Actomyosin sliding is attenuated in contractile biomimetic cortices

Myosin II motors embedded within the actin cortex generate contractile forces to modulate cell shape in essential behaviors, including polarization, migration, and division. In sarcomeres, myosin II–mediated sliding of antiparallel F-actin is tightly coupled to myofibril contraction. By contrast, cortical F-actin is highly disordered in polarity, orientation, and length. How the disordered nature of the actin cortex affects actin and myosin movements and resultant contraction is unknown. Here we reconstitute a model cortex in vitro to monitor the relative movements of actin and myosin under conditions that promote or abrogate network contraction. In weakly contractile networks, myosin can translocate large distances across stationary F-actin. By contrast, the extent of relative actomyosin sliding is attenuated during contraction. Thus actomyosin sliding efficiently drives contraction in actomyosin networks despite the high degree of disorder. These results are consistent with the nominal degree of relative actomyosin movement observed in actomyosin assemblies in nonmuscle cells.     

Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.     

Reconstitution of contractile actomyosin bundles

Contractile actomyosin bundles are critical for numerous aspects of muscle and nonmuscle cell physiology. Due to the varying composition and structure of actomyosin bundles in vivo, the minimal requirements for their contraction remain unclear. Here, we demonstrate that actin filaments and filaments of smooth muscle myosin motors can self-assemble into bundles with contractile elements that efficiently transmit actomyosin forces to cellular length scales. The contractile and force-generating potential of these minimal actomyosin bundles is sharply sensitive to the myosin density. Above a critical myosin density, these bundles are contractile and generate large tensile forces. Below this threshold, insufficient cross-linking of F-actin by myosin thick filaments prevents efficient force transmission and can result in rapid bundle disintegration. For contractile bundles, the rate of contraction decreases as forces build and stalls under loads of ∼0.5 nN. The dependence of contraction speed and stall force on bundle length is consistent with bundle contraction occurring by several contractile elements connected in series. Thus, contraction in reconstituted actomyosin bundles captures essential biophysical characteristics of myofibrils while lacking numerous molecular constituents and structural signatures of sarcomeres. These results provide insight into nonsarcomeric mechanisms of actomyosin contraction found in smooth muscle and nonmuscle cells.     

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles’ cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.     

Mechanical Coupling between Myosin Molecules Causes Differences between Ensemble and Single-Molecule Measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.     

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.     

Cross-Correlated TIRF/AFM Reveals Asymmetric Distribution of Force-Generating Heads along Self-Assembled, “Synthetic” Myosin Filaments

Myosin-II's rod-like tail drives filament assembly with a head arrangement that is often considered to be a symmetric bipole that generates equal and opposite contractile forces on actin. Self-assembled myosin filaments are shown here to be asymmetric in physiological buffer based on cross-correlated images from both atomic force microscopy and total internal reflection fluorescence. Quantitative cross-correlation of these orthogonal methods produces structural information unavailable to either method alone in showing that fluorescence intensity along the filament length is proportional to height. This implies that myosin heads form a shell around the filament axis, consistent with F-actin binding. A motor density of ∼50-100 heads/micrometer is further estimated but with an average of 32% more motors on one half of any given filament compared to the other, regardless of length. A purely entropic pyramidal lattice model is developed and mapped onto the Dyck paths problem that qualitatively captures this lack of length dependence and the distribution of filament asymmetries. Such strongly asymmetric bipoles are likely to produce an unbalanced contractile force in cells and in actin-myosin gels and thereby contribute to motility as well as cytoskeletal tension.     

Actin bundle architecture and mechanics regulate myosin II force generation

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.     

Multiple- and single-molecule analysis of the actomyosin motor by nanometer-piconewton manipulation with a microneedle: unitary steps and forces.

We have developed a new technique for measurements of piconewton forces and nanometer displacements in the millisecond time range caused by actin-myosin interaction in vitro by manipulating single actin filaments with a glass microneedle. Here, we describe in full the details of this method. Using this method, the elementary events in energy transduction by the actomyosin motor, driven by ATP hydrolysis, were directly recorded from multiple and single molecules. We found that not only the velocity but also the force greatly depended on the orientations of myosin relative to the actin filament axis. Therefore, to avoid the effects of random orientation of myosin and association of myosin with an artificial substrate in the surface motility assay, we measured forces and displacements by myosin molecules correctly oriented in single synthetic myosin rod cofilaments. At a high myosin-to-rod ratio, large force fluctuations were observed when the actin filament interacted in the correct orientation with a cofilament. The noise analysis of the force fluctuations caused by a small number of heads showed that the myosin head generated a force of 5.9 +/- 0.8 pN at peak and 2.1 +/- 0.4 pN on average over the whole ATPase cycle. The rate constants for transitions into (k+) and out of (k-) the force generation state and the duty ratio were 12 +/- 2 s-1, and 22 +/- 4 s-1, and 0.36 +/- 0.07, respectively. The stiffness was 0.14 pN nm-1 head-1 for slow length change (100 Hz), which would be approximately 0.28 pN nm-1 head-1 for rapid length change or in rigor. At a very low myosin-to-rod ratio, distinct actomyosin attachment, force generation (the power stroke), and detachment events were directly detected. At high load, one power stroke generated a force spike with a peak value of 5-6 pN and a duration of 50 ms (k(-)-1), which were compatible with those of individual myosin heads deduced from the force fluctuations. As the load was reduced, the force of the power stroke decreased and the needle displacement increased. At near zero load, the mean size of single displacement spikes, i.e., the unitary steps caused by correctly oriented myosin, which were corrected for the stiffness of the needle-to-myosin linkage and the randomizing effect by the thermal vibration of the needle, was approximately 20 nm.     

