Micro- and macrorheological properties of actin networks effectively cross-linked by depletion forces

The structure and rheology of cytoskeletal networks are regulated by actin binding proteins. Aside from these specific interactions, depletion forces can also alter the properties of cytoskeletal networks. Here we demonstrate that the addition of poly(ethylene glycol) (PEG) as a depletion agent results not only in severe structural changes, but also in alterations in mechanical properties of actin solutions. In the plateau of the elastic modulus two regimes can be distinguished by micro and macrorheological methods. In the first, the elastic modulus increases only slightly with increasing depletion agent, whereas above a critical concentration c*, a strong increase of cPEG6k3.5 is observed in a distinct second regime. Microrheological data and electron microscopy images show a homogenous network of actin filaments in the first regime, whereas at higher PEG concentrations a network of actin bundles is observed. The concentration dependence of the plateau modulus G0, the shift in entanglement time taue, and the nonlinear response indicate that below c* the network becomes effectively cross-linked, whereas above c* G0(cPEG6k) is primarily determined by the network of bundles that exhibits a linearly increasing bundle thickness.     

Isolation and characterization of covalently cross-linked actin dimer

Covalently cross-linked actin dimer was isolated from rabbit skeletal muscle F-actin reacted with phenylenebismaleimide (Knight, P., and Offer, G. (1978) Biochem. J. 175, 1023-1032). The UV spectrum of the purified cross-linked actin dimer, in a nonpolymerizing buffer, was very similar to that of native F-actin and not to the spectrum of G-actin. Cross-linked actin dimer polymerized to filaments that were indistinguishable in the electron microscope from F-actin made from native G-actin and that were similar to native F-actin in their ability to activate the Mg2+-ATPase of myosin subfragment-1. The critical concentrations of polymerization of cross-linked actin dimer in 0.5 mM and 2.0 mM MgCl2, 2 to 4 microM, and 1 to 2 microM, respectively, were similar to the values for native G-actin. Cross-linked actin dimer contained 2 mol of bound nucleotide/mol of dimer. One bound nucleotide exchanged with ATP in solution with a t 1/2 of 55 min and with ADP with a t 1/2 of 5 h. The second bound nucleotide exchanged much more slowly. The more rapidly exchangeable site contained 10 to 15% bound ADP.Pi and 85 to 90% bound ATP while the second site contained much less, if any, bound ADP.Pi. Cross-linked actin dimer had an ATPase activity in 0.5 mM MgCl2 that was 7 times greater than the ATPase activity of native G-actin and that was also stimulated by cytochalasin D. These data are discussed in relation to the possible role of ATP in actin polymerization and function with the speculation that the cross-linked actin dimer may serve simultaneously as a useful model for each of the two different ends of native F-actin.     

A chemo-mechanical constitutive model for transiently cross-linked actin networks and a theoretical assessment of their viscoelastic behaviour

Biological materials can undergo large deformations and also show viscoelastic behaviour. One such material is the network of actin filaments found in biological cells, giving the cell much of its mechanical stiffness. A theory for predicting the relaxation behaviour of actin networks cross-linked with the cross-linker α-actinin is proposed. The constitutive model is based on a continuum approach involving a neo-Hookean material model, modified in terms of concentration of chemically activated cross-links. The chemical model builds on work done by Spiros (Doctoral thesis, University of British Columbia, Vancouver, Canada, 1998) and has been modified to respond to mechanical stress experienced by the network. The deformation is split into a viscous and elastic part, and a thermodynamically motivated rate equation is assigned for the evolution of viscous deformation. The model predictions were evaluated for stress relaxation tests at different levels of strain and found to be in good agreement with experimental results for actin networks cross-linked with α-actinin.     

