Cytoskeletal Polymer Networks: Viscoelastic Properties are Determined by the Microscopic Interaction Potential of Cross-links

Although the structure of cross-linking molecules mainly determines the structural organization of actin filaments and with that the static elastic properties of the cytoskeleton, it is largely unknown how the biochemical characteristics of transiently cross-linking proteins (actin-binding proteins (ABPs)) affect the viscoelasticity of actin networks. In this study, we show that the macroscopic network response of reconstituted actin networks can be traced back to the microscopic interaction potential of an individual actin/ABP bond. The viscoelastic response of cross-linked actin networks is set by the cross-linker off-rate, the binding energy, and the characteristic bond length of individual actin/ABP interactions.     

Nonlinear Viscoelasticity of Actin Transiently Cross-linked with Mutant α-Actinin-4

Filamentous actin and associated actin binding proteins play an essential role in governing the mechanical properties of eukaryotic cells. They can also play a critical role in disease; for example, mutations in α-actinin-4 (Actn4), a dynamic actin cross-linking protein, cause proteinuric disease in humans and mice. Amino acid substitutions strongly affect the binding affinity and protein structure of Actn4. To study the physical impact of such substitutions on the underlying cytoskeletal network, we examine the bulk mechanical behavior of in vitro actin networks cross-linked with wild-type and mutant Actn4. These networks exhibit a complex viscoelastic response and are characterized by fluid-like behavior at the longest timescales, a feature that can be quantitatively accounted for through a model governed by dynamic cross-linking. The elastic behavior of the network is highly nonlinear, becoming much stiffer with applied stress. This nonlinear elastic response is also highly sensitive to the mutations of Actn4. In particular, we observe that actin networks cross-linked with Actn4 bearing the disease-causing K255E mutation are more brittle, with a lower breaking stress in comparison to networks cross-linked with wild-type Actn4. Furthermore, a mutation that ablates the first actin binding site (ABS1) in Actn4 abrogates the network's ability to stress-stiffen is standard nomenclature. These changes in the mechanical properties of actin networks cross-linked with mutant Actn4 may represent physical determinants of the underlying disease mechanism in inherited focal segmental glomerulosclerosis.     

Desmin and Vimentin Intermediate Filament Networks: Their Viscoelastic Properties Investigated by Mechanical Rheometry

We have investigated the viscoelastic properties of the cytoplasmic intermediate filament (IF) proteins desmin and vimentin. Mechanical measurements were supported by time-dependent electron microscopy studies of the assembly process under similar conditions. Network formation starts within 2 min, but it takes more than 30 min until equilibrium mechanical network strength is reached. Filament bundling is more pronounced for desmin than for vimentin. Desmin filaments (persistence length l_p ≈ 900 nm) are stiffer than vimentin filaments (l_p ≈ 400 nm), but both IFs are much more flexible than microfilaments. The concentration dependence of the plateau modulus G₀ ∼ c^α is much weaker than predicted theoretically for networks of semiflexible filaments. This is more pronounced for vimentin (α = 0.47) than for desmin (α = 0.70). Both networks exhibit strain stiffening at large shear deformations. At the transition from linear to nonlinear viscoelastic response, only desmin shows characteristics of nonaffine network deformation. Strain stiffening and the maximum modulus occur at strain amplitudes about an order of magnitude larger than those for microfilaments. This is probably attributable to axial slippage within the tetramer building blocks of the IFs. Network deformation beyond a critical strain γ_max results in irreversible damage. Strain stiffening sets in at lower concentrations, is more pronounced, and is less sensitive to ionic strength for desmin than for vimentin. Hence, desmin exhibits strain stiffening even at low-salt concentrations, which is not observed for vimentin, and we conclude that the strength of electrostatic repulsion compared to the strength of attractive interactions forming the network junctions is significantly weaker for desmin than for vimentin filaments. These findings indicate that both IFs exhibit distinct mechanical properties that are adapted to their respective cellular surroundings [i.e., myocytes (desmin) and fibroblasts (vimentin)].     

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.     

