Shape oscillations of non-adhering fibroblast cells

Friction forces determine cytoplasmic reorganization and shape changes of ascidian oocytes upon fertilization

Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole-a protuberance of the zygote's vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces.

Computational approaches for simulating luminogenesis

Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.

The nuclear piston activates mechanosensitive ion channels to generate cell migration paths in confining microenvironments

Cell migration in confining microenvironments is limited by the ability of the stiff nucleus to deform through pores when migration paths are preexisting and elastic, but how cells generate these paths remains unclear. Here, we reveal a mechanism by which the nucleus mechanically generates migration paths for mesenchymal stem cells (MSCs) in confining microenvironments. MSCs migrate robustly in nanoporous, confining hydrogels that are viscoelastic and plastic but not in hydrogels that are more elastic. To migrate, MSCs first extend thin protrusions that widen over time because of a nuclear piston, thus opening up a migration path in a confining matrix. Theoretical modeling and experiments indicate that the nucleus pushing into the protrusion activates mechanosensitive ion channels, leading to an influx of ions that increases osmotic pressure, which outcompetes hydrostatic pressure to drive protrusion expansion. Thus, instead of limiting migration, the nucleus powers migration by generating migration paths.

The Relative Densities of Cytoplasm and Nuclear Compartments Are Robust against Strong Perturbation

The cell nucleus is a compartment in which essential processes such as gene transcription and DNA replication occur. Although the large amount of chromatin confined in the finite nuclear space could install the picture of a particularly dense organelle surrounded by less dense cytoplasm, recent studies have begun to report the opposite. However, the generality of this newly emerging, opposite picture has so far not been tested. Here, we used combined optical diffraction tomography and epi-fluorescence microscopy to systematically quantify the mass densities of cytoplasm, nucleoplasm, and nucleoli of human cell lines, challenged by various perturbations. We found that the nucleoplasm maintains a lower mass density than cytoplasm during cell cycle progression by scaling its volume to match the increase of dry mass during cell growth. At the same time, nucleoli exhibited a significantly higher mass density than the cytoplasm. Moreover, actin and microtubule depolymerization and changing chromatin condensation altered volume, shape, and dry mass of those compartments, whereas the relative distribution of mass densities was generally unchanged. Our findings suggest that the relative mass densities across membrane-bound and membraneless compartments are robustly conserved, likely by different as-of-yet unknown mechanisms, which hints at an underlying functional relevance. This surprising robustness of mass densities contributes to an increasing recognition of the importance of physico-chemical properties in determining cellular characteristics and compartments.

Motion magnification analysis of microscopy videos of biological cells

It is well recognized that isolated cardiac muscle cells beat in a periodic manner. Recently, evidence indicates that other, non-muscle cells, also perform periodic motions that are either imperceptible under conventional lab microscope lens or practically not easily amenable for analysis of oscillation amplitude, frequency, phase of movement and its direction. Here, we create a real-time video analysis tool to visually magnify and explore sub-micron rhythmic movements performed by biological cells and the induced movements in their surroundings. Using this tool, we suggest that fibroblast cells perform small fluctuating movements with a dominant frequency that is dependent on their surrounding substrate and its stiffness.

Motility and morphodynamics of confined cells

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model, the cell is driven out of equilibrium by an active cytsokeleton force that acts on the membrane. The cell cytoplasm, described as a viscous droplet in the Darcy flow regime, contains a diffusive solute that actively transduces the applied cytoskeleton force. While fairly simple and analytically tractable, this quasi-two-dimensional model predicts a range of compelling dynamic behaviours. A linear stability analysis of the system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.

Rhythmicity and waves in the cortex of single cells

Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information.

This article is part of the theme issue ‘Self-organization in cell biology’.

Excitable RhoA dynamics drive pulsed contractions in the early C. elegans embryo

Pulsed actomyosin contractility underlies many morphogenetic processes. Here, Michaux et al. show that, in early C. elegans embryos, pulsed contractions are generated by intrinsically excitable RhoA dynamics, involving fast autoactivation of RhoA and delayed negative feedback through local actin-dependent recruitment of the RhoGAPs RGA-3/4.

