Optimal orientation in branched cytoskeletal networks

Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these properties, using the dendritic nucleation model as a basis for cytoskeletal restructuring, a kinetic-population model with orientational-dependent branching (birth) and capping (death) is constructed and analyzed. Optimizing for growth yields a relation between the branch angle and filament orientation that explains the two characteristic peaks. The model also exhibits a subdominant population that allows for more accurate modeling of recent measurements of filamentous actin density along the leading edge of lamellipodia in keratocytes. Finally, we explore the relationship between orientational and spatial organization of filamentous actin in lamellipodia and address recent observations of a prevalence of overlapping filaments to branched filaments-a finding that is claimed to be in contradiction with the dendritic nucleation model.     

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.     

Inhibition of the Arp2/3 complex-nucleated actin polymerization and branch formation by tropomyosin

The actin filament network immediately under the plasma membrane at the leading edge of rapidly moving cells consists of short, branched filaments, while those deeper in the cortex are much longer and are rarely branched. Nucleation by the Arp2/3 complex activated by membrane-bound factors (Rho-family GTPases and PIP(2)) is postulated to account for the formation of the branched network. Tropomyosin (TM) binds along the sides of filaments and protects them from severing proteins and pointed-end depolymerization in vitro. Here, we show that TM inhibits actin filament branching and nucleation by the Arp2/3 complex activated by WASp-WA. Tropomyosin increases the lag at the outset of polymerization, reduces the concentration of ends by 75%, and reduces the number of branches by approximately 50%. We conclude that TM bound to actin filaments inhibits their ability to act as secondary activators of nucleation by the Arp2/3 complex. This is the first example of inhibition of branching by an actin binding protein. We suggest that TM suppresses the nucleation of actin filament branches from actin filaments in the deep cortex of motile cells. Other abundant actin binding proteins may also locally regulate the branching nucleation by the Arp2/3 complex in cells.     

Actin dynamics: growth from dendritic branches

The dendritic nucleation model was devised to explain the cycle of actin dynamics resulting in actin filament network assembly and disassembly in two contexts--at the leading edge of motile cells and in the actin comet tails of intracellular pathogenic bacteria and viruses. Due to the detailed nature of its biochemical predictions, the model has provided an excellent focus for subsequent experimentation. This review summarizes recent work on actin dynamics in the context of the dendritic nucleation model. One outcome of this research is the possibility that additional proteins, as well as the six proteins included in the original model, might increase the efficiency of dendritic nucleation or modify the resulting actin network. In addition, actin dynamics at the leading edge might be influenced by a second actin filament network, independent of dendritic nucleation.     

The F-actin side binding activity of the Arp2/3 complex is essential for actin nucleation and lamellipod extension

Most eukaryotic cells rely on localized actin polymerization to generate and sustain the protrusion activity necessary for cell movement [1, 2]. Such protrusions are often in the form of a flat lamellipod with a leading edge composed of a dense network of actin filaments [3, 4]. The Arp2/3 complex localizes within that network in vivo [3, 4] and nucleates actin polymerization and generates a branched network of actin filaments in vitro [5-7]. The complex has thus been proposed to generate the actin network at the leading edge of crawling cells in vivo [3, 4, 8]. However, the relative contributions of nucleation and branching to protrusive force are still unknown. We prepared antibodies to the p34 subunit of the Arp2/3 complex that selectively inhibit side binding of the complex to F-actin. We demonstrate that side binding is required for efficient nucleation and branching by the Arp2/3 complex in vitro. However, microinjection of these antibodies into cells specifically inhibits lamellipod extension without affecting the EGF-stimulated appearance of free barbed ends in situ. These results indicate that while the side binding activity of the Arp2/3 complex is required for nucleation in vitro and for protrusive force in vivo, it is not required for EGF-stimulated increases in free barbed ends in vivo. This suggests that the branching activity of the Arp2/3 complex is essential for lamellipod extension, while the generation of nucleation sites for actin polymerization is not sufficient.     

