Strain field in actin filament network in lamellipodia of migrating cells: Implication for network reorganization

Cell motility is spatiotemporally regulated by interactions among mechanical and biochemical factors involved in the regulation of cytoskeletal actin structure reorganization. Although the molecular mechanisms underlying cell motility have been well investigated, the contributions of mechanical factors such as strain in the network reorganization remain unclear. In this study, we have quantitatively evaluated the strain field in the actin filament network forming the lamellipodia of migrating fish keratocytes to elucidate the mechanism by which actin filament network reorganization is regulated by biomechanical factors. The results highlight the existence of a negative (compressive) strain in the lamellipodia whose direction is parallel to that of cell movement. A close correlation was found between the distributions of the strain and the actin filament density in the lamellipodia, suggesting that negative strain may be involved in filament depolymerization. Based on this result, we propose a selective depolymerization model which suggests that negative strain may couple with biomechanical factors such as ADF/cofilin to promote selective depolymerization of filaments oriented in the direction of the deformation because such filaments experience relatively higher levels of the deformation. This model, in conjunction with others, may explain the observed reduction in filament density and the reorganization of actin filament network at the back of the lamellipodia of migrating fish keratocytes. Thus, we suggest that by coupling with biochemical factors, mechanical factors are involved in the regulation of actin filament depolymerization, thereby contributing to the regulation of cell motility.     

Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior

The microstructure of tissues and tissue equivalents (TEs) plays a critical role in determining the mechanical properties thereof. One of the key challenges in constitutive modeling of TEs is incorporating the kinematics at both the macroscopic and the microscopic scale. Models of fibrous microstructure commonly assume fibrils to move homogeneously, that is affine with the macroscopic deformation. While intuitive for situations of fibril-matrix load transfer, the relevance of the affine assumption is less clear when primary load transfer is from fibril to fibril. The microstructure of TEs is a hydrated network of collagen fibrils, making its microstructural kinematics an open question. Numerical simulation of uniaxial extensile behavior in planar TE networks was performed with fibril kinematics dictated by the network model and by the affine model. The average fibril orientation evolved similarly with strain for both models. The individual fibril kinematics, however, were markedly different. There was no correlation between fibril strain and orientation in the network model, and fibril strains were contained by extensive reorientation. As a result, the macroscopic stress given by the network model was roughly threefold lower than the affine model. Also, the network model showed a toe region, where fibril reorientation precluded the development of significant fibril strain. We conclude that network fibril kinematics are not governed by affine principles, an important consideration in the understanding of tissue and TE mechanics, especially when load bearing is primarily by an interconnected fibril network.     

A mechanochemical model of actin filaments

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.     

Quantitation of liquid-crystalline ordering in F-actin solutions.

Actin filaments (F-actin) are important determinants of cellular shape and motility. These functions depend on the collective organization of numerous filaments with respect to both position and orientation in the cytoplasm. Much of the orientational organization arises spontaneously through liquid crystal formation in concentrated F-actin solutions. In studying this phenomenon, we found that solutions of purified F-actin undergo a continuous phase transition, from the isotropic state to a liquid crystalline state, when either the mean filament length or the actin concentration is increased above its respective threshold value. The phase diagram representing the threshold filament lengths and concentrations at which the phase transition occurs is consistent with that predicted by Flory's theory on solutions of noninteracting, rigid cylinders (Flory, 1956b). However, in contrast to other predictions based on this model, we found no evidence for the coexistence of isotropic and anisotropic phases. Furthermore, the phase transition proved to be temperature dependent, which suggests the existence of orientation-dependent interfilament interactions or of a temperature-dependent filament flexibility. We developed a simple method for growing undistorted fluorescent acrylodan-labeled F-actin liquid crystals; and we derived a simple theoretical treatment by which polarization-of-fluorescence measurements could be used to quantitate, for the first time, the degree of spontaneous filament ordering (nematic order parameter) in these F-actin liquid crystals. This order parameter was found to increase monotonically with both filament length and concentration. Actin liquid crystals can readily become distorted by a process known as "texturing." Zigzaging and helicoidal liquid crystalline textures which persisted in the absence of ATP were observed through the polarizing microscope. Possible texturing mechanisms are discussed.     

