Determinants of Fluidlike Behavior and Effective Viscosity in Cross-Linked Actin Networks

The actin cortex has a well-documented ability to rapidly remodel and flow while maintaining long-range connectivity, but how this is achieved remains poorly understood. Here, we use computer simulations to explore how stress relaxation in cross-linked actin networks subjected to extensional stress depends on the interplay between network architecture and turnover. We characterize a regime in which a network response is nonaffine and stress relaxation is governed by the continuous dissipation of elastic energy via cyclic formation, elongation, and turnover of tension-bearing elements. Within this regime, for a wide range of network parameters, we observe a constant deformation (creep) rate that is linearly proportional to the rate of filament turnover, leading to a constant effective viscosity that is inversely proportional to turnover rate. Significantly, we observe a biphasic dependence of the creep rate on applied stress: below a critical stress threshold, the creep rate increases linearly with applied stress; above that threshold, the creep rate becomes independent of applied stress. We show that this biphasic stress dependence can be understood in terms of the nonlinear force-extension behavior of individual force-transmitting network elements. These results have important implications for understanding the origins and control of viscous flows both in the cortex of living cells and in other polymer networks.     

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

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

Creep measurements on gelatin gels

The present work describes creep measurements on a series of concentrations of gelatin gels well above the critical gel concentration C0, using a high precision constant stress rheometer. Results for the concentration dependence of compliance are close to those expected both from theory and from dynamic oscillatory measurements of gel modulus. The concentration dependence of viscosity follows an approximate power law behaviour, with eta proportional C1.1. This exponent is consistent with relaxation in the sol fraction, and in regions of dangling chain attached to the gel. At concentrations closer to C0 we predict that a higher power law regime will prevail.     

Network dynamics of the nonlinear power-law relaxation of cell cortex

Living cells are known to exhibit universal power-law rheological behaviors, but their underlying biomechanical principles are still not fully understood. Here, we present a network dynamics picture to decipher the nonlinear power-law relaxation of cortical cytoskeleton. Under step strains, we present a scaling relation between instantaneous differential stiffness and external stress as a result of chain reorientation. Then, during the relaxation, we show how the scaling law theoretically originates from an exponential form of cortical disorder, with the scaling exponent decreased by the imposed strain or crosslinker density in the nonlinear regime. We attribute this exponent variation to the molecular realignment along the stretch direction or the transition of network structure from in-series to in-parallel modes, both solidifying the network toward our one-dimensional theoretical limit. In addition, the rebinding of crosslinkers is found to be crucial for moderating the relaxation speed under small strains. Together with the disorder nature, we demonstrate that the structural effects of networks provide a unified interpretation for the nonlinear power-law relaxation of cell cortex, and may help to understand cell mechanics from the molecular scale.     

The orthotropic viscoelastic behavior of aortic elastin

In this paper, we studied the viscoelastic behaviors of isolated aortic elastin using combined modeling and experimental approaches. Biaxial stress relaxation and creep experiments were performed to study the time-dependent behavior of elastin. Experimental results reveal that stress relaxation preconditioning is necessary in order to obtain repeatable stress relaxation responses. Elastin exhibits less stress relaxation than intact or decellularized aorta. The rate of stress relaxation of intact and decellularized aorta is linearly dependent on the initial stress levels. The rate of stress relaxation for elastin increases linearly at stress levels below about 60 kPa; however, the rate changes very slightly at higher initial stress levels. Experimental results also show that creep response is negligible for elastin, and the intact or decellularized aorta. A quasi-linear viscoelasticity model was incorporated into a statistical mechanics based eight-chain microstructural model at the fiber level to simulate the orthotropic viscoelastic behavior of elastin. A user material subroutine was developed for finite element analysis. Results demonstrate that this model is suitable to capture both the orthotropic hyperelasticity and viscoelasticity of elastin.     

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.     

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.     

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.     

In vivo creep and stress relaxation experiments to determine the wall extensibility and yield threshold for the sporangiophores of phycomyces

The pressure probe was used to conduct in vivo creep and in vivo stress relaxation experiments on the sporangiophores of Phycomyces blakesleeanus. The in vivo creep and in vivo stress relaxation methods are compared with respect to their utility for determining the irreversible wall extensibility and the yield threshold. The results of the in vivo stress relaxation experiments demonstrate that the growth usually does not cease when the external water supply is removed, and the turgor pressure does not decay for hours afterwards. A successful stress relaxation experiment requires that the cell enlargement rate (growth rate) be zero during the turgor pressure decay. In a few experiments, the growth rate was zero during the turgor pressure decay. However, in general only the yield threshold could be determined.

In vivo creep experiments proved to be easier to conduct and more useful in determining values for both the irreversible wall extensibility and the yield threshold. The results of the in vivo creep experiments demonstrate that small steps-up in turgor pressure, generally <0.02 MPa, elicit increases in growth rate as predicted by the growth equations and the augmented growth equations. The irreversible wall extensibility and the yield threshold were determined from these results. The results also demonstrate that steps-up in turgor pressure larger than 0.02 MPa, produce a different response; a decrease in growth rate. The decreased growth rate behavior is related to the magnitude of the step-up, and in general, larger steps-up in turgor pressure produce larger decreases in growth rate and longer periods of decreased growth rate. Qualitatively, this growth behavior is very similar to the “stretch response” previously reported by Dennison and Roth (1967).

