-cellular variation in viscosity also predicted weak nonergodicity in GEM diffusion, consistent with the experimental data. To probe the origin of this variation, we found that the variance in GEM diffusivity was largely independent of factors such as temperature, the actin and microtubule cytoskeletons, cell-cyle stage, and spatial locations, but was magnified by hyperosmotic shocks. Taken together, our results provide a striking demonstration that the cytoplasm is not "well-mixed" but represents a highly heterogeneous environment in which subcellular components at the 40 nm size scale experience dramatically different effective viscosities within an individual cell, as well as in different cells in a genetically identical population. These findings carry significant implications for the origins and regulation of biological noise at cellular and subcellular levels.

Partitioning of ribonucleoprotein complexes from the cellular actin cortex

The cell cortex plays a crucial role in cell mechanics, signaling, and development. However, little is known about the influence of the cortical meshwork on the spatial distribution of cytoplasmic biomolecules. Here, we describe a fluorescence microscopy method with the capacity to infer the intracellular distribution of labeled biomolecules with subresolution accuracy. Unexpectedly, we find that RNA binding proteins are partially excluded from the cytoplasmic volume adjacent to the plasma membrane that corresponds to the actin cortex. Complementary diffusion measurements of RNA-protein complexes suggest that a rudimentary model based on excluded volume interactions can explain this partitioning effect. Our results suggest the actin cortex meshwork may play a role in regulating the biomolecular content of the volume immediately adjacent to the plasma membrane.

Blebs—Formation, Regulation, Positioning, and Role in Amoeboid Cell Migration

In the context of development, tissue homeostasis, immune surveillance, and pathological conditions such as cancer metastasis and inflammation, migrating amoeboid cells commonly form protrusions called blebs. For these spherical protrusions to inflate, the force for pushing the membrane forward depends on actomyosin contraction rather than active actin assembly. Accordingly, blebs exhibit distinct dynamics and regulation. In this review, we first examine the mechanisms that control the inflation of blebs and bias their formation in the direction of the cell’s leading edge and present current views concerning the role blebs play in promoting cell locomotion. While certain motile amoeboid cells exclusively form blebs, others form blebs as well as other protrusion types. We describe factors in the environment and cell-intrinsic activities that determine the proportion of the different forms of protrusions cells produce.

Biofilm Growth under Elastic Confinement

Bacteria often form surface-bound communities, embedded in a self-produced extracellular matrix, called biofilms. Quantitative studies of bioflim growth have typically focused on unconfined expansion above solid or semisolid surfaces, leading to exponential radial growth. This geometry does not accurately reflect the natural or biomedical contexts in which biofilms grow in confined spaces. Here, we consider one of the simplest confined geometries: a biofilm growing laterally in the space between a solid surface and an overlying elastic sheet. A poroelastic framework is utilized to derive the radial growth rate of the biofilm; it reveals an additional self-similar expansion regime, governed by the Poisson's ratio of the matrix, leading to a finite maximum radius, consistent with our experimental observations of growing Bacillus subtilis biofilms confined by polydimethylsiloxane.

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.

Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization

The cytoplasm is a crowded, visco-elastic environment whose physical properties change according to physiological or developmental states. How the physical properties of the cytoplasm impact cellular functions in vivo remains poorly understood. Here, we probe the effects of cytoplasmic concentration on microtubules by applying osmotic shifts to fission yeast, moss, and mammalian cells. We show that the rates of both microtubule polymerization and depolymerization scale linearly and inversely with cytoplasmic concentration; an increase in cytoplasmic concentration decreases the rates of microtubule polymerization and depolymerization proportionally, whereas a decrease in cytoplasmic concentration leads to the opposite. Numerous lines of evidence indicate that these effects are due to changes in cytoplasmic viscosity rather than cellular stress responses or macromolecular crowding per se. We reconstituted these effects on microtubules in vitro by tuning viscosity. Our findings indicate that, even in normal conditions, the viscosity of the cytoplasm modulates the reactions that underlie microtubule dynamic behaviors.

