In silico reconstitution of actin-based symmetry breaking and motility

Myosin-I synergizes with Arp2/3 complex to enhance the pushing forces of branched actin networks

Class I myosins (myosin-Is) colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by the Arp2/3 complex on the surface of beads coated with myosin-I and nucleation-promoting factor. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Myosin-I triggered symmetry breaking and comet tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations, suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

Reconstitution of Arp2/3-Nucleated Actin Assembly with CP, V-1 and CARMIL

Actin polymerization is often associated with membrane proteins containing capping-protein-interacting (CPI) motifs, such as CARMIL, CD2AP, and WASHCAP/Fam21. CPI motifs bind directly to actin capping protein (CP), and this interaction weakens the binding of CP to barbed ends of actin filaments, lessening the ability of CP to functionally cap those ends. The protein V-1 / myotrophin binds to the F-actin binding site on CP and sterically blocks CP from binding barbed ends. CPI-motif proteins also weaken the binding between V-1 and CP, which decreases the inhibitory effects of V-1, thereby freeing CP to cap barbed ends. Here, we address the question of whether CPI-motif proteins on a surface analogous to a membrane lead to net activation or inhibition of actin assembly nucleated by Arp2/3 complex. Using reconstitution with purified components, we discovered that CARMIL at the surface promotes and enhances actin assembly, countering the inhibitory effects of V-1 and thus activating CP. The reconstitution involves the presence of an Arp2/3 activator on the surface, along with Arp2/3 complex, V-1, CP, profilin and actin monomers in solution, recreating key features of cell physiology.

Myosin-I Synergizes with Arp2/3 Complex to Enhance Pushing Forces of Branched Actin Networks

Myosin-Is colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by Arp2/3 complex on the surface of beads coated with myosin-I and the WCA domain of N-WASP. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Remarkably, myosin-I triggered symmetry breaking and comet-tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

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.

Elastic wrinkling of keratocyte lamellipodia driven by myosin-induced contractile stress

During actin-based cell migration, the actin cytoskeleton in the lamellipodium both generates and responds to force, which has functional consequences for the ability of the cell to extend protrusions. However, the material properties of the lamellipodial actin network and its response to stress on the timescale of motility are incompletely understood. Here, we describe a dynamic wrinkling phenotype in the lamellipodium of fish keratocytes, in which the actin sheet buckles upward away from the ventral membrane of the cell, forming a periodic pattern of wrinkles perpendicular to the cell's leading edge. Cells maintain an approximately constant wrinkle wavelength over time despite new wrinkle formation and the lateral movement of wrinkles in the cell frame of reference, suggesting that cells have a preferred or characteristic wrinkle wavelength. Generation of wrinkles is dependent upon myosin contractility, and their wavelength scales directly with the density of the actin network and inversely with cell adhesion. These results are consistent with a simple physical model for wrinkling in an elastic sheet under compression and suggest that the lamellipodial cytoskeleton behaves as an elastic material on the timescale of cell migration despite rapid actin turnover.

Evolutionarily diverse LIM domain-containing proteins bind stressed actin filaments through a conserved mechanism

The actin cytoskeleton assembles into diverse load-bearing networks, including stress fibers (SFs), muscle sarcomeres, and the cytokinetic ring to both generate and sense mechanical forces. The LIM (Lin11, Isl- 1, and Mec-3) domain family is functionally diverse, but most members can associate with the actin cytoskeleton with apparent force sensitivity. Zyxin rapidly localizes via its LIM domains to failing SFs in cells, known as strain sites, to initiate SF repair and maintain mechanical homeostasis. The mechanism by which these LIM domains associate with stress fiber strain sites (SFSS) is not known. Additionally, it is unknown how widespread strain sensing is within the LIM protein family. We identify that the LIM domain-containing region of 18 proteins from the Zyxin, Paxillin, Tes, and Enigma proteins accumulate to SFSS. Moreover, the LIM domain region from the fission yeast protein paxillin like 1 (Pxl1) also localizes to SFSS in mammalian cells, suggesting that the strain sensing mechanism is ancient and highly conserved. We then used sequence and domain analysis to demonstrate that tandem LIM domains contribute additively, for SFSS localization. Employing in vitro reconstitution, we show that the LIM domain-containing region from mammalian zyxin and fission yeast Pxl1 binds to mechanically stressed F-actin networks but does not associate with relaxed actin filaments. We propose that tandem LIM domains recognize an F-actin conformation that is rare in the relaxed state but is enriched in the presence of mechanical stress.

