Real-Time Dynamics of Emerging Actin Networks in Cell-Mimicking Compartments

Understanding the cytoskeletal functionality and its relation to other cellular components and properties is a prominent question in biophysics. The dynamics of actin cytoskeleton and its polymorphic nature are indispensable for the proper functioning of living cells. Actin bundles are involved in cell motility, environmental exploration, intracellular transport and mechanical stability. Though the viscoelastic properties of actin-based structures have been extensively probed, the underlying microstructure dynamics, especially their disassembly, is not fully understood. In this article, we explore the rich dynamics and emergent properties exhibited by actin bundles within flow-free confinements using a microfluidic set-up and epifluorescence microscopy. After forming entangled actin filaments within cell-sized quasi two-dimensional confinements, we induce their bundling using three different fundamental mechanisms: counterion condensation, depletion interactions and specific protein-protein interactions. Intriguingly, long actin filaments form emerging networks of actin bundles via percolation leading to remarkable properties such as stress generation and spindle-like intermediate structures. Simultaneous sharing of filaments in different links of the network is an important parameter, as short filaments do not form networks but segregated clusters of bundles instead. We encounter a hierarchical process of bundling and its subsequent disassembly. Additionally, our study suggests that such percolated networks are likely to exist within living cells in a dynamic fashion. These observations render a perspective about differential cytoskeletal responses towards numerous stimuli.     

On the elasticity of cytoskeletal networks.

Models relating to the gelation and elasticity of complex cytoskeletal networks are formulated and investigated. Kinetic equations for reversible elongation of nucleated actin filaments are analyzed when the filaments are acted upon by capping proteins and cross-linking factors. Analytical expressions are obtained that relate the low frequency elastic shear modulus of a network, G, to chain growth kinetics, the number of nucleation sites, monomer concentration, and the amount of capping and cross-linking protein. Elasticity curves that relate G to such factors as the association constant for cross-linking are derived and then used to determine solation-gelation phase contours.     

Spectrin-actin associations studied by electron microscopy of shadowed preparations

By shadowing specimens dried onto mica sheets we have obtained clear images of actin crosslinked by spectrin, an actin-binding protein found in erythrocytes. We conclude that spectrin dimers possess a single binding site for F actin. Tetramers formed by head-to-head association of two dimers possess two actin binding sites, one at each tail. Polymerizing G actin in the presence of spectrin tetramers or mixing preformed F actin with spectrin tetramer plus band 4.1 results in an extensively crosslinked network of actin filaments. When G actin is polymerized in the presence of spectrin at spectrin:actin mole ratios close to that present on the erythrocyte membrane, large amorphous protein networks are formed. These networks are clusters of spectrin around 25 nm diameter structures which may be actin protofilaments. These networks are similar to the cytoskeletal network seen after erythrocyte membranes are extracted with detergent, and may represent the first in vitro assembly of a cytoskeletal complex resembling that of the native cell both biochemically and structurally.     

Simulations of dynamically cross-linked actin networks: Morphology,rheology, and hydrodynamic interactions

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.     

Softness, strength and self-repair in intermediate filament networks

One cellular function of intermediate filaments is to provide cells with compliance to small deformations while strengthening them when large stresses are applied. How IFs accomplish this mechanical role is revealed by recent studies of the elastic properties of single IF protein polymers and by viscoelastic characterization of the networks they form. IFs are unique among cytoskeletal filaments in withstanding large deformations. Single filaments can stretch to more than 3 times their initial length before breaking, and gels of IF withstand strains greater than 100% without damage. Even after mechanical disruption of gels formed by crossbridged neurofilaments, the elastic modulus of these gels rapidly recovers under conditions where gels formed by actin filaments are irreversibly ruptured. The polyelectrolyte properties of IFs may enable crossbridging by multivalent counterions, but identifying the mechanisms by which IFs link into bundles and networks in vivo remains a challenge.     

The viscoelastic properties of actin solutions

The viscoelastic properties in actin solutions were investigated by measuring their elastic modulus and viscous modulus using a rheometer. The polymerization/gelation process of actin solutions was accompanied by an increase of both parameters, indicating the formation of a protein network. High shear rotational motion destroyed this network which, however, would reanneal if left undisturbed. At 25 °C under low ionic strength conditions, the viscoelastic moduli of a Spudich-Watt globular (G) actin preparation increased with time, while G-actin, purified by gel filtration maintained low viscoelastic moduli. The rigidity of the filamentous (F) actin network in a solution of Spudich-Watt actin, measured by the elastic modulus, was somewhat lower than that of gel-filtration-purified actin at the same protein concentration. The crosslink density of these F-actin networks was estimated, using models from rubber elasticity theory. The calculated density was 1 crosslink/50 actin monomers for the purified actin and 1 crosslink/120 actin monomers for Spudich-Watt actin. The results are consistent with the idea that a small amount of regulatory factor(s), which could be removed by the gel filtration step, modulates the structure of an actin network.     