Divalent Cations Crosslink Vimentin Intermediate Filament Tail Domains to Regulate Network Mechanics

Intermediate filament networks in the cytoplasm and nucleus are critical for the mechanical integrity of metazoan cells. However, the mechanism of crosslinking in these networks and the origins of their mechanical properties are not understood. Here, we study the elastic behavior of in vitro networks of the intermediate filament protein vimentin. Rheological experiments reveal that vimentin networks stiffen with increasing concentrations of Ca²⁺ and Mg²⁺, showing that divalent cations act as crosslinkers. We quantitatively describe the elastic response of vimentin networks over five decades of applied stress using a theory that treats the divalent cations as crosslinkers: at low stress, the behavior is entropic in origin, and increasing stress pulls out thermal fluctuations from single filaments, giving rise to a nonlinear response; at high stress, enthalpic stretching of individual filaments significantly modifies the nonlinearity. We investigate the elastic properties of networks formed by a series of protein variants with stepwise tail truncations and find that the last 11 amino acids of the C-terminal tail domain mediate crosslinking by divalent ions. We determined the single-filament persistence length, l_P ≈ 0.5 μm, and Young's modulus, Y ≈ 9 MPa; both are consistent with literature values. Our results provide insight into a crosslinking mechanism for vimentin networks and suggest that divalent ions may help regulate the cytoskeletal structure and mechanical properties of cells.     

Mutations in Desmin's Carboxy-Terminal “Tail” Domain Severely Modify Filament and Network Mechanics

Inherited mutations in the gene coding for the intermediate filament protein desmin have been demonstrated to cause severe skeletal and cardiac myopathies. Unexpectedly, some of the mutated desmins, in particular those carrying single amino acid alterations in the non-α-helical carboxy-terminal domain (“tail”), have been demonstrated to form apparently normal filaments both in vitro and in transfected cells. Thus, it is not clear if filament properties are affected by these mutations at all. For this reason, we performed oscillatory shear experiments with six different desmin “tail” mutants in order to characterize the mesh size of filament networks and their strain stiffening properties. Moreover, we have carried out high-frequency oscillatory squeeze flow measurements to determine the bending stiffness of the respective filaments, characterized by the persistence length l_p. Interestingly, mesh size was not altered for the mutant filament networks, except for the mutant DesR454W, which apparently did not form proper filament networks. Also, the values for bending stiffness were in the same range for both the “tail” mutants (l_p = 1.0-2.0 μm) and the wild-type desmin (l_p = 1.1 ± 0.5 μm). However, most investigated desmin mutants exhibited a distinct reduction in strain stiffening compared to wild-type desmin and promoted nonaffine network deformation. Therefore, we conclude that the mutated amino acids affect intrafilamentous architecture and colloidal interactions along the filament in such a way that the response to applied strain is significantly altered.In order to explore the importance of the “tail” domain as such for filament network properties, we employed a “tail”-truncated desmin. Under standard conditions, it formed extended regular filaments, but failed to generate strain stiffening. Hence, these data strongly indicate that the “tail” domain is responsible for attractive filament-filament interactions. Moreover, these types of interactions may also be relevant to the network properties of the desmin cytoskeleton in patient muscle.     

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.     

Modeling myosin Va liposome transport through actin filament networks reveals a percolation threshold that modulates transport properties

Myosin Va (myoVa) motors transport membrane-bound cargo through three-dimensional, intracellular actin filament networks. We developed a coarse-grained, in silico model to predict how actin filament density (3-800 filaments) within a randomly oriented actin network affects fluid-like liposome (350 nm vs. 1750 nm) transport by myoVa motors. Five thousand simulated liposomes transported within each network adopted one of three states: transport, tug-of-war, or diffusion. Diffusion due to liposome detachment from actin rarely occurred given at least 10 motors on the liposome surface. However, with increased actin density, liposomes transitioned from primarily directed transport on single actin filaments to an apparent random walk, resulting from a mixture of transport and tug-of-wars as the probability of encountering additional actin filaments increased. This phase transition arises from a percolation phase transition at a critical number of accessible actin filaments, N_c. N_c is a geometric property of the actin network that depends only on the position and polarity of the actin filaments, transport distance, and the liposome diameter, as evidenced by a fivefold increase in liposome diameter resulting in a fivefold decrease in N_c. Thus in cells, actin network density and cargo size may be regulated to match cargo delivery to the cell’s physiological demands.     

