Mechanical Heterogeneity Favors Fragmentation of Strained Actin Filaments

We present a general model of actin filament deformation and fragmentation in response to compressive forces. The elastic free energy density along filaments is determined by their shape and mechanical properties, which were modeled in terms of bending, twisting, and twist-bend coupling elasticities. The elastic energy stored in filament deformation (i.e., strain) tilts the fragmentation-annealing reaction free-energy profile to favor fragmentation. The energy gradient introduces a local shear force that accelerates filament intersubunit bond rupture. The severing protein, cofilin, renders filaments more compliant in bending and twisting. As a result, filaments that are partially decorated with cofilin are mechanically heterogeneous (i.e., nonuniform) and display asymmetric shape deformations and energy profiles distinct from mechanically homogenous (i.e., uniform), bare actin, or saturated cofilactin filaments. The local buckling strain depends on the relative size of the compliant segment as well as the bending and twisting rigidities of flanking regions. Filaments with a single bare/cofilin-decorated boundary localize energy and force adjacent to the boundary, within the compliant cofilactin segment. Filaments with small cofilin clusters were predicted to fragment within the compliant cofilactin rather than at boundaries. Neglecting contributions from twist-bend coupling elasticity underestimates the energy density and gradients along filaments, and thus the net effects of filament strain to fragmentation. Spatial confinement causes compliant cofilactin segments and filaments to adopt higher deformation modes and store more elastic energy, thereby promoting fragmentation. The theory and simulations presented here establish a quantitative relationship between actin filament fragmentation thermodynamics and elasticity, and reveal how local discontinuities in filament mechanical properties introduced by regulatory proteins can modulate both the severing efficiency and location along filaments. The emergent behavior of mechanically heterogeneous filaments, particularly under confinement, emphasizes that severing in cells is likely to be influenced by multiple physical and chemical factors.     

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.     

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.     

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.     

A 'hot-spot' mutation alters the mechanical properties of keratin filament networks

Keratins 5 and 14 polymerize to form the intermediate filament network in the progenitor basal cells of many stratified epithelia including epidermis, where it provides crucial mechanical support. Inherited mutations in K5 or K14 result in epidermolysis bullosa simplex (EBS), a skin-fragility disorder. The impact that such mutations exert on the intrinsic mechanical properties of K5/K14 filaments is unknown. Here we show, by using differential interference contrast microscopy, that a 'hot-spot' mutation in K14 greatly reduces the ability of reconstituted mutant filaments to bundle under crosslinking conditions. Rheological assays measure similar small-deformation mechanical responses for crosslinked solutions of wild-type and mutant keratins. The mutation, however, markedly reduces the resilience of crosslinked networks against large deformations. Single-particle tracking, which probes the local organization of filament networks, shows that the mutant polymer exhibits highly heterogeneous structures compared to those of wild-type filaments. Our results indicate that the fragility of epithelial cells expressing mutant keratin may result from an impaired ability of keratin polymers to be crosslinked into a functional network.     

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.     

Building distinct actin filament networks in a common cytoplasm

Eukaryotic cells generate a diversity of actin filament networks in a common cytoplasm to optimally perform functions such as cell motility, cell adhesion, endocytosis and cytokinesis. Each of these networks maintains precise mechanical and dynamic properties by autonomously controlling the composition of its interacting proteins and spatial organization of its actin filaments. In this review, we discuss the chemical and physical mechanisms that target distinct sets of actin-binding proteins to distinct actin filament populations after nucleation, resulting in the assembly of actin filament networks that are optimized for specific functions.     

Micromechanics and ultrastructure of actin filament networks crosslinked by human fascin: a comparison with alpha-actinin.

