Interplay between Brownian motion and cross-linking controls bundling dynamics in actin networks

Morphology changes in cross-linked actin networks are important in cell motility, division, and cargo transport. Here, we study the transition from a weakly cross-linked network of actin filaments to a heavily cross-linked network of actin bundles through microscopic Brownian dynamics simulations. We show that this transition occurs in two stages: first, a composite bundle network of small and highly aligned bundles evolves from cross-linking of individual filaments and, second, small bundles coalesce into the clustered bundle state. We demonstrate that Brownian motion speeds up the first stage of this process at a faster rate than the second. We quantify the time to reach the composite bundle state and show that it strongly increases as the mesh size increases only when the concentration of cross-links is small and that it remains roughly constant if we decrease the relative ratio of cross-linkers as we increase the actin concentration. Finally, we examine the dependence of the bundling timescale on filament length, finding that shorter filaments bundle faster because they diffuse faster.     

Kinetics of filament bundling with attractive interactions

We study the kinetics of filament bundling by variable time-step Brownian-dynamics simulations employing a simplified attractive potential based on earlier atomic-level calculations for actin filaments. Our results show that collisions often cluster in time, due to memory in the random walk. The clustering increases the bundling opportunities. Small-angle collisions and collisions with short center-to-center distance are more likely to lead to bundling. Increasing the monomer-monomer attraction decreases the bundling time to a diffusional limit, which is determined by the capture cross-section and diffusion coefficients. The simulations clearly show that the bundling process consists of two sequential phases: rotation, by which two filaments align parallel to each other; and sliding, by which they maximize their contact length. Whether two filaments bundle or not is determined by the competition between rotation to a parallel state and escape. Increasing the rotational diffusion coefficient and attraction enhances rotation; decreasing attraction and increasing the translational diffusion coefficients enhance escape. Because of several competing effects, the filament length only affects the bundling time weakly.     

Polymerization and bundling kinetics of FtsZ filaments

FtsZ is a tubulin homolog essential for prokaryotic cell division. In living bacteria, FtsZ forms a ringlike structure (Z-ring) at the cell midpoint. Cell division coincides with a gradual contraction of the Z-ring, although the detailed molecular structure of the Z-ring is unknown. To reveal the structural properties of FtsZ, an understanding of FtsZ filament and bundle formation is needed. We develop a kinetic model that describes the polymerization and bundling mechanism of FtsZ filaments. The model reveals the energetics of the FtsZ filament formation and the bundling energy between filaments. A weak lateral interaction between filaments is predicted by the model. The model is able to fit the in vitro polymerization kinetics data of another researcher, and explains the cooperativity observed in FtsZ kinetics and the critical concentration in different buffer media. The developed model is also applicable for understanding the kinetics and energetics of other bundling biopolymer filaments.     

Affinity of alpha-actinin for actin determines the structure and mechanical properties of actin filament gels.

Proteins that cross-link actin filaments can either form bundles of parallel filaments or isotropic networks of individual filaments. We have found that mixtures of actin filaments with alpha-actinin purified from either Acanthamoeba castellanii or chicken smooth muscle can form bundles or isotropic networks depending on their concentration. Low concentrations of alpha-actinin and actin filaments form networks indistinguishable in electron micrographs from gels of actin alone. Higher concentrations of alpha-actinin and actin filaments form bundles. The threshold for bundling depends on the affinity of the alpha-actinin for actin. The complex of Acanthamoeba alpha-actinin with actin filaments has a Kd of 4.7 microM and a bundling threshold of 0.1 microM; chicken smooth muscle has a Kd of 0.6 microM and a bundling threshold of 1 microM. The physical properties of isotropic networks of cross-linked actin filaments are very different from a gel of bundles: the network behaves like a solid because each actin filament is part of a single structure that encompasses all the filaments. Bundles of filaments behave more like a very viscous fluid because each bundle, while very long and stiff, can slip past other bundles. We have developed a computer model that predicts the bundling threshold based on four variables: the length of the actin filaments, the affinity of the alpha-actinin for actin, and the concentrations of actin and alpha-actinin.     

