Soft Listeria: actin-based propulsion of liquid drops

Synthetic control of actin polymerization and symmetry breaking in active protocells

Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.

Emergence of inertia in the low-Reynolds regime of self-diffusiophoretic motion

For isotropic swimming particles driven by self-diffusiophoresis at zero Reynolds number (where particle velocity responds instantaneously to applied force), the diffusive timescale of emitted solute can produce an emergent quasi-inertial behavior. These particles can orbit in a central potential and reorient under second-order dynamics, not the first-order dynamics of classical zero-Reynolds motion. They are described by a simple effective model that embeds their history-dependent behavior as an effective inertia, this being the most primitive expression of memory. The system can be parameterized with dynamic quantities such as particle size and swimming speed, without detailed knowledge of the diffusiophoretic mechanism.

Reconstitution of actin-based cellular processes: Why encapsulation changes the rules

While in vitro reconstitution of cellular processes is progressing rapidly, the encapsulation of biomimetic systems to reproduce the cellular environment is a major challenge. Here we review the difficulties, using reconstitution of processes dependent on actin polymerization as an example. Some of the problems are purely technical, due to the need for engineering strategies to encapsulate concentrated solutions in micrometer-sized compartments. However, other significant issues arise from the reduction of experimental volumes, which alters the chemical evolution of these non-equilibrium systems. Important parameters to consider for successful reconstitutions are the amount of each component, their consumption and renewal rates to guarantee their continuous availability.

Spatial Control of Arp2/3-Induced Actin Polymerization on Phase-Separated Giant Unilamellar Vesicles

Deciphering the physical mechanisms underlying cell shape changes, while avoiding the cellular interior's complexity, involves the development of controlled basic biomimetic systems that imitate cell functions. In particular, the reconstruction of cytoskeletal dynamics on cell-sized giant unilamellar vesicles (GUVs) has allowed for the reconstituting of some cell-like processes in vitro. In fact, such a bottom-up strategy could be the basis for forming protocells able to reorganize or even move autonomously. However, reconstituting the subtle and controlled dynamics of the cytoskeleton-membrane interface in vitro remains an experimental challenge. Taking advantage of the lipid-induced segregation of an actin polymerization activator, we present a system that targets actin polymerization in specific domains of phase-separated GUVs. We observe actin networks localized on Lo, Ld, or on both types of domains and the actin-induced deformation or reorganization of these domains. These results suggest that the system we have developed here could pave the way for future experiments further detailing the interplay between actin dynamics and membrane heterogeneities.

Phenotyping polarization dynamics of immune cells using a lipid droplet-cell pairing microfluidic platform

The immune synapse is the tight contact zone between a lymphocyte and a cell presenting its cognate antigen. This structure serves as a signaling platform and entails a polarization of intracellular components necessary to the immunological function of the cell. While the surface properties of the presenting cell are known to control the formation of the synapse, their impact on polarization has not yet been studied. Using functional lipid droplets as tunable artificial presenting cells combined with a microfluidic pairing device, we simultaneously observe synchronized synapses and dynamically quantify polarization patterns of individual B cells. By assessing how ligand concentration, surface fluidity, and substrate rigidity impact lysosome polarization, we show that its onset and kinetics depend on the local antigen concentration at the synapse and on substrate rigidity. Our experimental system enables a fine phenotyping of monoclonal cell populations based on their synaptic readout.

Studying actin-induced cell shape changes using Giant Unilamellar Vesicles and reconstituted actin networks

Cell shape changes that are fuelled by the dynamics of the actomyosin cytoskeleton control cellular processes such as motility and division. However, the mechanisms of interplay between cell membranes and actomyosin are complicated to decipher in the complex environment of the cytoplasm. Using biomimetic systems offers an alternative approach to studying cell shape changes in assays with controlled biochemical composition. Biomimetic systems allow quantitative experiments that can help to build physical models describing the processes of cell shape changes. This article reviews works in which actin networks are reconstructed inside or outside cell-sized Giant Unilamellar Vesicles (GUVs), which are models of cell membranes. We show how various actin networks affect the shape and mechanics of GUVs and how some cell shape changes can be reproduced in vitro using these minimal systems.