Pulsed actomyosin contractility underlies diverse modes of tissue morphogenesis, but the underlying mechanisms remain poorly understood. Here, we combined quantitative imaging with genetic perturbations to identify a core mechanism for pulsed contractility in early Caenorhabditis elegans embryos. We show that pulsed accumulation of actomyosin is governed by local control of assembly and disassembly downstream of RhoA. Pulsed activation and inactivation of RhoA precede, respectively, the accumulation and disappearance of actomyosin and persist in the absence of Myosin II. We find that fast (likely indirect) autoactivation of RhoA drives pulse initiation, while delayed, F-actin–dependent accumulation of the RhoA GTPase-activating proteins RGA-3/4 provides negative feedback to terminate each pulse. A mathematical model, constrained by our data, suggests that this combination of feedbacks is tuned to generate locally excitable RhoA dynamics. We propose that excitable RhoA dynamics are a common driver for pulsed contractility that can be tuned or coupled differently to actomyosin dynamics to produce a diversity of morphogenetic outcomes.

Synchronized mechanical oscillations at the cell-matrix interface in the formation of tensile tissue

The formation of uniaxial fibrous tissues with defined viscoelastic properties implies the existence of an orchestrated mechanical interaction between the cytoskeleton and the extracellular matrix. This study addresses the nature of this interaction. The hypothesis is that this mechanical interplay underpins the mechanical development of the tissue. In embryonic tendon tissue, an early event in the development of a mechanically robust tissue is the interaction of the pointed tips of extracellular collagen fibrils with the fibroblast plasma membrane to form stable interface structures (fibripositors). Here, we used a fibroblast-generated tissue that is structurally and mechanically matched to embryonic tendon to demonstrate homeostasis of cell-derived and external strain-derived tension over repeated cycles of strain and relaxation. A cell-derived oscillatory tension component is evident in this matrix construct. This oscillatory tension involves synchronization of individual cell forces across the construct and is induced in each strain cycle by transient relaxation and transient tensioning of the tissue. The cell-derived tension along with the oscillatory component is absent in the presence of blebbistatin, which disrupts actinomyosin force generation of the cell. The time period of this oscillation (60-90 s) is well-defined in each tissue sample and matches a primary viscoelastic relaxation time. We hypothesize that this mechanical oscillation of fibroblasts with plasma membrane anchored collagen fibrils is a key factor in mechanical sensing and feedback regulation in the formation of tensile tissues.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Many studies in cell biology employ global shape descriptors to probe mechanisms of cell morphogenesis. Here, we implement a framework in this paper to profile cellular morphodynamics very locally. We employ the Hilbert-Huang transform (HHT) to extract along the entire cell edge spectra of instantaneous edge motion frequency and magnitude and use them to classify overall cell behavior as well as subcellular edge sectors of distinct dynamics. We find in fibroblast-like COS7 cells that the marked heterogeneity in mobility of an unstimulated population is fully captured by differences in the magnitude spectra, while the frequency spectra are conserved between cells. Using optogenetics to acutely inhibit morphogenetic signaling pathways we find that these molecular shifts are reflected by changes in the frequency spectra but not in the magnitude spectra. After clustering cell edge sectors with distinct morphodynamics we observe in cells expressing a Rac1 activity biosensor that the sectors with different frequency spectra associate with different signaling intensity and dynamics. Together, these observations let us conclude that the frequency spectrum encodes the wiring of the molecular circuitry that regulates edge movements, whereas the magnitude captures the activation level of the circuitry.

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.

