Growing an actin gel on spherical surfaces

Pushing off the walls: a mechanism of cell motility in confinement

We propose a novel mechanism of cell motility, which relies on the coupling of actin polymerization at the cell membrane to geometric confinement. We consider a polymerizing viscoelastic cytoskeletal gel confined in a narrow channel, and show analytically that spontaneous motion occurs. Interestingly, this does not require specific adhesion with the channel walls, and yields velocities potentially larger than the polymerization velocity. The contractile activity of myosin motors is not necessary to trigger motility in this mechanism, but is shown quantitatively to increase the velocity. Our model qualitatively accounts for recent experiments which show that cells without specific adhesion proteins are motile only in confined environments while they are unable to move on a flat surface, and could help in understanding the mechanisms of cell migration in more complex confined geometries such as living tissues.

Optimizing intermittent reaction paths

Various examples of biochemical reactions in cells, such as DNA/protein interactions, reveal that in extremely diluted regimes reaction paths are not always simple brownian trajectories. They can rather be qualified as intermittent, since they combine slow diffusion phases on one hand and a second mode of faster transport on the other hand, which can be either a faster diffusion mode, as in the case of DNA-binding proteins, or a ballistic mode powered by molecular motors in the case of intracellular transport. In this article, we introduce simple theoretical models which permit to calculate explicitly the reaction rates for reactions limited by intermittent transport. This approach shows quantitatively that intermittent reaction pathways are actually very efficient, since they permit to significantly increase the reaction rates, which could explain why they are observed so often. Moreover, we give theoretical arguments which suggest that intermittent transport could also be useful for in vitro chemistry. Indeed, we show that intermittent transport naturally pops up in the context of reaction at interfaces, where reactants combine surface diffusion phases and bulk excursions, and could permit to enhance reactivity. In this case, adjusting chemically the affinity of reactants with the interface makes possible to optimize the reaction rate.

New proposed mechanism of actin-polymerization-driven motility

We present the first numerical simulation of actin-driven propulsion by elastic filaments. Specifically, we use a Brownian dynamics formulation of the dendritic nucleation model of actin-driven propulsion. We show that the model leads to a self-assembled network that exerts forces on a disk and pushes it with an average speed. This simulation approach is the first to observe a speed that varies nonmonotonically with the concentration of branching proteins (Arp2/3), capping protein, and depolymerization rate, in accord with experimental observations. Our results suggest a new interpretation of the origin of motility. When we estimate the speed that this mechanism would produce in a system with realistic rate constants and concentrations as well as fluid flow, we obtain a value that is within an order-of-magnitude of the polymerization speed deduced from experiments.

Models for actin polymerization motors

Actin polymerization drives cell membrane protrusions and the propulsion of intracellular pathogens. The molecular mechanisms driving actin polymerization are not yet fully understood. Various mathematical models have been proposed to explain how cells convert chemical energy released upon actin polymerization into a pushing force on a surface. These models have attempted to explain puzzling properties of actin-based motility, including persistent attachment of the network to the membrane during propulsion and the interesting trajectories of propelled particles. These models fall generally into two classes: those requiring filament (+)-ends to fluctuate freely from the membrane to add subunits, and those where filaments elongate with their (+)-ends persistently associated with surface through filament end-tracking proteins ("actoclampin" models). This review compares and contrasts the key predictions of these two classes of models with regard to force-velocity profiles, and evaluates them with respect to experiments with biomimetic particles, and the experimental evidence on the role of end-tracking proteins such as formins and nucleation-promoting factors in actin-based motility.

Nonlinear study of symmetry breaking in actin gels: implications for cellular motility

Force generation by actin polymerization is an important step in cellular motility and can induce the motion of organelles or bacteria, which move inside their host cells by trailing an actin tail behind. Biomimetic experiments on beads and droplets have identified the biochemical ingredients to induce this motion, which requires a spontaneous symmetry breaking in the absence of external fields. We find that the symmetry breaking can be captured on the basis of elasticity theory and linear flux-force relationships. Furthermore, we develop a phase-field approach to study the fully nonlinear regime and show that actin-comet formation is a robust feature, triggered by growth and mechanical stresses. We discuss the implications of symmetry breaking for self-propulsion.

Synthesis of asymmetric inorganic/polymer nanocomposite particles via localized substrate surface modification and miniemulsion polymerization

Asymmetric nanocomposite particle pairs of polystyrene and silica were prepared via one-step miniemulsion polymerization for the first time. The transmission electron microscopy images showed that these nanocomposite particle pairs were monodisperse and highly asymmetric in morphology. The key to obtaining the asymmetric nanocomposite particle pairs was the combination of miniemulsion polymerization and the local surface modification of silica substrates. Because of localized surface modification on the silica surface, the nucleation and formation of the polymer nodule in miniemulsion polymerization took place only in the modified area on the silica surface, thus ensuring the asymmetric morphology. The asymmetrical materials obtained by the facile and effective method will have significant potential applications in some areas including biomedical fields.