Arp2/3 Complex from Acanthamoeba Binds Profilin and Cross-links Actin Filaments

The Arp2/3 complex was first purified from Acanthamoeba castellanii by profilin affinity chromatography. The mechanism of interaction with profilin was unknown but was hypothesized to be mediated by either Arp2 or Arp3. Here we show that the Arp2 subunit of the complex can be chemically cross-linked to the actin-binding site of profilin. By analytical ultracentrifugation, rhodamine-labeled profilin binds Arp2/3 complex with a K_d of 7 μM, an affinity intermediate between the low affinity of profilin for barbed ends of actin filaments and its high affinity for actin monomers. These data suggest the barbed end of Arp2 is exposed, but Arp2 and Arp3 are not packed together in the complex exactly like two actin monomers in a filament. Arp2/3 complex also cross-links actin filaments into small bundles and isotropic networks, which are mechanically stiffer than solutions of actin filaments alone. Arp2/3 complex is concentrated at the leading edge of motile Acanthamoeba, and its localization is distinct from that of α-actinin, another filament cross-linking protein. Based on localization and actin filament nucleation and cross-linking activities, we propose a role for Arp2/3 in determining the structure of the actin filament network at the leading edge of motile cells.     

Why Are Two Different Cross-linkers Necessary for Actin Bundle Formation In Vivo and What Does Each Cross-link Contribute?

In developing Drosophila bristles two species of cross-linker, the forked proteins and fascin, connect adjacent actin filaments into bundles. Bundles form in three phases: (a) tiny bundles appear; (b) these bundles aggregate into larger bundles; and (c) the filaments become maximally cross-linked by fascin. In mutants that completely lack forked, aggregation of the bundles does not occur so that the mature bundles consist of <50 filaments versus ∼700 for wild type. If the forked concentration is genetically reduced to half the wild type, aggregation of the tiny bundles occurs but the filaments are poorly ordered albeit with small patches of fascin cross-linked filaments. In mutants containing an excess of forked, all the bundles tend to aggregate and the filaments are maximally crossbridged by fascin. Alternatively, if fascin is absent, phases 1 and 2 occur normally but the resultant bundles are twisted and the filaments within them are poorly ordered. By extracting fully elongated bristles with potassium iodide which removes fascin but leaves forked, the bundles change from being straight to twisted and the filaments within them become poorly ordered. From these observations we conclude that (a) forked is used early in development to aggregate the tiny bundles into larger bundles; and (b) forked facilitates fascin entry into the bundles to maximally cross-link the actin filaments into straight, compact, rigid bundles. Thus, forked aligns the filaments and then directs fascin binding so that inappropriate cross-linking does not occur.     

Cutoff variation induces different topological properties: A new discovery of amino acid network within protein

An increasing attention has been dedicated to the characterization of complex networks within the protein world. Before now most investigations about protein structures were only considered where the interactive cutoff distance R_c=5 or 7 Å. It is noteworthy that the length of peptide bond is about 1.5 Å, the length of hydrogen bond is about 3 Å, the range of London-van der Waals force is about 5 Å and the range of hydrophobic effect can reach to 12 Å in protein molecule. Present work reports a study on the topological properties of the amino acid network constructed by different interactions above. The results indicate that the small-world property of amino acid network constructed by the peptide and hydrogen bond, London-van der Waals force and the hydrophobic effect is strong, very strong and relatively weak, respectively. Besides, there exists a precise exponential relation C∝k^−0.5 at R_c=12 Å. It means that the amino acid network constructed by the hydrophobic effect tend to be hierarchical. Functional modules could be the cause for hierarchical modularity architecture in protein structures. This study on amino acid interactive network for different interactions facilitates the identification of binding sites which is strongly linked with protein function, and furthermore provides reasonable understanding of the underlying laws of evolution in genomics and proteomics.     

Elasticity in Ionically Cross-Linked Neurofilament Networks

Neurofilaments are found in abundance in the cytoskeleton of neurons, where they act as an intracellular framework protecting the neuron from external stresses. To elucidate the nature of the mechanical properties that provide this protection, we measure the linear and nonlinear viscoelastic properties of networks of neurofilaments. These networks are soft solids that exhibit dramatic strain stiffening above critical strains of 30-70%. Surprisingly, divalent ions such as Mg²⁺, Ca²⁺, and Zn²⁺ act as effective cross-linkers for neurofilament networks, controlling their solidlike elastic response. This behavior is comparable to that of actin-binding proteins in reconstituted filamentous actin. We show that the elasticity of neurofilament networks is entropic in origin and is consistent with a model for cross-linked semiflexible networks, which we use to quantify the cross-linking by divalent ions.     