Actin filament bundling by fimbrin is important for endocytosis, cytokinesis, and polarization in fission yeast

Through the coordinated action of diverse actin-binding proteins, cells simultaneously assemble actin filaments with distinct architectures and dynamics to drive different processes. Actin filament cross-linking proteins organize filaments into higher order networks, although the requirement of cross-linking activity in cells has largely been assumed rather than directly tested. Fission yeast Schizosaccharomyces pombe assembles actin into three discrete structures: endocytic actin patches, polarizing actin cables, and the cytokinetic contractile ring. The fission yeast filament cross-linker fimbrin Fim1 primarily localizes to Arp2/3 complex-nucleated branched filaments of the actin patch and by a lesser amount to bundles of linear antiparallel filaments in the contractile ring. It is unclear whether Fim1 associates with bundles of parallel filaments in actin cables. We previously discovered that a principal role of Fim1 is to control localization of tropomyosin Cdc8, thereby facilitating cofilin-mediated filament turnover. Therefore, we hypothesized that the bundling ability of Fim1 is dispensable for actin patches but is important for the contractile ring and possibly actin cables. By directly visualizing actin filament assembly using total internal reflection fluorescence microscopy, we determined that Fim1 bundles filaments in both parallel and antiparallel orientations and efficiently bundles Arp2/3 complex-branched filaments in the absence but not the presence of actin capping protein. Examination of cells exclusively expressing a truncated version of Fim1 that can bind but not bundle actin filaments revealed that bundling activity of Fim1 is in fact important for all three actin structures. Therefore, fimbrin Fim1 has diverse roles as both a filament "gatekeeper" and as a filament cross-linker.     

The bundling of actin with polyethylene glycol 8000 in the presence and absence of gelsolin.

Actin filament and bundle formation occur in the cytosol under conditions of very high total macromolecular concentration. In this study we have utilized the inert molecule polyethylene glycol 8000 (PEG) as a means of simulating crowded conditions in vitro. Column-purified Ca-actin was polymerized in the absence and presence of gelsolin (to regulate mean filament lengths between 50 and 5000 mers) and PEG (2-8%) using various concentrations of KCl and/or 2 mM divalent cations. Bundling was characterized by the scattered light intensity and mean diffusion coefficients obtained from dynamic light scattering, as well as by fluorescence and phase-contrast microscopy. The minimum concentration of KCl required for bundling decreases both with increasing concentration of PEG at a fixed mean filament length, and with decreasing filament length at a fixed concentration of PEG. In the absence of divalent cation, bundling is reversible on dilution, as determined by intensity levels, diffusion coefficients, and microscopy. However, with either 2 mM Mg2+ or Ca2+ added, bundling is irreversible under conditions of higher PEG concentrations or longer filaments, indicating that osmotic pressure effects cannot fully explain actin bundling with PEG. Weaker divalent cation-binding sites on actin as well as disulfide bonds appear to be involved in the irreversible bundling.     

The two actin-binding regions on the myosin heads of cardiac muscle

In the presence of myosin S1 or myosin heads, actin filaments tend to form bundles. The biological meaning of the bundling of actin filaments has been unclear. In this study, we found that the cardiac myosin heads can form the bundles of actin filaments more rapidly than can skeletal S1, as monitored by light scattering and electron microscopy. Moreover, the actin bundles formed by cardiac S1 were found to be more stable against mechanical agitation. The distance between actin filaments in the bundles was approximately 20 nm, which is comparable to the length of a myosin head and two actin molecules. This suggests the direct binding of S1 tails to the adjacent actin filament. The "essential" light chain of cardiac myosin could be cross-linked to the actin molecule in the bundle. When monomeric actin molecules were added to the bundle, the bundles could be dispersed into individual filaments. The three-dimensional structure of the dispersed actin filaments was reconstructed from electron cryo-microscopic images of the single actin filaments dispersed by monomer actin. We were able to demonstrate that cardiac myosin heads bind to two actin molecules: one actin molecule at the conventional actin-binding region and the other at the essential light-chain-binding region. This capability of cardiac myosin heads to bind two actin molecules is discussed in view of lower ATPase activity and slower shortening velocity than those of skeletal ones.     