Cellular fate of deformable needle-shaped PLGA-PEG fibers

Deformability of micro/nanometer sized particles plays an important role in particle-cell interactions and thus becomes a key parameter in carrier design in biomedicine application such as drug delivery and vaccinology. Yet the influence of material's deformability on the cellular fate of the particles as well as physiology response of live cells are to be understood. Here we show the cellular fate of needle shaped (high aspect ratio ~25) PLGA-PEG copolymer fibers depending on their deformability. We found that all the fibers entered murine macrophage cells (RAW 264.7) via phagocytosis. While the fibers of high apparent Young's modulus (average value = 872 kPa) maintained their original shape upon phagocytosis, their counterparts of low apparent Young's modulus (average value = 56 kPa) curled in cells. The observed deformation of fibers of low apparent Young's modulus in cells coincided with abnormal intracellular actin translocation and absence of lysosome/phagosome fusion in macrophages, suggesting the important role of material mechanical properties and mechano-related cellular pathway in affecting cell physiology. STATEMENT OF SIGNIFICANCE: Particles are increasingly important in the field of biomedicine, especially when they are serving as drug carriers. Physical cues, such as mechanical properties, were shown to provide insight into their stability and influence on physiology inside the cell. In the current study, we managed to fabricate 5 types of needle shaped PLGA-PEG fibers with controlled Young's modulus. We found that hard fibers maintained their original shape upon phagocytosis, while soft fibers were curled by actin compressive force inside the cell, causing abnormal actin translocation and impediment of lysosome/phagosome fusion, suggesting the important role of material mechanical properties and mechano-related cellular pathway in affecting cell physiology.

Ebola Virus Nucleocapsid-Like Structures Utilize Arp2/3 Signaling for Intracellular Long-Distance Transport

The intracellular transport of nucleocapsids of the highly pathogenic Marburg, as well as Ebola virus (MARV, EBOV), represents a critical step during the viral life cycle. Intriguingly, a population of these nucleocapsids is distributed over long distances in a directed and polar fashion. Recently, it has been demonstrated that the intracellular transport of filoviral nucleocapsids depends on actin polymerization. While it was shown that EBOV requires Arp2/3-dependent actin dynamics, the details of how the virus exploits host actin signaling during intracellular transport are largely unknown. Here, we apply a minimalistic transfection system to follow the nucleocapsid-like structures (NCLS) in living cells, which can be used to robustly quantify NCLS transport in live cell imaging experiments. Furthermore, in cells co-expressing LifeAct, a marker for actin dynamics, NCLS transport is accompanied by pulsative actin tails appearing on the rear end of NCLS. These actin tails can also be preserved in fixed cells, and can be visualized via high resolution imaging using STORM in transfected, as well as EBOV infected, cells. The application of inhibitory drugs and siRNA depletion against actin regulators indicated that EBOV NCLS utilize the canonical Arp2/3-Wave1-Rac1 pathway for long-distance transport in cells. These findings highlight the relevance of the regulation of actin polymerization during directed EBOV nucleocapsid transport in human cells.

A hybrid stochastic-deterministic mechanochemical model of cell polarization

Polarization is a crucial component in cell differentiation, development, and motility, but its details are not yet well understood. At the onset of cell locomotion, cells break symmetry to form well-defined cell fronts and rears. This polarity establishment varies across cell types: in Dictyostelium discoideum cells, it is mediated by biochemical signaling pathways and can function in the absence of a cytoskeleton, while in keratocytes, it is tightly connected to cytoskeletal dynamics and mechanics. Theoretical models that have been developed to understand the onset of polarization have explored either signaling or mechanical pathways, yet few have explored mechanochemical mechanisms. However, many motile cells rely on both signaling modules and actin cytoskeleton to break symmetry and achieve a stable polarized state. We propose a general mechanochemical polarization model based on coupling between a stochastic model for the segregation of signaling molecules and a simplified mechanical model for actin cytoskeleton network competition. We find that local linear coupling between minimally nonlinear signaling and cytoskeletal systems, separately not supporting stable polarization, yields a robustly polarized cell state. The model captures the essence of spontaneous polarization of neutrophils, which has been proposed to emerge due to the competition between frontness and backness pathways.

