Cross-linked F-actin Networks Research Articles

Measuring fluctuating dynamics of sparsely crosslinked actin gels with dual-feedback nonlinear microrheology.

We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.

Constraint Release for Reptating Filaments in Semiflexible Networks Depends on Background Fluctuations.

Entangled semiflexible polymer networks are usually described by the tube model, although this concept has not been able to explain all experimental observations. One of its major shortcomings is neglecting the thermal fluctuations of the polymers surrounding the examined test filament, such that disentanglement effects are not captured. In this study, we present experimental evidence that correlated constraint release which has been predicted theoretically occurs in entangled, but not in crosslinked semiflexible polymer networks. By tracking single semiflexible DNA nanotubes embedded both in entangled and crosslinked F-actin networks, we observed different reptation dynamics in both systems, emphasizing the need for a revision of the classical tube theory for entangled polymer solutions.

Three-Dimensional Balance of Cortical Tension and Axial Contractility Enables Fast Amoeboid Migration

Fast amoeboid migration requires cells to apply mechanical forces on their surroundings via transient adhesions. However, the mechanistic role of forces in controlling cell shape changes and cell migration speed remains largely unknown. To address these questions, we used three-dimensional force microscopy to measure the in-plane (tangential) and out-of-plane (normal) forces exerted by cells crawling on flat surfaces. From the measured normal forces, we estimated the cells’ cortical tension using a Young-Laplace's model. We examined chemotaxing wild-type Dictyostelium cells, as well as mutants with defects in contractility, internal F-actin crosslinking, and cortical integrity, and demonstrated that once the cells initiate their migration and polarize, they generate tangential traction forces by myosin II contractility, which requires an internal crosslinked F-actin network. Simultaneously, cortical tension provides an additional mechanism that generates the normal forces and that does not require myosin II. The 3-D pulling forces generated by both mechanisms are internally balanced by an increase in cytoplasmic pressure that allows cells to push down on their substrate without adhering to it. These compressive pressure-induced forces are not associated to adhesion sites, and may allow amoeboid cells to push off surrounding structures when migrating in complex three-dimensional environments. Our findings are consistent with a model in which the two force-generating cellular domains are mechanically connected by myosin I crosslinking that enables the communication of forces between the domains. Furthermore, we found that the balance between axial myosin II contractility and cortical tension is important to produce the cell shape changes needed for locomotion, as cell migration speed correlates with the ratio of the magnitudes of the tangential traction forces to the normal ones. These results reveal a novel role for 3-D cellular forces in establishing the efficiency of amoeboid cell movement.

Reply to comment on “Polymerization, bending, tension: What happens at the leading edge of motile cells?” by Falko Ziebert and Igor S. Aranson

We are grateful to Falko Ziebert and Igor Aranson, who continue with their comment on our publication [5] a discussion on modelling concepts. Ziebert and Aranson present in their contribution to this volume [14] a model concept for cell motility and morphodynamics focusing on gel flow and its determinants. This type of models is particularly useful for describing slow dynamics on the length scale of the whole cell and modelling of cell shape [1,8,11,13,14]. Our approach is set apart from the gel models by taking into account a weakly cross-linked F-actin network region close to the location of polymerization in the lamellipodia of motile cells (semi-flexible region) in addition to the gel in the bulk. This addition explains a variety of non-linear dynamic regimes in cellular and reconstituted systems, and the force-velocity relation of fish keratocytes. Ziebert and Aranson point out in their comment that 1) a more detailed modelling of gel processes may be required to capture large cell deformations, 2) the dynamics of adhesion strength and distribution may be relevant for understanding the relation between cell shape, the dynamic regime of motion and cell velocity, 3) coarse grained models may allow for unifying both concepts, and 4) fluctuations are important in morphodynamics.

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach.

