Buckling-induced F-actin fragmentation modulates the contraction of active cytoskeletal networks

Characterization, enrichment, and computational modeling of cross-linked actin networks in trabecular meshwork cells

Purpose

Cross-linked actin networks (CLANs) are prevalent in the glaucomatous trabecular meshwork (TM), yet their role in ocular hypertension remains unclear. We used a human TM cell line that spontaneously forms fluorescently-labeled CLANs (GTM3L) to explore the origin of CLANs, developed techniques to increase CLAN incidence in GMT3L cells, and computationally studied the biomechanical properties of CLAN-containing cells.

Methods

GTM3L cells were fluorescently sorted for viral copy number analysis. CLAN incidence was increased by (i) differential sorting of cells by adhesion, (ii) cell deswelling, and (iii) cell selection based on cell stiffness. GTM3L cells were also cultured on glass or soft hydrogel to determine substrate stiffness effects on CLAN incidence. Computational models were constructed to mimic and study the biomechanical properties of CLANs.

Results

All GTM3L cells had an average of 1 viral copy per cell. LifeAct-GFP expression level did not affect CLAN incidence rate, but CLAN rate was increased from ~0.28% to ~50% by a combination of adhesion selection, cell deswelling, and cell stiffness-based sorting. Further, GTM3L cells formed more CLANs on a stiff vs. a soft substrate. Computational modeling predicted that CLANs contribute to higher cell stiffness, including increased resistance of the nucleus to tensile stress when CLANs are physically linked to the nucleus.

Conclusions

It is possible to greatly enhance CLAN incidence in GTM3L cells. CLANs are mechanosensitive structures that affect cell biomechanical properties. Further research is needed to determine the effect of CLANs on TM biomechanics and mechanobiology as well as the etiology of CLAN formation in the TM.

Myosin-induced F-actin fragmentation facilitates contraction of actin networks

Mechanical forces play a crucial role in diverse physiological processes, such as cell migration, cytokinesis, and morphogenesis. The actin cytoskeleton generates a large fraction of the mechanical forces via molecular interactions between actin filaments (F-actins) and myosin motors. Recent studies have shown that the common tendency of actomyosin networks to contract into a smaller structure deeply involves F-actin buckling induced by motor activities, fragmentation of F-actins, and the force-dependent unbinding of cross-linkers that inter-connect F-actins. The fragmentation of F-actins was shown to originate from either buckling or tensile force from previous single-molecule experiments. While the role of buckling in network contraction has been studied extensively, to date, the role of tension-induced F-actin fragmentation in network contraction has not been investigated. In this study, we employed in vitro experiments and an agent-based computational model to illuminate when and how the tension-induced F-actin fragmentation facilitates network contraction. Our experiments demonstrated that F-actins can be fragmented due to tensile forces, immediately followed by catastrophic rupture and contraction of networks. Using the agent-based model, we showed that F-actin fragmentation by tension results in distinct rupture dynamics different from that observed in networks only with cross-linker unbinding. Moreover, we found that tension-induced F-actin fragmentation is particularly important for the contraction of networks with high connectivity. Results from our study shed light on an important regulator of the contraction of actomyosin networks which has been neglected. In addition, our results provide insights into the rupture mechanisms of polymeric network structures and bio-inspired materials.

Emergence of diverse patterns driven by molecular motors in the motility assay

Actomyosin contractility originating from interactions between F-actin and myosin motors in the actin cytoskeleton generates mechanical forces and drives a wide range of cellular processes including cell migration and cytokinesis. To probe the interactions between F-actin and myosin motors, the myosin motility assay has been popularly employed, which consists of myosin heads attached to a glass surface and F-actins gliding on the surface via interactions with the heads. Several experiments have shown that F-actins move in a collective fashion due to volume-exclusion effects between neighboring F-actins. Furthermore, Computational models have shown how changes in key parameters lead to diverse pattern formation in motility assay. However, in most of the computational models, myosin motors were implicitly considered by applying a constant propulsion force to filaments to reduce computational cost. This simplification limits the physiological relevance of the insights provided by the models and potentially leads to artifacts. In this study, we employed an agent-based computational model for the motility assay with explicit immobile motors interacting with filaments. We rigorously account for the kinetics of myosin motors including the force-velocity relationship for walking and the binding and unbinding behaviors. We probed the effects of the length, rigidity, and concentration of filaments and repulsive strength on collective movements and pattern formation. It was found that four distinct types of structures-homogeneous networks, flocks, bands, and rings-emerged as a result of collisions between gliding filaments. We further analyzed the frequency and morphology of these structures and the curvature, alignment, and rotational motions of filaments. Our study provides better insights into the origin and properties of patterns formed by gliding filaments beyond what was shown before.