Mathematical modeling of cell migration

Mathematical modeling has become increasingly important in many areas of biology during the past two decades, and the area of cell migration and motility has seen significant contributions from a wide range of modeling approaches. In this chapter, we cover examples from the broad range of work in this area, emphasizing the models' biological significance and the relationships between them. We focus on three specific areas: cell protrusion, cell adhesion, and retraction/whole-cell models. At the end of this chapter, we provide our perspective on issues that future models and experiments should consider in order to advance the boundaries of this field.

Stress field in actin gel growing on spherical substrate

Polymerization of actin to form an elastic gel is one of the main mechanisms responsible for cellular motility. The particular problem addressed here stems from the need to model theoretically the growth of actin gel under controlled conditions, as observed in experiments. A biomimetic in vitro system which consists of a spherical latex bead, coated by the enzymatic protein ActA, and a reconstituted cytoplasm within which such beads are placed, induces polymerization of actin on the surface of the bead in the form of successive elastic thin spherical layers. Each newly formed layer pushes outward, and is pushed inward by, the already formed spherical layers which altogether constitute an elastic spherical shell of thickness h varying with time. Thus, a stress field is created in the shell which in turn affects the rate of polymerization as well as that of dissociation of actin gel. Given this bio-chemo-mechanical coupling, the accurate determination of the stress field becomes a subject of great importance for the understanding of the process, and it is the main objective of this work. The problem is addressed by first assuming appropriate constitutive laws for the actin gel elastic material, and then solving the only non-trivial stress equilibrium differential equation along the radial direction assuming spherical symmetry. A linear and a non-linear constitutive model for isotropic elasticity is used, appropriate for small and finite strains, respectively, and the solution is found in closed analytical forms in both cases. Two important conclusions are reached. First, the stress field depends strongly on the compressibility of the actin gel medium via the value of the Poisson ratio, for both linear and non-linear analysis. Second, the linear and non-linear solutions are very close for small strains, but they diverge progressively as the strains increase from small to large. Guided by available experimental data on the observed strain levels, the analytical results are illustrated by selected graphs of stress variation along the radial direction. At the end some comments and suggestions on the bio-chemo-mechanical coupling of actin gel growth and resorption are presented, where the role of properly defined joint isotropic invariants of stress and a unit vector along the predominant direction of free ends of actin filaments at the polymerization site is introduced.

The forces behind cell movement

Cell movement is a complex phenomenon primarily driven by the actin network beneath the cell membrane, and can be divided into three general components: protrusion of the leading edge of the cell, adhesion of the leading edge and deadhesion at the cell body and rear, and cytoskeletal contraction to pull the cell forward. Each of these steps is driven by physical forces generated by unique segments of the cytoskeleton. This review examines the specific physics underlying these phases of cell movement and the origins of the forces that drive locomotion.

Spatial and temporal relationships between actin-filament nucleation, capping, and disassembly

BACKGROUND

The leading actin network in motile cells is composed of two compartments, the lamellipod and the lamellum. Construction of the lamellipod requires a set of conserved proteins that form a biochemical cycle. The timing of this cycle and the roles of its components in determining actin network architecture in vivo, however, are not well understood.

RESULTS

We performed fluorescent speckle microscopy on spreading Drosophila S2 cells by using labeled derivatives of actin, the Arp2/3 complex, capping protein, and tropomyosin. We find that capping protein and the Arp2/3 complex both incorporate at the cell edge but that capping protein dissociates after covering less than half the width of the lamellipod, whereas the Arp2/3 complex dissociates after crossing two thirds of the lamellipod. The lamellipodial actin network itself persists long after the loss of the Arp2/3 complex. Depletion of capping protein by RNAi results in the displacement of the Arp2/3 complex and disappearance of the lamellipod. In contrast, depletion of cofilin, slingshot, twinfilin, and tropomyosin, all factors that control the stability of actin filaments, dramatically expanded the lamellipod at the expense of the lamellum.

CONCLUSIONS

The Arp2/3 complex is incorporated into the lamellipodial network at the cell edge but debranches well before the lamellipodial network itself is disassembled. Capping protein is required for the formation of a lamellipodial network but dissociates from the network precisely when filament disassembly is first detected. Cofilin, twinfilin, and tropomyosin appear to play no role in lamellipodial network assembly but function to limit its size.

Cracking up: symmetry breaking in cellular systems

The shape of animal cells is, to a large extent, determined by the cortical actin network that underlies the cell membrane. Because of the presence of myosin motors, the actin cortex is under tension, and local relaxation of this tension can result in cortical flows that lead to deformation and polarization of the cell. Cortex relaxation is often regulated by polarizing signals, but the cortex can also rupture and relax spontaneously. A similar tension-induced polarization is observed in actin gels growing around beads, and we propose that a common mechanism governs actin gel rupture in both systems.

Cell-free extract systems and the cytoskeleton: preparation of biochemical experiments for transmission electron microscopy

Cell-free systems can be used to reconstitute complex actin or microtubule-based phenomena. For example, a number of extracts support actin-dependent propulsion of Listeria monocytogenes, whereas Xenopus laevis extracts support formation of a microtubule-based meiotic spindle. Working in vitro opens these complex processes to biochemical dissection. Here, we describe methods to view these in vitro preparations by thin-section electron microscopy.