Spontaneous Oscillations and Synchronization of Active Droplets on a Water Surface via Marangoni Convection

Shape-oscillations and synchronization are intriguing phenomena in many biological and physical systems. Here, we report the rhythmic mechanical oscillations and synchronization of aniline oil droplets on a water phase, which is induced by Marangoni convection during transfer of the solute. The repetitive increase and decrease in the surface concentration in the vicinity of the contact line leads to the oscillations of droplets through an imbalance in surface tensions. The nature of the oscillations depends on the diameter of the droplet, the depth of the bulk aqueous phase, and the concentration of the aqueous phase. A numerical simulation reproduces the essential behaviors of active oscillations of a droplet. Droplets sense each other through a surface tension gradient and advection, and hydrodynamic coupling in the bulk solution induces the synchronization of droplet oscillations.

Autonomous unimer-vesicle oscillation by totally synthetic diblock copolymers: effect of block length and polymer concentration on spatio-temporal structures

In this study, factors controlling autonomous vesicle oscillations exhibited by self-oscillating diblock copolymers were investigated. The self-oscillating diblock copolymer contains poly(ethylene oxide) (PEO) as the hydrophilic block and a random copolymer composed of N-isopropylacrylamide (NIPAAm) with side chains of ruthenium tris(2,2'-bipyridine) (Ru(bpy)₃), which catalyzes the Belousov-Zhabotinsky (BZ) reaction, as the self-oscillating block. Recently, our group has reported that a diblock copolymer exhibits a unique autonomous disintegration and reconstruction of the vesicles driven by the periodic redox changes of Ru(bpy)₃ in a catalyst-free BZ reaction solution. Nevertheless, the effect of the diblock copolymer architecture on the structure of the vesicles under equilibrium conditions, as well as their oscillation properties under non-equilibrium conditions, has not been clarified thus far. Hence, self-oscillating diblock copolymers with different block lengths were systematically synthesized, and the effects of the block length and polymer concentration on the spatio-temporal vesicle structures were comprehensively discussed.

Actin cortex architecture regulates cell surface tension

Animal cell shape is largely determined by the cortex, a thin actin network underlying the plasma membrane in which myosin-driven stresses generate contractile tension. Tension gradients result in local contractions and drive cell deformations. Previous cortical tension regulation studies have focused on myosin motors. Here, we show that cortical actin network architecture is equally important. First, we observe that actin cortex thickness and tension are inversely correlated during cell-cycle progression. We then show that the actin filament length regulators CFL1, CAPZB and DIAPH1 regulate mitotic cortex thickness and find that both increasing and decreasing thickness decreases tension in mitosis. This suggests that the mitotic cortex is poised close to a tension maximum. Finally, using a computational model, we identify a physical mechanism by which maximum tension is achieved at intermediate actin filament lengths. Our results indicate that actin network architecture, alongside myosin activity, is key to cell surface tension regulation.

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.

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.

Dynamic myosin activation promotes collective morphology and migration by locally balancing oppositional forces from surrounding tissue

A challenge for migrating collectives is to respond to physical changes in local environments. Border cells migrate collectively in the Drosophila ovary and require dynamic myosin to maintain their morphology. Border cells elevate active myosin in response to tissue compression. Myosin tension counteracts tissue constraints for collective movement.

Migrating cells need to overcome physical constraints from the local microenvironment to navigate their way through tissues. Cells that move collectively have the additional challenge of negotiating complex environments in vivo while maintaining cohesion of the group as a whole. The mechanisms by which collectives maintain a migratory morphology while resisting physical constraints from the surrounding tissue are poorly understood. Drosophila border cells represent a genetic model of collective migration within a cell-dense tissue. Border cells move as a cohesive group of 6−10 cells, traversing a network of large germ line–derived nurse cells within the ovary. Here we show that the border cell cluster is compact and round throughout their entire migration, a shape that is maintained despite the mechanical pressure imposed by the surrounding nurse cells. Nonmuscle myosin II (Myo-II) activity at the cluster periphery becomes elevated in response to increased constriction by nurse cells. Furthermore, the distinctive border cell collective morphology requires highly dynamic and localized enrichment of Myo-II. Thus, activated Myo-II promotes cortical tension at the outer edge of the migrating border cell cluster to resist compressive forces from nurse cells. We propose that dynamic actomyosin tension at the periphery of collectives facilitates their movement through restrictive tissues.