Strain hardening of actin filament networks. Regulation by the dynamic cross-linking protein alpha-actinin

Mechanical stresses applied to the plasma membrane of an adherent cell induces strain hardening of the cytoskeleton, i.e. the elasticity of the cytoskeleton increases with its deformation. Strain hardening is thought to mediate the transduction of mechanical signals across the plasma membrane through the cytoskeleton. Here, we describe the strain dependence of a model system consisting of actin filaments (F-actin), a major component of the cytoskeleton, and the F-actin cross-linking protein alpha-actinin, which localizes along contractile stress fibers and at focal adhesions. We show that the amplitude and rate of shear deformations regulate the resilience of F-actin networks. At low temperatures, for which the lifetime of binding of alpha-actinin to F-actin is long, F-actin/alpha-actinin networks exhibit strong strain hardening at short time scales and soften at long time scales. For F-actin networks in the absence of alpha-actinin or for F-actin/alpha-actinin networks at high temperatures, strain hardening appears only at very short time scales. We propose a model of strain hardening for F-actin networks, based on both the intrinsic rigidity of F-actin and dynamic topological constraints formed by the cross-linkers located at filaments entanglements. This model offers an explanation for the origin of strain hardening observed when shear stresses are applied against the cellular membrane.     

Viscoelasticity of F-actin and F-actin/gelsolin complexes

Actin is the major protein of eukaryote peripheral cytoplasm where its mechanical effects could determine cell shape and motility. The mechanical properties of purified F-actin, whether it is a viscoelastic fluid or an elastic solid, have been a subject of controversy. Mainstream polymer theory predicts that filaments as long as those found in purified F-actin are so interpenetrated as to appear immobile in measurements over a reasonable time with available instrumentation and that the fluidity of F-actin could only be manifest if the filaments were shortened. We show that the static and dynamic elastic moduli below a critical degree of shear strain are much higher than previously reported, consistent with extreme interpenetration, but that higher strain or treatment with very low concentrations of the F-actin severing protein gelsolin greatly diminish the moduli and cause F-actin to exhibit rheologic behavior expected for independent semidilute rods, and defined by the dimensions of the filaments, including shear rate independent viscosity below a critical shear rate. The findings show that shortening of actin filaments sufficiently to permit reasonable measurements brings out their viscoelastic fluid properties. Since gelsolin shortens F-actin, it is likely that the effect of high strain is also to fragment a population of long actin filaments. We confirmed recent findings that the viscosity of F-actin is inversely proportional to the shear rate, consistent with an indeterminate fluid, but found that gelsolin abolishes this unusual shear rate dependence, indicating that it results from filament disruption during the viscosity measurements.(ABSTRACT TRUNCATED AT 250 WORDS)     

The structure of the F-actin filament and the actin molecule.

A consensus view on the three-dimensional structure of the F-actin filament and the relative strength of the intersubunit contacts in the filament has been established from an atomic filament model and recent three-dimensional reconstructions from electron micrographs of F-actin filaments. Functional implications of recent structural and biochemical data indicating a rather dynamic filament structure are discussed.     

The novel intestinal filament organizer IFO-1 contributes to epithelial integrity in concert with ERM-1 and DLG-1

The nematode Caenorhabditis elegans is an excellent model system in which to study in vivo organization and function of the intermediate filament (IF) system for epithelial development and function. Using a transgenic ifb-2::cfp reporter strain, a mutagenesis screen was performed to identify mutants with aberrant expression patterns of the IF protein IFB-2, which is expressed in a dense network at the subapical endotube just below the microvillar brush border of intestinal cells. Two of the isolated alleles (kc2 and kc3) were mapped to the same gene, which we refer to as ifo-1 (intestinal filament organizer). The encoded polypeptide colocalizes with IF proteins and F-actin in the intestine. The apical localization of IFO-1 does not rely on IFB-2 but is dependent on LET-413, a basolateral protein involved in apical junction assembly and maintenance of cell polarity. In mutant worms, IFB-2 and IFC-2 are mislocalized in cytoplasmic granules and accumulate in large aggregates at the C. elegans apical junction (CeAJ) in a DLG-1-dependent fashion. Electron microscopy reveals loss of the prominent endotube and disordered but still intact microvilli. Semiquantitative fluorescence microscopy revealed a significant decrease of F-actin, suggesting a general role of IFO-1 in cytoskeletal organization. Furthermore, downregulation of the cytoskeletal organizer ERM-1 and the adherens junction component DLG-1, each of which leads to F-actin reduction on its own, induces a novel synthetic phenotype in ifo-1 mutants resulting in disruption of the lumen. We conclude that IFO-1 is a multipurpose linker between different cytoskeletal components of the C. elegans intestinal terminal web and contributes to proper epithelial tube formation.     