Deformations in actin comets from rocketing beads

The mechanical and dynamical properties of the actin network are essential for many cellular processes like motility or division, and there is a growing body of evidence that they are also important for adhesion and trafficking. The leading edge of migrating cells is pushed out by the polymerization of actin networks, a process orchestrated by cross-linkers and other actin-binding proteins. In vitro physical characterizations show that these same proteins control the elastic properties of actin gels. Here we use a biomimetic system of Listeria monocytogenes, beads coated with an activator of actin polymerization, to assess the role of various actin-binding proteins in propulsion. We find that the properties of actin-based movement are clearly affected by the presence of cross-linkers. By monitoring the evolution of marked parts of the comet, we provide direct experimental evidence that the actin gel continuously undergoes deformations during the growth of the comet. Depending on the protein composition in the motility medium, deformations arise from either gel elasticity or monomer diffusion through the actin comet. Our findings demonstrate that actin-based movement is governed by the mechanical properties of the actin network, which are fine-tuned by proteins involved in actin dynamics and assembly.

Contractility and retrograde flow in lamellipodium motion

We present a phenomenological description of cell locomotion on a solid substrate. The material properties of the actin cytoskeleton in the lamellipodium are described by the constitutive equations of a viscous polar gel with intrinsic activity. The polymerization of the gel takes place in a localized region near the leading edge. Using a simple two-dimensional description, we calculate in the steady state the thickness profile of the lamellipodium which at the rear connects to the cell body; we also calculate the flow profiles and the forces exerted on the substrate. The cell velocity is estimated as a function of externally applied forces. Our description is consistent with experimentally observed properties of motile cells such as the existence of a retrograde flow in the lamellipodium and a dipolar force distribution exerted by the cell on the substrate.

Diffusion rate limitations in actin-based propulsion of hard and deformable particles

The mechanism by which actin polymerization propels intracellular vesicles and invasive microorganisms remains an open question. Several recent quantitative studies have examined propulsion of biomimetic particles such as polystyrene microspheres, phospholipid vesicles, and oil droplets. In addition to allowing quantitative measurement of parameters such as the dependence of particle speed on its size, these systems have also revealed characteristic behaviors such a saltatory motion of hard particles and oscillatory deformation of soft particles. Such measurements and observations provide tests for proposed mechanisms of actin-based motility. In the actoclampin filament end-tracking motor model, particle-surface-bound filament end-tracking proteins are involved in load-insensitive processive insertion of actin subunits onto elongating filament plus-ends that are persistently tethered to the surface. In contrast, the tethered-ratchet model assumes working filaments are untethered and the free-ended filaments grow as thermal ratchets in a load-sensitive manner. This article presents a model for the diffusion and consumption of actin monomers during actin-based particle propulsion to predict the monomer concentration field around motile particles. The results suggest that the various behaviors of biomimetic particles, including dynamic saltatory motion of hard particles and oscillatory vesicle deformations, can be quantitatively and self-consistently explained by load-insensitive, diffusion-limited elongation of (+)-end-tethered actin filaments, consistent with predictions of the actoclampin filament-end tracking mechanism.

Symmetry-breaking motility

Locomotion of bacteria by actin polymerization and in vitro motion of spherical beads coated with a protein catalyzing polymerization are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.

Bacterial shape and ActA distribution affect initiation of Listeria monocytogenes actin-based motility

We have examined the process by which the intracellular bacterial pathogen Listeria monocytogenes initiates actin-based motility and determined the contribution of the variable surface distribution of the ActA protein to initiation and steady-state movement. To directly correlate ActA distributions to actin dynamics and motility of live bacteria, ActA was fused to a monomeric red fluorescent protein (mRFP1). Actin comet tail formation and steady-state bacterial movement rates both depended on ActA distribution, which in turn was tightly coupled to the bacterial cell cycle. Motility initiation was found to be a highly complex, multistep process for bacteria, in contrast to the simple symmetry breaking previously observed for ActA-coated spherical beads. F-actin initially accumulated along the sides of the bacterium and then slowly migrated to the bacterial pole expressing the highest density of ActA as a tail formed. Early movement was highly unstable with extreme changes in speed and frequent stops. Over time, saltatory motility and sensitivity to the immediate environment decreased as bacterial movement became robust at a constant steady-state speed.

Mechanism of actin-based motility: a dynamic state diagram

Cells move by a dynamical reorganization of their cytoskeleton, orchestrated by a cascade of biochemical reactions directed to the membrane. Designed objects or bacteria can hijack this machinery to undergo actin-based propulsion inside cells or in a cell-like medium. These objects can explore the dynamical regimes of actin-based propulsion, and display different regimes of motion, in a continuous or periodic fashion. We show that bead movement can switch from one regime to the other, by changing the size of the beads or the surface concentration of the protein activating actin polymerization. We experimentally obtain the state diagram of the bead dynamics, in which the transitions between the different regimes can be understood by a theoretical approach based on an elastic force opposing a friction force. Moreover, the experimental characteristics of the movement, such as the velocity and the characteristic times of the periodic movement, are predicted by our theoretical analysis.