Cortactin promotes and stabilizes Arp2/3-induced actin filament network formation

Cortactin is a c-src substrate associated with sites of dynamic actin assembly at the leading edge of migrating cells. We previously showed that cortactin binds to Arp2/3 complex, the essential molecular machine for nucleating actin filament assembly. In this study, we demonstrate that cortactin activates Arp2/3 complex based on direct visualization of filament networks and pyrene actin assays. Strikingly, cortactin potently inhibited the debranching of filament networks. When cortactin was added in combination with the active VCA fragment of N-WASp, they synergistically enhanced Arp2/3-induced actin filament branching. The N-terminal acidic and F-actin binding domains of cortactin were both necessary to activate Arp2/3 complex. These results support a model in which cortactin modulates actin filament dendritic nucleation by two mechanisms, (1) direct activation of Arp2/3 complex and (2) stabilization of newly generated filament branch points. By these mechanisms, cortactin may promote the formation and stabilization of the actin network that drives protrusion at the leading edge of migrating cells.     

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model’s ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.     

Morphology of the lamellipodium and organization of actin filaments at the leading edge of crawling cells

Lamellipodium extension, incorporating actin filament dynamics and the cell membrane, is simulated in three dimensions. The actin filament network topology and the role of actin-associated proteins such as Arp2/3 are examined. We find that the orientational pattern of the filaments is in accord with the experimental data only if the spatial orientation of the Arp2/3 complex is restricted during each branching event. We hypothesize that branching occurs when Arp2/3 is bound to Wiskott-Aldrich syndrome protein (WASP), which is in turn bound to Cdc42 signaling complex; Arp2/3 binding geometry is restricted by the membrane-bound complex. Using mechanical and energetic arguments, we show that any membrane protein that is conical or trapezoidal in shape preferentially resides at the curved regions of the plasma membrane. We hypothesize that the transmembrane receptors involved in the recruitment of Cdc42/WASP complex has this property and concentrate at the leading edge. These features, combined with the mechanical properties of the cell membrane, explain why lamellipodium is a flat organelle.     

Actin filament organization in the fish keratocyte lamellipodium

From recent studies of locomoting fish keratocytes it was proposed that the dynamic turnover of actin filaments takes place by a nucleation- release mechanism, which predicts the existence of short (less than 0.5 microns) filaments throughout the lamellipodium (Theriot, J. A., and T. J. Mitchison. 1991. Nature (Lond.). 352:126-131). We have tested this model by investigating the structure of whole mount keratocyte cytoskeletons in the electron microscope and phalloidin-labeled cells, after various fixations, in the light microscope. Micrographs of negatively stained keratocyte cytoskeletons produced by Triton extraction showed that the actin filaments of the lamellipodium are organized to a first approximation in a two-dimensional orthogonal network with the filaments subtending an angle of around 45 degrees to the cell front. Actin filament fringes grown onto the front edge of keratocyte cytoskeletons by the addition of exogenous actin showed a uniform polarity when decorated with myosin subfragment-1, consistent with the fast growing ends of the actin filaments abutting the anterior edge. A steady drop in filament density was observed from the mid- region of the lamellipodium to the perinuclear zone and in images of the more posterior regions of lower filament density many of the actin filaments could be seen to be at least several microns in length. Quantitative analysis of the intensity distribution of fluorescent phalloidin staining across the lamellipodium revealed that the gradient of filament density as well as the absolute content of F-actin was dependent on the fixation method. In cells first fixed and then extracted with Triton, a steep gradient of phalloidin staining was observed from the front to the rear of the lamellipodium. With the protocol required to obtain the electron microscope images, namely Triton extraction followed by fixation, phalloidin staining was, significantly and preferentially reduced in the anterior part of the lamellipodium. This resulted in a lower gradient of filament density, consistent with that seen in the electron microscope, and indicated a loss of around 45% of the filamentous actin during Triton extraction. We conclude, first that the filament organization and length distribution does not support a nucleation release model, but is more consistent with a treadmilling-type mechanism of locomotion featuring actin filaments of graded length. Second, we suggest that two layers of filaments make up the lamellipodium; a lower, stabilized layer associated with the ventral membrane and an upper layer associated with the dorsal membrane that is composed of filaments of a shorter range of lengths than the lower layer and which is mainly lost in Triton.     