The Arp2/3 complex enhances cell migration on elastic substrates

Cell migration on soft surfaces occurs in both physiological and pathological processes such as corticogenesis during embryonic development and cancer invasion and metastasis. The Arp2/3 complex in neural progenitor cells was previously demonstrated to be necessary for cell migration on soft elastic substrate but not on stiff surfaces, but the underlying mechanism was unclear. Here, we integrate computational and experimental approaches to elucidate how the Arp2/3 complex enables cell migration on soft surfaces. We found that lamellipodia comprised of a branched actin network nucleated by the Arp2/3 complex distribute forces over a wider area, thus decreasing stress in the substrate. Additionally, we found that interactions between parallel focal adhesions within lamellipodia prolong cell-substrate interactions by compensating for the failure of neighboring adhesions. Together with decreased substrate stress, this leads to the observed improvements in migratory ability on soft substrates in cells utilizing lamellipodia-dependent mesenchymal migration when compared with filopodia-based migration. These results show that the Arp2/3 complex-dependent lamellipodia provide multiple distinct mechanical advantages to gliomas migrating on soft 2D substrates, which can contribute to their invasive potential.

Myosin and [Formula: see text]-actinin regulation of stress fiber contractility under tensile stress

Stress fibers are actomyosin bundles that regulate cellular mechanosensation and force transduction. Interacting with the extracellular matrix through focal adhesion complexes, stress fibers are highly dynamic structures regulated by myosin motors and crosslinking proteins. Under external mechanical stimuli such as tensile forces, the stress fiber remodels its architecture to adapt to external cues, displaying properties of viscoelastic materials. How the structural remodeling of stress fibers is related to the generation of contractile force is not well understood. In this work, we simulate mechanochemical dynamics and force generation of stress fibers using the molecular simulation platform MEDYAN. We model stress fiber as two connecting bipolar bundles attached at the ends to focal adhesion complexes. The simulated stress fibers generate contractile force that is regulated by myosin motors and [Formula: see text]-actinin crosslinkers. We find that stress fibers enhance contractility by reducing the distance between actin filaments to increase crosslinker binding, and this structural remodeling ability depends on the crosslinker turnover rate. Under tensile pulling force, the stress fiber shows an instantaneous increase of the contractile forces followed by a slow relaxation into a new steady state. While the new steady state contractility after pulling depends only on the overlap between actin bundles, the short-term contractility enhancement is sensitive to the tensile pulling distance. We further show that this mechanical response is also sensitive to the crosslinker turnover rate. Our results provide new insights into the stress fiber mechanics that have significant implications for understanding cellular adaptation to mechanical signaling.

Zyxin and actin structure confer anisotropic YAP mechanotransduction

Tissues and the embedded cells experience anisotropic deformations due to their functions and anatomical locations. The resident cells, such as tenocytes and muscle cells, are often restricted by their extracellular matrix and organize parallel to their major loading direction, yet most studies on cellular responses to strains use isotropic substrates without predetermined organizations. To understand how confined cells sense and respond to anisotropic loading, we combine cell patterning and uniaxial stretch to have precise geometric control. Dynamic stretch parallel to the long axis of the cell activates YAP nuclear translocation, but not when stretched in the perpendicular direction. Looking at the initial cytoskeleton response, parallel stretch leads to actin breakage and repair within the first minute, mediated by zyxin, the focal adhesion protein. In addition, this zyxin-mediated repair response is controlled by focal adhesion kinase (FAK) and leads to YAP signaling. As these factors are intimately involved in a wide range of mechanical regulation, our findings point to new roles of zyxin and YAP in anisotropic mechanotransduction, and may provide additional perspectives in cellular adaptive responses and tissue homeostasis. STATEMENT OF SIGNIFICANCE: Structure and deformation of tissues control gene expression, migration, and proliferation of the resident cells. In an effort to understand the underlying mechanisms, we find that the transcription cofactor YAP respond to mechanical stretch in a direction-dependent manner. We demonstrate that parallel stretch induces actin cytoskeleton damage, focal adhesion kinase (FAK) activation, and zyxin relocation, which are involved in the anisotropic YAP signaling. Our findings provide additional perspectives in the interactions of tissue structure and cell mechanotransduction.