Optimal transport and control of active drops

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Generation, Transmission, and Regulation of Mechanical Forces in Embryonic Morphogenesis

Embryonic morphogenesis is a biological process which depicts shape forming of tissues and organs during development. Unveiling the roles of mechanical forces generated, transmitted, and regulated in cells and tissues through these processes is key to understanding the biophysical mechanisms governing morphogenesis. To this end, it is imperative to measure, simulate, and predict the regulation and control of these mechanical forces during morphogenesis. This article aims to provide a comprehensive review of the recent advances on mechanical properties of cells and tissues, generation of mechanical forces in cells and tissues, the transmission processes of these generated forces during cells and tissues, the tools and methods used to measure and predict these mechanical forces in vivo, in vitro, or in silico, and to better understand the corresponding regulation and control of generated forces. Understanding the biomechanics and mechanobiology of morphogenesis will not only shed light on the fundamental physical mechanisms underlying these concerted biological processes during normal development, but also uncover new information that will benefit biomedical research in preventing and treating congenital defects or tissue engineering and regeneration.

Molecular mechanisms of force production in clathrin-mediated endocytosis

During clathrin-mediated endocytosis (CME), a flat patch of membrane is invaginated and pinched off to release a vesicle into the cytoplasm. In yeast CME, over 60 proteins-including a dynamic actin meshwork-self-assemble to deform the plasma membrane. Several models have been proposed for how actin and other molecules produce the forces necessary to overcome the mechanical barriers of membrane tension and turgor pressure, but the precise mechanisms and a full picture of their interplay are still not clear. In this review, we discuss the evidence for these force production models from a quantitative perspective and propose future directions for experimental and theoretical work that could clarify their various contributions.

The 2018 biomembrane curvature and remodeling roadmap

The importance of curvature as a structural feature of biological membranes has been recognized for many years and has fascinated scientists from a wide range of different backgrounds. On the one hand, changes in membrane morphology are involved in a plethora of phenomena involving the plasma membrane of eukaryotic cells, including endo- and exocytosis, phagocytosis and filopodia formation. On the other hand, a multitude of intracellular processes at the level of organelles rely on generation, modulation, and maintenance of membrane curvature to maintain the organelle shape and functionality. The contribution of biophysicists and biologists is essential for shedding light on the mechanistic understanding and quantification of these processes. Given the vast complexity of phenomena and mechanisms involved in the coupling between membrane shape and function, it is not always clear in what direction to advance to eventually arrive at an exhaustive understanding of this important research area. The 2018 Biomembrane Curvature and Remodeling Roadmap of Journal of Physics D: Applied Physics addresses this need for clarity and is intended to provide guidance both for students who have just entered the field as well as established scientists who would like to improve their orientation within this fascinating area.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Cell-like pressure sensors reveal increase of mechanical stress towards the core of multicellular spheroids under compression

The surrounding microenvironment limits tumour expansion, imposing a compressive stress on the tumour, but little is known how pressure propagates inside the tumour. Here we present non-destructive cell-like microsensors to locally quantify mechanical stress distribution in three-dimensional tissue. Our sensors are polyacrylamide microbeads of well-defined elasticity, size and surface coating to enable internalization within the cellular environment. By isotropically compressing multicellular spheroids (MCS), which are spherical aggregates of cells mimicking a tumour, we show that the pressure is transmitted in a non-trivial manner inside the MCS, with a pressure rise towards the core. This observed pressure profile is explained by the anisotropic arrangement of cells and our results suggest that such anisotropy alone is sufficient to explain the pressure rise inside MCS composed of a single cell type. Furthermore, such pressure distribution suggests a direct link between increased mechanical stress and previously observed lack of proliferation within the spheroids core.

A variational approach to the growth dynamics of pre-stressed actin filament networks

In order to model the growth dynamics of elastic bodies with residual stresses a thermodynamically consistent approach is needed such that the cross-coupling between growth and mechanics can be correctly described. In the present work we apply a variational principle to the formulation of the interfacial growth dynamics of dendritic actin filament networks growing from biomimetic beads, an experimentally well studied system, where the buildup of residual stresses governs the network growth. We first introduce the material model for the network via a strain energy density for an isotropic weakly nonlinear elastic material and then derive consistently from this model the dynamic equations for the interfaces, i.e. for a polymerizing internal interface in contact with the bead and a depolymerizing external interface directed towards the solvent. We show that (i) this approach automatically preserves thermodynamic symmetry-properties, which is not the case for the often cited 'rubber-band-model' (Sekimoto et al 2004 Eur. Phys. J. E 13 247-59, Plastino et al 2004 Eur. Biophys. J. 33 310-20) and (ii) leads to a robust morphological instability of the treadmilling network interfaces. The nature of the instability depends on the interplay of the two dynamic interfaces. Depending on the biochemical conditions the network envelope evolves into a comet-like shape (i.e. the actin envelope thins out at one side and thickens on the opposite side of the bead) via a varicose instability or it breaks the symmetry via higher order zigzag modes. We conclude that morphological instabilities due to mechano-chemical coupling mechanisms and the presences of mechancial pre-stresses can play a major role in locally organizing the cytoskeleton of living cells.