Stress release drives symmetry breaking for actin-based movement

By using a simple assay composed of purified proteins, we studied the spontaneous polarization of actin networks polymerizing on spherical beads, which subsequently undergo movement. We show evidence that this symmetry breaking is based on the release of elastic energy, analogous to the fracture of polymer gels. The dynamics of this process and the thickness at which it occurs depend on the growth rate and mechanical properties of the actin gel. We explain our experimental results with a model based on elasticity theory and fracture mechanics.

Cortical actomyosin breakage triggers shape oscillations in cells and cell fragments

Cell shape and movements rely on complex biochemical pathways that regulate actin, microtubules, and substrate adhesions. Some of these pathways act through altering the cortex contractility. Here we examined cellular systems where contractility is enhanced by disassembly of the microtubules. We found that adherent cells, when detached from their substrate, developed a membrane bulge devoid of detectable actin and myosin. A constriction ring at the base of the bulge oscillated from one side of the cell to the other. The movement was accompanied by sequential redistribution of actin and myosin to the membrane. We observed this oscillatory behavior also in cell fragments of various sizes, providing a simplified, nucleus-free system for biophysical studies. Our observations suggest a mechanism based on active gel dynamics and inspired by symmetry breaking of actin gels growing around beads. The proposed mechanism for breakage of the actomyosin cortex may be used for cell polarization.

Force generation by cytoskeletal filament end-tracking proteins

Force generation in several types of cell motility is driven by rapidly elongating cytoskeletal filaments that are persistently tethered at their polymerizing ends to propelled objects. These properties are not easily explained by force-generation models that require free (i.e., untethered) filament ends to fluctuate away from the surface for addition of new monomers. In contrast, filament end-tracking proteins that processively advance on filament ends can facilitate rapid elongation and substantial force generation by persistently tethered filaments. Such processive end-tracking proteins, termed here filament end-tracking motors, maintain possession of filament ends and, like other biomolecular motors, advance by means of 5'-nucleoside triphosphate (NTP) hydrolysis-driven affinity-modulated interactions. On-filament NTP hydrolysis/phosphate release yields substantially more energy than that required for driving steady-state assembly/disassembly of free filament ends (i.e., filament treadmilling), as revealed by an energy inventory on the treadmilling cycle. The kinetic and thermodynamic properties of two simple end-tracking mechanisms (an end-tracking stepping motor and a direct-transfer end-tracking motor) are analyzed to illustrate the advantages of an end-tracking motor over free filament-end elongation, and over passive end-trackers that operate without the benefit of NTP hydrolysis, in terms of generating force, facilitating rapid monomer addition, and maintaining tight possession of the filament ends. We describe an additional cofactor-assisted end-tracking motor to account for suggested roles of cofactors in the affinity-modulated interactions, such as profilin in actin-filament end-tracking motors and EB1 in microtubule end-tracking motors.

Actin-filament cross-linking protein T-plastin increases Arp2/3-mediated actin-based movement

Increasing evidence suggests that actin cross-linking or bundling proteins might not only structure the cortical actin cytoskeleton but also control actin dynamics. Here, we analyse the effects of T-plastin/T-fimbrin, a representative member of an important actin-filament cross-linking protein by combining a quantitative biomimetic motility assay with biochemical and cell-based approaches. Beads coated with the VCA domain of the Wiskott/Aldrich-syndrome protein (WASP) recruit the actin-nucleating Arp2/3 complex, polymerize actin at their surface and undergo movement when placed in cell-free extracts. T-Plastin increased the velocity of VCA beads 1.5 times, stabilized actin comets and concomitantly displaced cofilin, an actin-depolymerizing protein. T-Plastin also decreased the F-actin disassembly rate and inhibited cofilin-mediated depolymerization of actin filaments in vitro. Importantly, a bundling-incompetent variant comprising the first actin-binding domain (ABD1) had similar effects. In cells, this domain induced the formation of long actin cables to which other actin-regulating proteins were recruited. Altogether, these results favor a mechanism in which binding of ABD1 controls actin turnover independently of cross-link formation. In vivo, this activity might contribute to the assembly and maintenance of the actin cytoskeleton of plasma-membrane protrusions.

Listeria's right-handed helical rocket-tail trajectories: Mechanistic implications for force generation in actin-based motility

Listeria monocytogenes forms right-handed helical rocket tail trajectories during actin-based motility in cell-free extracts, and this stereochemical feature is consistent with actoclampin's affinity-modulated, clamped-filament elongation model [Dickinson and Purich, 2002: Biophys J 82:605-617]. In that mechanism, right-handed torque is generated by an end-tracking molecular motor, each comprised of a filament barbed end and clamping protein that processively traces the right-handed helix of its filament partner. By contrast, torque is not a predicted property of those models (e.g., elastic propulsion, elastic Brownian ratchet, tethered ratchet, and insertional polymerization models) requiring filament barbed ends to depart/detach from the motile object's surface during/after each monomer-addition step. Helical trajectories also explain why Listeria undergoes longitudinal-axis rotation on a length-scale matching the helical periodicity of Listeria's rocket tails.