Compression-induced buckling of a semiflexible filament in two and three dimensions

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show the theory is highly sensitive to fluctuations in length in two dimensions, and that the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.

Rapid assembly of a polar network architecture drives efficient actomyosin contractility

Actin network architecture and dynamics play a central role in cell contractility and tissue morphogenesis. RhoA-driven pulsed contractions are a generic mode of actomyosin contractility, but the mechanisms underlying how their specific architecture emerges and how this architecture supports the contractile function of the network remain unclear. Here we show that, during pulsed contractions, the actin network is assembled by two subpopulations of formins: a functionally inactive population (recruited) and formins actively participating in actin filament elongation (elongating). We then show that elongating formins assemble a polar actin network, with barbed ends pointing out of the pulse. Numerical simulations demonstrate that this geometry favors rapid network contraction. Our results show that formins convert a local RhoA activity gradient into a polar network architecture, causing efficient network contractility, underlying the key function of kinetic controls in the assembly and mechanics of cortical network architectures.

RhoA-driven actomyosin contractility plays a key role in driving cell and tissue contractility during morphogenesis. Tracking individual formins, Costache et al. show that the network assembled downstream of RhoA displays a polar architecture, barbed ends pointing outward, a feature that supports efficient contractility and force transmission during pulsed contractions.

Cortical tension initiates the positive feedback loop between cadherin and F-actin

Adherens junctions physically link two cells at their contact interface via extracellular binding between cadherin molecules and intracellular interactions between cadherins and the actin cytoskeleton. Cadherin and actomyosin cytoskeletal dynamics are regulated reciprocally by mechanical and chemical signals, which subsequently determine the strength of cell-cell adhesions and the emergent organization and stiffness of the tissues they form. However, an understanding of the integrated system is lacking. We present a new mechanistic computational model of intercellular junction maturation in a cell doublet to investigate the mechanochemical cross talk that regulates adherens junction formation and homeostasis. The model couples a two-dimensional lattice-based simulation of cadherin dynamics with a reaction-diffusion representation of the reorganising actomyosin network through its regulation by Rho signalling at the intracellular junction. We demonstrate that local immobilization of cadherin induces cluster formation in a cis-less-dependent manner. We then recapitulate the process of cell-cell contact formation. Our model suggests that cortical tension applied on the contact rim can explain the ring distribution of cadherin and actin filaments (F-actin) on the cell-cell contact of the cell doublet. Furthermore, we propose and test the hypothesis that cadherin and F-actin interact like a positive feedback loop, which is necessary for formation of the ring structure. Different patterns of cadherin distribution were observed as an emergent property of disturbances of this positive feedback loop. We discuss these findings in light of available experimental observations on underlying mechanisms related to cadherin/F-actin binding and the mechanical environment.

Myosin and gelsolin cooperate in actin filament severing and actomyosin motor activity