Mechanism of Spontaneous Blebbing Motion of an Oil-Water Interface: Elastic Stress Generated by a Lamellar-Lamellar Transition

A quaternary system composed of surfactant, cosurfactant, oil, and water showing spontaneous motion of the oil-water interface under far-from-equilibrium condition is studied in order to understand nanometer-scale structures and their roles in spontaneous motion. The interfacial motion is characterized by the repetitive extension and retraction of spherical protrusions at the interface, i.e, blebbing motion. During the blebbing motion, elastic aggregates are accumulated, which were characterized as surfactant lamellar structures with mean repeat distances d of 25 to 40 nm. Still unclear is the relationship between the structure formation and the dynamics of the interfacial motion. In the present study, we find that a new lamellar structure with d larger than 80 nm is formed at the blebbing oil-water interface, while the resultant elastic aggregates, which are the one reported before, have a lamellar structure with smaller d (25 to 40 nm). Such transition of lamellar structures from the larger d to smaller d is induced by a penetration of surfactants from an aqueous phase into the aggregates. We propose a model in which elastic stress generated by the transition drives the blebbing motion at the interface. The present results explain the link between nanometer-scale transition of lamellar structure and millimeter-scale dynamics at an oil-water interface.

Modeling the Excess Cell Surface Stored in a Complex Morphology of Bleb-Like Protrusions

Cells transition from spread to rounded morphologies in diverse physiological contexts including mitosis and mesenchymal-to-amoeboid transitions. When these drastic shape changes occur rapidly, cell volume and surface area are approximately conserved. Consequently, the rounded cells are suddenly presented with a several-fold excess of cell surface whose area far exceeds that of a smooth sphere enclosing the cell volume. This excess is stored in a population of bleb-like protrusions (BLiPs), whose size distribution is shown by electron micrographs to be skewed. We introduce three complementary models of rounded cell morphologies with a prescribed excess surface area. A 2D Hamiltonian model provides a mechanistic description of how discrete attachment points between the cell surface and cortex together with surface bending energy can generate a morphology that satisfies a prescribed excess area and BLiP number density. A 3D random seed-and-growth model simulates efficient packing of BLiPs over a primary rounded shape, demonstrating a pathway for skewed BLiP size distributions that recapitulate 3D morphologies. Finally, a phase field model (2D and 3D) posits energy-based constitutive laws for the cell membrane, nematic F-actin cortex, interior cytosol, and external aqueous medium. The cell surface is equipped with a spontaneous curvature function, a proxy for the cell surface-cortex couple, that is a priori unknown, which the model “learns” from the thin section transmission electron micrograph image (2D) or the “seed and growth” model image (3D). Converged phase field simulations predict self-consistent amplitudes and spatial localization of pressure and stress throughout the cell for any posited stationary morphology target and cell compartment constitutive properties. The models form a general framework for future studies of cell morphological dynamics in a variety of biological contexts.

Individual cells must have the capability for rapid morphological transformations under various physiological conditions. One of the most drastic shape transformations occurs during the transition from spread to rounded morphologies. When this transition occurs rapidly, there is insufficient time for significant changes in surface area to occur, although the final size of the rounded cell indicates a significant reduction in apparent cell surface area at light microscope resolution. By contrast, high-resolution scanning electron micrographs of rapidly rounded cells reveal that a large amount of surface area is stored in a highly convoluted surface morphology consisting of bleb-like protrusions (BLiPs) and other small structures that are unrecognizable at lower resolution. This surface reserve is an important part of the mechanism that allows rapid and efficient large scale transformations of cell shape. Remarkably, although this convoluted morphology has been observed for decades, there has been very little effort recognizing and including this surface surplus in mathematical modeling of cell morphology and physiology. In this paper, we develop three complementary models to fill this void and lay the foundation for future investigations of the mechanisms that drive cellular morphological dynamics.

Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time τ(C). To explore the resulting interplay between active and polymeric dynamics, we first generalize a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of τ(C) and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τ(C) and persists even as τ(C)→∞. We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τ(C)→∞. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

Cortical Flow-Driven Shapes of Nonadherent Cells

Nonadherent polarized cells have been observed to have a pearlike, elongated shape. Using a minimal model that describes the cell cortex as a thin layer of contractile active gel, we show that the anisotropy of active stresses, controlled by cortical viscosity and filament ordering, can account for this morphology. The predicted shapes can be determined from the flow pattern only; they prove to be independent of the mechanism at the origin of the cortical flow, and are only weakly sensitive to the cytoplasmic rheology. In the case of actin flows resulting from a contractile instability, we propose a phase diagram of three-dimensional cell shapes that encompasses nonpolarized spherical, elongated, as well as oblate shapes, all of which have been observed in experiment.

Force fluctuations in three-dimensional suspended fibroblasts

Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. To test quantitatively forces generated by cells not attached to a substrate, we used a dual optical trap to suspend 3T3 fibroblasts between two fibronectin-coated beads. In this simple geometry, we measured both the cells' elastic properties and the force fluctuations they generate with high bandwidth. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. We show that cortical forces generated by non-muscle myosin II deform the cell from its rounded shape in the frequency regime from 0.1 to 10 Hz. The amplitudes of these forces were strongly reduced by blebbistatin and serum starvation, but were unaffected by depolymerization of microtubules. Force fluctuations show a spectrum that is characteristic for an elastic network activated by random sustained stresses with abrupt transitions.

Multiblock copolymers exhibiting spatio-temporal structure with autonomous viscosity oscillation

Here we report an ABA triblock copolymer that can express microscopic autonomous formation and break-up of aggregates under constant condition to generate macroscopic viscoelastic self-oscillation of the solution. The ABA triblock copolymer is designed to have hydrophilic B segment and self-oscillating A segment at the both sides by RAFT copolymerization. In the A segment, a metal catalyst of chemical oscillatory reaction, i.e., the Belousov-Zhabotinsky (BZ) reaction, is introduced as a chemomechanical transducer to change the aggregation state of the polymer depending on the redox states. Time-resolved DLS measurements of the ABA triblock copolymer confirm the presence of a transitional network structure of micelle aggregations in the reduced state and a unimer structure in the oxidized state. This autonomous oscillation of a well-designed triblock copolymer enables dynamic biomimetic softmaterials with spatio-temporal structure.

Mechanical checkpoint for persistent cell polarization in adhesion-naive fibroblasts

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.

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.

Elastic properties of epithelial cells probed by atomic force microscopy

Cellular mechanics plays a crucial role in many biological processes such as cell migration, cell growth, embryogenesis, and oncogenesis. Epithelia respond to environmental cues comprising biochemical and physical stimuli through defined changes in cell elasticity. For instance, cells can differentiate between certain properties such as viscoelasticity or topography of substrates by adapting their own elasticity and shape. A living cell is a complex viscoelastic body that not only exhibits a shell architecture composed of a membrane attached to a cytoskeleton cortex but also generates contractile forces through its actomyosin network. Here we review cellular mechanics of single cells in the context of epithelial cell layers responding to chemical and physical stimuli. This article is part of a Special Issue entitled: Mechanobiology.

