The actin cortex as an active wetting layer

Localized States in Active Fluids

Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is regulated by chemical species that are advected with flows resulting from gradients in the active stress. The mechanochemical localized patterns form via a subcritical bifurcation and for parameter values for which patterns do not exist in absence of the advective coupling. Our work identifies a generic mechanism underlying localized cellular patterns.

Modeling Receptor Motility along Advecting Lipid Membranes

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

3D printed protein-based robotic structures actuated by molecular motor assemblies

Upscaling motor protein activity to perform work in man-made devices has long been an ambitious goal in bionanotechnology. The use of hierarchical motor assemblies, as realized in sarcomeres, has so far been complicated by the challenges of arranging sufficiently high numbers of motor proteins with nanoscopic precision. Here, we describe an alternative approach based on actomyosin cortex-like force production, allowing low complexity motor arrangements in a contractile meshwork that can be coated onto soft objects and locally activated by ATP. The design is reminiscent of a motorized exoskeleton actuating protein-based robotic structures from the outside. It readily supports the connection and assembly of micro-three-dimensional printed modules into larger structures, thereby scaling up mechanical work. We provide an analytical model of force production in these systems and demonstrate the design flexibility by three-dimensional printed units performing complex mechanical tasks, such as microhands and microarms that can grasp and wave following light activation.

Pinching the cortex of live cells reveals thickness instabilities caused by myosin II motors

The cell cortex is a contractile actin meshwork, which determines cell shape and is essential for cell mechanics, migration, and division. Because its thickness is below optical resolution, there is a tendency to consider the cortex as a thin uniform two-dimensional layer. Using two mutually attracted magnetic beads, one inside the cell and the other in the extracellular medium, we pinch the cortex of dendritic cells and provide an accurate and time-resolved measure of its thickness. Our observations draw a new picture of the cell cortex as a highly dynamic layer, harboring large fluctuations in its third dimension because of actomyosin contractility. We propose that the cortex dynamics might be responsible for the fast shape-changing capacity of highly contractile cells that use amoeboid-like migration.

Active particles with polar alignment in ring-shaped confinement

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

Integer topological defects of cell monolayers: Mechanics and flows

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.

Drops and fibers - how biomolecular condensates and cytoskeletal filaments influence each other

The cellular cytoskeleton self-organizes by specific monomer-monomer interactions resulting in the polymerization of filaments. While we have long thought about the role of polymerization in cytoskeleton formation, we have only begun to consider the role of condensation in cytoskeletal organization. In this review, we highlight how the interplay between polymerization and condensation leads to the formation of the cytoskeleton.

Cell spread area and traction forces determine myosin-II-based cortex thickness regulation

Actomyosin network under the plasma membrane of cells forms a cortical layer that regulates cellular deformations during different processes. What regulates the cortex? Characterized by its thickness, it is believed to be regulated by actin dynamics, filament-length regulators and myosin motor proteins. However, its regulation by cellular morphology (e.g. cell spread area) or mechanical microenvironment (e.g. substrate stiffness) has remained largely unexplored. In this study, super- and high-resolution imaging of actin in CHO cells demonstrates that at high spread areas (>450 μm²), the cortex is thinner, better separated as layers, and sensitive to deactivation of myosin II motors or reduction of substrate stiffness (and traction forces). In less spread cells (<400 μm²) such perturbations do not elicit a response. Myosin IIA's mechanosensing is limited here due to its lowered actin-bound fraction and higher turnover rate. Cofilin, in line with its competitive inhibitory role, is found to be overexpressed in these cells. To establish the causal relation, we initiate a spread area drop by de-adhesion and find enhanced actin dynamics and fragmentation along with oscillations and increase in thickness. This is more correlated to the reduction of traction forces than the endocytosis-based reduction in cell volume. Cortex thickness control by spread area is also found be true during differentiation of THP-1 monocytes to macrophages. Thus, we propose that spread area regulates cortex and its thickness by traction-based mechanosensing of myosin II.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Macropinocytosis Overcomes Directional Bias in Dendritic Cells Due to Hydraulic Resistance and Facilitates Space Exploration

The migration of immune cells can be guided by physical cues imposed by the environment, such as geometry, rigidity, or hydraulic resistance (HR). Neutrophils preferentially follow paths of least HR in vitro, a phenomenon known as barotaxis. The mechanisms and physiological relevance of barotaxis remain unclear. We show that barotaxis results from the amplification of a small force imbalance by the actomyosin cytoskeleton, resulting in biased directional choices. In immature dendritic cells (DCs), actomyosin is recruited to the cell front to build macropinosomes. These cells are therefore insensitive to HR, as macropinocytosis allows fluid transport across these cells. This may enhance their space exploration capacity in vivo. Conversely, mature DCs down-regulate macropinocytosis and are thus barotactic. Modeling suggests that HR may help guide these cells to lymph nodes where they initiate immune responses. Hence, DCs can either overcome or capitalize on the physical obstacles they encounter, helping their immune-surveillance function.

