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.     

Water in actin polymerization.

We have addressed the question whether water is part of the G- to F-actin polymerization reaction. Under osmotic stress, the critical concentration for G-Ca-ATP actin was reduced for six different osmolytes. These results are interpreted as showing that reducing water activity favored the polymerized state. The magnitude of the effect correlated, then saturated, with increasing MW of the osmolyte and suggested that up to 10-12 fewer water molecules were associated with actin when it polymerized. By contrast, osmotic effects were insignificant for Mg-ATP actin. The nucleotide binding site of the Mg conformation is more closed than the Ca and more closely resembles the closed actin conformation in the polymerized state. These results suggest that the water may come from the cleft of the nucleotide binding site.     

In vivo imaging of the actin polymerization state with two-photon fluorescence anisotropy

Using two-photon fluorescence anisotropy imaging of actin-GFP, we have developed a method for imaging the actin polymerization state that is applicable to a broad range of experimental systems extending from fixed cells to live animals. The incorporation of expressed actin-GFP monomers into endogenous actin polymers enables energy migration FRET (emFRET, or homoFRET) between neighboring actin-GFPs. This energy migration reduces the normally high polarization of the GFP fluorescence. We derive a simple relationship between the actin-GFP fluorescence polarization anisotropy and the actin polymer fraction, thereby enabling a robust means of imaging the actin polymerization state with high spatiotemporal resolution and providing what to the best of our knowledge are the first direct images of the actin polymerization state in live, adult brain tissue and live, intact Drosophila larvae.     

Microtubules and actin microfilaments in the amphibian bladder granular cells

Microtubules and microfilaments were localized by an immunocytochemical method in the granular cells of the frog bladder after fixation and isolation. An extensive array of microtubules was observed in the granular cells with an orientation towards the luminal plasma membrane in the supranuclear zone. Actin filaments formed a continuous bundle that underlined the cellular membrane. After incubation in the presence of colchicine, nocodazole, or tubulozole, the microtubular network appeared fragmented but did not disappear completely. These observations are related to the role of the cytoskeleton in the permeability response of the frog bladder epithelium to vasopressin.     

Surface-induced polymerization of actin

Living cells contain a very large amount of membrane surface area, which potentially influences the direction, the kinetics, and the localization of biochemical reactions. This paper quantitatively evaluates the possibility that a lipid monolayer can adsorb actin from a nonpolymerizing solution, induce its polymerization, and form a 2D network of individual actin filaments, in conditions that forbid bulk polymerization. G- and F-actin solutions were studied beneath saturated Langmuir monolayers containing phosphatidylcholine (PC, neutral) and stearylamine (SA, a positively charged surfactant) at PC:SA = 3:1 molar ratio. Ellipsometry, tensiometry, shear elastic measurements, electron microscopy, and dark-field light microscopy were used to characterize the adsorption kinetics and the interfacial polymerization of actin. In all cases studied, actin follows a monoexponential reaction-limited adsorption with similar time constants (approximately 10(3) s). At a longer time scale the shear elasticity of the monomeric actin adsorbate increases only in the presence of lipids, to a 2D shear elastic modulus of mu approximately 30 mN/m, indicating the formation of a structure coupled to the monolayer. Electron microscopy shows the formation of a 2D network of actin filaments at the PC:SA surface, and several arguments strongly suggest that this network is indeed causing the observed elasticity. Adsorption of F-actin to PC:SA leads more quickly to a slightly more rigid interface with a modulus of mu approximately 50 mN/m.     

Polyamine-induced actin polymerization.