Actin Filaments Align into Hollow Comets for Rapid VASP-Mediated Propulsion

For cells, the growth of a dense array of branched actin filaments organized by the actin-related proteins 2 and 3 (Arp2/3) complex at the plasma membrane offers an explanation as to how movement is produced, and this arrangement is considered to be optimal for motility. Here, we challenged this assumption by using an in vitro system of polystyrene beads in cell extracts that contained a complex mix of actin polymerization proteins as in vivo. We employed the surface of the bead as a reactor where we mixed two different actin polymerization-activating factors, the Arp2/3 complex and the vasodilator-stimulated phosphoprotein (VASP), to examine their contribution to actin-based movement and filament organization. We varied the coating of the bead surface but left the extracts identical for all assays. We found that the degree of filament alignment in the actin comet tails depended on the surface ratio of VASP to Arp2/3. Alignment of actin filaments parallel to the direction of bead movement in the presence of VASP was accompanied by an abrupt 7-fold increase in velocity that was independent of bead size and by hollowing out of the comets. The actin filament-bundling proteins fimbrin and fascin did not appear to play a role in this transformation. Together with the idea that VASP enhances filament detachment and with the presence of pulling forces at the rear of the bead, a mesoscopic analysis of movement provides a possible explanation for our results.

The co-workers of actin filaments: from cell structures to signals

Cells have various surface architectures, which allow them to carry out different specialized functions. Actin microfilaments that are associated with the plasma membrane are important for generating these cell-surface specializations, and also provide the driving force for remodelling cell morphology and triggering new cell behaviour when the environment is modified. This phenomenon is achieved through a tight coupling between cell structure and signal transduction, a process that is modulated by the regulation of actin-binding proteins.

Soft Listeria: actin-based propulsion of liquid drops

We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pearlike shape under the action of the elastic stresses exerted by the actin comet, a tail of cross-linked actin filaments. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.

The Role of Substrate Curvature in Actin-Based Pushing Forces

The extension of the plasma membrane during cell crawling or spreading is known to require actin polymerization; however, the question of how pushing forces derive from actin polymerization remains open. A leading theory (herein referred to as elastic propulsion) illustrates how elastic stresses in networks growing on curved surfaces can result in forces that push particles. To date all examples of reconstituted motility have used curved surfaces, raising the possibility that such squeezing forces are essential for actin-based pushing. By contrast, other theories, such as molecular ratchets, neither require nor consider surface curvature to explain pushing forces. Here, we critically test the requirement of substrate curvature by reconstituting actin-based motility on polystyrene disks. We find that disks move through extracts in a manner that indicates pushing forces on their flat surfaces and that disks typically move faster than the spheres they are manufactured from. For a subset of actin tails that form on the perimeter of disks, we find no correlation between local surface curvature and tail position. Collectively the data indicate that curvature-dependent mechanisms are not required for actin-based pushing.

Biophysical parameters influence actin-based movement, trajectory, and initiation in a cell-free system

Using a biochemically complex cytoplasmic extract to reconstitute actin-based motility of Listeria monocytogenes and polystyrene beads coated with the bacterial protein ActA, we have systematically varied a series of biophysical parameters and examined their effects on initiation of motility, particle speed, speed variability, and path trajectory. Bead size had a profound effect on all aspects of motility, with increasing size causing slower, straighter movement and inhibiting symmetry-breaking. Speed also was reduced by extract dilution, by addition of methylcellulose, and paradoxically by addition of excess skeletal muscle actin, but it was enhanced by addition of nonmuscle (platelet) actin. Large, persistent individual variations in speed were observed for all conditions and their relative magnitude increased with extract dilution, indicating that persistent alterations in particle surface properties may be responsible for intrinsic speed variations. Trajectory curvature was increased for smaller beads and also for particles moving in the presence of methylcellulose or excess skeletal muscle actin. Symmetry breaking and movement initiation occurred by two distinct modes: either stochastic amplification of local variation for small beads in concentrated extracts, or gradual accumulation of strain in the actin gel for large beads in dilute extracts. Neither mode was sufficient to enable spherical particles to break symmetry in the cytoplasm of living cells.

Forces generated during actin-based propulsion: a direct measurement by micromanipulation

Dynamic actin networks generate forces for numerous types of movements such as lamellipodia protrusion or the motion of endocytic vesicles. The actin-based propulsive movement of Listeria monocytogenes or of functionalized microspheres have been extensively used as model systems to identify the biochemical components that are necessary for actin-based motility. However, quantitative force measurements are required to elucidate the mechanism of force generation, which is still under debate. To directly probe the forces generated in the process of actin-based propulsion, we developed a micromanipulation experiment. A comet growing from a coated polystyrene bead is held by a micropipette while the bead is attached to a force probe, by using a specially designed "flexible handle." This system allows us to apply both pulling and pushing external forces up to a few nanonewtons. By pulling the actin tail away from the bead at high speed, we estimate the elastic modulus of the gel and measure the force necessary to detach the tail from the bead. By applying a constant force in the range of -1.7 to 4.3 nN, the force-velocity relation is established. We find that the relation is linear for pulling forces and decays more weakly for pushing forces. This behavior is explained by using a dimensional elastic analysis.