Fascin is an actin crosslinking protein that organizes actin filaments into tightly packed bundles believed to mediate the formation of cellular protrusions and to provide mechanical support to stress fibers. Using quantitative rheological methods, we studied the evolution of the mechanical behavior of filamentous actin (F-actin) networks assembled in the presence of human fascin. The mechanical properties of F-actin/fascin networks were directly compared with those formed by alpha-actinin, a prototypical actin filament crosslinking/bundling protein. Gelation of F-actin networks in the presence of fascin (fascin to actin molar ratio >1:50) exhibits a non-monotonic behavior characterized by a burst of elasticity followed by a slow decline over time. Moreover, the rate of gelation shows a non-monotonic dependence on fascin concentration. In contrast, alpha-actinin increased the F-actin network elasticity and the rate of gelation monotonically. Time-resolved multiple-angle light scattering and confocal and electron microscopies suggest that this unique behavior is due to competition between fascin-mediated crosslinking and side-branching of actin filaments and bundles, on the one hand, and delayed actin assembly and enhanced network micro-heterogeneity, on the other hand. The behavior of F-actin/fascin solutions under oscillatory shear of different frequencies, which mimics the cell's response to forces applied at different rates, supports a key role for fascin-mediated F-actin side-branching. F-actin side-branching promotes the formation of interconnected networks, which completely inhibits the motion of actin filaments and bundles. Our results therefore show that despite sharing seemingly similar F-actin crosslinking/bundling activity, alpha-actinin and fascin display completely different mechanical behavior. When viewed in the context of recent microrheological measurements in living cells, these results provide the basis for understanding the synergy between multiple crosslinking proteins, and in particular the complementary mechanical roles of fascin and alpha-actinin in vivo.     

Mechanics of the F-actin cytoskeleton

Dynamic regulation of the filamentous actin (F-actin) cytoskeleton is critical to numerous physical cellular processes, including cell adhesion, migration and division. Each of these processes require precise regulation of cell shape and mechanical force generation which, to a large degree, is regulated by the dynamic mechanical behaviors of a diverse assortment of F-actin networks and bundles. In this review, we review the current understanding of the mechanics of F-actin networks and identify areas of further research needed to establish physical models. We first review our understanding of the mechanical behaviors of F-actin networks reconstituted in vitro, with a focus on the nonlinear mechanical response and behavior of “active” F-actin networks. We then explore the types of mechanical response measured of cytoskeletal F-actin networks and bundles formed in living cells and identify how these measurements correspond to those performed on reconstituted F-actin networks formed in vitro. Together, these approaches identify the challenges and opportunities in the study of living cytoskeletal matter.     

Mechanical Detection of a Long-Range Actin Network Emanating from a Biomimetic Cortex

Actin is ubiquitous globular protein that polymerizes into filaments and forms networks that participate in the force generation of eukaryotic cells. Such forces are used for cell motility, cytokinesis, and tissue remodeling. Among those actin networks, we focus on the actin cortex, a dense branched network beneath the plasma membrane that is of particular importance for the mechanical properties of the cell. Here we reproduce the cellular cortex by activating actin filament growth on a solid surface. We unveil the existence of a sparse actin network that emanates from the surface and extends over a distance that is at least 10 times larger than the cortex itself. We call this sparse actin network the “actin cloud” and characterize its mechanical properties with optical tweezers. We show, both experimentally and theoretically, that the actin cloud is mechanically relevant and that it should be taken into account because it can sustain forces as high as several picoNewtons (pN). In particular, it is known that in plant cells, actin networks similar to the actin cloud have a role in positioning the nucleus; in large oocytes, they play a role in driving chromosome movement. Recent evidence shows that such networks even prevent granule condensation in large cells.     

Viscoelastic properties of vimentin compared with other filamentous biopolymer networks

The cytoplasm of vertebrate cells contains three distinct filamentous biopolymers, the microtubules, microfilaments, and intermediate filaments. The basic structural elements of these three filaments are linear polymers of the proteins tubulin, actin, and vimentin or another related intermediate filament protein, respectively. The viscoelastic properties of cytoplasmic filaments are likely to be relevant to their biologic function, because their extreme length and rodlike structure dominate the rheologic behavior of cytoplasm, and changes in their structure may cause gel-sol transitions observed when cells are activated or begin to move. This paper describes parallel measurements of the viscoelasticity of tubulin, actin, and vimentin polymers. The rheologic differences among the three types of cytoplasmic polymers suggest possible specialized roles for the different classes of filaments in vivo. Actin forms networks of highest rigidity that fluidize at high strains, consistent with a role in cell motility in which stable protrusions can deform rapidly in response to controlled filament rupture. Vimentin networks, which have not previously been studied by rheologic methods, exhibit some unusual viscoelastic properties not shared by actin or tubulin. They are less rigid (have lower shear moduli) at low strain but harden at high strains and resist breakage, suggesting they maintain cell integrity. The differences between F-actin and vimentin are optimal for the formation of a composite material with a range of properties that cannot be achieved by either polymer alone. Microtubules are unlikely to contribute significantly to interphase cell rheology alone, but may help stabilize the other networks.     