Quantitative regulation of the dynamic steady state of actin networks

Principles of regulation of actin network dimensions are fundamentally important for cell functions, yet remain unclear. Using both in vitro and in silico approaches, we studied the effect of key parameters, such as actin density, ADF/Cofilin concentration and network width on the network length. In the presence of ADF/Cofilin, networks reached equilibrium and became treadmilling. At the trailing edge, the network disintegrated into large fragments. A mathematical model predicts the network length as a function of width, actin and ADF/Cofilin concentrations. Local depletion of ADF/Cofilin by binding to actin is significant, leading to wider networks growing longer. A single rate of breaking network nodes, proportional to ADF/Cofilin density and inversely proportional to the square of the actin density, can account for the disassembly dynamics. Selective disassembly of heterogeneous networks by ADF/Cofilin controls steering during motility. Our results establish general principles on how the dynamic steady state of actin network emerges from biochemical and structural feedbacks.

Forces drive basement membrane invasion in Caenorhabditis elegans

During invasion, cells breach basement membrane (BM) barriers with actin-rich protrusions. It remains unclear, however, whether actin polymerization applies pushing forces to help break through BM, or whether actin filaments play a passive role as scaffolding for targeting invasive machinery. Here, using the developmental event of anchor cell (AC) invasion in Caenorhabditis elegans, we observe that the AC deforms the BM and underlying tissue just before invasion, exerting forces in the tens of nanonewtons range. Deformation is driven by actin polymerization nucleated by the Arp2/3 complex and its activators, whereas formins and cross-linkers are dispensable. Delays in invasion upon actin regulator loss are not caused by defects in AC polarity, trafficking, or secretion, as appropriate markers are correctly localized in the AC even when actin is reduced and invasion is disrupted. Overall force production emerges from this study as one of the main tools that invading cells use to promote BM disruption in C. elegans.

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.

WH2 and proline-rich domains of WASP-family proteins collaborate to accelerate actin filament elongation

WASP‐family proteins are known to promote assembly of branched actin networks by stimulating the filament‐nucleating activity of the Arp2/3 complex. Here, we show that WASP‐family proteins also function as polymerases that accelerate elongation of uncapped actin filaments. When clustered on a surface, WASP‐family proteins can drive branched actin networks to grow much faster than they could by direct incorporation of soluble monomers. This polymerase activity arises from the coordinated action of two regulatory sequences: (i) a WASP homology 2 (WH2) domain that binds actin, and (ii) a proline‐rich sequence that binds profilin–actin complexes. In the absence of profilin, WH2 domains are sufficient to accelerate filament elongation, but in the presence of profilin, proline‐rich sequences are required to support polymerase activity by (i) bringing polymerization‐competent actin monomers in proximity to growing filament ends, and (ii) promoting shuttling of actin monomers from profilin–actin complexes onto nearby WH2 domains. Unoccupied WH2 domains transiently associate with free filament ends, preventing their growth and dynamically tethering the branched actin network to the WASP‐family proteins that create it. Collaboration between WH2 and proline‐rich sequences thus strikes a balance between filament growth and tethering. Our work expands the number of critical roles that WASP‐family proteins play in the assembly of branched actin networks to at least three: (i) promoting dendritic nucleation; (ii) linking actin networks to membranes; and (iii) accelerating filament elongation.

Network heterogeneity regulates steering in actin-based motility

The growth of branched actin networks powers cell-edge protrusions and motility. A heterogeneous density of actin, which yields to a tunable cellular response, characterizes these dynamic structures. We study how actin organization controls both the rate and the steering during lamellipodium growth. We use a high-resolution surface structuration assay combined with mathematical modeling to describe the growth of a reconstituted lamellipodium. We demonstrate that local monomer depletion at the site of assembly negatively impacts the network growth rate. At the same time, network architecture tunes the protrusion efficiency, and regulates the rate of growth. One consequence of this interdependence between monomer depletion and network architecture effects is the ability of heterogeneous network to impose steering during motility. Therefore, we have established that the general principle, by which the cell can modulate the rate and the direction of a protrusion, is by varying both density and architecture of its actin network.

