Ju n 20 15 Mechanical properties of branched actin filaments

Cells moving on a 2dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measured in lamellipodia. These networks reproduce both the weak and strong force response of lamellipodia as measured in force-velocity experiments. We compare properties of branched and unbranched networks. The ratio of the network average of the force per branched filament to the average force per unbranched filament depends on the orientation distribution of the filaments. The ratio exhibits compression dependence and may go up to about 4.5 in networks with a narrow orientation distribution. With orientation distributions measured in lamellipodia, it is about 2 and essentially independent from network compression, graft elasticity and filament persistence length. PACS numbers: 00.00, 20.00, 42.10

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title: An Adhesion-Dependent Switch between Mechanisms That Determine Motile Cell Shape
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title: Coupling actin flow, adhesion, and morphology in a computational cell motility model
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title: Electron tomography reveals unbranched networks of actin filaments in lamellipodia
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title: Reply: Visualizing branched actin filaments in lamellipodia by electron tomography
abstract: colleagues have questioned the dendritic nucleation model in a recent paper1. In their study, they challenge key evidence supporting the dendritic nucleation model; namely, visualization of branched actin filaments in lamellipodia by platinum-replica electron microscopy4,5. Urban et al. argue1 that the branched configuration of the actin filaments in these samples are an artefact of critical-point drying, a part of the sample preparation. To prove their hypothesis that the actin filaments in lamellipodia are long and unbranched, they analysed the structure of lamellipodia by cryo-electron microscopy, and did not detect branched actin filaments in lamellipodia1. Because the data from platinum-replica electron microscopy that demonstrate branched actin filaments in lamellipodia have been reported primarily by our group, and because we have received multiple requests from the scientific community to comment on the results of Urban et al., we would like to share our opinion with a broader audience through this commentary. Several points, including comparison of potential artefacts produced by the two electron microscopy techniques and evaluation of evidence for and against the dendritic nucleation model, have already been addressed6,7. However, one critical point has not been discussed; namely, the fundamental consistency between our results and those of Urban et al. in spite of the different interpretations. We have carefully analysed the primary data provided as Supplementary Information by Urban et al. Based on this analysis, we argue that a subset of their results provides strong supporting evidence for the dendritic nucleation model by showing branched actin filaments in lamellipodia. We have found that Supplementary Movie S6, showing an electron tomogram of the lamellipodium in a 3T3 cell, is of particularly good quality to illustrate this point. Several examples of branched actin filaments from this movie are shown in Fig. 1a as a montage of z planes. In these examples, one of two actin filaments never re-emerges on the other side of the second filament in adjacent movie frames, despite the fact that both filaments are in the same z plane in at least one frame of the series. These features demonstrate that the end of the former filament makes a contact with the side of the latter filament, but does not cross it, which is the definition of a branch. In the zoomed region of the movie that shows a cell area of ~0.53 μm2, we have found a total of 147 branches , which is in contrast to the authors’ statement that “branches at the sides of actin filaments were extremely rare”. Branched actin filaments can be also found in other Supplementary movies, but fewer branches can be clearly detected in these movies owing to their insufficient quality and selection of regions corresponding to filopodia or filopodial precursors, which contain long unbranched filaments. Remarkably, all branches identified in our analysis invariably contained a blob at the branch point that probably corresponds to the Arp2/3 complex. Furthermore, the angle between branched filaments was 70 ± 7 degrees (n = 57), consistent with the conventional angle of ~70° produced by the Arp2/3 complex in vitro8. The actin filament branches found in data from the Urban et al. paper are virtually indistinguishable by appearance from those obtained by Hanein using cryo-electron microscopy of actin branches reconstituted in vitro from the Arp2/3 complex and actin, and could even be fitted into the three-dimensional branch model developed in these studies9. In conclusion, existence of branched actin filaments in lamellipodia is supported by two different electron microscopy techniques that probably counterbalance their potential artefacts. We are not sure why Urban et al. failed to detect branches, but this is definitely an issue of seeing or not seeing, rather than a problem with the techniques. Thus, in our opinion there should be no controversy regarding the structural organization of actin filaments in lamellipodia, and the dendritic nucleation model can serve as a conceptual framework for subsequent studies in the field.