Poroelastic osmoregulation of living cell volume

Cells maintain their volume through fine intracellular osmolarity regulation. Osmotic challenges drive fluid into or out of cells causing swelling or shrinkage, respectively. The dynamics of cell volume changes depending on the rheology of the cellular constituents and on how fast the fluid permeates through the membrane and cytoplasm. We investigated whether and how poroelasticity can describe volume dynamics in response to osmotic shocks. We exposed cells to osmotic perturbations and used defocusing epifluorescence microscopy on membrane-attached fluorescent nanospheres to track volume dynamics with high spatiotemporal resolution. We found that a poroelastic model that considers both geometrical and pressurization rates captures fluid-cytoskeleton interactions, which are rate-limiting factors in controlling volume changes at short timescales. Linking cellular responses to osmotic shocks and cell mechanics through poroelasticity can predict the cell state in health, disease, or in response to novel therapeutics.

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Cell height changes can be finely captured by defocusing microscopy

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Water permeation and cellular deformability regulate dynamics of cell volume changes

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Poroelasticity describes the dynamics of cell volume changes

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The response of cell to hypo or hyperosmotic shocks are modeled by poroelasticity

A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells

Living cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

Different types of cells exhibit a universal power-law rheological behavior which to this date has not been captured by a single theoretical model. Here, the authors propose a self-similar hierarchical cellular model that can naturally reproduce the universal power-law characteristics of cell rheology.

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.

Nonlinear Elastic and Inelastic Properties of Cells

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

Poroelasticity of (bio)polymer networks during compression: theory and experiment

Soft living tissues like cartilage can be considered as biphasic materials comprising a fibrous complex biopolymer network and a viscous background liquid. Here, we show by a combination of experiment and theoretical analysis that both the hydraulic permeability and the elastic properties of (bio)polymer networks can be determined with simple ramp compression experiments in a commercial rheometer. In our approximate closed-form solution of the poroelastic equations of motion, we find the normal force response during compression as a combination of network stress and fluid pressure. Choosing fibrin as a biopolymer model system with controllable pore size, measurements of the full time-dependent normal force during compression are found to be in excellent agreement with the theoretical calculations. The inferred elastic response of large-pore (μm) fibrin networks depends on the strain rate, suggesting a strong interplay between network elasticity and fluid flow. Phenomenologically extending the calculated normal force into the regime of nonlinear elasticity, we find strain-stiffening of small-pore (sub-μm) fibrin networks to occur at an onset average tangential stress at the gel-plate interface that depends on the polymer concentration in a power-law fashion. The inferred permeability of small-pore fibrin networks scales approximately inverse squared with the fibrin concentration, implying with a microscopic cubic lattice model that the number of protofibrils per fibrin fiber cross-section decreases with protein concentration. Our theoretical model provides a new method to obtain the hydraulic permeability and the elastic properties of biopolymer networks and hydrogels with simple compression experiments, and paves the way to study the relation between fluid flow and elasticity in biopolymer networks during dynamical compression.

F-Actin Interactome Reveals Vimentin as a Key Regulator of Actin Organization and Cell Mechanics in Mitosis

Most metazoan cells entering mitosis undergo characteristic rounding, which is important for accurate spindle positioning and chromosome separation. Rounding is driven by contractile tension generated by myosin motors in the sub-membranous actin cortex. Recent studies highlight that alongside myosin activity, cortical actin organization is a key regulator of cortex tension. Yet, how mitotic actin organization is controlled remains poorly understood. To address this, we characterized the F-actin interactome in spread interphase and round mitotic cells. Using super-resolution microscopy, we then screened for regulators of cortex architecture and identified the intermediate filament vimentin and the actin-vimentin linker plectin as unexpected candidates. We found that vimentin is recruited to the mitotic cortex in a plectin-dependent manner. We then showed that cortical vimentin controls actin network organization and mechanics in mitosis and is required for successful cell division in confinement. Together, our study highlights crucial interactions between cytoskeletal networks during cell division.