Corticosterone treatment results in enhanced release of peptidergic vesicles in astrocytes via cytoskeletal rearrangements

While the effect of stress on neuronal physiology is widely studied, its effect on the functionality of astrocytes is not well understood. We studied the effect of high doses of stress hormone corticosterone, on two physiological properties of astrocytes, i.e., gliotransmission and interastrocytic calcium waves. To study the release of peptidergic vesicles from astrocytes, hippocampal astrocyte cultures were transfected with a plasmid to express pro-atrial natriuretic peptide (ANP) fused with the emerald green fluorescent protein (ANP.emd). The rate of decrease in fluorescence of ANP.emd on application of ionomycin, a calcium ionophore was monitored. Significant increase in the rate of calcium-dependent exocytosis of ANP.emd was observed with the 100 nM and 1 μM corticosterone treatments for 3 h, which depended on the activation of the glucocorticoid receptor. ANP.emd tagged vesicles exhibited increased mobility in astrocyte culture upon corticosterone treatment. Increasing corticosterone concentrations also resulted in concomitant increase in the calcium wave propagation velocity, initiated by focal ATP application. Corticosterone treatment also resulted in increased GFAP expression and F-actin rearrangements. FITC-Phalloidin immunostaining revealed increased formation of cross linked F-actin networks with the 100 nM and 1 μM corticosterone treatment. Alternatively, blockade of actin polymerization and disruption of microtubules prevented the corticosterone-mediated increase in ANP.emd release kinetics. This study reports for the first time the effect of corticosterone on gliotransmission via modulation of cytoskeletal elements. As ANP acts on both neurons and blood vessels, modulation of its release could have functional implications in neurovascular coupling under pathophysiological conditions of stress.

A combined finite element-Langevin dynamics (FEM-LD) approach for analyzing the mechanical response of bio-polymer networks

A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.

Actin Assembly Factors Regulate the Gelation Kinetics and Architecture of F-actin Networks

Dynamic regulation of the actin cytoskeleton is required for diverse cellular processes. Proteins regulating the assembly kinetics of the cytoskeletal biopolymer F-actin are known to impact the architecture of actin cytoskeletal networks in vivo, but the underlying mechanisms are not well understood. Here, we demonstrate that changes to actin assembly kinetics with physiologically relevant proteins profilin and formin (mDia1 and Cdc12) have dramatic consequences on the architecture and gelation kinetics of otherwise biochemically identical cross-linked F-actin networks. Reduced F-actin nucleation rates promote the formation of a sparse network of thick bundles, whereas increased nucleation rates result in a denser network of thinner bundles. Changes to F-actin elongation rates also have marked consequences. At low elongation rates, gelation ceases and a solution of rigid bundles is formed. By contrast, rapid filament elongation accelerates dynamic arrest and promotes gelation with minimal F-actin density. These results are consistent with a recently developed model of how kinetic constraints regulate network architecture and underscore how molecular control of polymer assembly is exploited to modulate cytoskeletal architecture and material properties.

An affine micro-sphere-based constitutive model, accounting for junctional sliding, can capture F-actin network mechanics

Actin filaments are a major component of the cytoskeleton and play a crucial role in cell mechanotransduction. F-actin networks can be reconstituted in vitro and their mechanical behaviour has been studied experimentally. Constitutive models that assume an idealised network structure, in combination with a non-affine network deformation, have been successful in capturing the elastic response of the network. In this study, an affine network deformation is assumed, in which we propose an alternative 3D finite strain constitutive model. The model makes use of a micro-sphere to calculate the strain energy density of the network, which is represented as a continuous distribution of filament orientations in space. By incorporating a simplified sliding mechanism at the filament-to-filament junctions, premature filament locking, inherent to affine network deformation, could be avoided. The model could successfully fit experimental shear data for a specific cross-linked F-actin network, demonstrating the potential of the novel model.

Assembly kinetics determine the architecture of α-actinin crosslinked F-actin networks

The actin cytoskeleton is organized into diverse meshworks and bundles that support many aspects of cell physiology. Understanding the self-assembly of these actin-based structures is essential for developing predictive models of cytoskeletal organization. Here we show that the competing kinetics of bundle formation with the onset of dynamic arrest arising from filament entanglements and cross-linking determine the architecture of reconstituted actin networks formed with α-actinin cross-links. Cross-link mediated bundle formation only occurs in dilute solutions of highly mobile actin filaments. As actin polymerization proceeds, filament mobility and bundle formation are arrested concomitantly. By controlling the onset of dynamic arrest, perturbations to actin assembly kinetics dramatically alter the architecture of biochemically identical samples. Thus, the morphology of reconstituted F-actin networks is a kinetically determined structure similar to those formed by physical gels and glasses. These results establish mechanisms controlling the structure and mechanics in diverse semi-flexible biopolymer networks.