Actin is a major intracellular protein with key functions in cellular motility, signaling, and structural rearrangements. Its dynamic behavior, such as polymerization and depolymerization of actin filaments in response to intracellular and extracellular cues, is regulated by an abundance of actin binding proteins. Out of these, gelsolin is one of the most potent for filament severing. However, myosin motor activity also fragments actin filaments through motor-induced forces, suggesting that these two proteins could cooperate to regulate filament dynamics and motility. To test this idea, we used an in vitro motility assay, where actin filaments are propelled by surface-adsorbed heavy meromyosin (HMM) motor fragments. This allows studies of both motility and filament dynamics using isolated proteins. Gelsolin, at both nanomolar and micromolar Ca²⁺ concentration, appreciably enhanced actin filament severing caused by HMM-induced forces at 1 mM MgATP, an effect that was increased at higher HMM motor density. This finding is consistent with cooperativity between actin filament severing by myosin-induced forces and by gelsolin. We also observed reduced sliding velocity of the HMM-propelled filaments in the presence of gelsolin, providing further support of myosin-gelsolin cooperativity. Total internal reflection fluorescence microscopy–based single molecule studies corroborated that the velocity reduction was a direct effect of gelsolin binding to the filament and revealed different filament severing pattern of stationary and HMM propelled filaments. Overall, the results corroborate cooperative effects between gelsolin-induced alterations in the actin filaments and changes due to myosin motor activity leading to enhanced F-actin severing of possible physiological relevance.

Collective and contractile filament motions in the myosin motility assay

Cells require mechanical forces for their physiological functions. The forces are generated mainly from molecular interactions between actin filaments, cross-linking proteins, and myosin motors in the actin cytoskeleton. To better understand the molecular interactions, many studies employed myosin motility assays with actin filaments propelled by myosin heads fixed on a surface. Various interesting behaviors of actin filaments have been observed in the motility assay experiments. Despite the popularity of the motility assays, there were only a few computational models designed for simulating the motility assay systems. Most of the previous models have limitations which precluded full understanding of molecular origins for behaviors of actin filaments. In this study, we used an agent-based computational model based on Brownian dynamics for simulating the motility assay system. Our model rigorously describes the mechanics, dynamics, and interactions of actin filaments, cross-linking proteins, and molecular motors. Using the model, we first investigated how properties of actin filaments and motors affect gliding motions of actin filaments without volume-exclusion effects as a base study. We found that actin filaments can continuously glide at relative fast speed only when they are sufficiently longer than the average spacing between neighboring motors and that the gliding speed of F-actins shows a biphasic dependence on processivity of motors. Then, we showed that volume-exclusion effects between actin filaments can induce diverse collective movements and alignment of actin filaments, thus creating thick bundles and ring-like structures in the absence of cross-linking proteins. Lastly, we demonstrated that cross-linking proteins can lead to distinct contractile behaviors of actin networks depending on the density and kinetics of the cross-linking proteins. Results from our study show the ability of our model to simulate the motility assay system under various conditions and provide insights into understanding of different behaviors of actin filaments.

Filament Nucleation Tunes Mechanical Memory in Active Polymer Networks

Incorporating growth into contemporary material functionality presents a grand challenge in materials design. The F-actin cytoskeleton is an active polymer network which serves as the mechanical scaffolding for eukaryotic cells, growing and remodeling in order to determine changes in cell shape. Nucleated from the membrane, filaments polymerize and grow into a dense network whose dynamics of assembly and disassembly, or 'turnover', coordinates both fluidity and rigidity. Here, we vary the extent of F-actin nucleation from a membrane surface in a biomimetic model of the cytoskeleton constructed from purified protein. We find that nucleation of F-actin mediates the accumulation and dissipation of polymerization-induced F-actin bending energy. At high and low nucleation, bending energies are low and easily relaxed yielding an isotropic material. However, at an intermediate critical nucleation, stresses are not relaxed by turnover and the internal energy accumulates 100-fold. In this case, high filament curvatures template further assembly of F-actin, driving the formation and stabilization of vortex-like topological defects. Thus, nucleation coordinates mechanical and chemical timescales to encode shape memory into active materials.

Advanced Artificial Muscle for Flexible Material-Based Reconfigurable Soft Robots

Flexible material-based soft robots are widely used in various areas. In many situations, the suitable soft robots should be rapidly fabricated to complete the urgent tasks (such as rescue), so the facile fabricating methods of the multifunctional soft robots are still in urgent needs. In this work, the origami structure is employed to design vacuum-powered silicone rubber artificial muscles, which can perform multiple motions, including contraction, bending, twisting, and radial motions. Artificial muscles can be used for rapid reconfiguration of different soft robots, just like the "building bricks". Based on these artificial muscles, four soft robots with different functions, including an omnidirectional quadruped robot, a flexible gripper, a flexible wrist, and a pipe-climbing robot, are reconfigured to complete different tasks. The proposed origami artificial muscles offer a facile and rapid fabricating method of flexible material-based soft robots, and also greatly improve the utilization rate of flexible materials.