Controlled deformation of vesicles by flexible structured media

Liquid crystalline (LC) materials, such as actin or tubulin networks, are known to be capable of deforming the shape of cells. Here, elements of that behavior are reproduced in a synthetic system, namely, a giant vesicle suspended in a LC, which we view as a first step toward the preparation of active, anisotropic hybrid systems that mimic some of the functionality encountered in biological systems. To that end, we rely on a coupled particle-continuum representation of deformable networks in a nematic LC represented at the level of a Landau-de Gennes free energy functional. Our results indicate that, depending on its elastic properties, the LC is indeed able to deform the vesicle until it reaches an equilibrium, anisotropic shape. The magnitude of the deformation is determined by a balance of elastic and surface forces. For perpendicular anchoring at the vesicle, a Saturn ring defect forms along the equatorial plane, and the vesicle adopts a pancake-like, oblate shape. For degenerate planar anchoring at the vesicle, two boojum defects are formed at the poles of the vesicle, which adopts an elongated, spheroidal shape. During the deformation, the volume of the topological defects in the LC shrinks considerably as the curvature of the vesicle increases. These predictions are confirmed by our experimental observations of spindle-like shapes in experiments with giant unilamellar vesicles with planar anchoring. We find that the tension of the vesicle suppresses vesicle deformation, whereas anchoring strength and large elastic constants promote shape anisotropy.

A toolbox to explore the mechanics of living embryonic tissues

The sculpting of embryonic tissues and organs into their functional morphologies involves the spatial and temporal regulation of mechanics at cell and tissue scales. Decades of in vitro work, complemented by some in vivo studies, have shown the relevance of mechanical cues in the control of cell behaviors that are central to developmental processes, but the lack of methodologies enabling precise, quantitative measurements of mechanical cues in vivo have hindered our understanding of the role of mechanics in embryonic development. Several methodologies are starting to enable quantitative studies of mechanics in vivo and in situ, opening new avenues to explore how mechanics contributes to shaping embryonic tissues and how it affects cell behavior within developing embryos. Here we review the present methodologies to study the role of mechanics in living embryonic tissues, considering their strengths and drawbacks as well as the conditions in which they are most suitable.

Toward the reconstitution of synthetic cell motility

Cellular motility is a fundamental process essential for embryonic development, wound healing, immune responses, and tissues development. Cells are mostly moving by crawling on external, or inside, substrates which can differ in their surface composition, geometry, and dimensionality. Cells can adopt different migration phenotypes, e.g., bleb-based and protrusion-based, depending on myosin contractility, surface adhesion, and cell confinement. In the few past decades, research on cell motility has focused on uncovering the major molecular players and their order of events. Despite major progresses, our ability to infer on the collective behavior from the molecular properties remains a major challenge, especially because cell migration integrates numerous chemical and mechanical processes that are coupled via feedbacks that span over large range of time and length scales. For this reason, reconstituted model systems were developed. These systems allow for full control of the molecular constituents and various system parameters, thereby providing insight into their individual roles and functions. In this review we describe the various reconstituted model systems that were developed in the past decades. Because of the multiple steps involved in cell motility and the complexity of the overall process, most of the model systems focus on very specific aspects of the individual steps of cell motility. Here we describe the main advancement in cell motility reconstitution and discuss the main challenges toward the realization of a synthetic motile cell.