The biochemical composition of the actomyosin network sets the magnitude of cellular traction forces

The regulation of cellular force production relies on the complex interplay between a well-conserved set of proteins of the cytoskeleton: actin, myosin, and α-actinin. Despite our deep knowledge of the role of these proteins in force production at the molecular scale, our understanding of the biochemical regulation of the magnitude of traction forces generated at the entire-cell level has been limited, notably by the technical challenge of measuring traction forces and the endogenous biochemical composition in the same cell. In this study, we developed an alternative Traction-Force Microscopy (TFM) assay, which used a combination of hydrogel micropatterning to define cell adhesion and shape and an intermediate fixation/immunolabeling step to characterize strain energies and the endogenous protein contents in single epithelial cells. Our results demonstrated that both the signal intensity and the area of the Focal Adhesion (FA)–associated protein vinculin showed a strong positive correlation with strain energy in mature FAs. Individual contents from actin filament and phospho-myosin displayed broader deviation in their linear relationship to strain energies. Instead, our quantitative analyzes demonstrated that their relative amount exhibited an optimum ratio of phospho-myosin to actin, allowing maximum force production by cells. By contrast, although no correlation was identified between individual α-actinin content and strain energy, the ratio of α-actinin to actin filaments was inversely related to strain energy. Hence, our results suggest that, in the cellular model studied, traction-force magnitude is dictated by the relative numbers of molecular motors and cross-linkers per actin filament, rather than the amounts of an individual component in the cytoskeletal network. This assay offers new perspectives to study in more detail the complex interplay between the endogenous biochemical composition of individual cells and the force they produce.     

Force-dependent detachment of kinesin-2 biases track switching at cytoskeletal filament intersections

Intracellular trafficking of organelles often involves cytoskeletal track switching. Organelles such as melanosomes are transported by multiple motors including kinesin-2, dynein, and myosin-V, which drive switching between microtubules and actin filaments during dispersion and aggregation. Here, we used optical trapping to determine the unitary and ensemble forces of kinesin-2, and to reconstitute cargo switching at cytoskeletal intersections in a minimal system with kinesin-2 and myosin-V motors bound to beads. Single kinesin-2 motors exerted forces up to ～5 pN, similar to kinesin-1. However, kinesin-2 motors were more likely to detach at submaximal forces, and the duration of force maintenance was short as compared to kinesin-1. In multimotor assays, force increased with kinesin-2 density but was not affected by the presence of myosin-V. In crossed filament assays, switching frequencies of motor-bound beads were dependent on the starting track. At equal average forces, beads tended to switch from microtubules onto overlying actin filaments consistent with the relatively faster detachment of kinesin-2 at near-maximal forces. Thus, in addition to relative force, switching probability at filament intersections is determined by the dynamics of motor-filament interaction, such as the quick detachment of kinesin-2 under load. This may enable fine-tuning of filament switching in the cell.     

A quantitative analysis of contractility in active cytoskeletal protein networks

Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of purified F-actin, muscle myosin II motors, and α-actinin cross-linkers. We show that contractility occurs above a threshold motor concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of ∼1 μN, or ∼100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the (local) activity of molecular motors and the cross-linker density and binding affinity.     

Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay

The force generated between actin and myosin acts predominantly along the direction of the actin filament, resulting in relative sliding of the thick and thin filaments in muscle or transport of myosin cargos along actin tracks. Previous studies have also detected lateral forces or torques that are generated between actin and myosin, but the origin and biological role of these sideways forces is not known. Here we adapt an actin gliding filament assay to measure the rotation of an actin filament about its axis (“twirling”) as it is translocated by myosin. We quantify the rotation by determining the orientation of sparsely incorporated rhodamine-labeled actin monomers, using polarized total internal reflection microscopy. To determine the handedness of the filament rotation, linear incident polarizations in between the standard s- and p-polarizations were generated, decreasing the ambiguity of our probe orientation measurement fourfold. We found that whole myosin II and myosin V both twirl actin with a relatively long (∼1 μm), left-handed pitch that is insensitive to myosin concentration, filament length, and filament velocity.     

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.     