Differentially oriented populations of actin filaments generated in lamellipodia collaborate in pushing and pausing at the cell front

Eukaryotic cells advance in phases of protrusion, pause and withdrawal. Protrusion occurs in lamellipodia, which are composed of diagonal networks of actin filaments, and withdrawal terminates with the formation of actin bundles parallel to the cell edge. Using correlated live-cell imaging and electron microscopy, we have shown that actin filaments in protruding lamellipodia subtend angles from 15-90 degrees to the front, and that transitions from protrusion to pause are associated with a proportional increase in filaments oriented more parallel to the cell edge. Microspike bundles of actin filaments also showed a wide angular distribution and correspondingly variable bilateral polymerization rates along the cell front. We propose that the angular shift of filaments in lamellipodia serves in adapting to slower protrusion rates while maintaining the filament densities required for structural support; further, we suggest that single filaments and microspike bundles contribute to the construction of the lamella behind and to the formation of the cell edge when protrusion ceases. Our findings provide an explanation for the variable turnover dynamics of actin filaments in lamellipodia observed by fluorescence speckle microscopy and are inconsistent with a current model of lamellipodia structure that features actin filaments branching at 70 degrees in a dendritic array.     

Form-Finding Model Shows How Cytoskeleton Network Stiffness Is Realized

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.     

Kinetics of the formation and dissociation of actin filament branches mediated by Arp2/3 complex

The actin filament network at the leading edge of motile cells relies on localized branching by Arp2/3 complex from "mother" filaments growing near the plasma membrane. The nucleotide bound to the mother filaments (ATP, ADP and phosphate, or ADP) may influence the branch dynamics. To determine the effect of the nucleotide bound to the subunits of the mother filament on the formation and stability of branches, we compared the time courses of actin polymerization in bulk samples measured using the fluorescence of pyrene actin with observations of single filaments by total internal reflection fluorescence microscopy. Although the branch nucleation rate in bulk samples was nearly the same regardless of the nucleotide on the mother filaments, we observed fewer branches by microscopy on ADP-bound filaments than on ADP-P(i)-bound filaments. Observation of branches in the microscope depends on their binding to the slide. Since the probability that a branch binds to the slide is directly related to its lifetime, we used counts of branches to infer their rates of dissociation from mother filaments. We conclude that the nucleotide on the mother filament does not affect the initial branching event but that branches are an order of magnitude more stable on the sides of new ATP- or ADP-P(i) filaments than on ADP-actin filaments.     

Relationship between Arp2/3 complex and the barbed ends of actin filaments at the leading edge of carcinoma cells after epidermal growth factor stimulation

Using both light and high resolution electron microscopy, we analyzed the spatial and temporal relationships between the Arp2/3 complex and the nucleation activity that is required for lamellipod extension in mammary carcinoma cells after epidermal growth factor stimulation. A rapid two- to fourfold increase in filament barbed end number occurs transiently after stimulation and remains confined almost exclusively to the extreme outer edge of the extending lamellipod (within 100-200 nm of the plasma membrane). This is accompanied by an increase in filament density at the leading edge and a general decrease in filament length, with a specific loss of long filaments. Concomitantly, the Arp2/3 complex is recruited with a 1.5-fold increase throughout the entire cortical filament network extending 1-1.5 microm in depth from the membrane at the leading edge. The recruitment of the Arp2/3 complex at the membrane of the extending lamellipod indicates that Arp2/3 may be involved in initial generation of growing filaments. However, only a small subset of the complex present in the cortical network colocalizes near free barbed ends. This suggests that the 100-200-nm submembraneous compartment at the leading edge of the extending lamellipod constitutes a special biochemical microenvironment that favors the generation and maintenance of free barbed ends, possibly through the locally active Arp2/3 complex, severing or decreasing the on-rate of capping protein. Our results are inconsistent with the hypothesis suggesting uncapping is the dominant mechanism responsible for the generation of nucleation activity. However, they support the hypothesis of an Arp2/3-mediated capture of actin oligomers that formed close to the membrane by other mechanisms such as severing. They also support pointed-end capping by the Arp2/3 complex, accounting for its wide distribution at the leading edge.     