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Comparison of the F-actin interactome in spread interphase and round mitotic cells

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Proteomics identifies vimentin and plectin as key regulators of the mitotic cortex

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Vimentin intermediate filaments localize under the actin cortex in mitosis

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Sub-cortical vimentin regulates actin cortex organization and mechanics in mitosis

Hypotonic Challenge of Endothelial Cells Increases Membrane Stiffness with No Effect on Tether Force

Regulation of cell volume is a fundamental property of all mammalian cells. Multiple signaling pathways are known to be activated by cell swelling and to contribute to cell volume homeostasis. Although cell mechanics and membrane tension have been proposed to couple cell swelling to signaling pathways, the impact of swelling on cellular biomechanics and membrane tension have yet to be fully elucidated. In this study, we use atomic force microscopy under isotonic and hypotonic conditions to measure mechanical properties of endothelial membranes including membrane stiffness, which reflects the stiffness of the submembrane cytoskeleton complex, and the force required for membrane tether formation, reflecting membrane tension and membrane-cytoskeleton attachment. We find that hypotonic swelling results in significant stiffening of the endothelial membrane without a change in membrane tension/membrane-cytoskeleton attachment. Furthermore, depolymerization of F-actin, which, as expected, results in a dramatic decrease in the cellular elastic modulus of both the membrane and the deeper cytoskeleton, indicating a collapse of the cytoskeleton scaffold, does not abrogate swelling-induced stiffening of the membrane. Instead, this swelling-induced stiffening of the membrane is enhanced. We propose that the membrane stiffening should be attributed to an increase in hydrostatic pressure that results from an influx of solutes and water into the cells. Most importantly, our results suggest that increased hydrostatic pressure, rather than changes in membrane tension, could be responsible for activating volume-sensitive mechanisms in hypotonically swollen cells.

Nonlinear Cellular Mechanical Behavior Adaptation to Substrate Mechanics Identified by Atomic Force Microscope

Cell–substrate interaction plays an important role in intracellular behavior and function. Adherent cell mechanics is directly regulated by the substrate mechanics. However, previous studies on the effect of substrate mechanics only focused on the stiffness relation between the substrate and the cells, and how the substrate stiffness affects the time-scale and length-scale of the cell mechanics has not yet been studied. The absence of this information directly limits the in-depth understanding of the cellular mechanotransduction process. In this study, the effect of substrate mechanics on the nonlinear biomechanical behavior of living cells was investigated using indentation-based atomic force microscopy. The mechanical properties and their nonlinearities of the cells cultured on four substrates with distinct mechanical properties were thoroughly investigated. Furthermore, the actin filament (F-actin) cytoskeleton of the cells was fluorescently stained to investigate the adaptation of F-actin cytoskeleton structure to the substrate mechanics. It was found that living cells sense and adapt to substrate mechanics: the cellular Young’s modulus, shear modulus, apparent viscosity, and their nonlinearities (mechanical property vs. measurement depth relation) were adapted to the substrates’ nonlinear mechanics. Moreover, the positive correlation between the cellular poroelasticity and the indentation remained the same regardless of the substrate stiffness nonlinearity, but was indeed more pronounced for the cells seeded on the softer substrates. Comparison of the F-actin cytoskeleton morphology confirmed that the substrate affects the cell mechanics by regulating the intracellular structure.

Membrane Stiffening in Osmotic Swelling: Analysis of Membrane Tension and Elastic Modulus

The effects of osmotic swelling on key cellular biomechanical properties are explored in this chapter. We present the governing equations and theoretical backgrounds of the models employed to estimate cell membrane tension and elastic moduli from experimental methods, and provide a summary of the prevailing experimental approaches used to obtain these biomechanical parameters. A detailed analysis of the current evidence of the effects of osmotic swelling on membrane tension and elastic moduli is provided. Briefly, due to the buffering effect of unfolding membrane reservoirs, mild hypotonic swelling does not change membrane tension or the adhesion of the membrane to the underlying cytoskeleton. Conversely, osmotic swelling causes the cell membrane envelope to stiffen, measured as an increase in the membrane elastic modulus.