title: Orientational order of the lamellipodial actin network as demonstrated in living motile cells.
abstract: Lamellipodia of crawling cells represent both the motor for cell advance and the primary building site for the actin cytoskeleton. The organization of actin in the lamellipodium reflects actin dynamics and is of critical importance for the mechanism of cell motility. In previous structural studies, the lamellipodial actin network was analyzed primarily by electron microscopy (EM). An understanding of lamellipodial organization would benefit significantly if the EM data were complemented and put into a kinetic context by establishing correspondence with structural features observable at the light microscopic level in living cells. Here, we use an enhanced phase contrast microscopy technique to visualize an apparent long-range diagonal actin meshwork in the advancing lamellipodia of living cells. Visualization of this meshwork permitted a correlative light and electron microscopic approach that validated the underlying organization of lamellipodia. The linear features in the light microscopic meshwork corresponded to regions of greater actin filament density. Orientation of features was analyzed quantitatively and compared with the orientation of actin filaments at the EM level. We infer that the light microscopic meshwork reflects the orientational order of actin filaments which, in turn, is related to their branching angle.

title: Reconstructing the orientation distribution of actin filaments in the lamellipodium of migrating keratocytes from electron microscopy tomography data
abstract: Migration of motile cells on flat substrates is usually driven by the polymerization of a flat actin filament network. Theoretical models have made different predictions regarding the distribution of the filament orientation in the lamellipodium with respect to the direction of motion. Here we show how one can automatically reconstruct the orientation distribution of actin filaments in the lamellipodium of migrating keratocytes from electron microscopy tomography data. We use two different image analysis methods, an algorithm which explicitly extracts an abstract network representation and an analysis of the gray scale information based on the structure tensor. We show that the two approaches give similar results, both for simulated data and for electron microscopy tomography data from migrating keratocytes. For the lamellipodium at the leading edge of fast moving cells, we find an orientation distribution that is peaked at +35/−35 degrees. For the lamellipodium at the leading edge of slow moving cells as well as for the lamellipodium at the flanks of fast moving cells, one broad peak around 0 degree dominates the distribution.

title: Simulation of cell motility that reproduces the force–velocity relationship
abstract: Many cells crawl by extending an actin-rich pseudopod. We have devised a simulation that describes how the polymerization kinetics of a branched actin filament network, coupled with excluded volume effects, powers the motility of crawling cells such as amoebae and fish keratocytes. Our stochastic simulation is based on the key fundamental properties of actin polymerization, namely growth, shrinkage, capping, branching, and nucleation, and also includes contributions from the creation and breaking of adhesive contacts with the substrate together with excluded volume effects related to filament packing. When reasonable values for appropriate constants were employed, this simulation generated a force–velocity relationship that resembled closely that observed experimentally. Our simulations indicated that excluded volume effects associated with actin filament branching lead to a decreased packing efficiency and resultant swelling of the cytoskeleton gel that contributes substantially to lamellipod protrusion.

title: A role for actin arcs in the leading-edge advance of migrating cells
abstract: Epithelial cell migration requires coordination of two actin modules at the leading edge: one in the lamellipodium and one in the lamella. How the two modules connect mechanistically to regulate directed edge motion is not understood. Using live-cell imaging and photoactivation approaches, we demonstrate that the actin network of the lamellipodium evolves spatio-temporally into the lamella. This occurs during the retraction phase of edge motion, when myosin II redistributes to the lamellipodial actin and condenses it into an actin arc parallel to the edge. The new actin arc moves rearward, slowing down at focal adhesions in the lamella. We propose that net edge extension occurs by nascent focal adhesions advancing the site at which new actin arcs slow down and form the base of the next protrusion event. The actin arc thereby serves as a structural element underlying the temporal and spatial connection between the lamellipodium and the lamella during directed cell motion.

title: Actin branching in the initiation and maintenance of lamellipodia
abstract: Using correlated live-cell imaging and electron tomography we found that actin branch junctions in protruding and treadmilling lamellipodia are not concentrated at the front as previously supposed, but link actin filament subsets in which there is a continuum of distances from a junction to the filament plus ends, for up to at least 1 μm. When branch sites were observed closely spaced on the same filament their separation was commonly a multiple of the actin helical repeat of 36 nm. Image averaging of branch junctions in the tomograms yielded a model for the in vivo branch at 2.9 nm resolution, which was comparable with that derived for the in vitro actin–Arp2/3 complex. Lamellipodium initiation was monitored in an intracellular wound-healing model and was found to involve branching from the sides of actin filaments oriented parallel to the plasmalemma. Many filament plus ends, presumably capped, terminated behind the lamellipodium tip and localized on the dorsal and ventral surfaces of the actin network. These findings reveal how branching events initiate and maintain a network of actin filaments of variable length, and provide the first structural model of the branch junction in vivo. A possible role of filament capping in generating the lamellipodium leaflet is discussed and a mathematical model of protrusion is also presented.