Enzymatic mineralization of hydrogels for bone tissue engineering by incorporation of alkaline phosphatase

Alkaline phosphatase (ALP), an enzyme involved in mineralization of bone, is incorporated into three hydrogel biomaterials to induce their mineralization with calcium phosphate (CaP). These are collagen type I, a mussel-protein-inspired adhesive consisting of PEG substituted with catechol groups, cPEG, and the PEG/fumaric acid copolymer OPF. After incubation in Ca-GP solution, FTIR, EDS, SEM, XRD, SAED, ICP-OES, and von Kossa staining confirm CaP formation. The amount of mineral formed decreases in the order cPEG?>?collagen?>?OPF. The mineral:polymer ratio decreases in the order collagen?>?cPEG?>?OPF. Mineralization increases Young's modulus, most profoundly for cPEG. Such enzymatically mineralized hydrogel/CaP composites may find application as bone regeneration materials.     

Geometrical nonlinear elasticity of axon under tension: A coarse-grained computational study

Axon bundles cross-linked by microtubule (MT) associate proteins and bounded by a shell skeleton are critical for normal function of neurons. Understanding effects of the complexly geometrical parameters on their mechanical properties can help gain a biomechanical perspective on the neurological functions of axons and thus brain disorders caused by the structural failure of axons. Here, the tensile mechanical properties of MT bundles cross-linked by tau proteins are investigated by systematically tuning MT length, axonal cross-section radius, and tau protein spacing in a bead-spring coarse-grained model. Our results indicate that the stress-strain curves of axons can be divided into two regimes, a nonlinear elastic regime dominated by rigid-body like inter-MT sliding, and a linear elastic regime dominated by affine deformation of both tau proteins and MTs. From the energetic analyses, first, the tau proteins dominate the mechanical performance of axons under tension. In the nonlinear regime, tau proteins undergo a rigid-body like rotating motion rather than elongating, whereas in the nonlinear elastic regime, tau proteins undergo a flexible elongating deformation along the MT axis. Second, as the average spacing between adjacent tau proteins along the MT axial direction increases from 25 to 125 nm, the Young’s modulus of axon experiences a linear decrease whereas with the average space varying from 125 to 175 nm, and later reaches a plateau value with a stable fluctuation. Third, the increment of the cross-section radius of the MT bundle leads to a decrease in Young’s modulus of axon, which is possibly attributed to the decrease in MT numbers per cross section. Overall, our research findings offer a new perspective into understanding the effects of geometrical parameters on the mechanics of MT bundles as well as serving as a theoretical basis for the development of artificial MT complexes potentially toward medical applications.     

Morphogenesis of liposomes encapsulating actin depends on the type of actin-crosslinking

To study the morphogenesis of cells caused by the organization of their internal cytoskeletal network, we characterized the transformation of liposomes encapsulating actin and its crosslinking proteins, fascin, alpha-actinin, or filamin, using real-time high-intensity dark-field microscopy. With increasing temperature, the encapsulated G-actin polymerized into actin filaments and formed bundles or gels, depending on the type of actin-crosslinking protein that was co-encapsulated, causing various morphological changes of liposomes. The differences in morphology among transformed liposomes indicate that actin-crosslinking proteins determine liposome shape by organizing their specific actin networks. Morphological analysis reveals that the crosslinking manner, i.e. distance and angular flexibility between adjacent crosslinked actin filaments, is essential for the morphogenesis rather than their binding affinity and stoichiometry to actin filaments.     

Form-Finding Model Shows How Cytoskeleton Network Stiffness Is Realized

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.     

Computational Analysis of Viscoelastic Properties of Crosslinked Actin Networks

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G′) increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G′ as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a ‘supportive framework,’ as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.     