Mobility of Molecular Motors Regulates Contractile Behaviors of Actin Networks

Cells generate mechanical forces primarily from interactions between F-actin, cross-linking proteins, myosin motors, and other actin-binding proteins in the cytoskeleton. To understand how molecular interactions between the cytoskeletal elements generate forces, a number of in vitro experiments have been performed but are limited in their ability to accurately reproduce the diversity of motor mobility. In myosin motility assays, myosin heads are fixed on a surface and glide F-actin. By contrast, in reconstituted gels, the motion of both myosin and F-actin is unrestricted. Because only these two extreme conditions have been used, the importance of mobility of motors for network behaviors has remained unclear. In this study, to illuminate the impacts of motor mobility on the contractile behaviors of the actin cytoskeleton, we employed an agent-based computational model based on Brownian dynamics. We find that if motors can bind to only one F-actin like myosin I, networks are most contractile at intermediate mobility. In this case, less motor mobility helps motors stably pull F-actins to generate tensile forces, whereas higher motor mobility allows F-actins to aggregate into larger clustering structures. The optimal intermediate motor mobility depends on the stall force and affinity of motors that are regulated by mechanochemical rates. In addition, we find that the role of motor mobility can vary drastically if motors can bind to a pair of F-actins. A network can exhibit large contraction with high motor mobility because motors bound to antiparallel pairs of F-actins can exert similar forces regardless of their mobility. Results from this study imply that the mobility of molecular motors may critically regulate contractile behaviors of actin networks in cells.

Capturing 3D large-strain Euler-bending filament dynamics in fibrous media simulations; sample case of compression collapse in dendritic actin network

Cytoskeletal networks to transmission towers are comprised of slender elements. Slender filaments bend and buckle more easily than stretch. Therefore a deforming network is expected to exhaust all possible bending-based modes before engaging filament stretch. While the large-strain bending critically determines fibrous-media response, simulations use small-strain and jointed approximations. At low resolution, these approximations inflate bending resistance and delay buckling onset. The proposed string-of-continuous-beams (SOCB) approach captures 3D nonlinear Euler bending of filaments with high fidelity at low cost. Bending geometry (i.e. angles and its differentials) is solved as primary variables, to fit a 5th order polynomial of the contour angle. Displacement, solved simultaneously as length conservation, is predicted with C3 and C6 smoothness between and within segments, using only 2 nodes. In the chosen analysis frame, in-plane and out-plane moments can be decoupled for arbitrarily-curved segments. Complex crosslink force-transfers can be specified. Simulations show that when a daughter branch is appended, the buckling resistance of a filament changes from linear to nonlinear before reversible collapse. An actin outcrop with 8 generations of mother-daughter branching produced the linear, nonlinear, and collapse regimes observed in compression experiments. 'Collapse' was a redistribution of outcrop forces following the buckling of few strands.

Balance between Force Generation and Relaxation Leads to Pulsed Contraction of Actomyosin Networks

Actomyosin contractility regulates various biological processes, including cell migration and cytokinesis. The cell cortex underlying the membrane of eukaryote cells exhibits dynamic contractile behaviors facilitated by actomyosin contractility. Interestingly, the cell cortex shows reversible aggregation of actin and myosin called "pulsed contraction" in diverse cellular phenomena, such as embryogenesis and tissue morphogenesis. Although contractile behaviors of actomyosin machinery have been studied extensively in several in vitro experiments and computational studies, none of them successfully reproduced the pulsed contraction observed in vivo. Recent experiments have suggested the pulsed contraction is dependent upon the spatiotemporal expression of a small GTPase protein called RhoA. This only indicates the significance of biochemical signaling pathways during the pulsed contraction. In this study, we reproduced the pulsed contraction with only the mechanical and dynamic behaviors of cytoskeletal elements. First, we observed that small pulsed clusters or clusters with fluctuating sizes may appear when there is subtle balance between force generation from motors and force relaxation induced by actin turnover. However, the size and duration of these clusters differ from those of clusters observed during the cellular phenomena. We found that clusters with physiologically relevant size and duration can appear only with both actin turnover and angle-dependent F-actin severing resulting from buckling induced by motor activities. We showed how parameters governing F-actin severing events regulate the size and duration of pulsed clusters. Our study sheds light on the underestimated significance of F-actin severing for the pulsed contraction observed in physiological processes.