Muscle actin has been found to polymerize reversibly upon addition of low concentrations of polyamines. This polymerization, studied by centrifugation, has shown a linear relationship between the actin polymerization yield and the chain length of the polyamine. Among the biological polyamines tested, spermidine and spermine are the most efficient. The polymerization of actin can also be induced by the corresponding mono or diguanidine derivatives of these polyamines but monoamines or amino acids are inactive at the same concentration. The transformation of actin from a globular to a fibrous from upon addition of spermidine is also demonstrated by the changes in the near-ultraviolet circular dichoroic spectrum of this protein. Moreover, the polyamine-induced F -actin exhibits the same properties as the salt-induced F -actin: it strongly activates the Mg2+ -ATPase of myosin, its specific viscosity is enhanced to the same extent and electron micrographs show homogeneous thin filaments.     

Effects of jasplakinolide on the kinetics of actin polymerization. An explanation for certain in vivo observations

Jasplakinolide paradoxically stabilizes actin filaments in vitro, but in vivo it can disrupt actin filaments and induce polymerization of monomeric actin into amorphous masses. A detailed analysis of the effects of jasplakinolide on the kinetics of actin polymerization suggests a resolution to this paradox. Jasplakinolide markedly enhances the rate of actin filament nucleation. This increase corresponds to a change in the size of actin oligomer capable of nucleating filament growth from four to approximately three subunits, which is mechanistically consistent with the localization of the jasplakinolide-binding site at an interface of three actin subunits. Because jasplakinolide both decreases the amount of sequestered actin (by lowering the critical concentration of actin) and augments nucleation, the enhancement of polymerization by jasplakinolide is amplified in the presence of actin-monomer sequestering proteins such as thymosin beta(4). Overall, the kinetic parameters in vitro define the mechanism by which jasplakinolide induces polymerization of monomeric actin in vivo. Expected consequences of jasplakinolide function are consistent with the experimental observations and include de novo nucleation resulting in disordered polymeric actin and in insufficient monomeric actin to allow for remodeling of stress fibers.     

Competition between Blown fuse and WASP for WIP binding regulates the dynamics of WASP-dependent actin polymerization in vivo

Dynamic rearrangements of the actin cytoskeleton play a key role in numerous cellular processes. In Drosophila, fusion between a muscle founder cell and a fusion competent myoblast (FCM) is mediated by an invasive, F-actin-enriched podosome-like structure (PLS). Here, we show that the dynamics of the PLS is controlled by Blown fuse (Blow), a cytoplasmic protein required for myoblast fusion but whose molecular function has been elusive. We demonstrate that Blow is an FCM-specific protein that colocalizes with WASP, WIP/Solitary, and the actin focus within the PLS. Biochemically, Blow modulates the stability of the WASP-WIP complex by competing with WASP for WIP binding, leading to a rapid exchange of WASP, WIP and G-actin within the PLS, which, in turn, actively invades the adjacent founder cell to promote fusion pore formation. These studies identify a regulatory protein that modulates the actin cytoskeletal dynamics by controlling the stability of the WASP-WIP complex.     

In vivo evaluation of hsp27 as an inhibitor of actin polymerization: hsp27 limits actin stress fiber and focal adhesion formation after heat shock

The role of hsp27 as an inhibitor of actin polymerization was considered in the context of the actin cytoskeleton and its relationship with focal adhesion formation. The aim of this study was to evaluate the potential effects of hsp27 on focal adhesion formation as a relevant biological consequence of actin stress fiber formation. When hsp27 was overexpressed in stably transfected cells, cell attachment was delayed and recovery of disrupted stress fibers and focal adhesions was limited. In ROS 17/2.8 cells, heat shock caused the reversible disruption of stress fibers and focal adhesions. The loss of stress fibers and focal adhesions was associated with reduced phosphotyrosine on the focal adhesion kinase (FAK). Microinjection of recombinant 6-His hsp27 and phosphorylated 6-His hsp27 was used to demonstrate that nonphosphorylated hsp27 prevented the recovery of stress fibers and focal adhesions. These results provide in vivo evidence that hsp27 acts as an inhibitor of actin polymerization that can alter cellular interactions with extracellular environments by perturbation of stress fibers, and subsequently focal adhesions.     

