Geometric trade-off between contractile force and viscous drag determines the actomyosin-based motility of a cell-sized droplet.

Cell migration in confined environments is fundamental for diverse biological processes from cancer invasion to leukocyte trafficking. The cell body is propelled by the contractile force of actomyosin networks transmitted from the cell membrane to the external substrates. However, physical determinants of actomyosin-based migration capacity in confined environments are not fully understood. Here, we develop an in vitro migratory cell model, where cytoplasmic actomyosin networks are encapsulated into droplets surrounded by a lipid monolayer membrane. We find that the droplet can move when the actomyosin networks are bound to the membrane, in which the physical interaction between the contracting actomyosin networks and the membrane generates a propulsive force. The droplet moves faster when it has a larger contact area with the substrates, while narrower confinement reduces the migration speed. By combining experimental observations and active gel theory, we propose a mechanism where the balance between sliding friction force, which is a reaction force of the contractile force, and viscous drag determines the migration speed, providing a physical basis of actomyosin-based motility in confined environments.

Mechanically Distinct Microtubule Arrays Determine the Length and Force Response of the Meiotic Spindle.

The microtubule-based spindle is subjected to various mechanical forces during cell division. How the structure generates and responds to forces while maintaining overall integrity is unknown because we have a poor understanding of the relationship between filament architecture and mechanics. Here, to fill this gap, we combine microneedle-based quantitative micromanipulation with high-resolution imaging, simultaneously analyzing forces and local filament motility in the Xenopus meiotic spindle. We find that microtubules exhibit a compliant, fluid-like mechanical response at the middle of the spindle half, being distinct from those near the pole and the equator. A force altering spindle length induces filament sliding at this compliant array, where parallel microtubules predominate, without influencing equatorial antiparallel filament dynamics. Molecular perturbations suggest that kinesin-5 and dynein contribute to the spindle's local mechanical difference. Together, our data establish a link between spindle architecture and mechanics and uncover the mechanical design of this essential cytoskeletal assembly.

Analyzing the micromechanics of the cell division apparatus.

Cell division involves mechanical processes, such as chromosome transport and centrosome separation. Quantitative micromanipulation-based approaches have been central to dissecting the forces driving these processes. We highlight two biophysical assays that can be employed for such analyses. First, an in vitro "mini-spindle" assay is described that can be used to examine the collective mechanics of mitotic motor proteins cross-linking two microtubules. In the spindle, motor proteins (e.g., kinesin-5, kinesin-14, and dynein) can localize to overlapping microtubules that slide relative to each other, work as an ensemble, and equilibrate between cytoplasm and the microtubules. The "mini-spindle" assay can recapitulate these features and allows measurements of forces generated between adjacent microtubules and their dependence on filament orientation, sliding speed, overlap length, and motor protein density. Second, we describe a force-calibrated microneedle-based "whole-spindle" micromechanics assay. Microneedle-based micromanipulation can be a useful technique to examine cellular scale mechanics, but its use has been restricted by the difficulty in getting probes to penetrate the plasma membrane without disrupting cell physiology. As detailed here, the use of cell-free extracts prepared from metaphase-arrested Xenopus eggs can address this limitation. These micromanipulation studies also benefit from the use of frozen stocks of Xenopus egg extract. Together, these approaches can be used to decipher how micromechanics and biochemical activities ensure successful cell division.

Insights into the micromechanical properties of the metaphase spindle.

The microtubule-based metaphase spindle is subjected to forces that act in diverse orientations and over a wide range of timescales. Currently, we cannot explain how this dynamic structure generates and responds to forces while maintaining overall stability, as we have a poor understanding of its micromechanical properties. Here, we combine the use of force-calibrated needles, high-resolution microscopy, and biochemical perturbations to analyze the vertebrate metaphase spindle's timescale- and orientation-dependent viscoelastic properties. We find that spindle viscosity depends on microtubule crosslinking and density. Spindle elasticity can be linked to kinetochore and nonkinetochore microtubule rigidity, and also to spindle pole organization by kinesin-5 and dynein. These data suggest a quantitative model for the micromechanics of this cytoskeletal architecture and provide insight into how structural and functional stability is maintained in the face of forces, such as those that control spindle size and position, and can result from deformations associated with chromosome movement.

Regulatory mechanism of length-dependent activation in skinned porcine ventricular muscle: role of thin filament cooperative activation in the Frank-Starling relation.