Probe diffusion in cross-linked actin gels

The diffusion of monodisperse polystyrene latex spheres (PLS) in column-purified 0.65 mg/mL actin solutions, polymerized with 100 mM KCl in the absence and presence of a cross-linker, actin binding protein (ABP), has been studied using dynamic light scattering. Measurements over a wide range of scattering angles from 90 degrees to 8 degrees, corresponding to inverse scattering vector probing distances of about 40-400 nm, respectively, give a measure of both the fraction of PLS mobile over the probing distance (from the normalized time autocorrelation function amplitude) and the average diffusion coefficient of the mobile PLS. Both 100- and 500-nm diameter PLS are fully mobile in polymerized actin solutions over distances of less than 100 nm, as reported previously (Newman, J., Schick, K. S. & Gukelberger, G. Biophys. J. 53, 573a, and Newman, J., Mroczka, N. & Schick, K. L. Biopolymers, 28, 655-666). At increasing probing distances, or when ABP is added at molar ratios of 1:750 or 1:150, greater fractions of the PLS are immobilized, up to almost 99% at the conditions of a 400-nm probing distance with 500-nm probes and at a ratio of 1:150 added ABP to actin. The degree of immobilization correlated well with the amount of added ABP, the size of the PLS, and the probing distance. At increasing probe distances, as the degree of immobilization increases, the remaining mobile fraction of PLS has an increasing average diffusion coefficient. These results suggest a range of pore sizes in the actin gels with a mean size of a few hundred nanometers.     

Organization and dynamics of cross-linked actin filaments in confined environments

The organization of the actin cytoskeleton is impacted by the interplay between physical confinement, features of cross-linking proteins, and deformations of semiflexible actin filaments. Some cross-linking proteins preferentially bind filaments in parallel, although others bind more indiscriminately. However, a quantitative understanding of how the mode of binding influences the assembly of actin networks in confined environments is lacking. Here we employ coarse-grained computer simulations to study the dynamics and organization of semiflexible actin filaments in confined regions upon the addition of cross-linkers. We characterize how the emergent behavior is influenced by the system shape, the number and type of cross-linking proteins, and the length of filaments. Structures include isolated clusters of filaments, highly connected filament bundles, and networks of interconnected bundles and loops. Elongation of one dimension of the system promotes the formation of long bundles that align with the elongated axis. Dynamics are governed by rapid cross-linking into aggregates, followed by a slower change in their shape and connectivity. Cross-linking decreases the average bending energy of short or sparsely connected filaments by suppressing shape fluctuations. However, it increases the average bending energy in highly connected networks because filament bundles become deformed, and small numbers of filaments exhibit long-lived, highly unfavorable configurations. Indiscriminate cross-linking promotes the formation of high-energy configurations due to the increased likelihood of unfavorable, difficult-to-relax configurations at early times. Taken together, this work demonstrates physical mechanisms by which cross-linker binding and physical confinement impact the emergent behavior of actin networks, which is relevant both in cells and in synthetic environments.     

Mechanical properties of actin filament networks depend on preparation, polymerization conditions, and storage of actin monomers.

This study investigates possible sources for the variance of more than two orders of magnitude in the published values for the shear moduli of purified actin filaments. Two types of forced oscillatory rheometers used in some of our previous work agree within a factor of three for identical samples. Polymers assembled in EGTA and Mg2+ from fresh, gel-filtered ATP-actin at 1 mg/ml typically have an elastic storage modulus (G') of approximately 1 Pa at a deformation frequency of 0.1-1 Hz. G' is slightly higher when actin is polymerized in KCl with Ca2+ and Mg2+. Gel filtration removes minor contaminants from actin but has little effect on G' for most preparations of actin from acetone powder. Storage of actin monomers without frequent changes of buffer containing fresh ATP and dithiothreitol can result in changes that increase the G' of filaments by more than a factor of 10. Frozen storage can preserve the properties of monomeric actin, but care is necessary to prevent protein denaturation or aggregation due to freezing or thawing.     

Interaction of gelsolin with covalently cross-linked actin dimer.