title: Branching Microtubule Nucleation in Xenopus Egg Extracts Mediated by Augmin and TPX2
abstract: The microtubules that comprise mitotic spindles in animal cells are nucleated at centrosomes and by spindle assembly factors that are activated in the vicinity of chromatin. Indirect evidence has suggested that microtubules also might be nucleated from pre-existing microtubules throughout the spindle, but this process has not been observed directly. Here, we demonstrate microtubule nucleation from the sides of existing microtubules in meiotic Xenopus egg extracts. Daughter microtubules grow at a low branch angle and with the same polarity as mother filaments. Branching microtubule nucleation requires γ-tubulin and augmin and is stimulated by factors previously implicated in chromatin-stimulated nucleation, guanosine triphosphate(GTP)-bound Ran and its effector, TPX2. Because of the rapid amplification of microtubule numbers and the preservation of microtubule polarity, microtubule-dependent microtubule nucleation is well suited for spindle assembly and maintenance.

title: Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape
abstract: Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin- labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.

title: The interaction of Arp2/3 complex with actin: nucleation, high affinity pointed end capping, and formation of branching networks of filaments.
abstract: The Arp2/3 complex is a stable assembly of seven protein subunits including two actin-related proteins (Arp2 and Arp3) and five novel proteins. Previous work showed that this complex binds to the sides of actin filaments and is concentrated at the leading edges of motile cells. Here, we show that Arp2/3 complex purified from Acanthamoeba caps the pointed ends of actin filaments with high affinity. Arp2/3 complex inhibits both monomer addition and dissociation at the pointed ends of actin filaments with apparent nanomolar affinity and increases the critical concentration for polymerization at the pointed end from 0.6 to 1.0 microM. The high affinity of Arp2/3 complex for pointed ends and its abundance in amoebae suggest that in vivo all actin filament pointed ends are capped by Arp2/3 complex. Arp2/3 complex also nucleates formation of actin filaments that elongate only from their barbed ends. From kinetic analysis, the nucleation mechanism appears to involve stabilization of polymerization intermediates (probably actin dimers). In electron micrographs of quick-frozen, deep-etched samples, we see Arp2/3 bound to sides and pointed ends of actin filaments and examples of Arp2/3 complex attaching pointed ends of filaments to sides of other filaments. In these cases, the angle of attachment is a remarkably constant 70 +/- 7 degrees. From these in vitro biochemical properties, we propose a model for how Arp2/3 complex controls the assembly of a branching network of actin filaments at the leading edge of motile cells.

title: Visualizing branched actin filaments in lamellipodia by electron tomography
abstract: Urban et al.1 recently challenged the dendritic nucleation model of lamellipodia protrusion based on their inability to detect branched actin filaments in lamellipodia by electron tomography. We have carefully analysed the primary data that was provided as Supplementary Information by Urban et al., and report that there are numerous branches that have been overlooked by the authors. Lamellipodia are thin veil-like protrusions of the cell edge that have important roles in cell migration. Their advance is driven by the polymerization of actin filaments. The exact mechanisms of lamellipodia protrusion are still debated, owing in part to controversy regarding the structural organization of the actin filaments in lamellipodia. Initial structural data obtained by Small et al.2 using negative-staining electron microscopy suggested that lamellipodia contained a network of long diagonally oriented actin filaments. Based on this structure, the authors proposed a treadmilling model of lamellipodia protrusion stating that actin filaments continuously elongate at their distal barbed (plus) ends, thus pushing the membrane, and continuously depolymerize from the proximal pointed (minus) ends, thus maintaining actin turnover. A large body of structural, biochemical, kinetic and functional data accumulated over the subsequent three decades has led to a revised model of lamellipodia protrusion, termed the dendritic nucleation model3. A key additional point of this model is that the actin filaments in lamellipodia are constantly nucleated by the Arp2/3 complex as branches on pre-existing filaments. However, despite the compelling evidence, Small and

title: Antagonism between Ena/VASP Proteins and Actin Filament Capping Regulates Fibroblast Motility
abstract: Cell motility requires lamellipodial protrusion, a process driven by actin polymerization. Ena/VASP proteins accumulate in protruding lamellipodia and promote the rapid actin-driven motility of the pathogen Listeria. In contrast, Ena/VASP negatively regulate cell translocation. To resolve this paradox, we analyzed the function of Ena/VASP during lamellipodial protrusion. Ena/VASP-deficient lamellipodia protruded slower but more persistently, consistent with their increased cell translocation rates. Actin networks in Ena/VASP-deficient lamellipodia contained shorter, more highly branched filaments compared to controls. Lamellipodia with excess Ena/VASP contained longer, less branched filaments. In vitro, Ena/VASP promoted actin filament elongation by interacting with barbed ends, shielding them from capping protein. We conclude that Ena/VASP regulates cell motility by controlling the geometry of actin filament networks within lamellipodia.