Inelastic mechanics: A unifying principle in biomechanics

Many soft materials are classified as viscoelastic. They behave mechanically neither quite fluid-like nor quite solid-like - rather a bit of both. Biomaterials are often said to fall into this class. Here, we argue that this misses a crucial aspect, and that biomechanics is essentially damage mechanics, at heart. When deforming an animal cell or tissue, one can hardly avoid inducing the unfolding of protein domains, the unbinding of cytoskeletal crosslinkers, the breaking of weak sacrificial bonds, and the disruption of transient adhesions. We classify these activated structural changes as inelastic. They are often to a large degree reversible and are therefore not plastic in the proper sense, but they dissipate substantial amounts of elastic energy by structural damping. We review recent experiments involving biological materials on all scales, from single biopolymers over cells to model tissues, to illustrate the unifying power of this paradigm. A deliberately minimalistic yet phenomenologically very rich mathematical modeling framework for inelastic biomechanics is proposed. It transcends the conventional viscoelastic paradigm and suggests itself as a promising candidate for a unified description and interpretation of a wide range of experimental data. This article is part of a Special Issue entitled: Mechanobiology.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Self-beating artificial cells: design of cross-linked polymersomes showing self-oscillating motion

Biomimetic cross-linked polymersomes that exhibit a self-beating motion without any on-off switching are developed. The polymersomes are made from a well-defined synthetic thermoresponsive diblock copolymer, and the thermoresponsive segment includes ruthenium catalysts for the oscillatory chemical reaction and vinylidene groups to cross-link the polymersomes. Autonomous volume and shape oscillations of the cross-linked polymersomes are realized following redox changes of the catalysts.

Spontaneous oscillations of elastic contractile materials with turnover

Single and collective cellular oscillations driven by the actomyosin cytoskeleton have been observed in numerous biological systems. Here, we propose that these oscillations can be accounted for by a generic oscillator model of a material turning over and contracting against an elastic element. As an example, we show that during dorsal closure of the Drosophila embryo, experimentally observed changes in actomyosin concentration and oscillatory cell shape changes can, indeed, be captured by the dynamic equations studied here. We also investigate the collective dynamics of an ensemble of such contractile elements and show that the relative contribution of viscous and friction losses yields different regimes of collective oscillations. Taking into account the diffusion of force-producing molecules between contractile elements, our theoretical framework predicts the appearance of traveling waves, resembling the propagation of actomyosin waves observed during morphogenesis.

Cytoskeletal transition in patterned cells correlates with interfacial energy model

A cell's morphology is intricately regulated by microenvironmental cues and intracellular feedback signals. Besides biochemical factors, cell fate can be influenced by the mechanics and geometry of the surrounding matrix. The latter point was addressed herein, by studying cell adhesion on two-dimensional micropatterns. Endothelial cells were grown on maleic acid copolymer surfaces structured with stripes of fibronectin by microcontact printing. Experiments showed a biphasic behaviour of actin stress fibre spacing in dependence on the stripe width with a critical size of approx. 15 μm. In a concurrent modelling effort, cells on stripes were simulated as droplet-like structures, including variations of interfacial energy, total volume and dimensions of the nucleus. A biphasic behaviour with regard to cell morphology and area was found, triggered by the minimum of interfacial energy, with the phase transition occurring at a critical stripe width close to the critical stripe width found in the cell experiment. The correlation of experiment and simulation suggests a possible mechanism of the cytoskeletal rearrangements based on interfacial energy arguments.

Impact of heating on passive and active biomechanics of suspended cells

A cell is a complex material whose mechanical properties are essential for its normal functions. Heating can have a dramatic effect on these mechanical properties, similar to its impact on the dynamics of artificial polymer networks. We investigated such mechanical changes by the use of a microfluidic optical stretcher, which allowed us to probe cell mechanics when the cells were subjected to different heating conditions at different time scales. We find that HL60/S4 myeloid precursor cells become mechanically more compliant and fluid-like when subjected to either a sudden laser-induced temperature increase or prolonged exposure to higher ambient temperature. Above a critical temperature of 52 ± 1°C, we observed active cell contraction, which was strongly correlated with calcium influx through temperature-sensitive transient receptor potential vanilloid 2 (TRPV2) ion channels, followed by a subsequent expansion in cell volume. The change from passive to active cellular response can be effectively described by a mechanical model incorporating both active stress and viscoelastic components. Our work highlights the role of TRPV2 in regulating the thermomechanical response of cells. It also offers insights into how cortical tension and osmotic pressure govern cell mechanics and regulate cell-shape changes in response to heat and mechanical stress.