One of the two actin molecules in the ternary actin-gelsolin complex was selectively cross-linked to gelsolin when benzophenonemaleimide-actin (BPM-actin) was used [Doi, Y., Banba, M., & Vertut-Doi (1991a) Biochemistry 30, 5769-5777]. Here, we examine the interaction between gelsolin and BPM-actin dimer in which BPM-actin is covalently conjugated to unlabeled actin by p-phenylenedimaleimide (pPDM). BPM-actin dimer having an apparent molecular mass of 115 kDa is photo-cross-linked to gelsolin (90 kDa) more effectively than BPM-actin monomer in the presence of Ca2+, forming a cross-linked actin dimer-gelsolin (1:1) complex with a molecular mass of 210 kDa. The tight direct association of the dimer to gelsolin is shown by the titration of gelsolin with the fluorescently labeled dimer and by the higher concentration of phosphatidylinositol 4,5-bisphosphate required to inhibit the formation of BPM-dimer complex with gelsolin than that of BPM-monomer complex. However, an attempt to cross-link the two actin molecules in the ternary actin-gelsolin (2:1) complex by pPDM fails. The results argue that the topography of the two actin molecules in the actin-gelsolin (2:1) complex is similar, but not identical, to that of the barbed end of an actin filament.     

Nucleotide-induced states of myosin subfragment 1 cross-linked to actin

Actomyosin interactions and the properties of weakly bound states in carbodiimide-cross-linked complexes of actin and myosin subfragment 1 (S-1) were probed in tryptic digestion, fluorescence, and thiol modification experiments. Limited proteolysis showed that the 50/20K junction on S-1 was protected in cross-linked acto-S-1 from trypsin even under high-salt conditions in the presence of MgADP, MgAMPPNP, and MgPPi (mu = 0.5 M). The same junction was exposed to trypsin by MgATP and MgATP gamma S but mainly on S-1 cross-linked via its 50K fragment to actin. p-Phenylenedimaleimide-bridged S-1, when cross-linked to actin, yielded similar tryptic cleavage patterns to those of cross-linked S-1 in the presence of MgATP. By using p-nitrophenylenemaleimide, it was found that the essential thiols of cross-linked S-1 were exposed to labeling in the presence of MgATP and MgATP gamma S in a state-specific manner. In contrast to this, the reactive thiols were protected from modification in the presence of MgADP, MgAMPPNP, and MgPPi at mu = 0.5 M. These modifications were compared with similar reactions on isolated S-1. Experiments with pyrene-actin cross-linked to S-1 showed enhancement of fluorescence intensity upon additions of MgATP and MgATP gamma S, indicating the release of the pyrene probe on actin from the sphere of S-1 influence. The results of this study contrast the "open" structure of weakly bound actomyosin states to the "tight" conformation of rigor complexes.     

Yeast actin patches are networks of branched actin filaments

Cortical actin patches are the most prominent actin structure in budding and fission yeast. Patches assemble, move, and disassemble rapidly. We investigated the mechanisms underlying patch actin assembly and motility by studying actin filament ultrastructure within a patch. Actin patches were partially purified from Saccharomyces cerevisiae and examined by negative-stain electron microscopy (EM). To identify patches in the EM, we correlated fluorescence and EM images of GFP-labeled patches. Patches contained a network of actin filaments with branches characteristic of Arp2/3 complex. An average patch contained 85 filaments. The average filament was only 50-nm (20 actin subunits) long, and the filament to branch ratio was 3:1. Patches lacking Sac6/fimbrin were unstable, and patches lacking capping protein were relatively normal. Our results are consistent with Arp2/3 complex-mediated actin polymerization driving yeast actin patch assembly and motility, as described by a variation of the dendritic nucleation model.     

