Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arise from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

F-actin architecture determines the conversion of chemical energy into mechanical work.

Mechanical work serves as the foundation for dynamic cellular processes, ranging from cell division to migration. A fundamental driver of cellular mechanical work is the actin cytoskeleton, composed of filamentous actin (F-actin) and myosin motors, where force generation relies on adenosine triphosphate (ATP) hydrolysis. F-actin architectures, whether bundled by crosslinkers or branched via nucleators, have emerged as pivotal regulators of myosin II force generation. However, it remains unclear how distinct F-actin architectures impact the conversion of chemical energy to mechanical work. Here, we employ in vitro reconstitution of distinct F-actin architectures with purified components to investigate their influence on myosin ATP hydrolysis (consumption). We find that F-actin bundles composed of mixed polarity F-actin hinder network contraction compared to non-crosslinked network and dramatically decelerate ATP consumption rates. Conversely, linear-nucleated networks allow network contraction despite reducing ATP consumption rates. Surprisingly, branched-nucleated networks facilitate high ATP consumption without significant network contraction, suggesting that the branched network dissipates energy without performing work. This study establishes a link between F-actin architecture and myosin energy consumption, elucidating the energetic principles underlying F-actin structure formation and the performance of mechanical work.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arises from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Membrane tension induces F-actin reorganization and flow in a biomimetic model cortex.

The accumulation and transmission of mechanical stresses in the cell cortex and membrane determines the mechanics of cell shape and coordinates essential physical behaviors, from cell polarization to cell migration. However, the extent that the membrane and cytoskeleton each contribute to the transmission of mechanical stresses to coordinate diverse behaviors is unclear. Here, we reconstitute a minimal model of the actomyosin cortex within liposomes that adheres, spreads and ultimately ruptures on a surface. During spreading, accumulated adhesion-induced (passive) stresses within the membrane drive changes in the spatial assembly of actin. By contrast, during rupture, accumulated myosin-induced (active) stresses within the cortex determine the rate of pore opening. Thus, in the same system, devoid of biochemical regulation, the membrane and cortex can each play a passive or active role in the generation and transmission of mechanical stress, and their relative roles drive diverse biomimetic physical behaviors.

Dysregulation of TSP2-Rac1-WAVE2 axis in diabetic cells leads to cytoskeletal disorganization, increased cell stiffness, and dysfunction.

Fibroblasts are a major cell population that perform critical functions in the wound healing process. In response to injury, they proliferate and migrate into the wound space, engaging in extracellular matrix (ECM) production, remodeling, and contraction. However, there is limited knowledge of how fibroblast functions are altered in diabetes. To address this gap, several state-of-the-art microscopy techniques were employed to investigate morphology, migration, ECM production, 2D traction, 3D contraction, and cell stiffness. Analysis of cell-derived matrix (CDM) revealed that diabetic fibroblasts produce thickened and less porous ECM that hindered migration of normal fibroblasts. In addition, diabetic fibroblasts were found to lose spindle-like shape, migrate slower, generate less traction force, exert limited 3D contractility, and have increased cell stiffness. These changes were due, in part, to a decreased level of active Rac1 and a lack of co-localization between F-actin and Waskott-Aldrich syndrome protein family verprolin homologous protein 2 (WAVE2). Interestingly, deletion of thrombospondin-2 (TSP2) in diabetic fibroblasts rescued these phenotypes and restored normal levels of active Rac1 and WAVE2-F-actin co-localization. These results provide a comprehensive view of the extent of diabetic fibroblast dysfunction, highlighting the regulatory role of the TSP2-Rac1-WAVE2-actin axis, and describing a new function of TSP2 in regulating cytoskeleton organization.

F-actin architecture determines constraints on myosin thick filament motion.

Active stresses are generated and transmitted throughout diverse F-actin architectures within the cell cytoskeleton, and drive essential behaviors of the cell, from cell division to migration. However, while the impact of F-actin architecture on the transmission of stress is well studied, the role of architecture on the ab initio generation of stresses remains less understood. Here, we assemble F-actin networks in vitro, whose architectures are varied from branched to bundled through F-actin nucleation via Arp2/3 and the formin mDia1. Within these architectures, we track the motions of embedded myosin thick filaments and connect them to the extent of F-actin network deformation. While mDia1-nucleated networks facilitate the accumulation of stress and drive contractility through enhanced actomyosin sliding, branched networks prevent stress accumulation through the inhibited processivity of thick filaments. The reduction in processivity is due to a decrease in translational and rotational motions constrained by the local density and geometry of F-actin.