Polymorphism of highly cross-linked F-actin networks: Probing multiple length scales

The assembly properties of F-actin filaments in the presence of different biological cross-linker concentrations and types have been investigated using a combined approach of fluorescence confocal microscopy and coarse-grained molecular dynamics simulation. In particular for highly cross-linked regimes, new network morphologies are observed. Complex network formation and the details of the resulting structure are strongly dependent on the ratio of cross-linkers to actin monomers and cross-linker shape but only weakly dependent on overall actin concentration and filament length. The work presented here may help to provide some fundamental understanding of how excessive cross-linkers interact with the actin filament solution, creating different structures in the cell under high cross-linker concentrations. F-actin is not only of biological importance but also, as an example of a semiflexible polymer, has attracted significant interest in its physical behavior. In combination with different cross-linkers semiflexible filaments may provide new routes to bio-materials development and act as the inspiration for new hierarchical network-based materials.

Mechanical reorganization of cross-linked F-actin networks at the air-buffer interface

The response of an F-actin network at the air-buffer interface to nonlinear compression is studied. We observe two distinct classes of behavior: a mechanically induced structural reorganization of the monolayer and a subsequent reversible, nonlinear mechanical response. Measurements of pressure area isotherms, bulk modulus, and the epifluorescence microscopy of tracer beads provide evidence that an initial structural reorganization occurs that corresponds to the mechanically induced formation of bundles of actin. Once a steady state structure is formed, subsequent compressions exhibit four distinct regimes as a function of decreasing total area: a low density fragile network, a relatively uniform film of cross-linked bundles, a region characterized by a buckling instability, and finally, a close packed region. Evidence for the distinct regions comes from the epifluorescence microscopy of tracer beads and measurements of the bulk modulus. Key features of the dynamics include domain rearrangements in the fragile network and an irregular, jerk-like motion during the buckling transition.

Molecular origin of strain softening in cross-linked F-actin networks

Two types of measurement are presented that relate molecular events to macroscopic behavior of F-actin networks. First, shear modulus is measured by oscillating an embedded microbead. Second, a microbead is translated at constant rate and transitions in the resisting force are observed. The loading rate dependence of the force at the transitions is similar to that of the molecular unbinding force, suggesting that they share a common origin. Reversibility tests of shear modulus provide further evidence that strain softening of F-actin networks is caused by force-induced rupture of cross-links.

Passive and active microrheology for cross-linked F-actin networks in vitro

Actin filament (F-actin) is one of the dominant structural constituents in the cytoskeleton. Orchestrated by various actin-binding proteins (ABPs), F-actin is assembled into higher-order structures such as bundles and networks that provide mechanical support for the cell and play important roles in numerous cellular processes. Although mechanical properties of F-actin networks have been extensively studied, the underlying mechanisms for network elasticity are not fully understood, in part because different measurements probe different length and force scales. Here, we developed both passive and active microrheology techniques using optical tweezers to estimate the mechanical properties of F-actin networks at a length scale comparable to cells. For the passive approach we tracked the motion of a thermally fluctuating colloidal sphere to estimate the frequency-dependent complex shear modulus of the network. In the active approach, we used an optical trap to oscillate an embedded microsphere and monitored the response in order to obtain network viscoelasticity over a physiologically relevant force range. While both active and passive measurements exhibit similar results at low strain, the F-actin network subject to high strain exhibits non-linear behavior which is analogous to the strain-hardening observed in macroscale measurements. Using confocal and total internal reflection fluorescent microscopy, we also characterize the microstructure of reconstituted F-actin networks in terms of filament length, mesh size and degree of bundling. Finally, we propose a model of network connectivity by investigating the effect of filament length on the mechanical properties and structure.

Cytoskeletal Deformation at High Strains and the Role of Cross-link Unfolding or Unbinding

Actin cytoskeleton has long been a focus of attention due to its biological significance and unique rheological properties. Although F-actin networks have been extensively studied experimentally and several theoretical models proposed, the detailed molecular interactions between actin binding proteins (ABPs) and actin filaments that regulate network behavior remain unclear. Here, using an in vitro assay that allows direct measurements on the bond between one actin cross-linking protein and two actin filaments, we demonstrate force-induced unbinding and unfolding of filamin. The critical forces prove to be similar, 70 ± 23 pN for unbinding and 57 ± 19 pN for unfolding, suggesting that both are important mechanisms governing cytoskeletal rheology. We also obtain the mechanical response of a cross-linked F-actin network to an optically trapped microbead and observe abrupt transitions implying rupture or unfolding of cross-links. These measurements are interpreted with the aid of a computational simulation of the experiment to provide greater insight into physical mechanisms.