Amplification of actin polymerization forces

The actin cytoskeleton drives many essential processes in vivo, using molecular motors and actin assembly as force generators. We discuss here the propagation of forces caused by actin polymerization, highlighting simple configurations where the force developed by the network can exceed the sum of the polymerization forces from all filaments.

Introduction

Mechanical amplification is something we experience every day, in the form of gears, pulleys, and levers. While climbing a hill on a bicycle, for instance, shifting gears increases the force on the wheels while limiting the pressure required on the pedals. However, energy has to be conserved, and because mechanical work is defined as force × displacement, an increase in force can only be obtained at the expense of displacement. Thus, although shifting gears allows one to develop the additional force needed to go uphill, speed is reduced as each pedal stroke produces a smaller turn of the wheels. Cells have similarly developed microscopic force amplification strategies during evolution. Here, we discuss some amplification schemes for one of the major force generators in the cell—actin polymerization.Actin plays a ubiquitous role in cell motility and morphogenesis, spanning many scales of space and time. In fission yeast, for example, a miniature actin machinery only ∼100 nm across can induce the invagination of an endocytic vesicle in just a few seconds (Picco et al., 2015). However, to sever the entire yeast cell, a cytokinetic ring forms with an initial perimeter of ∼10 µm and requires ∼30 min to drive division (Proctor et al., 2012). These assemblies differ dramatically in both size and duration. In other species, considerably larger actin assemblies exist that reach the scale of centimeters, such as in muscle cells. Clearly, actin and its associated factors need to be specifically organized to achieve these different functions (Fig. 1). From a functional point of view, a key problem is to understand how the global architecture of an actin network allows forces that are produced at the molecular scale to be productive for the cell. In this respect, we can distinguish two sorts of components. Active components generate forces from chemical sources of energy and include molecular motors, as well as actin itself, which can push by polymerizing (Kovar and Pollard, 2004) and possibly pull while depolymerizing. Passive components, such as actin cross-linkers, are essential but can only transmit forces generated by other elements.Open in a separate windowFigure 1.Different actin networks. Networks of actin filaments are essential for many biological processes at the cellular level, and the organization of the filaments in space must be adapted to the task. Here, polymerization force (orange) of actin filaments (red) occurs near the plasma membrane (blue). Linear filopodia bundles with fascin (black) can produce high speeds, but represent a weak configuration for force generation. Lamellipodia are thin cellular extensions in which filaments are nearly parallel to the substrate on which the cell is crawling. The 2D branched network, created by Arp2/3 actin-nucleating complexes (black), can produce higher forces at the expense of displacement. During endocytosis in yeast, actin forms a 3D network at the site of the invagination that appears roughly spherical, but the organization of actin filaments in space is not known. The coat structure (yellow) enables actin to pull the membrane inward and actin polymerizes near the base of the structure, where Arp2/3 nucleators are shown in black (Picco et al., 2015). Endocytosis requires strong force amplification to pull the invagination against the turgor pressure.The forces developed by an actin meshwork are determined by the organization of its components. Ultimately, these forces must be sufficient to drive biological processes, and thus their scale depends on the physical characteristics of the cell. For example, in the case of endocytosis in yeast, the turgor pressure pushing the surface of the invagination outward reaches ∼1,000 pN, which the actin machinery must overcome (Basu et al., 2014). During cytokinesis, the actomyosin ring also works against the turgor pressure, which produces high forces on the furrow (Proctor et al., 2012). For both cases, these forces have been calculated from measured cellular parameters, particularly the turgor pressure and the dimensions over which the membrane is deformed. Hence, for these processes at least, the two ends of the problem are known: the forces produced by the molecular components make up the input and the force required for the cellular process to occur represents the output. Yet the force balance within the system must be considered to understand how the actin machinery harvests the input to produce this output.In this comment, we focus on the transmission of forces produced by the polymerization of actin, setting aside turnover and the contribution of molecular motors. We discuss specifically how the arrangement of the filaments in the system regulates the amount of productive force. In many ways, the actin machinery behaves analogously to a cyclist: though its power is limited, it can “shift gears” to favor either more displacement (high gears) or more force (low gears).