Interplay between substrate rigidity and tissue fluidity regulates cell monolayer spreading.

Coordinated and cooperative motion of cells is essential for embryonic development, tissue morphogenesis, wound healing and cancer invasion. A predictive understanding of the emergent mechanical behaviors in collective cell motion is challenging due to the complex interplay between cell-cell interactions, cell-matrix adhesions and active cell behaviors. To overcome this challenge, we develop a predictive cellular vertex model that can delineate the relative roles of substrate rigidity, tissue mechanics and active cell properties on the movement of cell collectives. We apply the model to the specific case of collective motion in cell aggregates as they spread into a two-dimensional cell monolayer adherent to a soft elastic matrix. Consistent with recent experiments, we find that substrate stiffness regulates the driving forces for the spreading of cellular monolayer, which can be pressure-driven or crawling-based depending on substrate rigidity. On soft substrates, cell monolayer spreading is driven by an active pressure due to the influx of cells coming from the aggregate, whereas on stiff substrates, cell spreading is driven primarily by active crawling forces. Our model predicts that cooperation of cell crawling and tissue pressure drives faster spreading, while the spreading rate is sensitive to the mechanical properties of the tissue. We find that solid tissues spread faster on stiff substrates, with spreading rate increasing with tissue tension. By contrast, the spreading of fluid tissues is independent of substrate stiffness and is slower than solid tissues. We compare our theoretical results with experimental results on traction force generation and spreading kinetics of cell monolayers, and provide new predictions on the role of tissue fluidity and substrate rigidity on collective cell motion.

In Vitro Reconstitution of the Actin Cytoskeleton Inside Giant Unilamellar Vesicles.

The actin cytoskeleton, the principal mechanical machinery in the cell, mediates numerous essential physical cellular activities, including cell deformation, division, migration, and adhesion. However, studying the dynamics and structure of the actin network in vivo is complicated by the biochemical and genetic regulation within live cells. To build a minimal model devoid of intracellular biochemical regulation, actin is encapsulated inside giant unilamellar vesicles (GUVs, also called liposomes). The biomimetic liposomes are cell-sized and facilitate a quantitative insight into the mechanical and dynamical properties of the cytoskeleton network, opening a viable route for bottom-up synthetic biology. To generate liposomes for encapsulation, the inverted emulsion method (also referred to as the emulsion transfer method) is utilized, which is one of the most successful techniques for encapsulating complex solutions into liposomes to prepare various cell-mimicking systems. With this method, a mixture of proteins of interest is added to the inner buffer, which is later emulsified in a phospholipid-containing mineral oil solution to form monolayer lipid droplets. The desired liposomes are generated from monolayer lipid droplets crossing a lipid/oil-water interface. This method enables the encapsulation of concentrated actin polymers into the liposomes with desired lipid components, paving the way for in vitro reconstitution of a biomimicking cytoskeleton network.

Correction: The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions.

Correction for 'The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions' by Dong Wang et al., Soft Matter, 2021, 17, 9901-9915, DOI: 10.1039/D1SM01228B.

The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions.

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈G〉 scales with pressure P as 〈G〉 ∼ Pß, with ß ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, ß ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

Detailed Balance Broken by Catch Bond Kinetics Enables Mechanical-Adaptation in Active Materials.

Unlike nearly all engineered materials which contain bonds that weaken under load, biological materials contain "catch" bonds which are reinforced under load. Consequently, materials, such as the cell cytoskeleton, can adapt their mechanical properties in response to their state of internal, non-equilibrium (active) stress. However, how large-scale material properties vary with the distance from equilibrium is unknown, as are the relative roles of active stress and binding kinetics in establishing this distance. Through course-grained molecular dynamics simulations, the effect of breaking of detailed balance by catch bonds on the accumulation and dissipation of energy within a model of the actomyosin cytoskeleton is explored. It is found that the extent to which detailed balance is broken uniquely determines a large-scale fluid-solid transition with characteristic time-reversal symmetries. The transition depends critically on the strength of the catch bond, suggesting that active stress is necessary but insufficient to mount an adaptive mechanical response.

Irreversibility in dynamical phases and transitions.