Cytoskeletal bundle mechanics

The mechanical properties of cytoskeletal actin bundles play an essential role in numerous physiological processes, including hearing, fertilization, cell migration, and growth. Cells employ a multitude of actin-binding proteins to actively regulate bundle dimensions and cross-linking properties to suit biological function. The mechanical properties of actin bundles vary by orders of magnitude depending on diameter and length, cross-linking protein type and concentration, and constituent filament properties. Despite their importance to cell function, the molecular design principles responsible for this mechanical behavior remain unknown. Here, we examine the mechanics of cytoskeletal bundles using a molecular-based model that accounts for the discrete nature of constituent actin filaments and their distinct cross-linking proteins. A generic competition between filament stretching and cross-link shearing determines three markedly different regimes of mechanical response that are delineated by the relative values of two simple design parameters, revealing the universal nature of bundle-bending mechanics. In each regime, bundle-bending stiffness displays distinct scaling behavior with respect to bundle dimensions and molecular composition, as observed in reconstituted actin bundles in vitro. This mechanical behavior has direct implications on the physiological bending, buckling, and entropic stretching behavior of cytoskeletal processes, as well as reconstituted actin systems. Results are used to predict the bending regimes of various in vivo cytoskeletal bundles that are not easily accessible to experiment and to generate hypotheses regarding implications of the isolated behavior on in vivo bundle function.     

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.     

The intermediate filament network in cultured human keratinocytes is remarkably extensible and resilient

The prevailing model of the mechanical function of intermediate filaments in cells assumes that these 10 nm diameter filaments make up networks that behave as entropic gels, with individual intermediate filaments never experiencing direct loading in tension. However, recent work has shown that single intermediate filaments and bundles are remarkably extensible and elastic in vitro, and therefore well-suited to bearing tensional loads. Here we tested the hypothesis that the intermediate filament network in keratinocytes is extensible and elastic as predicted by the available in vitro data. To do this, we monitored the morphology of fluorescently-tagged intermediate filament networks in cultured human keratinocytes as they were subjected to uniaxial cell strains as high as 133%. We found that keratinocytes not only survived these high strains, but their intermediate filament networks sustained only minor damage at cell strains as high as 100%. Electron microscopy of stretched cells suggests that intermediate filaments are straightened at high cell strains, and therefore likely to be loaded in tension. Furthermore, the buckling behavior of intermediate filament bundles in cells after stretching is consistent with the emerging view that intermediate filaments are far less stiff than the two other major cytoskeletal components F-actin and microtubules. These insights into the mechanical behavior of keratinocytes and the cytokeratin network provide important baseline information for current attempts to understand the biophysical basis of genetic diseases caused by mutations in intermediate filament genes.     

Foam-like compression behavior of fibrin networks

The rheological properties of fibrin networks have been of long-standing interest. As such there is a wealth of studies of their shear and tensile responses, but their compressive behavior remains unexplored. Here, by characterization of the network structure with synchronous measurement of the fibrin storage and loss moduli at increasing degrees of compression, we show that the compressive behavior of fibrin networks is similar to that of cellular solids. A nonlinear stress–strain response of fibrin consists of three regimes: (1) an initial linear regime, in which most fibers are straight, (2) a plateau regime, in which more and more fibers buckle and collapse, and (3) a markedly nonlinear regime, in which network densification occurs by bending of buckled fibers and inter-fiber contacts. Importantly, the spatially non-uniform network deformation included formation of a moving “compression front” along the axis of strain, which segregated the fibrin network into compartments with different fiber densities and structure. The Young’s modulus of the linear phase depends quadratically on the fibrin volume fraction while that in the densified phase depends cubically on it. The viscoelastic plateau regime corresponds to a mixture of these two phases in which the fractions of the two phases change during compression. We model this regime using a continuum theory of phase transitions and analytically predict the storage and loss moduli which are in good agreement with the experimental data. Our work shows that fibrin networks are a member of a broad class of natural cellular materials which includes cancellous bone, wood and cork.     

Modelling the dynamics of F-actin in the cell

The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter ϕ, denoting the relative binding affinity and concentration of the actin binding proteins.     

Binding of tropomyosin-troponin to actin increases filament bending stiffness

Rheologic measurements show that the association of tropomyosin-troponin with actin filaments is responsible for the reduction of the internal chain dynamic and increase in the mechanical rigidity of actin filaments. Basing calculations on the linear relation between the plateau modulus, G(N)('), and bending modulus, kappa, I find that tropomyosin-troponin at r(AT) = 7 increases actin filament stiffness by approximately 50%. This is confirmed by dynamic light scattering. Further increases are observed at rising F-actin and constant tropomyosin-troponin concentrations. Tropomyosin-troponin also delays actin assembly and subsequent network formation and increases filament stiffness over time.     