Microheterogeneity controls the rate of gelation of actin filament networks

Rapid sol-gel transitions of the actin cytoskeleton are required for many key cellular processes, including cell spreading and cell locomotion. Actin monomers assemble into semiflexible polymers that rapidly intertwine into a network, a process that in vitro takes approximately 1 min for an actin concentration of 1 mg/ml. The same actin filament network, however, takes approximately 1 h to exhibit a steady-state elasticity. We hypothesize that the slow gelation of F-actin is due to the slow establishment of a homogeneous meshwork. Using a novel method, time-resolved multiple particle tracking, which monitors the range of thermally excited displacements of microspheres imbedded in the network, we show that the increase in elasticity in a polymerizing solution of actin parallels the progressive decline of the network microheterogeneity. The rates of gelation and network homogenization slightly decrease with actin concentration and in the presence of the F-actin cross-linking proteins alpha-actinin and fascin, whereas the rate of actin polymerization increases dramatically with actin concentration. Our measurements show that the slow spatial homogenization of the actin filament network, not actin polymerization or the formation of polymer overlaps, is the rate-limiting step in the establishment of an elastic actin network and suggest that a new activity of F-actin binding proteins may be required for the rapid formation of a homogeneous stiff gel.     

On the computation of stress in affine versus nonaffine fibril kinematics within planar collagen network models

Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment.     

Electron Tomography of Cryofixed,Isometrically Contracting Insect Flight Muscle Reveals Novel Actin-Myosin Interactions

Background

Isometric muscle contraction, where force is generated without muscle shortening, is a molecular traffic jam in which the number of actin-attached motors is maximized and all states of motor action are trapped with consequently high heterogeneity. This heterogeneity is a major limitation to deciphering myosin conformational changes in situ.

Methodology

We used multivariate data analysis to group repeat segments in electron tomograms of isometrically contracting insect flight muscle, mechanically monitored, rapidly frozen, freeze substituted, and thin sectioned. Improved resolution reveals the helical arrangement of F-actin subunits in the thin filament enabling an atomic model to be built into the thin filament density independent of the myosin. Actin-myosin attachments can now be assigned as weak or strong by their motor domain orientation relative to actin. Myosin attachments were quantified everywhere along the thin filament including troponin. Strong binding myosin attachments are found on only four F-actin subunits, the “target zone”, situated exactly midway between successive troponin complexes. They show an axial lever arm range of 77°/12.9 nm. The lever arm azimuthal range of strong binding attachments has a highly skewed, 127° range compared with X-ray crystallographic structures. Two types of weak actin attachments are described. One type, found exclusively in the target zone, appears to represent pre-working-stroke intermediates. The other, which contacts tropomyosin rather than actin, is positioned M-ward of the target zone, i.e. the position toward which thin filaments slide during shortening.

Conclusion

We present a model for the weak to strong transition in the myosin ATPase cycle that incorporates azimuthal movements of the motor domain on actin. Stress/strain in the S2 domain may explain azimuthal lever arm changes in the strong binding attachments. The results support previous conclusions that the weak attachments preceding force generation are very different from strong binding attachments.     

Scinderin,a Ca2+-Dependent Actin Filament Severing Protein that Controls Cortical Actin Network Dynamics During Secretion

Secretory vesicles are localized in specific compartments within neurosecretory cells. These are different pools in which vesicles are in various states of releasability. The transit of vesicles between compartments is controlled and regulated by Ca²⁺, scinderin and the cortical F-actin network. Cortical F-actin disassembly is produced by the filament severing activity of scinderin. This Ca²⁺-dependent activity of scinderin together with its Ca²⁺-independent actin nucleating activity, control cortical F-actin dynamics during the secretory cycle. A good understanding of the interaction of actin with scinderin and of the role of this protein in secretion has been provided by the analysis of the molecular structure of scinderin together with the use of recombinant proteins corresponding to its different domains.     

Functional synergy of actin filament cross-linking proteins

The organization of filamentous actin (F-actin) in resilient networks is coordinated by various F-actin cross-linking proteins. The relative tolerance of cells to null mutations of genes that code for a single actin cross-linking protein suggests that the functions of those proteins are highly redundant. This apparent functional redundancy may, however, reflect the limited resolution of available assays in assessing the mechanical role of F-actin cross-linking/bundling proteins. Using reconstituted F-actin networks and rheological methods, we demonstrate how alpha-actinin and fascin, two F-actin cross-linking/bundling proteins that co-localize along stress fibers and in lamellipodia, could synergistically enhance the resilience of F-actin networks in vitro. These two proteins can generate microfilament arrays that "yield" at a strain amplitude that is much larger than each one of the proteins separately. F-actin/alpha-actinin/fascin networks display strain-induced hardening, whereby the network "stiffens" under shear deformations, a phenomenon that is non-existent in F-actin/fascin networks and much weaker in F-actin/alpha-actinin networks. Strain-hardening is further enhanced at high rates of deformation and high concentrations of actin cross-linking proteins. A simplified model suggests that the optimum results of the competition between the increased stiffness of bundles and their decreased density of cross-links. Our studies support a re-evaluation of the notion of functional redundancy among cytoskeletal regulatory proteins.     