Mechanical Detection of a Long-Range Actin Network Emanating from a Biomimetic Cortex

Actin is ubiquitous globular protein that polymerizes into filaments and forms networks that participate in the force generation of eukaryotic cells. Such forces are used for cell motility, cytokinesis, and tissue remodeling. Among those actin networks, we focus on the actin cortex, a dense branched network beneath the plasma membrane that is of particular importance for the mechanical properties of the cell. Here we reproduce the cellular cortex by activating actin filament growth on a solid surface. We unveil the existence of a sparse actin network that emanates from the surface and extends over a distance that is at least 10 times larger than the cortex itself. We call this sparse actin network the “actin cloud” and characterize its mechanical properties with optical tweezers. We show, both experimentally and theoretically, that the actin cloud is mechanically relevant and that it should be taken into account because it can sustain forces as high as several picoNewtons (pN). In particular, it is known that in plant cells, actin networks similar to the actin cloud have a role in positioning the nucleus; in large oocytes, they play a role in driving chromosome movement. Recent evidence shows that such networks even prevent granule condensation in large cells.     

Properties of intermediate filament networks assembled from keratin 8 and 18 in the presence of mg(2+)

The mechanical properties of epithelial cells are modulated by structural changes in keratin intermediate filament networks. To investigate the relationship between network architecture and viscoelasticity, we assembled keratin filaments from recombinant keratin proteins 8 (K8) and 18 (K18) in the presence of divalent ions (Mg²⁺). We probed the viscoelastic modulus of the network by tracking the movement of microspheres embedded in the network during assembly, and studied the network architecture using scanning electron microscopy. Addition of Mg²⁺ at physiological concentrations (<1 mM) resulted in networks whose structure was similar to that of keratin networks in epithelial cells. Moreover, the elastic moduli of networks assembled in vitro were found to be within the same magnitude as those measured in keratin networks of detergent-extracted epithelial cells. These findings suggest that Mg²⁺-induced filament cross-linking represents a valid model for studying the cytoskeletal mechanics of keratin networks.     

Diffusing wave spectroscopy microrheology of actin filament networks.

Filamentous actin (F-actin), one of the constituents of the cytoskeleton, is believed to be the most important participant in the motion and mechanical integrity of eukaryotic cells. Traditionally, the viscoelastic moduli of F-actin networks have been measured by imposing a small mechanical strain and quantifying the resulting stress. The magnitude of the viscoelastic moduli, their concentration dependence and strain dependence, as well as the viscoelastic nature (solid-like or liquid-like) of networks of uncross-linked F-actin, have been the subjects of debate. Although this paper helps to resolve the debate and establishes the extent of the linear regime of F-actin networks' rheology, we report novel measurements of the high-frequency behavior of networks of F-actin, using a noninvasive light-scattering based technique, diffusing wave spectroscopy (DWS). Because no external strain is applied, our optical assay generates measurements of the mechanical properties of F-actin networks that avoid many ambiguities inherent in mechanical measurements. We observe that the elastic modulus has a small magnitude, no strain dependence, and a weak concentration dependence. Therefore, F-actin alone is not sufficient to generate the elastic modulus necessary to sustain the structural rigidity of most cells or support new cellular protrusions. Unlike previous studies, our measurements show that the mechanical properties of F-actin are highly dependent on the frequency content of the deformation. We show that the loss modulus unexpectedly dominates the elastic modulus at high frequencies, which are key for fast transitions. Finally, the measured mean square displacement of the optical probes, which is also generated by DWS measurements, offers new insight into the local bending fluctuations of the individual actin filaments and shows how they generate enhanced dissipation at short time scales.     

Actin and myosin function in acanthamoeba

We have studied the functions of contractile proteins in Acanthamoeba by a combination of structural, biochemical and physiological approaches. We used electron microscopy and image processing to determine the three-dimensional structure of actin and the orientation of the molecule in the actin filament. We measured the rate constants for actin filament elongation and re-evaluated the effect of MgCl2 on the filament nucleation process. In Acanthamoeba actin polymerization is regulated, at least in part, by profilin, which binds to actin monomers, and by capping protein, which both nucleates polymerization and blocks monomer addition at the 'barbed' end of the filament. To test for physiological functions of myosin-II, we produced a monoclonal antibody that inhibits the actin-activated ATPase. When microinjected into living cells, this active-site-specific antibody inhibits amoeboid locomotion. We expect that similar experiments can be used to test for the physiological functions of the other components of the Acanthamoeba contractile system.     