Measuring Molecular Interaction between Actin Filament and Actin Binding Protein Governing Mechanical Properties of Cross-Linked F-Actin Network

Actin binding proteins (ABPs) regulate the assembly of actin filaments (F-actin) into various structures that provide physical support for the cell and play important roles in numerous cellular processes. Although the mechanical properties of F-actin networks have been extensively studied, a full understanding of how molecular interactions between ABPs and actin filaments influence the network mechanical properties of F-actin network is lacking. Here, we study the molecular interaction between ABPs and actin filaments and the mechanical rupture of a cross-linked F-actin network. A single molecule assay was used to measure the rupture force of a complex formed by an ABP filamin linking two actin filaments by pulling one of the filaments with the optical tweezers. The rupture forces for filamin/F-actin complex were 88±34 pN for loading rates of 1209±119 pN/s. About 20% of the force-extension traces exhibited a sawtooth pattern with intervals ∼30 nm comparable to length changes due to unfolding of individual immunoglobulin domains of filamin. We also prepared the F-actin gels and monitored their mechanical responses while an embedded bead was displaced at constant speed. Compared to similar experiments with an entangled F-actin solution, the force-extension curves for the filamin/F-actin network exhibited multiple transitions in the force of 37±17 pN, suggestive of bond rupture. In addition, using the optical tweezers, active microrheology was used to measure the strain-dependent mechanical properties of the filamin/F-actin network. Results demonstrate the network to be highly nonlinear and irreversible. Support from the NIGMS (GM-076689) is gratefully acknowledged.

Rheology of two-dimensional F-actin networks associated with a lipid interface

We report on the surface rheology of cross-linked F-actin networks associated with a lipid monolayer at the air-water interface of a Langmuir monolayer. The rheological measurements are made using a Couette cell. These data demonstrate that the network has a finite elastic modulus that grows as a function of the cross-linking concentration. We also note that under steady-state flow the system behaves as a power-law fluid in which the effective viscosity decreases with imposed shear.

Three-Dimensional Cross-Linked F-Actin Networks: Relation between Network Architecture and Mechanical Behavior

Numerical simulations are reported for the response of three-dimensional cross-linked F-actin networks when subjected to large deformations. In addition to the physiological parameters such as actin and cross-linker concentration, the model explicitly accounts for filament properties and network architecture. Complementary to two-dimensional studies, we find that the strain-stiffening characteristics depend on network architecture through the local topology around cross-links.

Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro.

The organization of individual actin filaments into higher-order structures is controlled by actin-binding proteins (ABPs). Although the biological significance of the ABPs is well documented, little is known about how bundling and cross-linking quantitatively affect the microstructure and mechanical properties of actin networks. Here we quantify the effect of the ABP scruin on actin networks by using imaging techniques, cosedimentation assays, multiparticle tracking, and bulk rheology. We show how the structure of the actin network is modified as the scruin concentration is varied, and we correlate these structural changes to variations in the resultant network elasticity.

Angiotensin II Inhibits Cell Proliferation and Stimulates Protein Synthesis in Rat Glomerulosa Cells

Angiotensin II (Ang Il) is one of the most important stimuli of rat adrenaI glomerulosa cells. The aim of the present study was to investigate whether Ang Il can stimulate cell proliferation and/or hypertrophy and to investigate pathways of these two specific growth responses. Results reveal that a 3-day treatment with Ang Il abolished cell proliferation observed in control cells, but increased protein synthesis. Preincubation with PD98059 (a MEK inhibitor) diminished basal proliferation and affected basal protein synthesis. In contrast, the p38 MAPK inhibitor, SB203580, reversed the inhibitory effect on cell proliferation and abolished the increase in protein synthesis, although the JNK inhibitor had no effect. Time-course studies indeed indicate that Ang II stimulates phosphorylation of p42/p44 mapk (peak at 5 min with a sustained plateau) and of p38 mapk (rapid and transient effect at 2 min), but did not activate JNK. Preincubation with cytochalasin B abolished basal proliferation. Immunofluorescence studies indicate that Ang II favored the formation of a peripheral cortical actin ring, but a depolymerization of the cross-linked F-actin network. Together, these results indicate that a well-developed network of microfilaments is necessary to promote basal cell proliferation, while microfilament disruption are involved in Ang II