Emergent mechanics of actomyosin drive punctuated contractions and shape network morphology in the cell cortex

Filamentous actin (F-actin) and non-muscle myosin II motors drive cell motility and cell shape changes that guide large scale tissue movements during embryonic morphogenesis. To gain a better understanding of the role of actomyosin in vivo, we have developed a two-dimensional (2D) computational model to study emergent phenomena of dynamic unbranched actomyosin arrays in the cell cortex. These phenomena include actomyosin punctuated contractions, or "actin asters" that form within quiescent F-actin networks. Punctuated contractions involve both formation of high intensity aster-like structures and disassembly of those same structures. Our 2D model allows us to explore the kinematics of filament polarity sorting, segregation of motors, and morphology of F-actin arrays that emerge as the model structure and biophysical properties are varied. Our model demonstrates the complex, emergent feedback between filament reorganization and motor transport that generate as well as disassemble actin asters. Since intracellular actomyosin dynamics are thought to be controlled by localization of scaffold proteins that bind F-actin or their myosin motors we also apply our 2D model to recapitulate in vitro studies that have revealed complex patterns of actomyosin that assemble from patterning filaments and motor complexes with microcontact printing. Although we use a minimal representation of filament, motor, and cross-linker biophysics, our model establishes a framework for investigating the role of other actin binding proteins, how they might alter actomyosin dynamics, and makes predictions that can be tested experimentally within live cells as well as within in vitro models.

Recent genetic and mechanical studies of embryonic development reveal a critical role for intracellular scaffolds in generating the shape of the embryo and constructing internal organs. In this paper we developed computer simulations of these scaffolds, composed of filamentous actin (F-actin), a rod-like protein polymer, and mini-thick filaments, composed of non-muscle myosin II, forming a two headed spring-like complex of motor proteins that can walk on, and remodel F-actin networks. Using simulations of these dynamic interactions, we can carry out virtual experiments where we change the physics and chemistry of F-actin polymers, their associated myosin motors, and cross-linkers and observe the changes in scaffolds that emerge. For example, by modulating the motor stiffness of the myosin motors in our model we can observe the formation or loss of large aster-like structures. Such fine-grained control over the physical properties of motors or filaments within simulations are not currently possible with biological experiments, even where mutant proteins or small molecule inhibitors can be targeted to specific sites on filaments or motors. Our approach reflects a growing adoption of simulation methods to investigate microscopic features that shape actomyosin arrays and the mesoscale effects of molecular scale processes. We expect predictions from these models will drive more refined experimental approaches to expose the many roles of actomyosin in development.

Polarity sorting drives remodeling of actin-myosin networks

Cytoskeletal networks of actin filaments and myosin motors drive many dynamic cell processes. A key characteristic of these networks is their contractility. Despite intense experimental and theoretical efforts, it is not clear what mechanism favors network contraction over expansion. Recent work points to a dominant role for the nonlinear mechanical response of actin filaments, which can withstand stretching but buckle upon compression. Here we present an alternative mechanism. We study how interactions between actin and myosin-2 at the single filament level translate into contraction at the network scale by performing time-lapse imaging on reconstituted quasi-2D-networks mimicking the cell cortex. We observe myosin end-dwelling after it runs processively along actin filaments. This leads to transport and clustering of actin filament ends and the formation of transiently stable bipolar structures. Further we show that myosin-driven polarity sorting produces polar actin asters, which act as contractile nodes that drive contraction in crosslinked networks. Computer simulations comparing the roles of the end-dwelling mechanism and a buckling-dependent mechanism show that the relative contribution of end-dwelling contraction increases as the network mesh-size decreases.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.