Rap1 activation in collagen phagocytosis is dependent on nonmuscle myosin II-A

Rap1 enhances integrin-mediated adhesion but the link between Rap1 activation and integrin function in collagen phagocytosis is not defined. Mass spectrometry of Rap1 immunoprecipitates showed that the association of Rap1 with nonmuscle myosin heavy-chain II-A (NMHC II-A) was enhanced by cell attachment to collagen beads. Rap1 colocalized with NM II-A at collagen bead-binding sites. There was a transient increase in myosin light-chain phosphorylation after collagen-bead binding that was dependent on myosin light-chain kinase but not Rho kinase. Inhibition of myosin light-chain phosphorylation, but not myosin II-A motor activity inhibited collagen-bead binding and Rap activation. In vitro binding assays demonstrated binding of Rap1A to filamentous myosin rods, and in situ staining of permeabilized cells showed that NM II-A filaments colocalized with F-actin at collagen bead sites. Knockdown of NM II-A did not affect talin, actin, or β1-integrin targeting to collagen beads but targeting of Rap1 and vinculin to collagen was inhibited. Conversely, knockdown of Rap1 did not affect localization of NM II-A to beads. We conclude that MLC phosphorylation in response to initial collagen-bead binding promotes NM II-A filament assembly; binding of Rap1 to myosin filaments enables Rap1-dependent integrin activation and enhanced collagen phagocytosis.     

The Three Filament Model of Skeletal Muscle Stability and Force Production

Ever since the 1950s, muscle force regulation has been associated with the cross-bridge interactions between the two contractile filaments, actin and myosin. This gave rise to what is referred to as the "two-filament sarcomere model". This model does not predict eccentric muscle contractions well, produces instability of myosin alignment and force production on the descending limb of the force-length relationship, and cannot account for the vastly decreased ATP requirements of actively stretched muscles. Over the past decade, we and others, identified that a third myofilament, titin, plays an important role in stabilizing the sarcomere and the myosin filament. Here, we demonstrate additionally how titin is an active participant in muscle force regulation by changing its stiffness in an activation/force dependent manner and by binding to actin, thereby adjusting its free spring length. Therefore, we propose that skeletal muscle force regulation is based on a three filament model that includes titin, rather than a two filament model consisting only of actin and myosin filaments.     

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.     

Nonmuscle myosin IIA is required for lamellipodia formation through binding to WAVE2 and phosphatidylinositol 3,4,5-triphosphate

Investigation of the mechanism underlying cell membrane-targeted WAVE2 capture by phosphatidylinositol 3,4,5-triphosphate (PIP₃) through IRSp53 revealed an unidentified 250-kDa protein (p250) bound to PIP₃. We identified p250 as nonmuscle myosin IIA heavy chain (MYH9) by mass spectrometry and immunoblot analysis using anti-MYH9 antibody. After stimulation with insulin-like growth factor I (IGF-I), MYH9 colocalized with PIP₃ in lamellipodia at the leading edge of cells. Depletion of MYH9 expression by small interfering RNA (siRNA) and inhibition of myosin II activity by blebbistatin abrogated the formation of actin filament (F-actin) arcs and lamellipodia induced by IGF-I. MYH9 was constitutively associated with WAVE2, which was dependent on myosin II activity, and the MYH9-WAVE2 complex colocalized to PIP₃ at the leading edge after IGF-I stimulation. These results indicate that MYH9 is required for lamellipodia formation since it provides contractile forces and tension for the F-actin network to form convex arcs at the leading edge through constitutive binding to WAVE2 and colocalization with PIP₃ in response to IGF-I.     

Actin polymerization or myosin contraction: two ways to build up cortical tension for symmetry breaking

Cells use complex biochemical pathways to drive shape changes for polarization and movement. One of these pathways is the self-assembly of actin filaments and myosin motors that together produce the forces and tensions that drive cell shape changes. Whereas the role of actin and myosin motors in cell polarization is clear, the exact mechanism of how the cortex, a thin shell of actin that is underneath the plasma membrane, can drive cell shape changes is still an open question. Here, we address this issue using biomimetic systems: the actin cortex is reconstituted on liposome membranes, in an ‘outside geometry’. The actin shell is either grown from an activator of actin polymerization immobilized at the membrane by a biotin–streptavidin link, or built by simple adsorption of biotinylated actin filaments to the membrane, in the presence or absence of myosin motors. We show that tension in the actin network can be induced either by active actin polymerization on the membrane via the Arp2/3 complex or by myosin II filament pulling activity. Symmetry breaking and spontaneous polarization occur above a critical tension that opens up a crack in the actin shell. We show that this critical tension is reached by growing branched networks, nucleated by the Arp2/3 complex, in a concentration window of capping protein that limits actin filament growth and by a sufficient number of motors that pull on actin filaments. Our study provides the groundwork to understanding the physical mechanisms at work during polarization prior to cell shape modifications.