Polymer motors: pushing out the front and pulling up the back

Mechanical work in cells is performed by specialized motor proteins that operate in a continuous mechanochemical cycle. Less complex, but still efficient, 'one-shot' motors evolved based on the assembly and disassembly of polymers. We review the mechanisms of pushing and pulling by actin and microtubule filaments and the organizational principles of actin networks. We show how these polymer force generators are used for the propulsion of intracellular pathogens, protrusion of lamellipodia and mitotic movements. We discuss several examples of cellular forces generated by the assembly and disassembly of polymer gels.

Evidence implicating the 5' untranslated region of Listeria monocytogenes actA in the regulation of bacterial actin-based motility

The ActA protein of Listeria monocytogenes is a major virulence factor, essential for the recruitment and polymerization of host actin filaments that lead to intracellular motility and cell-to-cell spread of bacteria within the infected host. The expression of actA is tightly regulated and is strongly induced only when L. monocytogenes is within the host cytosol. Intracellular induction of actA expression is mediated through a single promoter element that directs the expression of a messenger RNA with a long (150 bp) 5' untranslated region (UTR). Deletion of the actA+3 to +130 upstream region was found to result in bacterial mutants that were no longer capable of intracellular actin recruitment or cell-to-cell spread, thus indicating that this region is important for actA expression. L. monocytogenes strains that contained smaller deletions (21-23 bp) within the actA upstream region demonstrated a range of actA expression levels that coincided with the amount of bacterial cell-to-cell spread observed within infected monolayers. A correlation appeared to exist between levels of actA expression and the ability of L. monocytogenes to transition from uniform actin accumulation surrounding individual bacteria (actin clouds) to directional assembly and the formation of actin tails. Bacterial mutants containing deletions that most significantly altered the predicted secondary structure of the actA mRNA 5' UTR had the largest reductions in actA expression. These results suggest that the actA 5' UTR is required for maximal ActA synthesis and that a threshold level of ActA synthesis must be achieved to promote the transition from bacteria-associated actin clouds to directional actin assembly and movement.

Role of tensile stress in actin gels and a symmetry-breaking instability

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a "comet" pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro.

The effect of diffusion, depolymerization and nucleation promoting factors on actin gel growth

In eukaryotic cells, localized actin polymerization is able to deform the plasma membrane and push the cell forward. Depolymerization of actin filaments and diffusion of actin monomers ensure the availability of monomers at sites of polymerization, and therefore these processes must play an active role in cellular actin dynamics. Here we reveal experimental evidence that actin gel growth can be limited by monomer diffusion, consistent with theoretical predictions. We study actin gels formed on beads coated with ActA (and ActA fragments), the bacterial factor responsible for actin-based movement of Listeria monocytogenes. We observe a saturation of gel thickness with increasing bead radius, the signature of diffusion control. Data analysis using an elastic model of actin gel growth gives an estimate of 2x10(-8) cm(-2) s(-1) for the diffusion coefficient of actin monomers through the gel, ten times less than in buffer, and in agreement with literature values in bulk cytoskeleton, providing corroboration of our model. The depolymerization rate of actin filaments and the elastic modulus of the gel are also evaluated. Furthermore, we qualitatively examine the different actin gels produced when ActA fragments interact with either VASP or the Arp2/3 complex.

Biomimetic Systems for Studying Actin-Based Motility

Actin polymerization provides a major driving force for eukaryotic cell motility. Successive intercalation of monomeric actin subunits between the plasma membrane and the filamentous actin network results in protrusions of the membrane enabling the cell to move or to change shape. One of the challenges in understanding eukaryotic cell motility is to dissect the elementary biochemical and biophysical steps that link actin polymerization to mechanical force generation. Recently, significant progress was made using biomimetic, in vitro systems that are inspired by the actin-based motility of bacterial pathogens such as Listeria monocytogenes. Polystyrene microspheres and synthetic phospholipid vesicles coated with proteins that initiate actin polymerization display motile behavior similar to Listeria, mimicking the leading edge of lamellipodia and filopodia. A major advantage of these biomimetic systems is that both biochemical and physical parameters can be controlled precisely. These systems provide a test bed for validating theoretical models on force generation and polarity establishment resulting from actin polymerization. In this review, we discuss recent experimental progress using biomimetic systems propelled by actin polymerization and discuss these results in the light of recent theoretical models on actin-based motility.