Perinuclear Arp2/3-driven actin polymerization enables nuclear deformation to facilitate cell migration through complex environments

Cell migration has two opposite faces: although necessary for physiological processes such as immune responses, it can also have detrimental effects by enabling metastatic cells to invade new organs. In vivo, migration occurs in complex environments and often requires a high cellular deformability, a property limited by the cell nucleus. Here we show that dendritic cells, the sentinels of the immune system, possess a mechanism to pass through micrometric constrictions. This mechanism is based on a rapid Arp2/3-dependent actin nucleation around the nucleus that disrupts the nuclear lamina, the main structure limiting nuclear deformability. The cells' requirement for Arp2/3 to pass through constrictions can be relieved when nuclear stiffness is decreased by suppressing lamin A/C expression. We propose a new role for Arp2/3 in three-dimensional cell migration, allowing fast-moving cells such as leukocytes to rapidly and efficiently migrate through narrow gaps, a process probably important for their function.

Common Themes in Cytoskeletal Remodeling by Intracellular Bacterial Effectors

Bacterial pathogens interact with various types of tissues to promote infection. Because it controls the formation of membrane extensions, adhesive processes, or the junction integrity, the actin cytoskeleton is a key target of pathogens during infection. We will highlight common and specific functions of the actin cytoskeleton during bacterial infections, by first reviewing the mechanisms of intracellular motility of invasive Shigella, Listeria, and Rickettsia. Through the models of EPEC/EHEC, Shigella, Salmonella, and Chlamydia spp., we will illustrate various strategies of diversion of actin cytoskeletal processes used by these bacteria to colonize or breach epithelial/endothelial barriers.

Reconstituting the actin cytoskeleton at or near surfaces in vitro

Actin filament dynamics have been studied for decades in pure protein solutions or in cell extracts, but a breakthrough in the field occurred at the turn of the century when it became possible to reconstitute networks of actin filaments, growing in a controlled but physiological manner on surfaces, mimicking the actin assembly that occurs at the plasma membrane during cell protrusion and cell shape changes. The story begins with the bacteria Listeria monocytogenes, the study of which led to the reconstitution of cellular actin polymerization on a variety of supports including plastic beads. These studies made possible the development of liposome-type substrates for filament assembly and micropatterning of actin polymerization nucleation. Based on the accumulated expertise of the last 15 years, many exciting approaches are being developed, including the addition of myosin to biomimetic actin networks to study the interplay between actin structure and contractility. The field is now poised to make artificial cells with a physiological and dynamic actin cytoskeleton, and subsequently to put these cells together to make in vitro tissues. This article is part of a Special Issue entitled: Mechanobiology.

Generation of biocompatible droplets for in vivo and in vitro measurement of cell-generated mechanical stresses

Here we describe a detailed protocol to produce biocompatible droplets that permit the measurement of mechanical stresses at cell and tissue scales. The droplets can be used as force transducers in vivo, ex vivo, and in vitro, to measure mechanical stresses in situ, in three dimensions and time. Versatile and modular droplet coatings using biotinylated molecules, such as ligands for specific adhesion receptors, enable the targeting of specific tissues or cells. Droplet sizes can be varied to measure forces at different scales (tissue and cell scales) and the range of measurable mechanical stresses ranges within approximately 0.3-100 kPa. The protocol described in this chapter is divided in three sections. First, we describe the generation and stabilization of biocompatible droplets. Next, we explain the steps necessary to functionalize the droplet surface. Finally, we describe how to characterize the mechanical properties of the droplets, so that they can be used as calibrated mechanical probes. The procedure to generate, stabilize, and functionalize the droplets is straightforward and can be completed in about 3h with basic laboratory resources. The calibration of the droplet's mechanical properties to perform quantitative stress measurements is also straightforward, but requires the proper equipment to measure interfacial tension (such as a tensiometer). Calibrated droplets can be used to quantify cell-generated mechanical stresses by analyzing the tridimensional shape of the droplet.

Force generation by endocytic actin patches in budding yeast

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel. The deformation of the gel is treated using a finite-element approach. We explore the effects and interplay of three different types of force driving invagination: 1), forces perpendicular to the membrane, generated by differences between actin polymerization rates at the edge of the patch and those at the center; 2), the inherent curvature of the coat-protein layer; and 3), forces parallel to the membrane that buckle the coat protein layer, generated by an actomyosin contractile ring. We find that with optimistic estimates for the stall stress of actin gel growth and the shear modulus of the actin gel, actin polymerization can generate almost enough force to overcome the turgor pressure. In combination with the other mechanisms, actin polymerization can the force over the critical value.