beta-actinin, a regulatory protein of muscle. Purification, characterization and function.

beta-Actinin, a minor regulatory protein of muscle, was purified from skeletal muscles of rabbit and chicken by DEAE-Sephadex chromatography. beta-Actinin consisted of two subunits, beta I and betaII, with chain weights of 37,000 and 34,000 daltons, respectively. The amino acid compositions were similar, though not identical. It appears that each of the two subunits is associated in solution. beta-Actinin had the following effects on actin: (1) inhibition of reassociation of F-actin fragments; (2) inhibition of network formation of F-actin; (3) inhibition of growth of F-actin fragments; (4) retardation of depolymerization of F-actin and (5) acceleration of polymerization of G-actin. All these actions of beta-actinin can be explained in terms of action as an "ending factor". Experimental evidence favored the view that beta-actinin is bound to one end of the F-actin filament, namely to the end opposite to the direction of polymerization. Fluorescence-labeled anti-beta-actinin stained the middle portion of the A band of myofibrils. Based on the finding that the stain was unchanged on removal of myosin, it is suggested that beta-actinin is located at the free ends of the I filaments of myofibrils. Thus is seems likely that beta-actinin functions as an ending factor for actin filaments.     

A three-dimensional random network model of the cytoskeleton and its role in mechanotransduction and nucleus deformation

We have developed a three-dimensional random network model of the intracellular actin cytoskeleton and have used it to study the role of the cytoskeleton in mechanotransduction and nucleus deformation. We use the model to predict the deformation of the nucleus when mechanical stresses applied on the plasma membrane are propagated through the random cytoskeletal network to the nucleus membrane. We found that our results agree with previous experiments utilizing micropipette pulling. Therefore, we propose that stress propagation through the random cytoskeletal network can be a mechanism to effect nucleus deformation, without invoking any biochemical signaling activity. Using our model, we also predict how nucleus strain and its relative displacement within the cytosol vary with varying concentrations of actin filaments and actin-binding proteins. We find that nucleus strain varies in a sigmoidal manner with actin filament concentration, while there exists an optimal concentration of actin-binding proteins that maximize nucleus displacement. We provide a theoretical analysis for these nonlinearities in terms of the connectivity of the random cytoskeletal network. Finally, we discuss laser ablation experiments that can be performed to validate these results in order to advance our understanding of the role of the cytoskeleton in mechanotransduction.     

Mechanics of F-actin characterized with microfabricated cantilevers

In this report we characterized the longitudinal elasticity of single actin filaments manipulated by novel silicon-nitride microfabricated levers. Single actin filaments were stretched from zero tension to maximal physiological tension, P(0). The obtained length-tension relation was nonlinear in the low-tension range (0-50 pN) with a resultant strain of approximately 0.4-0.6% and then became linear at moderate to high tensions (approximately 50-230 pN). In this region, the stretching stiffness of a single rhodamine-phalloidin-labeled, 1-microm-long F-actin is 34.5 +/- 3.5 pN/nm. Such a length-tension relation could be characterized by an entropic-enthalpic worm-like chain model, which ascribes most of the energy consumed in the nonlinear portion to overcoming thermal undulations arising from the filament's interaction with surrounding solution and the linear portion to the intrinsic stretching elasticity. By fitting the experimental data with such a worm-like chain model, an estimation of persistence length of approximately 8.75 microm was derived. These results suggest that F-actin is more compliant than previously thought and that thin filament compliance may account for a substantial fraction of the sarcomere's elasticity.     