     

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.     

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.     

Coronin 1B antagonizes cortactin and remodels Arp2/3-containing actin branches in lamellipodia

The dendritic actin network generated by the Arp2/3 complex in lamellipodia underlies formation of protrusions, directional sensing, and migration. While the generation of this network is well studied, the mechanisms regulating network disassembly are poorly understood. We report that Coronin 1B disassembles Arp2/3-containing actin filament branches by inducing Arp2/3 dissociation. This activity is antagonized by Cortactin, a filament branch stabilizer. Consistent with this biochemical competition, depletion of both proteins partially rescues defects in lamellipodial dynamics observed upon depletion of either protein alone. Coronin 1B targets actin branches in a manner that is mutually exclusive with the Arp2/3 complex and alters the branch angle. We conclude that Coronin 1B replaces the Arp2/3 complex at actin filament branches as the dendritic network matures and drives the turnover of branched actin networks.     

Mechanics of Biomimetic Liposomes Encapsulating an Actin Shell

Cell-shape changes are insured by a thin, dynamic, cortical layer of cytoskeleton underneath the plasma membrane. How this thin cortical structure impacts the mechanical properties of the whole cell is not fully understood. Here, we study the mechanics of liposomes or giant unilamellar vesicles, when a biomimetic actin cortex is grown at the inner layer of the lipid membrane via actin-nucleation-promoting factors. Using a hydrodynamic tube-pulling technique, we show that tube dynamics is clearly affected by the presence of an actin shell anchored to the lipid bilayer. The same force pulls much shorter tubes in the presence of the actin shell compared to bare membranes. However, in both cases, we observe that the dynamics of tube extrusion has two distinct features characteristic of viscoelastic materials: rapid elastic elongation, followed by a slower elongation phase at a constant rate. We interpret the initial elastic regime by an increase of membrane tension due to the loss of lipids into the tube. Tube length is considerably shorter for cortex liposomes at comparable pulling forces, resulting in a higher spring constant. The presence of the actin shell seems to restrict lipid mobility, as is observed in the corral effect in cells. The viscous regime for bare liposomes corresponds to a leakout of the internal liquid at constant membrane tension. The presence of the actin shell leads to a larger friction coefficient. As the tube is pulled from a patchy surface, membrane tension increases locally, leading to a Marangoni flow of lipids. As a conclusion, the presence of an actin shell is revealed by its action that alters membrane mechanics.     

Unconfined compression of hydrated viscoelastic tissues: a biphasic poroviscoelastic analysis

A biphasic poroviscoelastic theory was used to analyze the unconfined compression creep and stress relaxation of a hydrated viscoelastic tissue. The intrinsic shear properties of the tissue matrix was described by an integral-type viscoelastic constitutive law while the intrinsic bulk property of the matrix was assumed to be linearly elastic. Parametric data were presented to show how the two major energy dissipative mechanisms, namely the interstitial fluid flow and the intrinsic matrix viscoelasticity, may each contribute to the apparent viscoelastic behavior of the whole tissue under unconfined compression. The hydraulic permeability of the tissue was found to enter in only as a scaling factor for time.     

Protein friction and filament bending facilitate contraction of disordered actomyosin networks

We use mathematical modeling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semiflexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament systems to show that filament bending flexibility can facilitate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent filament aggregation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only arise because of additional regulatory mechanisms or more complex mechanical behavior.     

The effect of auxin on stress relaxation in isolated Avena coleoptiles

In order to characterize further the mechanical properties of coleoptile cell walls, stress relaxation measurements were made on methanol-boiled sections of Avena coleoptiles. Relaxation was measured both in mechanically conditioned specimens and in specimens which had not been previously extended. In both cases the relaxation was proportional to log time. Mechanical conditioning increased the relaxation modules and decreased the relative rate of relaxation. In contrast, pretreatment of the live coleoptiles with indoleacetic acid reduced the relaxation modulus and the absolute rate of relaxation but did not affect the relative rate of relaxation. Essentially similar pictures of the mechanical properties of coleoptile walls are obtained from stress relaxation and creep tests; the wall behaves as a nonlinear viscoelastic material.     

Dynamic role of cross-linking proteins in actin rheology

We develop a computational model to compare the relative importance of unbinding and unfolding of actin cross-linking proteins (ACPs) in the dynamic properties of the actin cytoskeleton. We show that in the strain-stiffening regime with typical physiological and experimental strain rates, unbinding events are predominant with negligible unfolding. ACPs unbound by greater forces experience larger displacements, with a tendency to rebind to different filaments. At constant strain, stress relaxes to physiological levels by unbinding only—not unfolding—of ACPs, which is consistent with experiments. Also, rebinding of ACPs dampens full relaxation of stress. When the network is allowed to return to a stress-free state after shear deformation, plastic deformation is observed only with unbinding. These results suggest that despite the possibility of unfolding, unbinding of ACPs is the major determinant for the rheology of the actin network.     

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.     

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.