Cardiac sarcomeres produce greater active force in response to stretch, forming the basis of the Frank-Starling mechanism of the heart. The purpose of this study was to provide the systematic understanding of length-dependent activation by investigating experimentally and mathematically how the thin filament "on-off" switching mechanism is involved in its regulation. Porcine left ventricular muscles were skinned, and force measurements were performed at short (1.9 µm) and long (2.3 µm) sarcomere lengths. We found that 3 mM MgADP increased Ca(2+) sensitivity of force and the rate of rise of active force, consistent with the increase in thin filament cooperative activation. MgADP attenuated length-dependent activation with and without thin filament reconstitution with the fast skeletal troponin complex (sTn). Conversely, 20 mM of inorganic phosphate (Pi) decreased Ca(2+) sensitivity of force and the rate of rise of active force, consistent with the decrease in thin filament cooperative activation. Pi enhanced length-dependent activation with and without sTn reconstitution. Linear regression analysis revealed that the magnitude of length-dependent activation was inversely correlated with the rate of rise of active force. These results were quantitatively simulated by a model that incorporates the Ca(2+)-dependent on-off switching of the thin filament state and interfilament lattice spacing modulation. Our model analysis revealed that the cooperativity of the thin filament on-off switching, but not the Ca(2+)-binding ability, determines the magnitude of the Frank-Starling effect. These findings demonstrate that the Frank-Starling relation is strongly influenced by thin filament cooperative activation.

Nonlinear force-length relationship in the ADP-induced contraction of skeletal myofibrils.

The regulatory mechanism of sarcomeric activity has not been fully clarified yet because of its complex and cooperative nature, which involves both Ca(2+) and cross-bridge binding to the thin filament. To reveal the mechanism of regulation mediated by the cross-bridges, separately from the effect of Ca(2+), we investigated the force-sarcomere length (SL) relationship in rabbit skeletal myofibrils (a single myofibril or a thin bundle) at SL > 2.2 microm in the absence of Ca(2+) at various levels of activation by exogenous MgADP (4-20 mM) in the presence of 1 mM MgATP. The individual SLs were measured by phase-contrast microscopy to confirm the homogeneity of the striation pattern of sarcomeres during activation. We found that at partial activation with 4-8 mM MgADP, the developed force nonlinearly depended on the length of overlap between the thick and the thin filaments; that is, contrary to the maximal activation, the maximal active force was generated at shorter overlap. Besides, the active force became larger, whereas this nonlinearity tended to weaken, with either an increase in [MgADP] or the lateral osmotic compression of the myofilament lattice induced by the addition of a macromolecular compound, dextran T-500. The model analysis, which takes into account the [MgADP]- and the lattice-spacing-dependent probability of cross-bridge formation, was successfully applied to account for the force-SL relationship observed at partial activation. These results strongly suggest that the cross-bridge works as a cooperative activator, the function of which is highly sensitive to as little as

Regulation of muscle contraction by Ca2+ and ADP: focusing on the auto-oscillation (SPOC).

A molecular motor in striated muscle, myosin II, is a non-processive motor that is unable to perform physiological functions as a single molecule and acts as an assembly of molecules. It is widely accepted that a myosin II motor is an independent force generator; the force generated at a steady state is usually considered to be a simple sum of those generated by each motor. This is the case at full activation (pCa < 5 in the presence of MgATP); however, we found that the myosin II motors show cooperative functions, i.e., non-linear auto-oscillation, named SPOC (SPontaneous Oscillatory Contraction), when the activation level is intermediate between those of contraction and relaxation (that is, at the intermediate level of pCa, 5-6, for cardiac muscle, or at the coexistence of MgATP, MgADP and inorganic phosphate (Pi) at higher pCa (> 7) for both skeletal and cardiac muscles). Here, we summarize the characteristics of SPOC phenomena, especially focusing on the physiological significance of SPOC in cardiac muscle. We propose a new concept that the auto-oscillatory property, which is inherent to the contractile system of cardiac muscle, underlies the molecular mechanism of heartbeat. Additionally, we briefly describe the dynamic properties of the thin filaments, i.e., the Ca(2+)-dependent flexibility change of the thin filaments, which may be the basis for the SPOC phenomena. We also describe a newly developed experimental system named "bio-nanomuscle," in which tension is asserted on a single reconstituted thin filament by interacting with crossbridges in the A-band composed of the thick filament lattice. This newly devised hybrid system is expected to fill the gap between the single-molecule level and the muscle system.