The Stepping Pattern of Myosin X Is Adapted for Processive Motility on Bundled Actin

Myosin X is a molecular motor that is adapted to select bundled actin filaments over single actin filaments for processive motility. Its unique form of motility suggests that myosin X's stepping mechanism takes advantage of the arrangement of actin filaments and the additional target binding sites found within a bundle. Here we use fluorescence imaging with one-nanometer accuracy to show that myosin X takes steps of ∼18 nm along a fascin-actin bundle. This step-size is well short of the 36-nm step-size observed in myosin V and myosin VI that corresponds to the actin pseudohelical repeat distance. Myosin X is able to walk along bundles with this step-size if it straddles two actin filaments, but would be quickly forced to spiral into the constrained interior of the bundle if it were to use only a single actin filament. We also demonstrate that myosin X takes many sideways steps as it walks along a bundle, suggesting that it can switch actin filament pairs within the bundle as it walks. Sideways steps to the left or the right occur on bundles with equal frequency, suggesting a degree of lateral flexibility such that the motor's working stroke does not bias it to the left or to the right. On single actin filaments, we find a broad mixture of 10-20-nm steps, which again falls short of the 36-nm actin repeat. Moreover, the motor leans to the right as it walks along single filaments, which may require myosin X to adopt strained configurations. As a control, we also tracked myosin V stepping along actin filaments and fascin-actin bundles. We find that myosin V follows a narrower path on both structures, walking primarily along one surface of an actin filament and following a single filament within a bundle while occasionally switching to neighboring filaments. Together, these results delineate some of the structural features of the motor and the track that allow myosin X to recognize actin filament bundles.     

A theoretical analysis of filament length fluctuations in actin and other polymers

Control of the structure and dynamics of the actin cytoskeleton is essential for cell motility and for maintaining the structural integrity of cells. Central to understanding the control of these features is an understanding of the dynamics of actin filaments, first as isolated filaments, then as integrated networks, and finally as networks containing higher-order structures such as bundles, stress fibers and acto-myosin complexes. It is known experimentally that single filaments can exhibit large fluctuations, but a detailed understanding of the transient dynamics involved is still lacking. Here we first study stochastic models of a general system involving two-monomer types that can be analyzed completely, and then we report stochastic simulations on the complete actin model with three monomer types. We systematically examine the transient behavior of filament length dynamics so as to gain a better understanding of the time scales involved in reaching a steady state. We predict the lifetime of a cap of one monomer type and obtain the mean and variance of the survival time of a cap at the filament end, which together determine the filament length fluctuations.     

Stochastic severing of actin filaments by actin depolymerizing factor/cofilin controls the emergence of a steady dynamical regime

Actin dynamics (i.e., polymerization/depolymerization) powers a large number of cellular processes. However, a great deal remains to be learned to explain the rapid actin filament turnover observed in vivo. Here, we developed a minimal kinetic model that describes key details of actin filament dynamics in the presence of actin depolymerizing factor (ADF)/cofilin. We limited the molecular mechanism to 1), the spontaneous growth of filaments by polymerization of actin monomers, 2), the ageing of actin subunits in filaments, 3), the cooperative binding of ADF/cofilin to actin filament subunits, and 4), filament severing by ADF/cofilin. First, from numerical simulations and mathematical analysis, we found that the average filament length, 〈L〉, is controlled by the concentration of actin monomers (power law: 5/6) and ADF/cofilin (power law: −2/3). We also showed that the average subunit residence time inside the filament, 〈T〉, depends on the actin monomer (power law: −1/6) and ADF/cofilin (power law: −2/3) concentrations. In addition, filament length fluctuations are ∼20% of the average filament length. Moreover, ADF/cofilin fragmentation while modulating filament length keeps filaments in a high molar ratio of ATP- or ADP-P_i versus ADP-bound subunits. This latter property has a protective effect against a too high severing activity of ADF/cofilin. We propose that the activity of ADF/cofilin in vivo is under the control of an affinity gradient that builds up dynamically along growing actin filaments. Our analysis shows that ADF/cofilin regulation maintains actin filaments in a highly dynamical state compatible with the cytoskeleton dynamics observed in vivo.     

Mechanism of actin filament bundling by fascin

Fascin is the main actin filament bundling protein in filopodia. Because of the important role filopodia play in cell migration, fascin is emerging as a major target for cancer drug discovery. However, an understanding of the mechanism of bundle formation by fascin is critically lacking. Fascin consists of four β-trefoil domains. Here, we show that fascin contains two major actin-binding sites, coinciding with regions of high sequence conservation in β-trefoil domains 1 and 3. The site in β-trefoil-1 is located near the binding site of the fascin inhibitor macroketone and comprises residue Ser-39, whose phosphorylation by protein kinase C down-regulates actin bundling and formation of filopodia. The site in β-trefoil-3 is related by pseudo-2-fold symmetry to that in β-trefoil-1. The two sites are ～5 nm apart, resulting in a distance between actin filaments in the bundle of ～8.1 nm. Residue mutations in both sites disrupt bundle formation in vitro as assessed by co-sedimentation with actin and electron microscopy and severely impair formation of filopodia in cells as determined by rescue experiments in fascin-depleted cells. Mutations of other areas of the fascin surface also affect actin bundling and formation of filopodia albeit to a lesser extent, suggesting that, in addition to the two major actin-binding sites, fascin makes secondary contacts with other filaments in the bundle. In a high resolution crystal structure of fascin, molecules of glycerol and polyethylene glycol are bound in pockets located within the two major actin-binding sites. These molecules could guide the rational design of new anticancer fascin inhibitors.     