Phase-synchronized state of oriented active fluids

We present a theory for self-driven fluids, such as motorized cytoskeletal extracts or microbial suspensions, that takes into account the underlying periodic duty cycle carried by the constituent active particles. We show that an orientationally ordered active fluid can undergo a transition to a state in which the particles synchronize their phases. This spontaneous breaking of time-translation invariance gives rise to flow instabilities distinct from those arising in phase-incoherent active matter. Our work is of relevance to the transport of fluids in living systems and makes predictions for concentrated active-particle suspensions and optically driven colloidal arrays.

The actin cortex as an active wetting layer

Using active gel theory we study theoretically the properties of the cortical actin layer of animal cells. The cortical layer is described as a non-equilibrium wetting film on the cell membrane. The actin density is approximately constant in the layer and jumps to zero at its edge. The layer thickness is determined by the ratio of the polymerization velocity and the depolymerization rate of actin.

Compression and dilation of the membrane-cortex layer generates rapid changes in cell shape

A cyclic process of membrane-cortex compression and dilation generates a traveling wave of cortical actin density that in turn generates oscillations in cell morphology.

Rapid changes in cellular morphology require a cell body that is highly flexible yet retains sufficient strength to maintain structural integrity. We present a mechanism that meets both of these requirements. We demonstrate that compression (folding) and subsequent dilation (unfolding) of the coupled plasma membrane–cortex layer generates rapid shape transformations in rounded cells. Two- and three-dimensional live-cell images showed that the cyclic process of membrane-cortex compression and dilation resulted in a traveling wave of cortical actin density. We also demonstrate that the membrane-cortex traveling wave led to amoeboid-like cell migration. The compression–dilation hypothesis offers a mechanism for large-scale cell shape transformations that is complementary to blebbing, where the plasma membrane detaches from the actin cortex and is initially unsupported when the bleb extends as a result of cytosolic pressure. Our findings provide insight into the mechanisms that drive the rapid morphological changes that occur in many physiological contexts, such as amoeboid migration and cytokinesis.

Contractile units in disordered actomyosin bundles arise from F-actin buckling

Bundles of filaments and motors are central to contractility in cells. The classic example is striated muscle, where actomyosin contractility is mediated by highly organized sarcomeres which act as fundamental contractile units. However, many contractile bundles in vivo and in vitro lack sarcomeric organization. Here we propose a model for how contractility can arise in bundles without sarcomeric organization and validate its predictions with experiments on a reconstituted system. In the model, internal stresses in frustrated arrangements of motors with diverse velocities cause filaments to buckle, leading to overall shortening. We describe the onset of buckling in the presence of stochastic motor head detachment and predict that buckling-induced contraction occurs in an intermediate range of motor densities. We then calculate the size of the "contractile units" associated with this process. Consistent with these results, our reconstituted actomyosin bundles show contraction at relatively high motor density, and we observe buckling at the predicted length scale.

A review of models of fluctuating protrusion and retraction patterns at the leading edge of motile cells

A characteristic feature of motile cells as they undergo a change in motile behavior is the development of fluctuating exploratory motions of the leading edge, driven by actin polymerization. We review quantitative models of these protrusion and retraction phenomena. Theoretical studies have been motivated by advances in experimental and computational methods that allow controlled perturbations, single molecule imaging, and analysis of spatiotemporal correlations in microscopic images. To explain oscillations and waves of the leading edge, most theoretical models propose nonlinear interactions and feedback mechanisms among different components of the actin cytoskeleton system. These mechanisms include curvature-sensing membrane proteins, myosin contraction, and autocatalytic biochemical reaction kinetics. We discuss how the combination of experimental studies with modeling promises to quantify the relative importance of these biochemical and biophysical processes at the leading edge and to evaluate their generality across cell types and extracellular environments.