Cytoskeletal Contribution to Cell Stiffness Due to Osmotic Swelling; Extending the Donnan Equilibrium

Cell volume regulation is commonly analyzed with a model of a closed semipermeable membrane filled with impermeant mobile solutes and the Donnan Equilibrium is used to predict the hydrostatic pressure. This traditional model ignores the fact that most cells are filled with a crosslinked cytoskeleton that is elastic and can be stretched or compressed like a sponge with no obvious need to move mobile solutes. However, calculations show that under osmotic stress, the elastic energy of the cytoskeleton is far greater than the elastic energy of the membrane. Here we expand the traditional Donnan model to include the elasticity of a cytoskeleton with fixed charges and show that cell stiffening happens without a membrane.

Ultrafast imaging of cell elasticity with optical microelastography

In wave physics, and especially seismology, uncorrelated vibrations could be exploited using “noise correlation” tools to reconstruct images of a medium. By using a high-frequency vibration, a high-speed tracking device, and a reconstruction technique based on temporal correlations of travelling waves we conceptualized an optical microelastography technique to map elasticity of internal cellular structures. This technique, unlike other methods, can provide an elasticity image in less than a millisecond, thus opening the possibility of studying dynamic cellular processes and elucidating new mechanocellular properties. We call this proposed technique “cell quake elastography.”

Elasticity is a fundamental cellular property that is related to the anatomy, functionality, and pathological state of cells and tissues. However, current techniques based on cell deformation, atomic force microscopy, or Brillouin scattering are rather slow and do not always accurately represent cell elasticity. Here, we have developed an alternative technique by applying shear wave elastography to the micrometer scale. Elastic waves were mechanically induced in live mammalian oocytes using a vibrating micropipette. These audible frequency waves were observed optically at 200,000 frames per second and tracked with an optical flow algorithm. Whole-cell elasticity was then mapped using an elastography method inspired by the seismology field. Using this approach we show that the elasticity of mouse oocytes is decreased when the oocyte cytoskeleton is disrupted with cytochalasin B. The technique is fast (less than 1 ms for data acquisition), precise (spatial resolution of a few micrometers), able to map internal cell structures, and robust and thus represents a tractable option for interrogating biomechanical properties of diverse cell types.

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.

Universal glass-forming behavior of in vitro and living cytoplasm

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.

Feedback-tracking microrheology in living cells

Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.

Cell Surface Mechanochemistry and the Determinants of Bleb Formation, Healing, and Travel Velocity

Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density.

Intracellular Pressure Dynamics in Blebbing Cells

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify the relationship among cytoplasmic rheology, pressure, and bleb expansion dynamics, and provide a more detailed picture of intracellular pressure dynamics. This study shows the elastic response of the cytoplasm relieves pressure and limits bleb size, and that both permeability and elasticity of the cytoplasm determine bleb expansion time. Our model with a poroelastic cytoplasm shows that pressure disturbances from bleb initiation propagate faster than the timescale of bleb expansion and that pressure equilibrates slower than the timescale of bleb expansion. The multiple timescales in intracellular pressure dynamics explain the apparent discrepancy in the interpretation of experimental results.

Physical view on migration modes

Cellular motility is essential for many processes such as embryonic development, wound healing processes, tissue assembly and regeneration, immune cell trafficing and diseases such as cancer. The migration efficiency and the migratory potential depend on the type of migration mode. The previously established migration modes such as epithelial (non-migratory) and mesenchymal (migratory) as well as amoeboid (squeezing motility) relay mainly on phenomenological criteria such as cell morphology and molecular biological criteria such as gene expression. However, the physical view on the migration modes is still not well understood. As the process of malignant cancer progression such as metastasis depends on the migration of single cancer cells and their migration mode, this review focuses on the different migration strategies and discusses which mechanical prerequisites are necessary to perform a special migration mode through a 3-dimensional microenvironment. In particular, this review discusses how cells can distinguish and finally switch between the migration modes and what impact do the physical properties of cells and their microenvironment have on the transition between the novel migration modes such as blebbing and protrusive motility.

Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy

Current measurements of the biomechanical properties of cells require physical contact with cells or lack subcellular resolution. Here we developed a label-free microscopy technique based on Brillouin light scattering that is capable of measuring an intracellular longitudinal modulus with optical resolution. The 3D Brillouin maps we obtained of cells in 2D and 3D microenvironments revealed mechanical changes due to cytoskeletal modulation and cell-volume regulation.

Actin-myosin spatial patterns from a simplified isotropic viscoelastic model

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.

Investigating cell mechanics with atomic force microscopy

Transmission of mechanical force is crucial for normal cell development and functioning. However, the process of mechanotransduction cannot be studied in isolation from cell mechanics. Thus, in order to understand how cells 'feel', we must first understand how they deform and recover from physical perturbations. Owing to its versatility, atomic force microscopy (AFM) has become a popular tool to study intrinsic cellular mechanical properties. Used to directly manipulate and examine whole and subcellular reactions, AFM allows for top-down and reconstitutive approaches to mechanical characterization. These studies show that the responses of cells and their components are complex, and largely depend on the magnitude and time scale of loading. In this review, we generally describe the mechanotransductive process through discussion of well-known mechanosensors. We then focus on discussion of recent examples where AFM is used to specifically probe the elastic and inelastic responses of single cells undergoing deformation. We present a brief overview of classical and current models often used to characterize observed cellular phenomena in response to force. Both simple mechanistic models and complex nonlinear models have been used to describe the observed cellular behaviours, however a unifying description of cell mechanics has not yet been resolved.

Furrow constriction in animal cell cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles' surface tension.

Cell mechanics: principles, practices, and prospects

Cells generate and sustain mechanical forces within their environment as part of their normal physiology. They are active materials that can detect mechanical stimulation by the activation of mechanosensitive signaling pathways, and respond to physical cues through cytoskeletal re-organization and force generation. Genetic mutations and pathogens that disrupt the cytoskeletal architecture can result in changes to cell mechanical properties such as elasticity, adhesiveness, and viscosity. On the other hand, perturbations to the mechanical environment can affect cell behavior. These transformations are often a hallmark and symptom of a variety of pathologies. Consequently, there are now a myriad of experimental techniques and theoretical models adapted from soft matter physics and mechanical engineering to characterize cell mechanical properties. Interdisciplinary research combining modern molecular biology with advanced cell mechanical characterization techniques now paves the way for furthering our fundamental understanding of cell mechanics and its role in development, physiology, and disease. We describe a generalized outline for measuring cell mechanical properties including loading protocols, tools, and data interpretation.We summarize recent advances in the field and explain how cell biomechanics research can be adopted by physicists, engineers, biologists, and clinicians alike.

Bioengineering paradigms for cell migration in confined microenvironments

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).

An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.

Regulation of T-cell receptor signaling by the actin cytoskeleton and poroelastic cytoplasm

The actin cytoskeleton plays essential roles in modulating T-cell activation. Most models of T-cell receptor (TCR) triggering signalosome assembly and immune synapse formation invoke actin-dependent mechanisms. As T cells are constitutively motile cells, TCR triggering and signaling occur against a cytoskeletal backdrop that is constantly remodeling. While the interplay between actin dynamics and TCR signaling have been the focus of research for many years, much of the work in T cells has considered actin largely for its 'scaffolding' function. We examine the roles of the actin cytoskeleton in TCR signaling and immune synapse formation with an emphasis on how poroelasticity, an ensemble feature of actin dynamics with the cytosol, relates to how T cells respond to stimulation.