The force generated by actin polymerization

Actin polymerization can produce force. Indeed if an actin monomer in solution binds the barbed end of a filament, there is a change of free energy (ΔG_p) and polymerization will occur if ΔG_p < 0 (Fig. 2 A). This reaction depends on the concentration (C) of monomeric actin and will take place only above a critical concentration (C* of ∼0.14 µM; Pollard, 1986). It is associated with ΔG_p = −k_BT ln(C/C*), where k_B is the Boltzmann constant and T is the absolute temperature. If actin is polymerizing against a load and producing work (W), the change in free energy is ΔG_p + W. In this case, polymerization will occur spontaneously if the change is negative, i.e., ΔG_p + W < 0. Consider an actin filament pushing against a force (f) applied parallel to the filament axis (Fig. 2 B). Because the addition of one actin monomer produces a displacement (δ = 2.75 nm; Holmes et al., 1990), the mechanical work is W = f × δ. Forces that are antagonistic to elongation can impede actin assembly (Peskin et al., 1993). The critical force under which the filament would cease to elongate is called the polymerization force (f_a). Using a physiological concentration (C of ∼40 µM; Wu and Pollard, 2005), the polymerization force is thermodynamically limited to k_BT ln(C/C*)/δ = ∼9 pN (Hill, 1981). Within such limits, the force developed by polymerization will depend on the conditions of assembly. Direct measurements of the polymerization force using single-molecule techniques are scarce. A first study used optical traps on bare filaments, giving a force of ∼1 pN (Footer et al., 2007). By monitoring the buckling of filaments capped with formins, a second study found the force to be ∼1.3 pN (Kovar and Pollard, 2004). In both cases, the concentration of actin was an order of magnitude lower than in vivo, and the measured forces were in fact close to the theoretical maximum under the experimental conditions. Here, we will thus consider that f_a is within 1 and 9 pN. We further assume that an actin filament is able to elongate as long as the parallel component of the antagonistic force at its barbed end remains lower than f_a, irrespective of the perpendicular components (Fig. 2 C). We discuss various examples of force amplification in which the network develops forces that exceed f_a per filament, without breaking the thermodynamic requirement for actin polymerization (ΔG_p + W < 0).Open in a separate windowFigure 2.Polymerization mechanics. (A) During polymerization, the addition of one actin monomer (orange) corresponds to an elongation (δ) at the barbed end of an actin filament (red) and is associated with a change of free energy (ΔG_p = −k_b T ln(C/C*)). (B) The work required to push a load over a distance (h) with a force (f) is f × h, and thus assembly remains favorable as long as ΔG_p + f × h < 0. In the case where polymerization occurs straight against a load (h = δ), the maximal force (f_a) is f_a = k_b T ln(C/C*)/δ (Hill, 1981). (C) If the filament encounters the load with an angle (θ), then h = δ sinθ and the maximal force is consequently increased: f_θ = f_a/sinθ. (D) In the branched network of a lamellipod, actin grows against the leading membrane at an angle (θ = ∼54°). In the absence of friction, the force between the polymerizing tip (orange) of the actin and the membrane (blue) is perpendicular to the membrane. It can then reach a maximum magnitude of f_a/sinθ. The sum of the forces produced by the two filaments is then ∼2.5 f_a. (E) Higher forces arise by polymerizing with shallow angles. The device illustrated here is composed of a growing actin filament with a “leg” on its side. By elongating, the filament will induce rotation around the pivot point, where the leg is contacting the membrane. High forces can be exerted on a load supported at the branch point, as a result of the amplification achieved by the lever arm and contact angle. (F) The highest forces are generated if a filament polymerizes parallel to the surface. In the illustrated configuration, elongation of the filament will cause a load (green dome) to separate from the membrane. The maximal force is calculated as in E, except that anchoring has to be assumed at the pivot point to balance forces horizontally. The device can sustain high forces applied on the top of the dome because the upward movement is small compared with the elongation of the filament.