Protrusive cellular structures contain a heterogeneous density of actin, but whether this influences motility is not known. Using an in vitro system and modelling, here the authors show that local actin monomer depletion and network architecture can tune the rate of network growth to impose steering during motility.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Statistics of actin-propelled trajectories in noisy environments

Actin polymerization is ubiquitously utilized to power the locomotion of eukaryotic cells and pathogenic bacteria in living systems. Inevitably, actin polymerization and depolymerization proceed in a fluctuating environment that renders the locomotion stochastic. Previously, we have introduced a deterministic model that manages to reproduce actin-propelled trajectories in experiments, but not to address fluctuations around them. To remedy this, here we supplement the deterministic model with noise terms. It enables us to compute the effects of fluctuating actin density and forces on the trajectories. Specifically, the mean-squared displacement (MSD) of the trajectories is computed and found to show a super-ballistic scaling with an exponent 3 in the early stage, followed by a crossover to a normal, diffusive scaling of exponent 1 in the late stage. For open-end trajectories such as straights and S-shaped curves, the time of crossover matches the decay time of orientational order of the velocities along trajectories, suggesting that it is the spreading of velocities that leads to the crossover. We show that the super-ballistic scaling of MSD arises from the initial, linearly increasing correlation of velocities, before time translational symmetry is established. When the spreading of velocities reaches a steady state in the long-time limit, short-range correlation then yields a diffusive scaling in MSD. In contrast, close-loop trajectories like circles exhibit localized periodic motion, which inhibits spreading. The initial super-ballistic scaling of MSD arises from velocity correlation that both linearly increases and oscillates in time. Finally, we find that the above statistical features of the trajectories transcend the nature of noises, be it additive or multiplicative, and generalize to other self-propelled systems that are not necessarily actin based.

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.

Methods of myofibrillogenesis modeling

Organization in the heart is important on multiple length scales. Myofibrillogenesis processes control the assembly of this multi-scale architecture. Understanding myofibrillogenesis might allow us to better control self-assembly of cardiac tissues. One approach consists of creating phenomenological models and comparing these models to in vitro data from primary myocytes. In this chapter, we present a method for building these models to recapitulate different aspects of myofibrillogenesis. We present a specific example for a cardiomyocyte model, but the same procedure can be used to model fibrillogenesis with other mechanisms such as motility. In sum, the models allow for a better understanding of mechanisms behind self-assembly.

CPI motif interaction is necessary for capping protein function in cells

Capping protein (CP) has critical roles in actin assembly in vivo and in vitro. CP binds with high affinity to the barbed end of actin filaments, blocking the addition and loss of actin subunits. Heretofore, models for actin assembly in cells generally assumed that CP is constitutively active, diffusing freely to find and cap barbed ends. However, CP can be regulated by binding of the 'capping protein interaction' (CPI) motif, found in a diverse and otherwise unrelated set of proteins that decreases, but does not abolish, the actin-capping activity of CP and promotes uncapping in biochemical experiments. Here, we report that CP localization and the ability of CP to function in cells requires interaction with a CPI-motif-containing protein. Our discovery shows that cells target and/or modulate the capping activity of CP via CPI motif interactions in order for CP to localize and function in cells.

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.

Reconstitution of proteins on electroformed giant unilamellar vesicles

In vitro reconstitution of simplified biological systems from molecular parts has proven to be a powerful method for investigating the biochemical and biophysical principles underlying cellular processes. In recent years, there has been a growing interest in reconstitution of protein-membrane interactions to understand the critical role played by membranes in organizing molecular-scale events into micron-scale patterns and protrusions. However, while all reconstitution experiments depend on identifying and isolating an essential set of soluble biomolecules, such as proteins, DNA, and RNA, reconstitution of membrane-based processes involves the additional challenge of forming and working with lipid bilayer membranes with composition, fluidity, and mechanical properties appropriate for the process at hand. Here we discuss a selection of methods for forming synthetic lipid bilayer membranes and present a versatile electroformation protocol that our lab uses for reconstituting proteins on giant unilamellar vesicles. This synthetic membrane-based approach to reconstitution offers the ability to study protein organization and activity at membranes under more cell-like conditions, addressing a central challenge to accomplishing the grand goal of "building the cell."