The toxoplasma Acto-MyoA motor complex is important but not essential for gliding motility and host cell invasion

Apicomplexan parasites are thought to actively invade the host cell by gliding motility. This movement is powered by the parasite's own actomyosin system, and depends on the regulated polymerisation and depolymerisation of actin to generate the force for gliding and host cell penetration. Recent studies demonstrated that Toxoplasma gondii can invade the host cell in the absence of several core components of the invasion machinery, such as the motor protein myosin A (MyoA), the microneme proteins MIC2 and AMA1 and actin, indicating the presence of alternative invasion mechanisms. Here the roles of MyoA, MLC1, GAP45 and Act1, core components of the gliding machinery, are re-dissected in detail. Although important roles of these components for gliding motility and host cell invasion are verified, mutant parasites remain invasive and do not show a block of gliding motility, suggesting that other mechanisms must be in place to enable the parasite to move and invade the host cell. A novel, hypothetical model for parasite gliding motility and invasion is presented based on osmotic forces generated in the cytosol of the parasite that are converted into motility.

An equatorial contractile mechanism drives cell elongation but not cell division

A cytokinesis-like contractile mechanism is co-opted in a different developmental scenario to achieve cell elongation instead of cell division in Ciona intestinalis.

Cell shape changes and proliferation are two fundamental strategies for morphogenesis in animal development. During embryogenesis of the simple chordate Ciona intestinalis, elongation of individual notochord cells constitutes a crucial stage of notochord growth, which contributes to the establishment of the larval body plan. The mechanism of cell elongation is elusive. Here we show that although notochord cells do not divide, they use a cytokinesis-like actomyosin mechanism to drive cell elongation. The actomyosin network forming at the equator of each notochord cell includes phosphorylated myosin regulatory light chain, α-actinin, cofilin, tropomyosin, and talin. We demonstrate that cofilin and α-actinin are two crucial components for cell elongation. Cortical flow contributes to the assembly of the actomyosin ring. Similar to cytokinetic cells, membrane blebs that cause local contractions form at the basal cortex next to the equator and participate in force generation. We present a model in which the cooperation of equatorial actomyosin ring-based constriction and bleb-associated contractions at the basal cortex promotes cell elongation. Our results demonstrate that a cytokinesis-like contractile mechanism is co-opted in a completely different developmental scenario to achieve cell shape change instead of cell division. We discuss the occurrences of actomyosin rings aside from cell division, suggesting that circumferential contraction is an evolutionally conserved mechanism to drive cell or tissue elongation.

The actomyosin cytoskeleton is the primary force that drives cell shape changes. These fibers are organized in elaborate structures that form sarcomeres in the muscle and the contractile ring during cytokinesis. In cytokinesis, the establishment of an equatorial actomyosin ring is preceded and regulated by many cell cycle events, and the ring itself is a complex and dynamic structure. Here we report the presence of an equatorial circumferential actomyosin structure with remarkable similarities to the cytokinetic ring formed in postmitotic notochord cells of sea squirt Ciona intestinalis. The notochord is a transient rod-like structure found in all embryos that belong to the phylum Chordata, and in Ciona, a simple chordate, it consists of only 40 cylindrical cells arranged in a single file, which elongate individually during development. Our study shows that the activity of the equatorial actomyosin ring is required for the elongation of the notochord cells. We also find that cortical flow contributes significantly to the formation of the ring at the equator. Similar to cytokinetic cells, we observe the formation of membrane blebs outside the equatorial region. Our analyses suggest that cooperation of actomyosin ring-based circumferential constriction and bleb-associated contractions drive cell elongation in Ciona. We conclude that cells can utilize a cytokinesis-like force generation mechanism to promote cell shape change instead of cell division.

Measurement of spatiotemporal intracellular deformation of cells adhered to collagen matrix during freezing of biomaterials