Compression forces generated by actin comet tails on lipid vesicles

Polymerizing networks of actin filaments generate force for a variety of movements in living cells, including protrusion of filopodia and lamellipodia, intra- and intercellular motility of certain bacterial and viral pathogens, and motility of endocytic vesicles and other membrane-bound organelles. During actin-based motility, coexisting populations of actin filaments exert both pushing and retarding forces on the moving cargo. To examine the distribution and magnitude of forces generated by actin, we have developed a model system where large artificial lipid vesicles coated with the protein ActA from the bacterial pathogen Listeria monocytogenes are propelled by actin polymerization in cytoplasmic extract. We find that motile vesicles associated with actin comet tails are significantly deformed due to an inward compression force exerted by actin polymerization orthogonal to the direction of motion, which is >10-fold greater in magnitude than the component of the force exerted in the direction of motion. Furthermore, there is a spatial segregation of the pushing and retarding forces, such that pushing predominates along the sides of the vesicle, although retarding forces predominate at the rear. We estimate that the total net (pushing minus retarding) force generated by the actin comet tail is approximately 0.4-4 nN. In addition, actin comet tail formation is associated with polarization of the ActA protein on the fluid vesicle surface, which may reinforce the persistence of unidirectional motion by helping to maintain a persistent asymmetry of actin filament density.

Probing polymerization forces by using actin-propelled lipid vesicles

Actin polymerization provides a powerful propulsion force for numerous types of cell motility. Although tremendous progress has been made in identifying the biochemical components necessary for actin-based motility, the precise biophysical mechanisms of force generation remain unclear. To probe the polymerization forces quantitatively, we introduce an experimental system in which lipid vesicles coated with the Listeria monocytogenes virulence factor ActA are propelled by actin polymerization. The polymerization forces cause significant deformations of the vesicle. We have used these deformations to obtain a spatially resolved measure of the forces exerted on the membrane using a model based on the competition between osmotic pressure and membrane stretching. Our results indicate that actin exerts retractile or propulsive forces depending on the local membrane curvature and that the membrane is strongly bound to the actin gel. These results are consistent with the observed dynamics. After a slow elongation of the vesicle from a spherical shape, the strong bonds between the actin gel and the membrane rupture if the retractile forces exceed a critical value, leading to a rapid release of the vesicle's trailing edge.

Local force induced conical protrusions of phagocytic cells

Magnetic tweezers were used to study the passive and active response of macrophages to local centripetal nanonewton forces on beta1 integrins. Superparamagnetic beads coated with the beta1-integrin-binding protein invasin were attached to J774 murine macrophages to mimic phagocytosis of bacterial pathogens. Forces exceeding approximately 0.5 nN induce the active formation of trumpet-like protrusions resembling pseudopodia after an initial elastic deflection and a response time of approximately 30 seconds. The speed of advancement of the protrusion is <v>=0.065+/-0.020 micro m second(-1) and is force independent. After saturation (after about 100 seconds) the protrusion stops abruptly and is completely retracted again against forces exceeding 5 nN with an effective relaxation time of approximately 30 seconds. The active protrusion is tentatively attributed to the growth of the actin cortex in the direction of the force, and evidence for the involvement of actin is provided by the finding that Latrunculin A abolishes the activated cone growth. The growth is assumed to be activated by cell signaling mediated by the invasin-specific integrins (exhibiting beta1 chains) and could play a role in phagocytic and protrusive events during immune response by macrophages.

Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.

A biomimetic motility assay provides insight into the mechanism of actin-based motility

Abiomimetic motility assay is used to analyze the mechanism of force production by site-directed polymerization of actin. Polystyrene microspheres, functionalized in a controlled fashion by the N-WASP protein, the ubiquitous activator of Arp2/3 complex, undergo actin-based propulsion in a medium that consists of five pure proteins. We have analyzed the dependence of velocity on N-WASP surface density, on the concentration of capping protein, and on external force. Movement was not slowed down by increasing the diameter of the beads (0.2 to 3 microm) nor by increasing the viscosity of the medium by 10(5)-fold. This important result shows that forces due to actin polymerization are balanced by internal forces due to transient attachment of filament ends at the surface. These forces are greater than the viscous drag. Using Alexa488-labeled Arp2/3, we show that Arp2/3 is incorporated in the actin tail like G-actin by barbed end branching of filaments at the bead surface, not by side branching, and that filaments are more densely branched upon increasing gelsolin concentration. These data support models in which the rates of filament branching and capping control velocity, and autocatalytic branching of filament ends, rather than filament nucleation, occurs at the particle surface.

Actin-based motility as a self-organized system: mechanism and reconstitution in vitro

Site-directed actin polymerisation in response to signalling is responsible for the formation of cell protrusions. These elementary 'actin-based motility processes' are involved in cell locomotion, cell metastasis, organ morphogenesis and microbial pathogenesis. We have reconstituted actin-based propulsive movement of particles of various sizes and geometries (rods, microspheres) in a minimum motility medium containing five pure proteins. The ATP-supported treadmilling of actin filaments, regulated by Actin Depolymerizing Factor (ADF/cofilin), profilin and capping proteins provides the thermodynamic basis for sustained actin-based movement. Local activation of Arp2/3 complex at the surface of the particle promotes autocatalytic barbed end branching of filaments, generating a polarized arborescent array. Barbed end growth of branched filaments against the surface generates a propulsive force and is eventually arrested by capping proteins. Understanding the mechanism of actin-based movement requires elucidation of the biochemical properties and mode of action of Arp2/3 complex in filament branching, in particular the role of ATP binding and hydrolysis in Arp2/3, and a physical analysis of the movement of functionalised particles. Because the functionalisation of the particle by an activator of Arp2/3 complex (N-WASP or the Listeria protein ActA) and the concentrations of effectors in the medium are controlled, the reconstituted motility assay allows an analysis of the mechanism of force production at the mesoscopic and molecular levels.