Growth of branched actin networks against obstacles

A method for simulating the growth of branched actin networks against obstacles has been developed. The method is based on simple stochastic events, including addition or removal of monomers at filament ends, capping of filament ends, nucleation of branches from existing filaments, and detachment of branches; the network structure for several different models of the branching process has also been studied. The models differ with regard to their inclusion of effects such as preferred branch orientations, filament uncapping at the obstacle, and preferential branching at filament ends. The actin ultrastructure near the membrane in lamellipodia is reasonably well produced if preferential branching in the direction of the obstacle or barbed-end uncapping effects are included. Uncapping effects cause the structures to have a few very long filaments that are similar to those seen in pathogen-induced "actin tails." The dependence of the growth velocity, branch spacing, and network density on the rate parameters for the various processes is quite different among the branching models. An analytic theory of the growth velocity and branch spacing of the network is described. Experiments are suggested that could distinguish among some of the branching models.     

How tropomyosin regulates lamellipodial actin‐based motility: a combined biochemical and reconstituted motility approach

At the leading edge of migrating cells, protrusive forces are developed by the assembly of actin filaments organised in a lamellipodial dendritic array at the front and a more distal lamellar linear array. Whether these two arrays are distinct or functionally linked and how they contribute to cell migration is an open issue. Tropomyosin severely inhibits lamellipodium formation and facilitates the lamellar array while enhancing migration, by a mechanism that is not understood. Here we show that the complex in vivo effects of tropomyosin are recapitulated in the reconstituted propulsion of neural Wiskott–Aldrich syndrome protein (N‐WASP)‐functionalised beads, which is based on the sole formation of a dendritic array of actin‐related protein (Arp)2/3‐branched filaments. Actin‐depolymerising factor (ADF) and tropomyosin control the length of the actin tail. By competing with Arp2/3 during filament branching, tropomyosin displays opposite effects on propulsion depending on the surface density of N‐WASP. Tropomyosin binding to the dendritic array is facilitated following filament debranching, causing its enrichment at the rear of the actin tail, like in vivo. These results unveil the mechanism by which tropomyosin generates two morphologically and dynamically segregated actin networks from a single one.     

Capping Protein Terminates but Does Not Initiate Chemoattractant-induced Actin Assembly in Dictyostelium

The first step in the directed movement of cells toward a chemotactic source involves the extension of pseudopods initiated by the focal nucleation and polymerization of actin at the leading edge of the cell. We have previously isolated a chemoattractant-regulated barbed-end capping activity from Dictyostelium that is uniquely associated with capping protein, also known as cap32/34. Although uncapping of barbed ends by capping protein has been proposed as a mechanism for the generation of free barbed ends after stimulation, in vitro and in situ analysis of the association of capping protein with the actin cytoskeleton after stimulation reveals that capping protein enters, but does not exit, the cytoskeleton during the initiation of actin polymerization. Increased association of capping protein with regions of the cell containing free barbed ends as visualized by exogenous rhodamine-labeled G-actin is also observed after stimulation. An approximate threefold increase in the number of filaments with free barbed ends is accompanied by increases in absolute filament number, whereas the average filament length remains constant. Therefore, a mechanism in which preexisting filaments are uncapped by capping protein, in response to stimulation leading to the generation of free barbed ends and filament elongation, is not supported. A model for actin assembly after stimulation, whereby free barbed ends are generated by either filament severing or de novo nucleation is proposed. In this model, exposure of free barbed ends results in actin assembly, followed by entry of free capping protein into the actin cytoskeleton, which acts to terminate, not initiate, the actin polymerization transient.     

Emergence and maintenance of variable-length actin filaments in a limiting pool of building blocks

Actin is one of the key structural components of the eukaryotic cytoskeleton that regulates cellular architecture and mechanical properties. Dynamic regulation of actin filament length and organization is essential for the control of many physiological processes including cell adhesion, motility and division. While previous studies have mostly focused on the mechanisms controlling the length of single actin filaments, it remains poorly understood how distinct actin filament populations in cells maintain different lengths using the same set of molecular building blocks. Here, we develop a theoretical model for the length regulation of multiple actin filaments by nucleation and growth-rate modulation by actin-binding proteins in a limiting pool of monomers. We first show that spontaneous nucleation of actin filaments naturally leads to heterogeneities in filament length distribution. We then investigate the effects of filament growth inhibition by capping proteins and growth promotion by formin proteins on filament length distribution. We find that filament length heterogeneity can be increased by growth inhibition, whereas growth promoters do not significantly affect length heterogeneity. Interestingly, a competition between filament growth inhibitors and growth promoters can give rise to bimodal filament length distribution as well as a highly heterogeneous length distribution with large statistical dispersion. We quantitatively predict how heterogeneity in actin filament length can be modulated by tuning filamentous actin nucleation and growth rates in order to create distinct filament subpopulations with different lengths.     