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechanochemical coupling mechanisms that guide the growth process are poorly understood, and a general continuum description combining growth and mechanics is lacking. We develop a theory that bridges the gap between mesoscale and continuum limit and propose a general framework providing the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

Collision dynamics of traveling bands in systems of deformable self-propelled particles

We study the soliton-like character of traveling bands in systems of interacting deformable self-propelled particles in two dimensions. The collision dynamics of the model in which migration velocity increases with increasing local density is investigated numerically by changing the relaxation rate of deformations. The bands are unstable upon head-on collisions for larger relaxation rates. This clearly indicates that deformability plays a crucial role of the soliton-like behavior.

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

Actin dynamics, architecture, and mechanics in cell motility

Tight coupling between biochemical and mechanical properties of the actin cytoskeleton drives a large range of cellular processes including polarity establishment, morphogenesis, and motility. This is possible because actin filaments are semi-flexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" (in laymen's terms, shock absorbers or fluidizers) able to exert or resist against force in a cellular environment. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. In this review we describe the feedback loop between biochemical and mechanical properties of actin organization at the molecular level in vitro, then we integrate this knowledge into our current understanding of cellular actin organization and its physiological roles.

Quantifying cell-generated mechanical forces within living embryonic tissues

Cell-generated mechanical forces play a critical role during tissue morphogenesis and organ formation in the embryo. However, little is known about how these forces shape embryonic organs, mainly because it has not been possible to measure cellular forces within developing three-dimensional (3D) tissues in vivo. Here we present a method to quantify cell-generated mechanical stresses that are exerted locally within living embryonic tissues using fluorescent, cell-sized, oil microdroplets with defined mechanical properties and coated with surface integrin or cadherin receptor ligands. After introducing a droplet between cells in a tissue, local stresses are determined from the droplet shape deformations, which are obtained via fluorescence microscopy and computerized image analysis. Using this method, we quantify the anisotropic stresses generated by mammary epithelial cells cultured within 3D aggregates and confirm that these stresses (3.4 nN/µm²) are dependent on myosin II activity and more than two-fold larger than the stresses generated by cells of embryonic tooth mesenchyme when analyzed within similar cultured aggregates or in developing whole mouse mandibles.

Control of actin-based motility through localized actin binding

A wide variety of cell biological and biomimetic systems use actin polymerization to drive motility. It has been suggested that an object such as a bacterium can propel itself by self-assembling a high concentration of actin behind it, if it is repelled by actin. However, it is also known that it is essential for the moving object to bind actin. Therefore, a key question is how the actin tail can propel an object when it both binds and repels the object. We present a physically consistent Brownian dynamics model for actin-based motility that includes the minimal components of the dendritic nucleation model and allows for both attractive and repulsive interactions between actin and a moveable disc. We find that the concentration gradient of filamentous actin generated by polymerization is sufficient to propel the object, even with moderately strong binding interactions. Additionally, actin binding can act as a biophysical cap, and may directly control motility through modulation of network growth. Overall, this mechanism is robust in that it can drive motility against a load up to a stall pressure that depends on the Young's modulus of the actin network and can explain several aspects of actin-based motility.

Actin polymerization or myosin contraction: two ways to build up cortical tension for symmetry breaking

Cells use complex biochemical pathways to drive shape changes for polarization and movement. One of these pathways is the self-assembly of actin filaments and myosin motors that together produce the forces and tensions that drive cell shape changes. Whereas the role of actin and myosin motors in cell polarization is clear, the exact mechanism of how the cortex, a thin shell of actin that is underneath the plasma membrane, can drive cell shape changes is still an open question. Here, we address this issue using biomimetic systems: the actin cortex is reconstituted on liposome membranes, in an 'outside geometry'. The actin shell is either grown from an activator of actin polymerization immobilized at the membrane by a biotin-streptavidin link, or built by simple adsorption of biotinylated actin filaments to the membrane, in the presence or absence of myosin motors. We show that tension in the actin network can be induced either by active actin polymerization on the membrane via the Arp2/3 complex or by myosin II filament pulling activity. Symmetry breaking and spontaneous polarization occur above a critical tension that opens up a crack in the actin shell. We show that this critical tension is reached by growing branched networks, nucleated by the Arp2/3 complex, in a concentration window of capping protein that limits actin filament growth and by a sufficient number of motors that pull on actin filaments. Our study provides the groundwork to understanding the physical mechanisms at work during polarization prior to cell shape modifications.