High‐ and low‐frequency mechanical properties of living starfish oocytes

We studied the mechanical properties of living starfish oocytes belonging to two species, Astropecten Auranciacus and Asterina pectinifera, over a wide range of timescales. We monitored the Brownian motion of microspheres injected in the cytoplasm using laser particle‐tracking (LPT) and video multiple‐particle‐tracking (MPT) techniques, to explore high‐ and low‐frequency response ranges, respectively. The analysis of the mean‐square‐displacements (MSD) allowed us to characterize the samples on different timescales. The MSD behavior is explained by three power‐law exponents: for short times (τ < 1 ms) it reflects the semiflexible behavior of the actin network; for intermediate timescales (1 ms < τ < 1 s) it is similar to that of a soft‐glass material; finally for long times (τ > 1 s) it behaves mainly like a viscous medium. We computed and compared the viscoelastic moduli using a recently proposed model describing the frequency response of the cell material. The large fluctuations found in the MSD over hundreds of trajectories indicate and confirm the significant cytoplasm heterogeneity. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion rate limitations in actin-based propulsion of hard and deformable particles

The mechanism by which actin polymerization propels intracellular vesicles and invasive microorganisms remains an open question. Several recent quantitative studies have examined propulsion of biomimetic particles such as polystyrene microspheres, phospholipid vesicles, and oil droplets. In addition to allowing quantitative measurement of parameters such as the dependence of particle speed on its size, these systems have also revealed characteristic behaviors such a saltatory motion of hard particles and oscillatory deformation of soft particles. Such measurements and observations provide tests for proposed mechanisms of actin-based motility. In the actoclampin filament end-tracking motor model, particle-surface-bound filament end-tracking proteins are involved in load-insensitive processive insertion of actin subunits onto elongating filament plus-ends that are persistently tethered to the surface. In contrast, the tethered-ratchet model assumes working filaments are untethered and the free-ended filaments grow as thermal ratchets in a load-sensitive manner. This article presents a model for the diffusion and consumption of actin monomers during actin-based particle propulsion to predict the monomer concentration field around motile particles. The results suggest that the various behaviors of biomimetic particles, including dynamic saltatory motion of hard particles and oscillatory vesicle deformations, can be quantitatively and self-consistently explained by load-insensitive, diffusion-limited elongation of (+)-end-tethered actin filaments, consistent with predictions of the actoclampin filament-end tracking mechanism.     

Local rheology of human neutrophils investigated using atomic force microscopy

During the immune response, neutrophils display localized mechanical events by interacting with their environment through the micro-vascular transit, trans-endothelial, and trans-epithelial migration. Nano-mechanical studies of human neutrophils on localized nano-domains could provide the essential information for understanding their immune responsive functions. Using the Atomic Force Microscopy (AFM)-based micro-rheology, we have investigated rheological properties of the adherent human neutrophils on local nano-domains. We have applied the modified Hertz model to obtain the viscoelastic moduli from the relatively thick body regions of the neutrophils. In addition, by using more advanced models to account for the substrate effects, we have successfully characterized the rheological properties of the thin leading and tail regions as well. We found a regional difference in the mechanical compliances of the adherent neutrophils. The central regions of neutrophils were significantly stiffer (1,548 ± 871 Pa) than the regions closer to the leading edge (686 ± 801 Pa), while the leading edge and the tail (494 ± 537 Pa) regions were mechanically indistinguishable. The frequency-dependent elastic and viscous moduli also display a similar regional difference. Over the studied frequency range (100 to 300 Hz), the complex viscoelastic moduli display the partial rubber plateau behavior where the elastic moduli are greater than the viscous moduli for a given frequency. The non-disparaging viscous modulus indicates that the neutrophils display a viscoelastic dynamic behavior rather than a perfect elastic behavior like polymer gels. In addition, we found no regional difference in the structural damping coefficient between the leading edge and the cell body. Thus, we conclude that despite the lower loss and storage moduli, the leading edges of the human neutrophils display partially elastic properties similar to the cell body. These results suggest that the lower elastic moduli in the leading edges are more favorable for the elastic fluctuation of actin filaments, which supports the polymerization of the actin filaments leading to the active protrusion during the immune response.