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.

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.

Directed actin assembly and motility

The actin cytoskeleton is a key component of the cellular architecture. However, understanding actin organization and dynamics in vivo is a complex challenge. Reconstitution of actin structures in vitro, in simplified media, allows one to pinpoint the cellular biochemical components and their molecular interactions underlying the architecture and dynamics of the actin network. Previously, little was known about the extent to which geometrical constraints influence the dynamic ultrastructure of these networks. Therefore, in order to study the balance between biochemical and geometrical control of complex actin organization, we used the innovative methodologies of UV and laser patterning to design a wide repertoire of nucleation geometries from which we assembled branched actin networks. Using these methods, we were able to reconstitute complex actin network organizations, closely related to cellular architecture, to precisely direct and control their 3D connections. This methodology mimics the actin networks encountered in cells and can serve in the fabrication of innovative bioinspired systems.

Purification of native Arp2/3 complex from bovine thymus

The Arp2/3 complex is an actin filament nucleator involved in cell motility and vesicle trafficking. Owing to the role the complex plays in important and fundamental cell biological processes, the purified complex is used in biochemical assays, reconstituted motility assays, and structural biology. As this is a eukaryotic complex assembled from seven polypeptides, the complex is purified from eukaryotic sources. Described here is a detailed method for purification of the complex from a mammalian tissue, bovine thymus.

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.

Cell polarity: mechanochemical patterning

Nearly every cell type exhibits some form of polarity, yet the molecular mechanisms vary widely. Here we examine what we term 'chemical systems' where cell polarization arises through biochemical interactions in signaling pathways, 'mechanical systems' where cells polarize due to forces, stresses and transport, and 'mechanochemical systems' where polarization results from interplay between mechanics and chemical signaling. To reveal potentially unifying principles, we discuss mathematical conceptualizations of several prototypical examples. We suggest that the concept of local activation and global inhibition - originally developed to explain spatial patterning in reaction-diffusion systems - provides a framework for understanding many cases of cell polarity. Importantly, we find that the core ingredients in this framework - symmetry breaking, self-amplifying feedback, and long-range inhibition - involve processes that can be chemical, mechanical, or even mechanochemical in nature.

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.

Cell polarity: quantitative modeling as a tool in cell biology

Among a number of innovative approaches that have modernized cell biology, modeling has a prominent yet unusual place. One popular view is that we progress linearly, from conceptual to ever more detailed models. We review recent discoveries of cell polarity mechanisms, in which modeling played an important role, to demonstrate that the experiment-theory feedback loop requires diverse models characterized by varying levels of biological detail and mathematical complexity. We argue that a quantitative model is a tool that has to fit an experimental study, and the model's value should be judged not by how complex and detailed it is, but by what could be learned from it.

How actin network dynamics control the onset of actin-based motility

Cells use their dynamic actin network to control their mechanics and motility. These networks are made of branched actin filaments generated by the Arp2/3 complex. Here we study under which conditions the microscopic organization of branched actin networks builds up a sufficient stress to trigger sustained motility. In our experimental setup, dynamic actin networks or "gels" are grown on a hard bead in a controlled minimal protein system containing actin monomers, profilin, the Arp2/3 complex and capping protein. We vary protein concentrations and follow experimentally and through simulations the shape and mechanical properties of the actin gel growing around beads. Actin gel morphology is controlled by elementary steps including "primer" contact, growth of the network, entanglement, mechanical interaction and force production. We show that varying the biochemical orchestration of these steps can lead to the loss of network cohesion and the lack of effective force production. We propose a predictive phase diagram of actin gel fate as a function of protein concentrations. This work unveils how, in growing actin networks, a tight biochemical and physical coupling smoothens initial primer-caused heterogeneities and governs force buildup and cell motility.