The F-actin cytoskeleton in syncytia from non-clonal progenitor cells

The actin cytoskeleton of plant syncytia (a multinucleate cell arising through fusion) is poorly known: to date, there have only been reports about F-actin organization in plant syncytia induced by parasitic nematodes. To broaden knowledge regarding this issue, we analyzed F-actin organization in special heterokaryotic Utricularia syncytia, which arise from maternal sporophytic tissues and endosperm haustoria. In contrast to plant syncytia induced by parasitic nematodes, the syncytia of Utricularia have an extensive F-actin network. Abundant F-actin cytoskeleton occurs both in the region where cell walls are digested and the protoplast of nutritive tissue cells fuse with the syncytium and also near a giant amoeboid in the shape nuclei in the central part of the syncytium. An explanation for the presence of an extensive F-actin network and especially F-actin bundles in the syncytia is probably that it is involved in the movement of nuclei and other organelles and also the transport of nutrients in these physiological activity organs which are necessary for the development of embryos in these unique carnivorous plants. We observed that in Utricularia nutritive tissue cells, actin forms a randomly arranged network of F-actin, and later in syncytium, two patterns of F-actin were observed, one characteristic for nutritive cells and second—actin bundles—characteristic for haustoria and suspensors, thus syncytia inherit their F-actin patterns from their progenitors.     

MARCKS-Related Protein Binds to Actin without Significantly Affecting Actin Polymerization or Network Structure

Actinis a 42-kDa protein which, due to its ability to polymerize into filaments (F-actin), is one of the major constituents of the cytoskeleton. It has been proposed that MARCKS (an acronym for myristoylated alanine-rich C kinase substrate) proteins play an important role in regulating the structure and mechanical properties of the actin cytoskeleton by cross-linking actin filaments. We have recently reported that peptides corresponding to the effector domain of MARCKS proteins promote actin polymerization and cause massive bundling of actin filaments. We now investigate the effect of MARCKS-related protein, a 20-kDa member of the MARCKS family, on both filament structure and the kinetics of actin polymerization in vitro. Our experiments document that MRP binds to F-actin with micromolar affinity and that the myristoyl chain at the N-terminus of MRP is not required for this interaction. In marked contrast to the effector peptide, binding of MRP is not accompanied by an acceleration of actin polymerization kinetics, and we also could not reliably observe an actin cross-linking activity of MRP.     

Multiple actin binding domains of Ena/VASP proteins determine actin network stiffening

Vasodilator-stimulated phosphoprotein (Ena/VASP) is an actin binding protein, important for actin dynamics in motile cells and developing organisms. Though VASP’s main activity is the promotion of barbed end growth, it has an F-actin binding site and can form tetramers, and so could additionally play a role in actin crosslinking and bundling in the cell. To test this activity, we performed rheology of reconstituted actin networks in the presence of wild-type VASP or mutants lacking the ability to tetramerize or to bind G-actin and/or F-actin. We show that increasing amounts of wild-type VASP increase network stiffness up to a certain point, beyond which stiffness actually decreases with increasing VASP concentration. The maximum stiffness is 10-fold higher than for pure actin networks. Confocal microscopy shows that VASP forms clustered actin filament bundles, explaining the reduction in network elasticity at high VASP concentration. Removal of the tetramerization site results in significantly reduced bundling and bundle clustering, indicating that VASP’s flexible tetrameric structure causes clustering. Removing either the F-actin or the G-actin binding site diminishes VASP’s effect on elasticity, but does not eliminate it. Mutating the F-actin and G-actin binding site together, or mutating the F-actin binding site and saturating the G-actin binding site with monomeric actin, eliminates VASP’s ability to increase network stiffness. We propose that, in the cell, VASP crosslinking confers only moderate increases in linear network elasticity, and unlike other crosslinkers, VASP’s network stiffening activity may be tuned by the local concentration of monomeric actin.     

High microfilament concentration results in barbed-end ADP caps.

Current theory and experiments describing actin polymerization suggest that site-specific cleavage of bound nucleotide following F-actin filament formation causes the barbed ends of microfilaments to be capped first with ATP subunits, then with ADP bound to inorganic phosphate (ADP.Pi) at steady-state. The barbed ends of depolymerizing filaments consist of ADP subunits. The decrease in stability of the barbed-end cap accompanying the transition from ADP.Pi to ADP allows nucleotide hydrolysis and subsequent loss of Pi to regulate F-actin filament dynamics. We describe a novel computational model of nucleotide capping that simulates both the spatial and temporal properties of actin polymerization. This model has been used to test the effects of high filament concentration on the behavior of the ATP hydrolysis cycle observed during polymerization. The model predicts that under conditions of high microfilament concentration an ADP cap can appear during steady-state at the barbed ends of filaments. We show that the presence of the cap can be accounted for by a kinetic model and predict the relationship between the nucleotide concentration ratio [ATP]/[ADP], the F-actin filament concentration, and the steady-state distribution of barbed-end ADP cap lengths. The possible consequences of this previously unreported phenomenon as a regulator of cytoskeletal behavior are discussed.