Oscillatory motions of an active deformable particle

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of n- and 2n-mode deformations for n=1, and those for n=2. We show that an oscillatory bifurcation occurs for n=2, which corresponds mathematically to the bifurcation for n=1 where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Spinning motion of a deformable self-propelled particle in two dimensions

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

Mesoscopic model of actin-based propulsion

Two theoretical models dominate current understanding of actin-based propulsion: microscopic polymerization ratchet model predicts that growing and writhing actin filaments generate forces and movements, while macroscopic elastic propulsion model suggests that deformation and stress of growing actin gel are responsible for the propulsion. We examine both experimentally and computationally the 2D movement of ellipsoidal beads propelled by actin tails and show that neither of the two models can explain the observed bistability of the orientation of the beads. To explain the data, we develop a 2D hybrid mesoscopic model by reconciling these two models such that individual actin filaments undergoing nucleation, elongation, attachment, detachment and capping are embedded into the boundary of a node-spring viscoelastic network representing the macroscopic actin gel. Stochastic simulations of this ‘in silico’ actin network show that the combined effects of the macroscopic elastic deformation and microscopic ratchets can explain the observed bistable orientation of the actin-propelled ellipsoidal beads. To test the theory further, we analyze observed distribution of the curvatures of the trajectories and show that the hybrid model's predictions fit the data. Finally, we demonstrate that the model can explain both concave-up and concave-down force-velocity relations for growing actin networks depending on the characteristic time scale and network recoil. To summarize, we propose that both microscopic polymerization ratchets and macroscopic stresses of the deformable actin network are responsible for the force and movement generation.

There are two major ideas about how actin networks generate force against an obstacle: one is that the force comes directly from the elongation and bending of individual actin filaments against the surface of the obstacle; the other is that a growing actin gel can build up stress around the obstacle to squeeze it forward. Neither of the two models can explain why actin-propelled ellipsoidal beads move with equal bias toward long- and short-axes. We propose a hybrid model by combining those two ideas so that individual actin filaments are embedded into the boundary of a deformable actin gel. Simulations of this model show that the combined effects of pushing from individual filaments and squeezing from the actin network explain the observed bi-orientation of ellipsoidal beads as well as the curvature of trajectories of spherical beads and the force-velocity relation of actin networks.

Plasma membrane reshaping during endocytosis is revealed by time-resolved electron tomography

Endocytosis, like many dynamic cellular processes, requires precise temporal and spatial orchestration of complex protein machinery to mediate membrane budding. To understand how this machinery works, we directly correlated fluorescence microscopy of key protein pairs with electron tomography. We systematically located 211 endocytic intermediates, assigned each to a specific time window in endocytosis, and reconstructed their ultrastructure in 3D. The resulting virtual ultrastructural movie defines the protein-mediated membrane shape changes during endocytosis in budding yeast. It reveals that clathrin is recruited to flat membranes and does not initiate curvature. Instead, membrane invagination begins upon actin network assembly followed by amphiphysin binding to parallel membrane segments, which promotes elongation of the invagination into a tubule. Scission occurs on average 9 s after initial bending when invaginations are ∼100 nm deep, releasing nonspherical vesicles with 6,400 nm2 mean surface area. Direct correlation of protein dynamics with ultrastructure provides a quantitative 4D resource.

Confinement induces actin flow in a meiotic cytoplasm

In vivo, F-actin flows are observed at different cell life stages and participate in various developmental processes during asymmetric divisions in vertebrate oocytes, cell migration, or wound healing. Here, we show that confinement has a dramatic effect on F-actin spatiotemporal organization. We reconstitute in vitro the spontaneous generation of F-actin flow using Xenopus meiotic extracts artificially confined within a geometry mimicking the cell boundary. Perturbations of actin polymerization kinetics or F-actin nucleation sites strongly modify the network flow dynamics. A combination of quantitative image analysis and biochemical perturbations shows that both spatial localization of F-actin nucleators and actin turnover play a decisive role in generating flow. Interestingly, our in vitro assay recapitulates several symmetry-breaking processes observed in oocytes and early embryonic cells.

Actin network growth under load

Many processes in eukaryotic cells, including the crawling motion of the whole cell, rely on the growth of branched actin networks from surfaces. In addition to their well-known role in generating propulsive forces, actin networks can also sustain substantial pulling loads thanks to their persistent attachment to the surface from which they grow. The simultaneous network elongation and surface attachment inevitably generate a force that opposes network growth. Here, we study the local dynamics of a growing actin network, accounting for simultaneous network elongation and surface attachment, and show that there exist several dynamical regimes that depend on both network elasticity and the kinetic parameters of actin polymerization. We characterize this in terms of a phase diagram and provide a connection between mesoscopic theories and the microscopic dynamics of an actin network at a surface. Our framework predicts the onset of instabilities that lead to the local detachment of the network and translate to oscillatory behavior and waves, as observed in many cellular phenomena and in vitro systems involving actin network growth, such as the saltatory dynamics of actin-propelled oil drops.