Spatiotemporal coordinated hierarchical properties of cellular protrusion revealed by multiscale analysis

We present a methodology for integrative multiscale analysis to highlight hierarchical properties of cellular protrusion and mechanochemical interactions in cellular protrusion based on live cell imaging data with high spatiotemporal resolution. As an appropriate experimental system, we selected non-polarized full-moon-shaped keratocytes that present balanced protrusion around the entire cell periphery at the cellular scale simultaneously with active protrusion and retraction at the subcellular scale. We achieved the observation of a whole cell with sub-micrometer spatial precision and sub-second time resolution for three minutes or more. The multiscale characteristics of cell peripheral activity and those of the cell peripheral shape were extracted from an identical image sequence by estimating the cell protrusion rates and the cell peripheral curvatures at various differential intervals. The spatiotemporal maps of the cell protrusion rates demonstrated a spatiotemporally nested structure of travelling waves of active protruding regions at the cellular and subcellular scales. Moreover, correlation analysis demonstrated the relationship between the cell protrusion rate and peripheral curvature at the subcellular scale. The novel integrative methodology presented here well highlighted the hierarchical properties of organized cellular protrusion, and further provided insight about the underlying mechanochemical interactions between the cell membrane and the actin filaments under the membrane.

Actin filament attachments for sustained motility in vitro are maintained by filament bundling

We reconstructed cellular motility in vitro from individual proteins to investigate how actin filaments are organized at the leading edge. Using total internal reflection fluorescence microscopy of actin filaments, we tested how profilin, Arp2/3, and capping protein (CP) function together to propel thin glass nanofibers or beads coated with N-WASP WCA domains. Thin nanofibers produced wide comet tails that showed more structural variation in actin filament organization than did bead substrates. During sustained motility, physiological concentrations of Mg(2+) generated actin filament bundles that processively attached to the nanofiber. Reduction of total Mg(2+) abolished particle motility and actin attachment to the particle surface without affecting actin polymerization, Arp2/3 nucleation, or filament capping. Analysis of similar motility of microspheres showed that loss of filament bundling did not affect actin shell formation or symmetry breaking but eliminated sustained attachments between the comet tail and the particle surface. Addition of Mg(2+), Lys-Lys(2+), or fascin restored both comet tail attachment and sustained particle motility in low Mg(2+) buffers. TIRF microscopic analysis of filaments captured by WCA-coated beads in the absence of Arp2/3, profilin, and CP showed that filament bundling by polycation or fascin addition increased barbed end capture by WCA domains. We propose a model in which CP directs barbed ends toward the leading edge and polycation-induced filament bundling sustains processive barbed end attachment to the leading edge.

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.

Cease-fire at the leading edge: new perspectives on actin filament branching, debranching, and cross-linking

Membrane protrusion at the leading edge of migrating cells is driven by the polymerization of actin. Recent studies using advanced imaging techniques raised a lively controversy about the morphology of these filaments; however, common ground between the two sides now appears to have been found. Here we discuss how the controversy has led to a deeper consideration of the architecture of actin networks underlying cell migration, and has helped define new challenges that lie ahead.

Modeling cellular processes in 3D

Recent advances in photonic imaging and fluorescent protein technology offer unprecedented views of molecular space-time dynamics in living cells. At the same time, advances in computing hardware and software enable modeling of ever more complex systems, from global climate to cell division. As modeling and experiment become more closely integrated we must address the issue of modeling cellular processes in 3D. Here, we highlight recent advances related to 3D modeling in cell biology. While some processes require full 3D analysis, we suggest that others are more naturally described in 2D or 1D. Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.

Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We put forward the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle reproduces the stochastic nature of lamellipodia protrusion (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is a well-known signature of self-organized criticality and is confirmed by unique optical tweezer measurements performed in vivo on neuronal growth cones.

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 a quantitative understanding of mitotic spindle assembly and mechanics

The 'simple' view of the mitotic spindle is that it self-assembles as a result of microtubules (MTs) randomly searching for chromosomes, after which the spindle length is maintained by a balance of outward tension exerted by molecular motors on the MTs connecting centrosomes and chromosomes, and compression generated by other motors on the MTs connecting the spindle poles. This picture is being challenged now by mounting evidence indicating that spindle assembly and maintenance rely on much more complex interconnected networks of microtubules, molecular motors, chromosomes and regulatory proteins. From an engineering point of view, three design principles of this molecular machine are especially important: the spindle assembles quickly, it assembles accurately, and it is mechanically robust--yet malleable. How is this design achieved with randomly interacting and impermanent molecular parts? Here, we review recent interdisciplinary studies that have started to shed light on this question. We discuss cooperative mechanisms of spindle self-assembly, error correction and maintenance of its mechanical properties, speculate on analogy between spindle and lamellipodial dynamics, and highlight the role of quantitative approaches in understanding the mitotic spindle design.