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a measure of irreversibility we term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales. We use this scalar, dimensionless function to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We measure the total energetic cost of establishing synchronized biochemical oscillations while simultaneously quantifying the distribution of irreversibility across spatiotemporal frequencies.

Dynamic motions of molecular motors in the actin cytoskeleton.

During intracellular transport, cellular cargos, such as organelles, vesicles, and proteins, are transported within cells. Intracellular transport plays an important role in diverse cellular functions. Molecular motors walking on the cytoskeleton facilitate active intracellular transport, which is more efficient than diffusion-based passive transport. Active transport driven by kinesin and dynein walking on microtubules has been studied well during recent decades. However, mechanisms of active transport occurring in disorganized actin networks via myosin motors remain elusive. To provide physiologically relevant insights, we probed motions of myosin motors in actin networks under various conditions using our well-established computational model that rigorously accounts for the mechanical and dynamical behaviors of the actin cytoskeleton. We demonstrated that myosin motions can be confined due to three different reasons in the absence of F-actin turnover. We verified mechanisms of motor stalling using in vitro reconstituted actomyosin networks. We also found that with F-actin turnover, motors consistently move for a long time without significant confinement. Our study sheds light on the importance of F-actin turnover for effective active transport in the actin cytoskeleton.

Wound Healing Coordinates Actin Architectures to Regulate Mechanical Work.

How cells with diverse morphologies and cytoskeletal architectures modulate their mechanical behaviors to drive robust collective motion within tissues is poorly understood. During wound repair within epithelial monolayers in vitro, cells coordinate the assembly of branched and bundled actin networks to regulate the total mechanical work produced by collective cell motion. Using traction force microscopy, we show that the balance of actin network architectures optimizes the wound closure rate and the magnitude of the mechanical work. These values are constrained by the effective power exerted by the monolayer, which is conserved and independent of actin architectures. Using a cell-based physical model, we show that the rate at which mechanical work is done by the monolayer is limited by the transformation between actin network architectures and differential regulation of cell-substrate friction. These results and our proposed mechanisms provide a robust physical model for how cells collectively coordinate their non-equilibrium behaviors to dynamically regulate tissue-scale mechanical output.

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.

Spontaneous migration of cellular aggregates from giant keratocytes to running spheroids.

Despite extensive knowledge on the mechanisms that drive single-cell migration, those governing the migration of cell clusters, as occurring during embryonic development and cancer metastasis, remain poorly understood. Here, we investigate the collective migration of cell on adhesive gels with variable rigidity, using 3D cellular aggregates as a model system. After initial adhesion to the substrate, aggregates spread by expanding outward a cell monolayer, whose dynamics is optimal in a narrow range of rigidities. Fast expansion gives rise to the accumulation of mechanical tension that leads to the rupture of cell-cell contacts and the nucleation of holes within the monolayer, which becomes unstable and undergoes dewetting like a liquid film. This leads to a symmetry breaking and causes the entire aggregate to move as a single entity. Varying the substrate rigidity modulates the extent of dewetting and induces different modes of aggregate motion: "giant keratocytes," where the lamellipodium is a cell monolayer that expands at the front and retracts at the back; "penguins," characterized by bipedal locomotion; and "running spheroids," for nonspreading aggregates. We characterize these diverse modes of collective migration by quantifying the flows and forces that drive them, and we unveil the fundamental physical principles that govern these behaviors, which underscore the biological predisposition of living material to migrate, independent of length scale.

Entropy production rate is maximized in non-contractile actomyosin.

The actin cytoskeleton is an active semi-flexible polymer network whose non-equilibrium properties coordinate both stable and contractile behaviors to maintain or change cell shape. While myosin motors drive the actin cytoskeleton out-of-equilibrium, the role of myosin-driven active stresses in the accumulation and dissipation of mechanical energy is unclear. To investigate this, we synthesize an actomyosin material in vitro whose active stress content can tune the network from stable to contractile. Each increment in activity determines a characteristic spectrum of actin filament fluctuations which is used to calculate the total mechanical work and the production of entropy in the material. We find that the balance of work and entropy does not increase monotonically and the entropy production rate is maximized in the non-contractile, stable state of actomyosin. Our study provides evidence that the origins of entropy production and activity-dependent dissipation relate to disorder in the molecular interactions between actin and myosin.

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.