title: Tracer studies on f-actin fluctuations.
abstract: We present a study on the fluctuations of semiflexible actin filaments using fluorescence videomicroscopy, focusing on the end-to-end fluctuations of single filaments. In order to specifically measure the position of the polymer's ends, we developed a novel noninvasive method that consists of annealing short end tags to the filaments. This allows us to probe polymer fluctuations to a very high accuracy. We compared the distribution of the end-to-end distance with recent theoretical results, and found excellent agreement. We also studied the dynamics of the mean-square end-to-end distance deltaR2(t) and orientation of the ends, deltaTheta(2)(t), finding power laws t(3/4) and t(1/4), respectively. Scaling behavior for deltaR2(t) is observed over several decades in relaxation time in agreement with theoretical results.

title: Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins
abstract: Single actin filaments undergoing brownian movement in two dimensions were observed at 20 degrees C in fluorescence optical video microscopy. The persistence length (Lp) was derived from the analysis of either the cosine correlation function or the average transverse fluctuations of a series of recorded shapes of filaments assembled from rhodamine-action. Phalloidin-stabilized filaments had a persistence length of 18 +/- 1 micron, in agreement with recent observations. In the absence of phalloidin, rhodamine-labeled filaments could be observed under a variety of solution conditions once diluted in free unlabeled G-actin at the appropriate critical concentration. Such nonstabilized F-ADP- actin filaments had the same Lp of 9 +/- 0.5 microns, whether they had been assembled from ATP-G-actin or from ADP-G-actin, and independently of the tightly bound divalent metal ion. In the presence of BeF3-, which mimics the gamma-phosphate of ATP, F-ADP-BeF3-actin was appreciably more rigid, with Lp = 13.5 microns. Hence, newly formed F- ADP-Pi-actin filaments are more rigid than “old” F-ADP-actin filaments, a fact which has implications in actin-based motility processes. In the presence of skeletal tropomyosin and troponin, filaments were rigid (Lp = 20 +/- 1 micron) in the off state (-Ca2+), and flexible (Lp = 12 microns) in the on state (+Ca2+), consistent with the steric blocking model. In agreement with x-ray diffraction data, no appreciable difference was recorded between the off and on states using smooth muscle tropomyosin and caldesmon (Lp = 20 +/- 1 micron). In conclusion, this method allows accurate measurement of small (< or = 15%) changes in mechanical properties of actin filaments in correlation with their biological functions.

title: Cofilin increases the bending flexibility of actin filaments: implications for severing and cell mechanics.
abstract: We determined the flexural (bending) rigidities of actin and cofilactin filaments from a cosine correlation function analysis of their thermally driven, two-dimensional fluctuations in shape. The persistence length of actin filaments is 9.8 microm, corresponding to a flexural rigidity of 0.040 pN microm(2). Cofilin binding lowers the persistence length approximately 5-fold to a value of 2.2 microm and the filament flexural rigidity to 0.0091 pN microm(2). That cofilin-decorated filaments are more flexible than native filaments despite an increased mass indicates that cofilin binding weakens and redistributes stabilizing subunit interactions of filaments. We favor a mechanism in which the increased flexibility of cofilin-decorated filaments results from the linked dissociation of filament-stabilizing ions and reorganization of actin subdomain 2 and as a consequence promotes severing due to a mechanical asymmetry. Knowledge of the effects of cofilin on actin filament bending mechanics, together with our previous analysis of torsional stiffness, provide a quantitative measure of the mechanical changes in actin filaments associated with cofilin binding, and suggest that the overall mechanical and force-producing properties of cells can be modulated by cofilin activity.

title: Actin filament remodeling by actin depolymerization factor/cofilin
abstract: We investigate, using molecular dynamics, how the severing protein, actin depolymerization factor (ADF)/cofilin, modulates the structure, conformational dynamics, and mechanical properties of actin filaments. The actin and cofilactin filament bending stiffness and corresponding persistence lengths obtained from all-atom simulations are comparable to values obtained from analysis of thermal fluctuations in filament shape. Filament flexibility is strongly affected by the nucleotide-linked conformation of the actin subdomain 2 DNase-I binding loop and the filament radial mass density distribution. ADF/cofilin binding between subdomains 1 and 3 of a filament subunit triggers reorganization of subdomain 2 of the neighboring subunit such that the DNase-I binding loop (DB-loop) moves radially away from the filament. Repositioning of the neighboring subunit DB-loop significantly weakens subunit interactions along the long-pitch helix and lowers the filament bending rigidity. Lateral filament contacts between the hydrophobic loop and neighboring short-pitch helix monomers in native filaments are also compromised with cofilin binding. These works provide a molecular interpretation of biochemical solution studies documenting the disruption of filament subunit interactions and also reveal the molecular basis of actin filament allostery and its linkage to ADF/cofilin binding.