Cell ingression and apical shape oscillations during dorsal closure in Drosophila

Programmed patterns of gene expression, cell-cell signaling, and cellular forces cause morphogenic movements during dorsal closure. We investigated the apical cell-shape changes that characterize amnioserosa cells during dorsal closure in Drosophila embryos with in vivo imaging of green-fluorescent-protein-labeled DE-cadherin. Time-lapsed, confocal images were assessed with a novel segmentation algorithm, Fourier analysis, and kinematic and dynamical modeling. We found two generic processes, reversible oscillations in apical cross-sectional area and cell ingression characterized by persistent loss of apical area. We quantified a time-dependent, spatially-averaged sum of intracellular and intercellular forces acting on each cell's apical belt of DE-cadherin. We observed that a substantial fraction of amnioserosa cells ingress near the leading edges of lateral epidermis, consistent with the view that ingression can be regulated by leading-edge cells. This is in addition to previously observed ingression processes associated with zipping and apoptosis. Although there is cell-to-cell variability in the maximum rate for decreasing apical area (0.3-9.5 μm(2)/min), the rate for completing ingression is remarkably constant (0.83 cells/min, r(2) > 0.99). We propose that this constant ingression rate contributes to the spatiotemporal regularity of mechanical stress exerted by the amnioserosa on each leading edge during closure.

Dimensional and temporal controls of three-dimensional cell migration by zyxin and binding partners

Spontaneous molecular oscillations are ubiquitous in biology. But to our knowledge, periodic cell migratory patterns have not been observed. Here we report the highly regular, periodic migration of cells along rectilinear tracks generated inside three-dimensional matrices, with each excursion encompassing several cell lengths, a phenotype that does not occur on conventional substrates. Short hairpin RNA depletion shows that these one-dimensional oscillations are uniquely controlled by zyxin and binding partners α-actinin and p130Cas, but not vasodilator-stimulated phosphoprotein and cysteine-rich protein 1. Oscillations are recapitulated for cells migrating along one-dimensional micropatterns, but not on two-dimensional compliant substrates. These results indicate that although two-dimensional motility can be well described by speed and persistence, three-dimensional motility requires two additional parameters, the dimensionality of the cell paths in the matrix and the temporal control of cell movements along these paths. These results also suggest that the zyxin/α-actinin/p130Cas module may ensure that motile cells in a three-dimensional matrix explore the largest space possible in minimum time.

Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments

We present a model of cell motility generated by actomyosin contraction of the cell cortex. We identify, analytically, dynamical instabilities of the cortex and show that they yield steady-state cortical flows, which, in turn, can induce cell migration in three-dimensional environments. This mechanism relies on the regulation of contractility by myosin, whose transport is explicitly taken into account in the model. Theoretical predictions are compared to experimental data of tumor cells migrating in three-dimensional matrigel and suggest that this mechanism could be a general mode of cell migration in three-dimensional environments.

Biomechanical regulation of contractility: spatial control and dynamics

Cells are active materials; they can change shape using internal energy to build contractile networks of actin filaments and myosin motors. Contractility of the actomyosin cortex is tightly regulated in space and time to orchestrate cell shape changes. Conserved biochemical pathways regulate actomyosin networks in subcellular domains which drive cell shape changes. Actomyosin networks display complex dynamics, such as flows and pulses, which participate in myosin distribution and provide a more realistic description of the spatial distribution and evolution of forces during morphogenesis. Such dynamics are influenced by the mechanical properties of actomyosin networks. Moreover, actomyosin can self-organize and respond to mechanical stimuli through multiple types of biomechanical feedback. In this review we propose a framework encapsulating spatiotemporal regulation of contractility from established pathways with the dynamics and mechanics of actomyosin networks. Through the comparison of cytokinesis, cell migration and epithelial morphogenesis, we delineate emergent properties of contractile activity, including self-organization, adaptability and robustness.

Fluctuations and symmetries in two-dimensional active gels

Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.