Dendritic organization of actin comet tails

Polymerization of actin filaments is necessary for both protrusion of the leading edge of crawling cells and propulsion of certain intracellular pathogens, and it is sufficient for generating force for bacterial motility in vitro. Motile intracellular pathogens are associated with actin-rich comet tails containing many of the same molecular components present in lamellipodia, and this suggests that these two systems use a similar mechanism for motility. However, available structural evidence suggests that the organization of comet tails differs from that of lamellipodia. Actin filaments in lamellipodia form branched arrays, which are thought to arise by dendritic nucleation mediated by the Arp2/3 complex. In contrast, comet tails have been variously described as consisting of short, randomly oriented filaments, with a higher degree of alignment at the periphery, or as containing long, straight axial filaments with a small number of oblique filaments. Because the assembly of pathogen-associated comet tails has been used as a model system for lamellipodial protrusion, it is important to resolve this apparent discrepancy. Here, using a platinum replica approach, we show that actin filament arrays in comet tails in fact have a dendritic organization with the Arp2/3 complex localizing to Y-junctions as in lamellipodia. Thus, comet tails and lamellipodia appear to share a common dendritic nucleation mechanism for protrusive motility. However, comet tails differ from lamellipodia in that their actin filaments are usually twisted and appear to be under significant torsional stress.     

The role of actin turnover in retrograde actin network flow in neuronal growth cones

The balance of actin filament polymerization and depolymerization maintains a steady state network treadmill in neuronal growth cones essential for motility and guidance. Here we have investigated the connection between depolymerization and treadmilling dynamics. We show that polymerization-competent barbed ends are concentrated at the leading edge and depolymerization is distributed throughout the peripheral domain. We found a high-to-low G-actin gradient between peripheral and central domains. Inhibiting turnover with jasplakinolide collapsed this gradient and lowered leading edge barbed end density. Ultrastructural analysis showed dramatic reduction of leading edge actin filament density and filament accumulation in central regions. Live cell imaging revealed that the leading edge retracted even as retrograde actin flow rate decreased exponentially. Inhibition of myosin II activity before jasplakinolide treatment lowered baseline retrograde flow rates and prevented leading edge retraction. Myosin II activity preferentially affected filopodial bundle disassembly distinct from the global effects of jasplakinolide on network turnover. We propose that growth cone retraction following turnover inhibition resulted from the persistence of myosin II contractility even as leading edge assembly rates decreased. The buildup of actin filaments in central regions combined with monomer depletion and reduced polymerization from barbed ends suggests a mechanism for the observed exponential decay in actin retrograde flow. Our results show that growth cone motility is critically dependent on continuous disassembly of the peripheral actin network.     

Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia.

The leading edge (approximately 1 microgram) of lamellipodia in Xenopus laevis keratocytes and fibroblasts was shown to have an extensively branched organization of actin filaments, which we term the dendritic brush. Pointed ends of individual filaments were located at Y-junctions, where the Arp2/3 complex was also localized, suggesting a role of the Arp2/3 complex in branch formation. Differential depolymerization experiments suggested that the Arp2/3 complex also provided protection of pointed ends from depolymerization. Actin depolymerizing factor (ADF)/cofilin was excluded from the distal 0.4 micrometer++ of the lamellipodial network of keratocytes and in fibroblasts it was located within the depolymerization-resistant zone. These results suggest that ADF/cofilin, per se, is not sufficient for actin brush depolymerization and a regulatory step is required. Our evidence supports a dendritic nucleation model (Mullins, R.D., J.A. Heuser, and T.D. Pollard. 1998. Proc. Natl. Acad. Sci. USA. 95:6181-6186) for lamellipodial protrusion, which involves treadmilling of a branched actin array instead of treadmilling of individual filaments. In this model, Arp2/3 complex and ADF/cofilin have antagonistic activities. Arp2/3 complex is responsible for integration of nascent actin filaments into the actin network at the cell front and stabilizing pointed ends from depolymerization, while ADF/cofilin promotes filament disassembly at the rear of the brush, presumably by pointed end depolymerization after dissociation of the Arp2/3 complex.