Acanthamoeba actin and profilin can be cross-linked between glutamic acid 364 of actin and lysine 115 of profilin

Acanthamoeba profilin was cross-linked to actin via a zero-length isopeptide bond using carbodiimide. The covalently linked 1:1 complex was purified and treated with cyanogen bromide. This cleaves actin into small cyanogen bromide (CNBr) peptides and leaves the profilin intact owing to its lack of methionine. Profilin with one covalently attached actin CNBr peptide was purified by gel filtration followed by gel electrophoresis and electroblotting on polybase-coated glass-fiber membranes. Since the NH2 terminus of profilin is blocked, Edman degradation gave only the sequence of the conjugated actin CNBr fragment beginning with Trp-356. The profilin-actin CNBr peptide conjugate was digested further with trypsin and the cross-linked peptide identified by comparison with the tryptic peptide pattern obtained from carbodiimide-treated profilin. Amino-acid sequence analysis of the cross-linked tryptic peptides produced two residues at each cycle. Their order corresponds to actin starting at Trp-356 and profilin starting at Ala-94. From the absence of the phenylthiohydantoin-amino acid residues in specific cycles, we conclude that actin Glu-364 is linked to Lys-115 in profilin. Experiments with the isoforms of profilin I and profilin II gave identical results. The cross-linked region in profilin is homologous with sequences in the larger actin filament capping proteins fragmin and gelsolin.     

Dynamic viscoelasticity of actin cross-linked with wild-type and disease-causing mutant alpha-actinin-4

The actin cross-linker α-actinin-4 has been found to be indispensable for the structural and functional integrity of podocytes; deficiency or alteration of this protein due to mutations results in kidney disease. To gain insight into the effect of the cross-linker on cytoskeletal mechanics, we studied the macroscopic rheological properties of actin networks cross-linked with wild-type and mutant α-actinin-4. The frequency-dependent viscoelasticity of the networks is characterized by an elastic plateau at intermediate frequencies, and relaxation toward fluid properties at low frequencies. The relaxation frequencies of networks with mutant α-actinin-4 are an order of magnitude lower than that with the wild-type, suggesting a slower reaction rate for the dissociation of actin and α-actinin for the mutant, consistent with a smaller observed equilibrium dissociation constant. This difference can be attributed to an additional binding site that is exposed as a result of the mutation, and can be interpreted as a difference in binding energy barriers. This is further supported by the Arrhenius-like temperature dependence of the relaxation frequencies.     

Growth velocities of branched actin networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.     

Curvature and torsion in growing actin networks

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque.     

Biochemical properties of intramolecularly cross-linked hemoglobin

The chemical modification of hemoglobin was conducted with the help of bifunctional crosslinking agent--glutaraldehyde. By SDS-polyacrylamide gel electrophoresis and gel-filtration it was shown that the final product contained 70% of modified protein which consisted of non-dissociating hemoglobin dimers and tetramers. It was also shown that the chemical modification didn't produce significant changes in the oxygen-transporting properties of the starting hemoglobin, but had influence on the character of the interaction with the allosteric regulator of reversible oxygenation (pyridoxal-5'-phosphate). The half-disappearance period in animals of the intramolecularly crosslinked hemoglobin was two times longer in comparison with the native protein.     