Table 1.

Physical characteristics of actin

GCS1, an Arf guanosine triphosphatase-activating protein in Saccharomyces cerevisiae, is required for normal actin cytoskeletal organization in vivo and stimulates actin polymerization in vitro

Recent cloning of a rat brain phosphatidylinositol 3,4, 5-trisphosphate binding protein, centaurin alpha, identified a novel gene family based on homology to an amino-terminal zinc-binding domain. In Saccharomyces cerevisiae, the protein with the highest homology to centaurin alpha is Gcs1p, the product of the GCS1 gene. GCS1 was originally identified as a gene conditionally required for the reentry of cells into the cell cycle after stationary phase growth. Gcs1p was previously characterized as a guanosine triphosphatase-activating protein for the small guanosine triphosphatase Arf1, and gcs1 mutants displayed vesicle-trafficking defects. Here, we have shown that similar to centaurin alpha, recombinant Gcs1p bound phosphoinositide-based affinity resins with high affinity and specificity. A novel GCS1 disruption strain (gcs1Delta) exhibited morphological defects, as well as mislocalization of cortical actin patches. gcs1Delta was hypersensitive to the actin monomer-sequestering drug, latrunculin-B. Synthetic lethality was observed between null alleles of GCS1 and SLA2, the gene encoding a protein involved in stabilization of the actin cytoskeleton. In addition, synthetic growth defects were observed between null alleles of GCS1 and SAC6, the gene encoding the yeast fimbrin homologue. Recombinant Gcs1p bound to actin filaments, stimulated actin polymerization, and inhibited actin depolymerization in vitro. These data provide in vivo and in vitro evidence that Gcs1p interacts directly with the actin cytoskeleton in S. cerevisiae.     

Microtubules in neurons as information carriers

Microtubules in neurons consist of highly dynamic regions as well as stable regions, some of which persist after bouts of severing as short mobile polymers. Concentrated at the plus ends of the highly dynamic regions are microtubule plus end tracking proteins called +TIPs that can interact with an array of other proteins and structures relevant to the plasticity of the neuron. It is also provocative to ponder that short mobile microtubules might similarly convey information with them as they transit within the neuron. Thus, beyond their known conventional functions in supporting neuronal architecture and organelle transport, microtubules may act as ‘information carriers’ in the neuron.

     

N-ethylmaleimide cannot inhibit actin polymerization in platelets

We investigated the effects of the N-ethylmaleimide (NEM), a sulfhydryl(SH) radical blocker, on platelet activation. Platelet aggregation and ATP release was suppressed by 0.2 mM NEM during ADP (20 microM) stimulation and by 0.5 mM NEM during A23187 (4 microM) stimulation. However the agent had no effect on actin polymerization in stimulated platelets. In the absence of a stimulant, NEM (over 1 mM) induced shape changes and slight (5%) actin polymerization, but not aggregation or ATP release. Although platelet aggregation and ATP release were suppressed by the addition of 1 mM NEM during the process of both reactions, the amount of polymerized actin was not influenced by the addition. The reconstructed system consisting of actin and partially purified regulatory proteins without myosin showed a dose-dependent increase in turbidity by the addition of NEM. From these findings, we concluded that NEM enhances actin polymerization, although actin molecules contain SH-radicals, and that actin polymerization has little affect on aggregation and release reaction.     

Surfing pathogens and the lessons learned for actin polymerization

A number of unrelated bacterial species as well as vaccinia virus (ab)use the process of actin polymerization to facilitate and enhance their infection cycle. Studies into the mechanism by which these pathogens hijack and control the actin cytoskeleton have provided many interesting insights into the regulation of actin polymerization in migrating cells. This review focuses on what we have learnt from the actin-based motilities of Listeria, Shigella and vaccinia and discusses what we would still like to learn from our nasty friends, including enteropathogenic Escherichia coli and Rickettsia