Preservation of structural integrity inside cells and at cell-extracellular matrix (ECM) interfaces is a key challenge during freezing of biomaterials. Since the post-thaw functionality of cells depends on the extent of change in the cytoskeletal structure caused by complex cell-ECM adhesion, spatiotemporal deformation inside the cell was measured using a newly developed microbead-mediated particle tracking deformetry (PTD) technique using fibroblast-seeded dermal equivalents as a model tissue. Fibronectin-coated 500 nm diameter microbeads were internalized in cells, and the microbead-labeled cells were used to prepare engineered tissue with type I collagen matrices. After a 24 h incubation the engineered tissues were directionally frozen, and the cells were imaged during the process. The microbeads were tracked, and spatiotemporal deformation inside the cells was computed from the tracking data using the PTD method. Effects of particle size on the deformation measurement method were tested, and it was found that microbeads represent cell deformation to acceptable accuracy. The results showed complex spatiotemporal deformation patterns in the cells. Large deformation in the cells and detachments of cells from the ECM were observed. At the cellular scale, variable directionality of the deformation was found in contrast to the one-dimensional deformation pattern observed at the tissue scale, as found from earlier studies. In summary, this method can quantify the spatiotemporal deformation in cells and can be correlated to the freezing-induced change in the structure of cytosplasm and of the cell-ECM interface. As a broader application, this method may be used to compute deformation of cells in the ECM environment for physiological processes, namely cell migration, stem cell differentiation, vasculogenesis, and cancer metastasis, which have relevance to quantify mechanotransduction.

Resiliency of the plasma membrane and actin cortex to large-scale deformation

The tight coupling between the plasma membrane and actin cortex allows cells to rapidly change shape in response to mechanical cues and during physiological processes. Mechanical properties of the membrane are critical for organizing the actin cortex, which ultimately governs the conversion of mechanical information into signaling. The cortex has been shown to rapidly remodel on timescales of seconds to minutes, facilitating localized deformations and bundling dynamics that arise during the exertion of mechanical forces and cellular deformations. Here, we directly visualized and quantified the time-dependent deformation and recovery of the membrane and actin cortex of HeLa cells in response to externally applied loads both on- and off-nucleus using simultaneous confocal and atomic force microscopy. The local creep-like deformation of the membrane and actin cortex depends on both load magnitude and duration and does not appear to depend on cell confluency. The membrane and actin cortex rapidly recover their initial shape after prolonged loading (up to 10 min) with large forces (up to 20 nN) and high aspect ratio deformations. Cytoplasmic regions surrounding the nucleus are shown to be more resistant to long-term creep than nuclear regions. These dynamics are highly regulated by actomyosin contractility and an intact actin cytoskeleton. Results suggest that in response to local deformations, the nucleus does not appear to provide significant resistance or play a major role in cell shape recovery. The membrane and actin cortex clearly possess remarkable mechanical stability, critical for the transduction of mechanical deformation into long term biochemical signals and cellular remodeling.

The role and regulation of blebs in cell migration

Blebs are cellular protrusions that have been shown to be instrumental for cell migration in development and disease. Bleb expansion is driven by hydrostatic pressure generated in the cytoplasm by the contractile actomyosin cortex. The mechanisms of bleb formation thus fundamentally differ from the actin polymerization-based mechanisms responsible for lamellipodia expansion. In this review, we summarize recent findings relevant for the mechanics of bleb formation and the underlying molecular pathways. We then review the processes involved in determining the type of protrusion formed by migrating cells, in particular in vivo, in the context of embryonic development. Finally, we discuss how cells utilize blebs for their forward movement in the presence or absence of strong substrate attachment.

Dynamics of elastic interactions in soft and biological matter

Cells probe their mechanical environment and can change the organization of their cytoskeletons when the elastic and viscous properties of their environment are modified. We use a model in which the forces exerted by small, contractile acto-myosin filaments (e.g., nascent stress fibers in stem cells) on the extracellular matrix are modeled as local force dipoles. In some cases, the strain field caused by these force dipoles propagates quickly enough so that only static elastic interactions need be considered. On the other hand, in the case of significant energy dissipation, strain propagation is slower and may be eliminated completely by the relaxation of the cellular cytoskeleton (e.g., by cross-link dissociation). Here, we consider several dissipative mechanisms that affect the propagation of the strain field in adhered cells and consider these effects on the interaction between force dipoles and their resulting mutual orientations. This is a first step in understanding the development of orientational (nematic) or layering (smectic) order in the cytoskeleton. We use the theory to estimate the propagation time of the strain fields over a cellular distance for different mechanisms and find that in some cases it can be of the order of seconds, thus competing with the cytoskeletal relaxation time. Furthermore, for a simple system of two force dipoles, we predict that in some cases the orientation of force dipoles might change significantly with time, e.g., for short times the dipoles exhibit parallel alignment while for later times they align perpendicularly.

