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.     

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.     

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.     

Structural and Viscoelastic Properties of Actin/Filamin Networks: Cross-Linked versus Bundled Networks

The high diversity of cytoskeletal actin structures is accomplished by myriads of actin binding proteins (ABPs). Depending on its concentration, even a single type of ABP can induce different actin microstructures. Thus, for an overall understanding of the cytoskeleton, a detailed characterization of the cross-linker's effect on structural and mechanical properties of actin networks is required for each ABP. Using confocal microscopy and macrorheology, we investigate both cross-linked and bundled actin/filamin networks and compare their microstructures as well as their viscoelastic properties in the linear and the nonlinear regime.     

The bimodal role of filamin in controlling the architecture and mechanics of F-actin networks

Reconstituted actin filament networks have been used extensively to understand the mechanics of the actin cortex and decipher the role of actin cross-linking proteins in the maintenance and deformation of cell shape. However, studies of the mechanical role of the F-actin cross-linking protein filamin have led to seemingly contradictory conclusions, in part due to the use of ill-defined mechanical assays. Using quantitative rheological methods that avoid the pitfalls of previous studies, we systematically tested the complex mechanical response of reconstituted actin filament networks containing a wide range of filamin concentrations and compared the mechanical function of filamin with that of the cross-linking/bundling proteins alpha-actinin and fascin. At steady state and within a well defined linear regime of small non-destructive deformations, F-actin solutions behave as highly dynamic networks (actin polymers are still sufficiently mobile to relax the stress) below the cross-linking-to-bundling threshold filamin concentration, and they behave as covalently cross-linked gels above that threshold. Under large deformations, F-actin networks soften at low filamin concentrations and strain-harden at high filamin concentrations. Filamin cross-links F-actin into networks that are more resilient, stiffer, more solid-like, and less dynamic than alpha-actinin and fascin. These results resolve the controversy by showing that F-actin/filamin networks can adopt diametrically opposed rheological behaviors depending on the concentration in cross-linking proteins.     

The mechanics of F-actin microenvironments depend on the chemistry of probing surfaces

To understand the microscopic mechanical properties of actin networks, we monitor the motion of embedded particles with controlled surface properties. The highly resolved Brownian motions of these particles reveal the viscoelastic character of the microenvironments around them. In both non-cross-linked and highly cross-linked actin networks, particles that bind F-actin report viscoelastic moduli comparable to those determined by macroscopic rheology experiments. By contrast, particles modified to prevent actin binding have weak microenvironments that are surprisingly insensitive to the introduction of filament cross-links. Even when adjacent in the same cross-linked gel, actin-binding and nonbinding particles report viscoelastic moduli that differ by two orders of magnitude at low frequencies (0.5-1.5 rad/s) but converge at high frequencies (> 10(4) rad/s). For all particle chemistries, electron and light microscopies show no F-actin recruitment or depletion, so F-actin microheterogeneities cannot explain the deep penetration (approximately 100 nm) of nonbinding particles. Instead, we hypothesize that a local depletion of cross-linking around nonbinding particles explains the phenomena. With implications for organelle mobility in cells, our results show that actin binding is required for microenvironments to reflect macroscopic properties, and conversely, releasing actin enhances particle mobility beyond the effects of mere biochemical untethering.     

A microstructurally informed model for the mechanical response of three-dimensional actin networks

We propose a class of microstructurally informed models for the linear elastic mechanical behaviour of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behaviour resulting from anisotropic filament distributions, and a power law scaling of the mechanical properties with the filament density. Mechanical models within the class are parameterized by seven different constants. We demonstrate a procedure for determining these constants using finite element models of three-dimensional actin networks. Actin filaments and cross-links were modelled as elastic rods, and the networks were constructed at physiological volume fractions and at the scale of an image voxel. We show the performance of the model in estimating the mechanical behaviour of the networks over a wide range of filament densities and degrees of anisotropy.     

A microstructurally informed model for the mechanical response of three-dimensional actin networks

We propose a class of microstructurally informed models for the linear elastic mechanical behaviour of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behaviour resulting from anisotropic filament distributions, and a power law scaling of the mechanical properties with the filament density. Mechanical models within the class are parameterized by seven different constants. We demonstrate a procedure for determining these constants using finite element models of three-dimensional actin networks. Actin filaments and cross-links were modelled as elastic rods, and the networks were constructed at physiological volume fractions and at the scale of an image voxel. We show the performance of the model in estimating the mechanical behaviour of the networks over a wide range of filament densities and degrees of anisotropy.     

Direct visualization of actin nematic network formation and dynamics

Various actin assemblies within the cell regulate many cellular processes such as cell shape and motility. The mechanical properties of these networks are challenging to measure in vivo. They have been studied in solution by indirect observation methods, such as multiple ball tracking. However, little is known about the behavior of such networks near the crowded cell membrane. Here we used in vitro TIRF microscopy to directly probe the formation of actin networks in real-time near a hydrophilic surface in the presence of crowding agents. We find that under these conditions actin does not form a mesh like network, but either textured nematic liquid crystals or a bundled network. We are directly able to follow the thermal fluctuations of actin filaments within these networks. Prearranged parallel networks of actin filaments near the crowded cell membrane could play a role in the rapid formation of stress fibers or microvilli.     

Affinity of alpha-actinin for actin determines the structure and mechanical properties of actin filament gels.

Proteins that cross-link actin filaments can either form bundles of parallel filaments or isotropic networks of individual filaments. We have found that mixtures of actin filaments with alpha-actinin purified from either Acanthamoeba castellanii or chicken smooth muscle can form bundles or isotropic networks depending on their concentration. Low concentrations of alpha-actinin and actin filaments form networks indistinguishable in electron micrographs from gels of actin alone. Higher concentrations of alpha-actinin and actin filaments form bundles. The threshold for bundling depends on the affinity of the alpha-actinin for actin. The complex of Acanthamoeba alpha-actinin with actin filaments has a Kd of 4.7 microM and a bundling threshold of 0.1 microM; chicken smooth muscle has a Kd of 0.6 microM and a bundling threshold of 1 microM. The physical properties of isotropic networks of cross-linked actin filaments are very different from a gel of bundles: the network behaves like a solid because each actin filament is part of a single structure that encompasses all the filaments. Bundles of filaments behave more like a very viscous fluid because each bundle, while very long and stiff, can slip past other bundles. We have developed a computer model that predicts the bundling threshold based on four variables: the length of the actin filaments, the affinity of the alpha-actinin for actin, and the concentrations of actin and alpha-actinin.