The use of a water-soluble carbodiimide to study the interaction between Chromatium vinosum flavocytochrome c-552 and cytochrome c

The interaction between horse heart cytochrome c and Chromatium vinosum flavocytochrome c-552 was studied using the water-soluble reagent 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC). Treatment of flavocytochrome c-552 with EDC was found to inhibit the sulfide: cytochrome c reductase activity of the enzyme. SDS gel electrophoresis studies revealed that EDC treatment led to modification of carboxyl groups in both the M_r 21000 heme peptide and the M_r 46000 flavin peptide, and also to the formation of a cross-linked heme peptide dimer with an M_r value of 42000. Both the inhibition of sulfide: cytochrome c reductase activity and the formation of the heme peptide dimer were decreased when the EDC modification was carried out in the presence of cytochrome c. In addition, two new cross-linked species with M_r values of 34000 and 59000 were formed. These were identified as cross-linked cytochrome c-heme peptide and cytochrome c-flavin peptide species, respectively. Neither of these species were formed in the presence of a cytochrome c derivative in which all of the lysine amino groups had been dimethylated, demonstrating that EDC had cross-linked lysine amino groups on native cytochrome c to carboxyl groups on the heme and flavin peptides. A complex between cytochrome c and flavocytochrome c-552 was required for cross-linking to occur, since ionic strengths above 100 mM inhibited cross-linking.     

Mechanical properties of elytra from Tribolium castaneum wild-type and body color mutant strains

Cuticle tanning in insects involves simultaneous cuticular pigmentation and hardening or sclerotization. The dynamic mechanical properties of the highly modified and cuticle-rich forewings (elytra) from Tribolium castaneum (red flour beetle) wild-type and body color mutant strains were investigated to relate body coloration and elytral mechanical properties. There was no statistically significant variation in the storage modulus E′ among the elytra from jet, cola, sooty and black mutants or between the mutants and the wild-type GA-1 strain: E′ averaged 5.1 ± 0.6 GPa regardless of body color. E′ is a power law function of oscillation frequency for all types. The power law exponent, n, averaged 0.032 ± 0.001 for elytra from all genotypes except black; this small value indicated that the elytra are cross-linked. Black elytra, however, displayed a significantly larger n of 0.047 ± 0.004 and an increased loss tangent (tan δ), suggesting that metabolic differences in the black mutant strain result in elytra that are less cross-linked and more pigmented than the other types. These results are consistent with the hypothesis that black elytra have a β-alanine-deficient and dopamine-abundant metabolism, leading to greater melanin (black pigment) production, probably at the expense of cross-linking of cuticular proteins mediated by N-β-alanyldopamine quinone.     

Time-resolved single-turnover of ba3 oxidase from Thermus thermophilus

The kinetics of the oxidation of fully-reduced ba₃ cytochrome c oxidase from Thermus thermophilus by oxygen were followed by time-resolved optical spectroscopy and electrometry. Four catalytic intermediates were resolved during this reaction. The chemical nature and the spectral properties of three intermediates (compounds A, P and O) reproduce the general features of aa₃-type oxidases. However the F intermediate in ba₃ oxidase has a spectrum identical to the P state. This indicates that the proton taken up during the P → F transition does not reside in the binuclear site but is rather transferred to the covalently cross-linked tyrosine near that site. The total charge translocation associated with the F → O transition in ba₃ oxidase is close to that observed during the F → O transition in the aa₃ oxidases. However, the P_R → F transition is characterized by significantly lower charge translocation, which probably reflects the overall lower measured pumping efficiency during multiple turnovers.     

Electrospinning of Cross-Linked Magnetic Chitosan Nanofibers for Protein Release

A poly(vinylalcohol) (PVA) electrospun/magnetic/chitosan nanocomposite fibrous cross-linked network was fabricated using in situ cross-linking electrospinning technique and used for bovine serum albumin (BSA) loading and release applications. Sodium tripolyphosphate (TPP) and glutaraldehyde (GA) were used as cross-linkers which modified magnetic-Fe₃O₄ chitosan as Fe₃O_4/CS/TPP and Fe₃O_4/CS/GA, respectively. BSA was used as a model protein drugs which was encapsulated to form Fe₃O₄/CS/TPP/BSA and Fe₃O₄/CS/GA/BSA nanoparticles. The composites were electrospun with PVA to form nanofibers. Nanofibers were characterized by field emission scanning electron microscopy (FESEM) and Fourier transform infrared spectroscopy (FTIR). The characterization results suggest that Fe₃O₄ nanoparticles with average size of 45 nm were successfully bound on the surface of chitosan. The cross-linked nanofibers were found to contain uniformly dispersed Fe₃O₄ nanoparticles. The size and morphology of the nanofibers network was controlled by varying the cross-linker type. FTIR data show that these two polymers have intermolecular interactions. The sample with TPP cross-linker showed an enhancement of the controlled release properties of BSA during 30-h experimental investigation.