Intracellular mechanochemical waves in an active poroelastic model

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.

Numerical study of cell cryo-preservation: a network model of intracellular ice formation

In this study, a new intracellular ice formation network model, coupled with an improved cell dehydration model has been developed. The non-uniform dehydration of the cell during freezing is simulated with moving boundary condition. Internal cell structures like cell nucleus are taken into consideration. The IIF network model is developed from classic diffusion limited IIF model in order to simulate spatial ice growth pattern inside cells. Simulation results suggest that cell nuclear plays a significant role in cryo-dehydration and would affect water/CPA concentration gradient inside the cell. At the same time, the ice growth pattern of exogenous IIF hypothesis is examined in the model. It is consistent with our previous experiments, in which we witnessed the intracellular ice first grown into the nucleus before spreading to the whole intercellular space. According to this model, the water concentration difference between nucleus and cytoplasm during cryo-dehydration could partly explain why ice crystal in the nucleus grows faster. However, it is not the dominate factor. Higher diffusion coefficient in cell nucleus might play a more important role in the phenomenon.

The cytoplasm of living cells behaves as a poroelastic material

The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales.

Contraction of cross-linked actomyosin bundles

Cross-linked actomyosin bundles retract when severed in vivo by laser ablation, or when isolated from the cell and micromanipulated in vitro in the presence of ATP. We identify the timescale for contraction as a viscoelastic time τ, where the viscosity is due to (internal) protein friction. We obtain an estimate of the order of magnitude of the contraction time τ ≈ 10-100 s, consistent with available experimental data for circumferential microfilament bundles and stress fibers. Our results are supported by an exactly solvable, hydrodynamic model of a retracting bundle as a cylinder of isotropic, active matter, from which the order of magnitude of the active stress is estimated.

Phosphatidylserine externalization and membrane blebbing are involved in the nonclassical export of FGF1

The mechanisms of nonclassical export of signal peptide-less proteins remain insufficiently understood. Here, we demonstrate that stress-induced unconventional export of FGF1, a potent and ubiquitously expressed mitogenic and proangiogenic protein, is associated with and dependent on the formation of membrane blebs and localized cell surface exposure of phosphatidylserine (PS). In addition, we found that the differentiation of promonocytic cells results in massive FGF1 release, which also correlates with membrane blebbing and exposure of PS. These findings indicate that the externalization of acidic phospholipids could be used as a pharmacological target to regulate the availability of FGF1 in the organism.

Electric field exposure triggers and guides formation of pseudopod-like blebs in U937 monocytes

We describe a new phenomenon of anodotropic pseudopod-like blebbing in U937 cells stimulated by nanosecond pulsed electric field (nsPEF). In contrast to "regular," round-shaped blebs, which are often seen in response to cell damage, pseudopod-like blebs (PLBs) formed as longitudinal membrane protrusions toward anode. PLB length could exceed the cell diameter in 2 min of exposure to 60-ns, 10-kV/cm pulses delivered at 10-20 Hz. Both PLBs and round-shaped nsPEF-induced blebs could be efficiently inhibited by partial isosmotic replacement of bath NaCl for a larger solute (sucrose), thereby pointing to the colloid-osmotic water uptake as the principal driving force for bleb formation. In contrast to round-shaped blebs, PLBs retracted within several minutes after exposure. Cells treated with 1 nM of the actin polymerization blocker cytochalasin D were unable to form PLBs and instead produced stationary, spherical blebs with no elongation or retraction capacity. Live cell fluorescent actin tagging showed that during elongation actin promptly entered the PLB interior, forming bleb cortex and scaffold, which was not seen in stationary blebs. Overall, PLB formation was governed by both passive (physicochemical) effects of membrane permeabilization and active cytoskeleton assembly in the living cell. To a certain extent, PLB mimics the membrane extension in the process of cell migration and can be employed as a nonchemical model for studies of cytomechanics, membrane-cytoskeleton interaction and cell motility.