Mechanics and regulation of cell shape during the cell cycle

Many cell types undergo dramatic changes in shape throughout the cell cycle. For individual cells, a tight control of cell shape is crucial during cell division, but also in interphase, for example during cell migration. Moreover, cell cycle-related cell shape changes have been shown to be important for tissue morphogenesis in a number of developmental contexts. Cell shape is the physical result of cellular mechanical properties and of the forces exerted on the cell. An understanding of the causes and repercussions of cell shape changes thus requires knowledge of both the molecular regulation of cellular mechanics and how specific changes in cell mechanics in turn effect global shape changes. In this chapter, we provide an overview of the current knowledge on the control of cell morphology, both in terms of general cell mechanics and specifically during the cell cycle.

A microscopic formulation for the actin-driven motion of listeria in curved paths

Using a generalized Brownian ratchet model that accounts for the interactions of actin filaments with the surface of Listeria mediated by proteins like ActA and Arp2/3, we have developed a microscopic model for the movement of Listeria. Specifically, we show that a net torque can be generated within the comet tail, causing the bacteria to spin about its long axis, which in conjunction with spatially varying polymerization at the surface leads to motions of bacteria in curved paths that include circles, sinusoidal-like curves, translating figure eights, and serpentine shapes, as observed in recent experiments. A key ingredient in our formulation is the coupling between the motion of Listeria and the force-dependent rate of filament growth. For this reason, a numerical scheme was developed to determine the kinematic parameters of motion and stress distribution among filaments in a self-consistent manner. We find that a 5-15% variation in polymerization rates can lead to radii of curvatures of the order of 4-20 microm, measured in experiments. In a similar way, our results also show that most of the observed trajectories can be produced by a very low degree of correlation, <10%, among filament orientations. Since small fluctuations in polymerization rate, as well as filament orientation, can easily be induced by various factors, our findings here provide a reasonable explanation for why Listeria can travel along totally different paths under seemingly identical experimental conditions. Besides trajectories, stress distributions corresponding to different polymerization profiles are also presented. We have found that although some actin filaments generate propelling forces that push the bacteria forward, others can exert forces opposing the movement of Listeria, consistent with recent experimental observations.

Eukaryotic chemotaxis: a network of signaling pathways controls motility, directional sensing, and polarity

Chemotaxis, the directed migration of cells in chemical gradients, is a vital process in normal physiology and in the pathogenesis of many diseases. Chemotactic cells display motility, directional sensing, and polarity. Motility refers to the random extension of pseudopodia, which may be driven by spontaneous actin waves that propagate through the cytoskeleton. Directional sensing is mediated by a system that detects temporal and spatial stimuli and biases motility toward the gradient. Polarity gives cells morphologically and functionally distinct leading and lagging edges by relocating proteins or their activities selectively to the poles. By exploiting the genetic advantages of Dictyostelium, investigators are working out the complex network of interactions between the proteins that have been implicated in the chemotactic processes of motility, directional sensing, and polarity.

Actin dynamics: from nanoscale to microscale

The dynamic nature of actin in cells manifests itself constantly. Polymerization near the cell edge is balanced by depolymerization in the interior, externally induced actin polymerization is followed by depolymerization, and spontaneous oscillations of actin at the cell periphery are frequently seen. I discuss how mathematical modeling relates quantitative measures of actin dynamics to the rates of underlying molecular level processes. The dynamic properties addressed include the rate of actin assembly at the leading edge of a moving cell, the disassembly rates of intracellular actin networks, the polymerization time course in externally stimulated cells, and spontaneous spatiotemporal patterns formed by actin. Although several aspects of actin assembly have been clarified by increasingly sophisticated models, our understanding of rapid actin disassembly is limited, and the origins of nonmonotonic features in externally stimulated actin polymerization remain unclear. Theory has generated several concrete, testable hypotheses for the origins of spontaneous actin waves and cell-edge oscillations. The development and use of more biomimetic systems applicable to the geometry of a cell will be key to obtaining a quantitative understanding of actin dynamics in cells.

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.