Choosing orientation: influence of cargo geometry and ActA polarization on actin comet tails

Networks of polymerizing actin filaments can propel intracellular pathogens and drive movement of artificial particles in reconstituted systems. While biochemical mechanisms activating actin network assembly have been well characterized, it remains unclear how particle geometry and large-scale force balance affect emergent properties of movement. We reconstituted actin-based motility using ellipsoidal beads resembling the geometry of Listeria monocytogenes. Beads coated uniformly with the L. monocytogenes ActA protein migrated equally well in either of two distinct orientations, with their long axes parallel or perpendicular to the direction of motion, while intermediate orientations were unstable. When beads were coated with a fluid lipid bilayer rendering ActA laterally mobile, beads predominantly migrated with their long axes parallel to the direction of motion, mimicking the orientation of motile L. monocytogenes. Generating an accurate biophysical model to account for our observations required the combination of elastic-propulsion and tethered-ratchet actin-polymerization theories. Our results indicate that the characteristic orientation of L. monocytogenes must be due to polarized ActA rather than intrinsic actin network forces. Furthermore, viscoelastic stresses, forces, and torques produced by individual actin filaments and lateral movement of molecular complexes must all be incorporated to correctly predict large-scale behavior in the actin-based movement of nonspherical particles.

Modeling morphodynamic phenotypes and dynamic regimes of cell motion

Many cellular processes and signaling pathways converge onto cell morphology and cell motion, which share important components. The mechanisms used for propulsion could also be responsible for shape changes, if they are capable of generating the rich observed variety of dynamic regimes. Additionally, the analysis of cell shape changes in space and time promises insight into the state of the cytoskeleton and signaling pathways controlling it. While this has been obvious for some time by now, little effort has been made to systematically and quantitatively explore this source of information. First pioneering experimental work revealed morphodynamic phenotypes which can be associated with dynamic regimes like oscillations and excitability. Here, we review the current state of modeling of morphodynamic phenotypes, the experimental results and discuss the ideas on the mechanisms driving shape changes which are suggested by modeling.

BIOMIMETIC SYSTEMS SHED LIGHT ON ACTIN-BASED MOTILITY DOWN TO THE MOLECULAR SCALE

Cell motility, one of the modular activities of living cells, elicits the response of the cell to extra-cellular signals, to move directionally, feed, divide or transport materials. The combined actions of molecular motors and re-modeling of the cytoskeleton generate forces and movement. Here we describe mechanistic approaches of force and movement produced by site-directed assembly of actin filaments. The insight derived from a biochemical analysis of the protein machineries involved in "actin-based motile processes" like cell protrusions, invaginations, organelle propulsion, is used to build reconstituted assays that mimic cellular processes, using several protein machineries known to initiate filament assembly by different mechanisms. Reconstitution of complex self-organized systems presents a broad variety of interests. Reconstituting actin-based movement of a functionalized particle from a minimum number of pure proteins, first used to prove the general thermodynamic principles at work in motility, then was the basis for fully controlled physical measurements of forces produced by polymerization of actin against an obstacle and of the mechanical properties of the resulting polymer arrays. In addition, measurements at the mesoscopic scale (trajectories, velocity, polymer mechanics, fluorescence of specifically labeled components of the actin array, use of mutated proteins) can provide further insight into the molecular mechanisms underlying motility.

Deformable self-propelled domain in an excitable reaction-diffusion system in three dimensions

We derive a set of equations of motion for an isolated domain in an excitable reaction-diffusion system in three dimensions. In the singular limit where the interface is infinitesimally thin, the motion of the center of mass coupled with deformation is investigated near the drift bifurcation where a motionless domain becomes unstable and undergoes migration. This is an extension of our previous theory in two dimensions. We show that there are three basic motions of a domain, straight motion, rotating motion, and helical motion. The last one is a characteristic of three dimensions. The phase diagram of these three solutions is given in the parameter space of the original reaction-diffusion equations.