Large-scale curvature sensing by directional actin flow drives cellular migration mode switching

Cell migration over heterogeneous substrates during wound healing or morphogenetic processes leads to shape changes driven by different organizations of the actin cytoskeleton and by functional changes including lamellipodial protrusions and contractile actin cables. Cells distinguish between cell-sized positive and negative curvatures in their physical environment by forming protrusions at positive ones and actin cables at negative ones; however, the cellular mechanisms remain unclear. Here, we report that concave edges promote polarized actin structures with actin flow directed towards the cell edge, in contrast to well-documented retrograde flow at convex edges. Anterograde flow and contractility induce a tension anisotropy gradient. A polarized actin network is formed, accompanied by a local polymerization-depolymerization gradient, together with leading-edge contractile actin cables in the front. These cables extend onto non-adherent regions while still maintaining contact with the substrate through focal adhesions. The contraction and dynamic reorganization of this actin structure allows forward movements enabling cell migration over non-adherent regions on the substrate. These versatile functional structures may help cells sense and navigate their environment by adapting to external geometric and mechanical cues.

Aurora A depletion reveals centrosome-independent polarization mechanism in Caenorhabditis elegans

How living systems break symmetry in an organized manner is a fundamental question in biology. In wild-type Caenorhabditis elegans zygotes, symmetry breaking during anterior-posterior axis specification is guided by centrosomes, resulting in anterior-directed cortical flows and a single posterior PAR-2 domain. We uncover that C. elegans zygotes depleted of the Aurora A kinase AIR-1 or lacking centrosomes entirely usually establish two posterior PAR-2 domains, one at each pole. We demonstrate that AIR-1 prevents symmetry breaking early in the cell cycle, whereas centrosomal AIR-1 instructs polarity initiation thereafter. Using triangular microfabricated chambers, we establish that bipolarity of air-1(RNAi) embryos occurs effectively in a cell-shape and curvature-dependent manner. Furthermore, we develop an integrated physical description of symmetry breaking, wherein local PAR-2-dependent weakening of the actin cortex, together with mutual inhibition of anterior and posterior PAR proteins, provides a mechanism for spontaneous symmetry breaking without centrosomes.

Mechanical Properties of the Cytoskeleton and Cells

SUMMARYThe cytoskeleton is the major mechanical structure of the cell; it is a complex, dynamic biopolymer network comprising microtubules, actin, and intermediate filaments. Both the individual filaments and the entire network are not simple elastic solids but are instead highly nonlinear structures. Appreciating the mechanics of biopolymer networks is key to understanding the mechanics of cells. Here, we review the mechanical properties of cytoskeletal polymers and discuss the implications for the behavior of cells.

Contractility in an extensile system

Essentially all biology is active and dynamic. Biological entities autonomously sense, compute, and respond using energy-coupled ratchets that can produce force and do work. The cytoskeleton, along with its associated proteins and motors, is a canonical example of biological active matter, which is responsible for cargo transport, cell motility, division, and morphology. Prior work on cytoskeletal active matter systems showed either extensile or contractile dynamics. Here, we demonstrate a cytoskeletal system that can control the direction of the network dynamics to be either extensile, contractile, or static depending on the concentration of filaments or weak, transient crosslinkers through systematic variation of the crosslinker or microtubule concentrations. Based on these new observations and our previously published results, we created a simple one-dimensional model of the interaction of filaments within a bundle. Despite its simplicity, our model recapitulates the observed activities of our experimental system, implying that the dynamics of our finite networks of bundles are driven by the local filament-filament interactions within the bundle. Finally, we show that contractile phases can result in autonomously motile networks that resemble cells. Our results reveal a fundamentally important aspect of cellular self-organization: weak, transient interacting species can tune their interaction strength directly by tuning the local concentration to act like a rheostat. In this case, when the weak, transient proteins crosslink microtubules, they can tune the dynamics of the network to change from extensile to contractile to static. Our experiments and model allow us to gain a deeper understanding of cytoskeletal dynamics and provide an new understanding of the importance of weak, transient interactions to soft and biological systems.

Dissecting the actin cortex density and membrane-cortex distance in living cells by super-resolution microscopy

Nanoscale spacing between the plasma membrane and the underlying cortical actin cytoskeleton profoundly modulates cellular morphology, mechanics, and function. Measuring this distance has been a key challenge in cell biology. Current methods for dissecting the nanoscale spacing either limit themselves to complex survey design using fixed samples or rely on diffraction-limited fluorescence imaging whose spatial resolution is insufficient to quantify distances on the nanoscale. Using dual-color super-resolution STED (stimulated-emission-depletion) microscopy, we here overcome this challenge and accurately measure the density distribution of the cortical actin cytoskeleton and the distance between the actin cortex and the membrane in live Jurkat T-cells. We found an asymmetric cortical actin density distribution with a mean width of 230 (+105/-125) nm. The spatial distances measured between the maximum density peaks of the cortex and the membrane were bi-modally distributed with mean values of 50  ±  15 nm and 120  ±  40 nm, respectively. Taken together with the finite width of the cortex, our results suggest that in some regions the cortical actin is closer than 10 nm to the membrane and a maximum of 20 nm in others.