Mechanical properties of actin

We used a cone and plate rheometer to evaluate the mechanical properties of actin over a wide range of oscillation frequencies and shear rates. Remarkably, both filamentous and nonfilamentous actin behaved as viscoelastic solids in both oscillatory and shear type experiments, providing that they were given ample time to equilibrate. Actin was purified by gel filtration from rabbit skeletal muscle and Acanthamoeba. Nonfilamentous actin in 2 different buffers had similar properties. In a low ionic strength buffer the absence of filaments was confirmed by electron microscopy, ultracentrifugation, and the fluorescence of pyrene-labeled actin. In 0.6 M KI, actin was monomeric by gel filtration. Filamentous actin had similar properties in 2 mM MgCl2 with either 50 mM KC1 or 500 mM KC1. Under all 4 of these conditions, actin required about 1000 min at 25 degrees C for the rheological properties to equilibrate. Under conditions where the oscillation of the rheometer did not affect the mechanical properties, all of the actin preparations had dynamic viscosities that were inverse functions of the frequency and dynamic elasticites that leveled off at low frequencies as expected for viscoelastic solids. For filamentous actin, the values of these parameters were about 2 times higher than for nonfilamentous actin. In shear experiments, both filamentous and nonfilamentous actin exhibited shear rate-dependent yield stresses. When filamentous and nonfilamentous actin structures were disrupted by transient shearing, the dynamic elasticity recovered to 90% in 30 min. Ovalbumin in the low ionic strength buffer also behaved as a viscoelastic material with elasticity and viscosity about 10 times lower than nonfilamentous actin, while cytochrome c behaved as a Newtonian fluid with a viscosity of 0.02 poise.     

Organization of actin networks in intact filopodia

Filopodia are finger-like extensions of the cell surface that are involved in sensing the environment, in attachment of particles for phagocytosis, in anchorage of cells on a substratum, and in the response to chemoattractants or other guidance cues. Filopodia present an excellent model for actin-driven membrane protrusion. They grow at their tips by the assembly of actin and are stabilized along their length by a core of bundled actin filaments. To visualize actin networks in their native membrane-anchored state, filopodia of Dictyostelium cells were subjected to cryo-electron tomography. At the site of actin polymerization, a peculiar structure, the "terminal cone," is built of short filaments fixed with their distal end to the filopod's tip and with their proximal end to the flank of the filopod. The backbone of the filopodia consists of actin filaments that are shorter than the entire filopod and aligned in parallel or obliquely to the filopod's axis. We hypothesize that growth of the highly dynamic filopodia of Dictyostelium is accompanied by repetitive nucleation of actin polymerization at the filopod tip, followed by the rearrangement of filaments within the shaft.     

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.     

Actin dynamics: assembly and disassembly of actin networks

Assembly of branched actin filament networks at the leading edge of migrating cells requires stimulation of the Arp2/3 complex by WASp proteins, in concert with the WASp activators Cdc42, PIP(2) and profilin. Network disassembly and debranching appears to be linked to actin-bound ATP hydrolysis as filaments age.     

Contraction mechanisms in composite active actin networks

Simplified in vitro systems are ideally suited for studying the principle mechanisms of the contraction of cytoskeletal actin systems. To shed light on the dependence of the contraction mechanism on the nature of the crosslinking proteins, we study reconstituted in vitro active actin networks on different length scales ranging from the molecular organization to the macroscopic contraction. Distinct contraction mechanisms are observed in polar and apolar crosslinked active gels whereas composite active gels crosslinked in a polar and apolar fashion at the same time exhibit both mechanisms simultaneously. In polar active actin/fascin networks initially bundles are formed which are then rearranged. In contrast, apolar cortexillin-I crosslinked active gels are bundled only after reorganization of actin filaments by myosin-II motor filaments.     

Dynamic rheological properties of native and cross-linked gliadin proteins

A comparison of cross-linked and native gliadin suspensions, with respect to the state of protein globular structure was carried out using small-angle X-ray scattering (SAXS), dynamic light scattering (DLS) and rheological analysis. Gliadin suspensions were also analyzed in the presence and absence of glycerol. DLS analysis showed that R(h) increased only with gliadin/EDC/NHS suspensions. However, Kratky plots revealed that gliadin and gliadin/l-cysteine maintained their globular shape even in absence or presence of glycerol. Rheological experiments revealed that gliadin and gliadin/l-cysteine suspension exhibited a similar profile with three main domains, and a sol-gel transition. Gliadin/EDC/NHS did not present any sol-gel transition, and this fact corroborates with DLS results and the hypothesis of lower protein-protein interaction, which are in agreement with G″>G'.