Identification of Novel Graded Polarity Actin Filament Bundles in Locomoting Heart Fibroblasts: Implications for the Generation of Motile Force

We have determined the structural organization and dynamic behavior of actin filaments in entire primary locomoting heart fibroblasts by S1 decoration, serial section EM, and photoactivation of fluorescence. As expected, actin filaments in the lamellipodium of these cells have uniform polarity with barbed ends facing forward. In the lamella, cell body, and tail there are two observable types of actin filament organization. A less abundant type is located on the inner surface of the plasma membrane and is composed of short, overlapping actin bundles (0.25–2.5 μm) that repeatedly alternate in polarity from uniform barbed ends forward to uniform pointed ends forward. This type of organization is similar to the organization we show for actin filament bundles (stress fibers) in nonlocomoting cells (PtK2 cells) and to the known organization of muscle sarcomeres. The more abundant type of actin filament organization in locomoting heart fibroblasts is mostly ventrally located and is composed of long, overlapping bundles (average 13 μm, but can reach up to about 30 μm) which span the length of the cell. This more abundant type has a novel graded polarity organization. In each actin bundle, polarity gradually changes along the length of the bundle. Actual actin filament polarity at any given point in the bundle is determined by position in the cell; the closer to the front of the cell the more barbed ends of actin filaments face forward.

By photoactivation marking in locomoting heart fibroblasts, as expected in the lamellipodium, actin filaments flow rearward with respect to substrate. In the lamella, all marked and observed actin filaments remain stationary with respect to substrate as the fibroblast locomotes. In the cell body of locomoting fibroblasts there are two dynamic populations of actin filaments: one remains stationary and the other moves forward with respect to substrate at the rate of the cell body.

This is the first time that the structural organization and dynamics of actin filaments have been determined in an entire locomoting cell. The organization, dynamics, and relative abundance of graded polarity actin filament bundles have important implications for the generation of motile force during primary heart fibroblast locomotion.

     

Mechanistic differences in actin bundling activity of two mammalian formins, FRL1 and mDia2

Formin proteins are regulators of actin dynamics, mediating assembly of unbranched actin filaments. These multidomain proteins are defined by the presence of a Formin Homology 2 (FH2) domain. Previous work has shown that FH2 domains bind to filament barbed ends and move processively at the barbed end as the filament elongates. Here we report that two FH2 domains, from mammalian FRL1 and mDia2, also bundle filaments, whereas the FH2 domain from mDia1 cannot under similar conditions. The FH2 domain alone is sufficient for bundling. Bundled filaments made by either FRL1 or mDia2 are in both parallel and anti-parallel orientations. A novel property that might contribute to bundling is the ability of the dimeric FH2 domains from both FRL1 and mDia2 to dissociate and recombine. This property is not observed for mDia1. A difference between FRL1 and mDia2 is that FRL1-mediated bundling is competitive with barbed end binding, whereas mDia2-mediated bundling is not. Mutation of a highly conserved isoleucine residue in the FH2 domain does not inhibit bundling by either FRL1 or mDia2, but inhibits barbed end activities. However, the severity of this mutation varies between formins. For mDia1 and mDia2, the mutation strongly inhibits all effects of barbed end binding, but affects FRL1 much less strongly. Furthermore, our results suggest that the Ile mutation affects processivity. Taken together, our data suggest that the bundling activities of FRL1 and mDia2, while producing phenotypically similar bundles, differ in mechanistic detail.     

Sarcomeric pattern formation by actin cluster coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.     

Effect of tensile force on the mechanical behavior of actin filaments

Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately -2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament.     