The dynamics of actin-based motility depend on surface parameters

In cells, actin polymerization at the plasma membrane is induced by the recruitment of proteins such as the Arp2/3 complex, and the zyxin/VASP complex. The physical mechanism of force generation by actin polymerization has been described theoretically using various approaches, but lacks support from experimental data. By the use of reconstituted motility medium, we find that the Wiskott Aldrich syndrome protein (WASP) subdomain, known as VCA, is sufficient to induce actin polymerization and movement when grafted on microspheres. Changes in the surface density of VCA protein or in the microsphere diameter markedly affect the velocity regime, shifting from a continuous to a jerky movement resembling that of the mutated 'hopping' Listeria. These results highlight how simple physical parameters such as surface geometry and protein density directly affect spatially controlled actin polymerization, and play a fundamental role in actin-dependent movement.

Clamped-filament elongation model for actin-based motors

Although actin-based motility drives cell crawling and intracellular locomotion of organelles and certain pathogens, the underlying mechanism of force generation remains a mystery. Recent experiments demonstrated that Listeria exhibit episodes of 5.4-nm stepwise motion corresponding to the periodicity of the actin filament subunits, and extremely small positional fluctuations during the intermittent pauses [S. C. Kuo and J. L. McGrath. 2000. Nature. 407:1026-1029]. These findings suggest that motile bacteria remain firmly bound to actin filament ends as they elongate, a behavior that appears to rule out previous models for actin-based motility. We propose and analyze a new mechanochemical model (called the "Lock, Load & Fire" mechanism) for force generation by means of affinity-modulated, clamped-filament elongation. During the locking step, the filament's terminal ATP-containing subunit binds tightly to a clamp situated on the surface of a motile object; in the loading step, actin.ATP monomer(s) bind to the filament end, an event that triggers the firing step, wherein ATP hydrolysis on the clamped subunit attenuates the filament's affinity for the clamp. This last step initiates translocation of the new ATP-containing terminus to the clamp, whereupon another cycle begins anew. This model explains how surface-tethered filaments can grow while exerting flexural or tensile force on the motile surface. Moreover, stochastic simulations of the model reproduce the signature motions of Listeria. This elongation motor, which we term actoclampin, exploits actin's intrinsic ATPase activity to provide a simple, high-fidelity enzymatic reaction cycle for force production that does not require elongating filaments to dissociate from the motile surface. This mechanism may operate whenever actin polymerization is called upon to generate the forces that drive cell crawling or intracellular organelle motility.

ActA and human zyxin harbour Arp2/3-independent actin-polymerization activity

The actin cytoskeleton is a dynamic network that is composed of a variety of F-actin structures. To understand how these structures are produced, we tested the capacity of proteins to direct actin polymerization in a bead assay in vitro and in a mitochondrial-targeting assay in cells. We found that human zyxin and the related protein ActA of Listeria monocytogenes can generate new actin structures in a vasodilator-stimulated phosphoprotein-dependent (VASP) manner, but independently of the Arp2/3 complex. These results are consistent with the concept that there are multiple actin-polymerization machines in cells. With these simple tests it is possible to probe the specific function of proteins or identify novel molecules that act upon cellular actin polymerization.

An elastic analysis of Listeria monocytogenes propulsion

The bacterium Listeria monocytogenes uses the energy of the actin polymerization to propel itself through infected tissues. In steady state, it continuously adds new polymerized filaments to its surface, pushing on its tail, which is made from previously cross-linked actin filaments. In this paper we introduce an elastic model to describe how the addition of actin filaments to the tail results in the propulsive force on the bacterium. Filament growth on the bacterial surface produces stresses that are relieved at the back of the bacterium as it moves forward. The model leads to a natural competition between growth from the sides and growth from the back of the bacterium, with different velocities and strengths for each. This competition can lead to the periodic motion observed in a Listeria mutant.

Motility powered by supramolecular springs and ratchets

Not all biological movements are caused by molecular motors sliding along filaments or tubules. Just as springs and ratchets can store or release energy and rectify motion in physical systems, their analogs can perform similar functions in biological systems. The energy of biological springs is derived from hydrolysis of a nucleotide or the binding of a ligand, whereas biological ratchets are powered by Brownian movements of polymerizing filaments. However, the viscous and fluctuating cellular environment and the mechanochemistry of soft biological systems constrain the modes of motion generated and the mechanisms for energy storage, control, and release.