Immersed Boundary Simulations of Active Fluid Droplets

We present numerical simulations of active fluid droplets immersed in an external fluid in 2-dimensions using an Immersed Boundary method to simulate the fluid droplet interface as a Lagrangian mesh. We present results from two example systems, firstly an active isotropic fluid boundary consisting of particles that can bind and unbind from the interface and generate surface tension gradients through active contractility. Secondly, a droplet filled with an active polar fluid with homeotropic anchoring at the droplet interface. These two systems demonstrate spontaneous symmetry breaking and steady state dynamics resembling cell motility and division and show complex feedback mechanisms with minimal degrees of freedom. The simulations outlined here will be useful for quantifying the wide range of dynamics observable in these active systems and modelling the effects of confinement in a consistent and adaptable way.

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.

Actin kinetics shapes cortical network structure and mechanics

The actin cortex of animal cells is the main determinant of cellular mechanics. The continuous turnover of cortical actin filaments enables cells to quickly respond to stimuli. Recent work has shown that most of the cortical actin is generated by only two actin nucleators, the Arp2/3 complex and the formin Diaph1. However, our understanding of their interplay, their kinetics, and the length distribution of the filaments that they nucleate within living cells is poor. Such knowledge is necessary for a thorough comprehension of cellular processes and cell mechanics from basic polymer physics principles. We determined cortical assembly rates in living cells by using single-molecule fluorescence imaging in combination with stochastic simulations. We find that formin-nucleated filaments are, on average, 10 times longer than Arp2/3-nucleated filaments. Although formin-generated filaments represent less than 10% of all actin filaments, mechanical measurements indicate that they are important determinants of cortical elasticity. Tuning the activity of actin nucleators to alter filament length distribution may thus be a mechanism allowing cells to adjust their macroscopic mechanical properties to their physiological needs.

Theoretical study of actin layers attachment and separation

We use the theory of active gels to study theoretically the merging and separation of two actin dense layers akin to cortical layers of animal cells. The layers bind at a distance equal to twice the thickness of a free layer, thus forming a single dense layer, similar in this sense to a lamellipodium. When that unique layer is stretched apart, it is resilient to break apart up to a critical length larger than twice the thickness of a free layer. We show that this behavior can result from the high contractile properties of the actomyosin gel due to the activity of myosin molecular motors. Furthermore, we establish that the stability of the stretched single layer is highly dependent on the properties of the gel. Indeed, the nematic order of the actin filaments along the polymerizing membranes is a destabilizing factor.

Assembly and positioning of actomyosin rings by contractility and planar cell polarity

The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

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.

Symmetry breaking in reconstituted actin cortices

The actin cortex plays a pivotal role in cell division, in generating and maintaining cell polarity and in motility. In all these contexts, the cortical network has to break symmetry to generate polar cytoskeletal dynamics. Despite extensive research, the mechanisms responsible for regulating cortical dynamics in vivo and inducing symmetry breaking are still unclear. Here we introduce a reconstituted system that self-organizes into dynamic actin cortices at the inner interface of water-in-oil emulsions. This artificial system undergoes spontaneous symmetry breaking, driven by myosin-induced cortical actin flows, which appears remarkably similar to the initial polarization of the embryo in many species. Our in vitro model system recapitulates the rich dynamics of actin cortices in vivo, revealing the basic biophysical and biochemical requirements for cortex formation and symmetry breaking. Moreover, this synthetic system paves the way for further exploration of artificial cells towards the realization of minimal model systems that can move and divide.

DOI:http://dx.doi.org/10.7554/eLife.01433.001

Cells are extremely complex because they have to perform a vast number of processes. However, this also makes it difficult for researchers to figure out how the individual parts of the cell work. There is interest, therefore, in developing simple artificial cells that can accurately mimic how specific parts of a cell behave.

An important process for a cell is called polarization. This is where the contents of the cell arrange themselves in a way that is not symmetrical. Polarization is necessary for many cellular functions, and is particularly important during embryonic development where it helps to form the complex shape of the developing embryo.

The cytoskeleton—a dynamic structure that supports the cell and enables it to move—is crucial for polarization. An important part of the cytoskeleton is the actin cortex. This is a thin active sheet made up of a network of tiny filaments of a protein called actin that assembles at the inner face of the cell membrane. Many aspects of the structure and behavior of the actin cortex are not understood.

Abu Shah and Keren have now developed an artificial cell system using aqueous droplets surrounded by oil that can reproduce the behavior of actin cortices in real cells. An actin cortex forms upon the localization of specific nucleation factors at the inner surface of the droplets.

The artificial cortices are capable of spontaneous symmetry breaking, similar to the initial polarization in embryonic cells during development. This symmetry breaking is driven by molecular motors called myosins and depends on the connectivity of the actin network in the cortex. Experiments on the artificial cells also rule out several other mechanisms that have been proposed to explain symmetry breaking.

The work of Abu Shah and Keren represents a further step towards the goal of creating simple artificial cells that can move and divide.

DOI:http://dx.doi.org/10.7554/eLife.01433.002

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.