Hypertonicity triggers RhoA-dependent assembly of myosin-containing striated polygonal actin networks in endothelial cells

Endothelial cells respond to mechanical stresses of the circulation with cytoskeletal rearrangements such as F-actin stress fiber alignment along the axis of fluid flow. Endothelial cells are exposed to hypertonic stress in the renal medulla or during mannitol treatment of cerebral edema. We report here that arterial endothelial cells exposed to hypertonic stress rearranged F-actin into novel actin-myosin II fibers with regular 0.5-µm striations, in which -actinin colocalizes with actin. These striated fibers assembled over hours into three-dimensional, irregular, polygonal actin networks most prominent at the cell base, and occasionally surrounding the nucleus in a geodesic-like structure. Hypertonicity-induced assembly of striated polygonal actin networks was inhibited by cytochalasin D, blebbistatin, cell ATP depletion, and intracellular Ca²⁺ chelation but did not require intact microtubules, regulatory volume increase, or de novo RNA or protein synthesis. Striated polygonal actin network assembly was insensitive to inhibitors of MAP kinases, tyrosine kinases, or phosphatidylinositol 3-kinase, but was prevented by C3 exotoxin, by the RhoA kinase inhibitor Y-27632, and by overexpressed dominant-negative RhoA. In contrast, overexpression of dominant-negative Rac or of dominant-negative cdc42 cDNAs did not prevent striated polygonal actin network assembly. The actin networks described here are novel in structure, as striated actin-myosin structures in nonmuscle cells, as a cellular response to hypertonicity, and as a cytoskeletal regulatory function of RhoA. Endothelial cells may use RhoA-dependent striated polygonal actin networks, possibly in concert with cytoskeletal load-bearing elements, as a contractile, tension-generating component of their defense against isotropic compressive forces. mannitol; Rho kinase; blebbistatin; bovine aortic endothelial cells     

Action of cytochalasin D on cytoskeletal networks

Extraction of SC-1 cells (African green monkey kidney) with the detergent Triton X-100 in combination with stereo high-voltage electron microscopy of whole mount preparations has been used as an approach to determine the mode of action of cytochalasin D on cells. The cytoskeleton of extracted BSC-1 cells consists of substrate-associated filament bundles (stress fibers) and a highly cross-linked network of four major filament types extending throughout the cell body; 10-nm filaments, actin microfilaments, microtubules, and 2- to 3-nm filaments. Actin filaments and 2- to 3-nm filaments form numerous end- to-side contacts with other cytoskeletal filaments. Cytochalasin D treatment severely disrupts network organization, increases the number of actin filament ends, and leads to the formation of filamentous aggregates or foci composed mainly of actin filaments. Metabolic inhibitors prevent filament redistribution, foci formation, and cell arborization, but not disorganization of the three-dimensional filament network. In cells first extracted and then treated with cytochalasin D, network organization is disrupted, and the number of free filament ends is increased. Supernates of preparations treated in this way contain both short actin filaments and network fragments (i.e., actin filaments in end-to-side contact with other actin filaments). It is proposed that the dramatic effects of cytochalasin D on cells result from both a direct interaction of the drug with the actin filament component of cytoskeletal networks and a secondary cellular response. The former leads to an immediate disruption of the ordered cytoskeletal network that appears to involve breaking of actin filaments, rather than inhibition of actin filament-filament interactions (i.e., disruption of end-to-side contacts). The latter engages network fragments in an energy-dependent (contractile) event that leads to the formation of filament foci.     

Mechanics of Individual Keratin Bundles in Living Cells

Along with microtubules and microfilaments, intermediate filaments are a major component of the eukaryotic cytoskeleton and play a key role in cell mechanics. In cells, keratin intermediate filaments form networks of bundles that are sparser in structure and have lower connectivity than, for example, actin networks. Because of this, bending and buckling play an important role in these networks. Buckling events, which occur due to compressive intracellular forces and cross-talk between the keratin network and other cytoskeletal components, are measured here in situ. By applying a mechanical model for the bundled filaments, we can access the mechanical properties of both the keratin bundles themselves and the surrounding cytosol. Bundling is characterized by a coupling parameter that describes the strength of the linkage between the individual filaments within a bundle. Our findings suggest that coupling between the filaments is mostly complete, although it becomes weaker for thicker bundles, with some relative movement allowed.