Graphical Abstract

Open in a separate windowᅟKEY WORDS: cross-linker, electrospun, magnetite, mano-composite, protein loading     

Cross-linking of contractile proteins from skeletal muscle by treatment with microbial transglutaminase.

The action on muscle proteins of microbial transglutaminase (MTGase), which catalyzes the formation of a "zero-length" covalent cross-link between glutamine and lysine residues in peptides, was studied in order to define a basis for future application of MTGase cross-linking to the study of muscle protein interaction. We examined the cross-linking of skeletal muscle myosin, myosin subfragments, actin, and myofibrils by treatment with MTGase and the possible side-effects of the cross-linking on the enzymic activity of myosin, and found that the rod portions of myosin in myosin filaments were quickly cross-linked to each other by the action of MTGase, but myosin subfragment 1 was not cross-linked to actin. The MgATPase activities at 0.5 M KCl of myosin, heavy meromyosin, subfragment 1, and subfragment 1-actin were not significantly affected by the MTGase reaction. A very small fraction of the head portion of heavy meromyosin was cross-linked to actin in their rigor complexes by MTGase, and the ATPase activity at 0.5 M KCl of the cross-linked heavy meromyosin-actin complexes was slightly enhanced.     

Unphosphorylated calponin enhances the binding force of unphosphorylated myosin to actin

Background

Smooth muscle has the distinctive ability to maintain force for long periods of time and at low energy costs. While it is generally agreed that this property, called the latch-state, is due to the dephosphorylation of myosin while attached to actin, dephosphorylated-detached myosin can also attach to actin and may contribute to force maintenance. Thus, we investigated the role of calponin in regulating and enhancing the binding force of unphosphorylated tonic muscle myosin to actin.

Methods

To measure the effect of calponin on the binding of unphosphorylated myosin to actin, we used the laser trap assay to quantify the average force of unbinding (F_unb) in the absence and presence of calponin or phosphorylated calponin.

Results

F_unb from F-actin alone (0.12 ± 0.01 pN; mean ± SE) was significantly increased in the presence of calponin (0.20 ± 0.02 pN). This enhancement was lost when calponin was phosphorylated (0.12 ± 0.01 pN). To further verify that this enhancement of F_unb was due to the cross-linking of actin to myosin by calponin, we repeated the measurements at high ionic strength. Indeed, the F_unb obtained at a [KCl] of 25 mM (0.21 ± 0.02 pN; mean ± SE) was significantly decreased at a [KCl] of 150 mM, (0.13 ± 0.01 pN).

Conclusions

This study provides direct molecular level-evidence that calponin enhances the binding force of unphosphorylated myosin to actin by cross-linking them and that this is reversed upon calponin phosphorylation. Thus, calponin might play an important role in the latch-state.

General significance

This study suggests a new mechanism that likely contributes to the latch-state, a fundamental and important property of smooth muscle that remains unresolved.     

Mechanics and multiple-particle tracking microheterogeneity of alpha-actinin-cross-linked actin filament networks

Cell morphology is controlled by the actin cytoskeleton organization and mechanical properties, which are regulated by the available contents in actin and actin regulatory proteins. Using rheometry and the recently developed multiple-particle tracking method, we compare the mechanical properties and microheterogeneity of actin filament networks containing the F-actin cross-linking protein alpha-actinin. The elasticity of F-actin/alpha-actinin networks increases with actin concentration more rapidly for a fixed molar ratio of actin to alpha-actinin than in the absence of alpha-actinin, for networks of fixed alpha-actinin concentration and of fixed actin concentration, but more slowly than theoretically predicted for a homogeneous cross-linked semiflexible polymer network. These rheological measurements are complemented by multiple-particle tracking of fluorescent microspheres imbedded in the networks. The distribution of the mean squared displacements of these microspheres becomes progressively more asymmetric and wider for increasing concentration in alpha-actinin and, to a lesser extent, for increasing actin concentration, which suggests that F-actin networks become progressively heterogeneous for increasing protein content. This may explain the slower-than-predicted rise in elasticity of F-actin/alpha-actinin networks. Together these in vitro results suggest that actin and alpha-actinin provides the cell with an unsuspected range of regulatory pathways to modulate its cytoskeleton's micromechanics and local organization in vivo.     

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

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