A model actin comet tail disassembling by severing

We use a numerical simulation to model an actin comet tail as it grows from the surface of a small object (a bead) and disassembles by severing. We explore the dependence of macroscopic properties such as the local tail radius and tail length on several controllable properties, namely the bead diameter, the bead velocity, the severing rate per unit length, and the actin gel mesh size. The model predicts an F-actin density with an initial exponential decay followed by an abrupt decay at the edge of the tail, and predicts that the comet tail diameter is constant along the length of the tail. The simulation results are used to fit a formula relating the comet tail length to the control parameters, and it is proposed that this formula offers a means to extract quantitative information on the actin gel mesh size and severing kinetics from simple macroscopic measurements.

Towards high throughput production of artificial egg oocytes using microfluidics

The production of micron-size droplets using microfluidic tools offers new opportunities to carry out biological assays in a controlled environment. We apply these strategies by using a flow-focusing microfluidic device to encapsulate Xenopus egg extracts, a biological system recapitulating key events of eukaryotic cell functions in vitro. We present a method to generate monodisperse egg extract-in-oil droplets and use high-speed imaging to characterize the droplet pinch-off dynamics leading to the production of trains of droplets. We use fluorescence microscopy to show that our method does not affect the biological activity of the encapsulated egg extract by observing the self-organization of microtubules and actin filaments, two main biopolymers of the cell cytoskeleton, encapsulated in the produced droplets. We anticipate that this assay might be useful for quantitative studies of biological systems in a confined environment as well as high throughput screenings for drug discovery.

Force generation of curved actin gels characterized by combined AFM-epifluorescence measurements

Polymerization of actin into branched filaments is the driving force behind active migration of eukaryotic cells and motility of intracellular organelles. The site-directed assembly of a polarized branched array forms an expanding gel that generates the force that pushes the membrane. Here, we use atomic force microscopy to understand the relation between actin polymerization and the produced force. Functionalized spherical colloidal probes of varying size and curvature are attached to the atomic force microscopy cantilever and initiate the formation of a polarized actin gel in a solution mimicking the in vivo context. The gel growth is recorded by epifluorescence microscopy both against the cantilever and in the perpendicular (lateral) nonconstrained direction. In this configuration, the gel growth stops simultaneously in both directions at the stall force, which corresponds to a pressure of 0.15 nN/microm(2). The results show that the growth of the gel is limited laterally, in the absence of external force, by internal mechanical stresses resulting from a combination of the curved geometry and the molecular mechanism of site-directed assembly of a cohesive branched filament array.

Autonomous motion of vesicle via ion exchange

The autonomous motion of vesicle is observed in a simple chemical system. A vesicle composed of didodecyldimethylammonium bromide DDAB breaks down by ion exchange from Br(-) to I(-). When an electrolyte is supplied to vesicles, some of them begin to move after an induction period. They continue to move, leaving behind the reaction products on the trail. The ion exchange decreases the vesicle size, and smaller vesicles remain after the motion. We examine the characteristics of this motion. The surface tension of the DDAB-containing aqueous phase depends on the KI concentration. Considering this result carefully, we conclude that vesicles can move when the ion exchange from Br(-) to I(-) proceeds irreversibly. Then, inhomogeneity in the vesicle membrane develops because of the coagulating nature of the product, didodecyldimethylammonium iodide (DDAI), which is sparingly soluble in water. Inhomogeneous properties of vesicle membranes are then generated, which induce surface transport of the reaction product and flow in the water pool. As a result, a couple of convection rolls appear in the water pool of the vesicle. The convection rolls drive vesicle motion. A simple model for the semiquantitative description is proposed.

Force-velocity relation for actin-polymerization-driven motility from Brownian dynamics simulations

We report numerical simulation results for the force-velocity relation for actin-polymerization-driven motility. We use Brownian dynamics to solve a physically consistent formulation of the dendritic nucleation model with semiflexible filaments that self-assemble and push a disk. We find that at small loads, the disk speed is independent of load, whereas at high loads, the speed decreases and vanishes at a characteristic stall pressure. Our results demonstrate that at small loads, the velocity is controlled by the reaction rates, whereas at high loads the stall pressure is determined by the mechanical properties of the branched actin network. The behavior is consistent with experiments and with our recently proposed self-diffusiophoretic mechanism for actin-polymerization-driven motility. New in vitro experiments to measure the force-velocity relation are proposed.