Actin‐induced dimerization of palladin promotes actin‐bundling

A subset of actin binding proteins is able to form crosslinks between two or more actin filaments, thus producing structures of parallel or networked bundles. These actin crosslinking proteins interact with actin through either bivalent binding or dimerization. We recently identified two binding sites within the actin binding domain of palladin, an actin crosslinking protein that plays an important role in normal cell adhesion and motility during wound healing and embryonic development. In this study, we show that actin induces dimerization of palladin. Furthermore, the extent of dimerization reflects earlier comparisons of actin binding and bundling between different domains of palladin. On the basis of these results we hypothesized that actin binding may promote a conformational change that results in dimerization of palladin, which in turn may drive the crosslinking of actin filaments. The proximal distance between two actin binding sites on crosslinking proteins determines the ultrastructural properties of the filament network, therefore we also explored interdomain interactions using a combination of chemical crosslinking experiments and actin cosedimentation assays. Limited proteolysis data reveals that palladin is less susceptible to enzyme digestion after actin binding. Our results suggest that domain movements in palladin are necessary for interactions with actin and are induced by interactions with actin filaments. Accordingly, we put forth a model linking the structural changes to functional dynamics.     

Polarized actin bundles formed by human fascin-1: their sliding and disassembly on myosin II and myosin V in vitro

Fascin-1 is a putative bundling factor of actin filaments in the filopodia of neuronal growth cones. Here, we examined the structure of the actin bundle formed by human fascin-1 (actin/fascin bundle), and its mode of interaction with myosin in vitro. The distance between cross-linked filaments in the actin/bundle was 8-9 nm, and the bundle showed the transverse periodicity of 36 nm perpendicular to the bundle axis, which was confirmed by electron microscopy. Decoration of the actin/fascin bundle with heavy meromyosin revealed that the arrowheads of filaments in the bundle pointed in the same direction, indicating that the bundle has polarity. This result suggested that fascin-1 plays an essential role in polarity of actin bundles in filopodia. In the in vitro motility assay, actin/fascin bundles slid as fast as single actin filaments on myosin II and myosin V. When myosin was attached to the surface at high density, the actin/fascin bundle disassembled to single filaments at the pointed end of the bundle during sliding. These results suggest that myosins may drive filopodial actin bundles backward by interacting with actin filaments on the surface, and may induce disassembly of the bundle at the basal region of filopodia.     

RhoB and the mammalian Diaphanous-related formin mDia2 in endosome trafficking

Rho GTPases and the dynamic assembly and disassembly of actin filaments have been shown to have critical roles in both the internalization and trafficking of growth factor receptors. While all three mammalian Diaphanous-related (mDia1/2/3) formin GTPase effector proteins have been localized on endosomes, a role for their actin nucleation, filament elongation, and/or bundling remains poorly understood in the context of intracellular trafficking. In a study of a functional relationship between RhoB, a GTPase known to associate with both early- and late-endosomes, and the formin mDia2, we show that 1) RhoB and mDia2 interact on endosomes; 2) GTPase activity-the ability to hydrolyze GTP to GDP-is required for the ability of RhoB to govern endosome dynamics; and 3) the actin dynamics controlled by RhoB and mDia2 is necessary for vesicle trafficking. These studies further suggest that Rho GTPases significantly influence the activity of mDia family formins in driving cellular membrane remodeling through the regulation of actin dynamics.     

Molecular Basis for the Dual Function of Eps8 on Actin Dynamics: Bundling and Capping

Actin capping and cross-linking proteins regulate the dynamics and architectures of different cellular protrusions. Eps8 is the founding member of a unique family of capping proteins capable of side-binding and bundling actin filaments. However, the structural basis through which Eps8 exerts these functions remains elusive. Here, we combined biochemical, molecular, and genetic approaches with electron microscopy and image analysis to dissect the molecular mechanism responsible for the distinct activities of Eps8. We propose that bundling activity of Eps8 is mainly mediated by a compact four helix bundle, which is contacting three actin subunits along the filament. The capping activity is mainly mediated by a amphipathic helix that binds within the hydrophobic pocket at the barbed ends of actin blocking further addition of actin monomers. Single-point mutagenesis validated these modes of binding, permitting us to dissect Eps8 capping from bundling activity in vitro. We further showed that the capping and bundling activities of Eps8 can be fully dissected in vivo, demonstrating the physiological relevance of the identified Eps8 structural/functional modules. Eps8 controls actin-based motility through its capping activity, while, as a bundler, is essential for proper intestinal morphogenesis of developing Caenorhabditis elegans.