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.

Controlling Physical and Biochemical Parameters of Actin Nucleation Using a Patterned Model Lipid Membrane.

Self-assembly of nanoscale actin cytoskeletal proteins into filamentous networks requires organizing actin nucleation areas on the plasma membrane through recruiting actin nucleators and nucleation-promoting factors (NPFs) to the areas. To investigate impacts of the nucleation geometry on actin network assembly, we localized NPF or nucleator on defined micropatterns of laterally mobile lipid bilayers confined in a framework of a polymerized lipid bilayer. We demonstrated that actin network assembly in purified protein mixtures was confined on NPF- or nucleator-localized fluid bilayers. By controlling the shape and size of nucleation areas as well as the density and types of localized NPFs and nucleators, we showed that these parameters regulate actin network architectures. Actin network assembly in Xenopus egg extracts was also spatially controlled by patterning bilayers containing phosphatidylinositol 4,5-bisphoshate (PI(4,5)P2), an essential lipid signaling mediator. Therefore, the system provides a promising platform to investigate the physical and biochemical principles for actin network assembly.

Microscopic Temperature Control Reveals Cooperative Regulation of Actin-Myosin Interaction by Drebrin E.

Drebrin E is a regulatory protein of intracellular force produced by actomyosin complexes, that is, myosin molecular motors interacting with actin filaments. The expression level of drebrin E in nerve cells decreases as the animal grows, suggesting its pivotal but unclarified role in neuronal development. Here, by applying the microscopic heat pulse method to actomyosin motility assay, the regulatory mechanism is examined from the room temperature up to 37 °C without a thermal denaturing of proteins. We show that the inhibition of actomyosin motility by drebrin E is eliminated immediately and reversibly during heating and depends on drebrin E concentration. The direct observation of quantum dot-labeled drebrin E implies its stable binding to actin filaments during the heat-induced sliding. Our results suggest that drebrin E allosterically modifies the actin filament structure to regulate cooperatively the actomyosin activity at the maintained in vivo body temperature.

Spatial confinement of active microtubule networks induces large-scale rotational cytoplasmic flow.

Collective behaviors of motile units through hydrodynamic interactions induce directed fluid flow on a larger length scale than individual units. In cells, active cytoskeletal systems composed of polar filaments and molecular motors drive fluid flow, a process known as cytoplasmic streaming. The motor-driven elongation of microtubule bundles generates turbulent-like flow in purified systems; however, it remains unclear whether and how microtubule bundles induce large-scale directed flow like the cytoplasmic streaming observed in cells. Here, we adopted Xenopus egg extracts as a model system of the cytoplasm and found that microtubule bundle elongation induces directed flow for which the length scale and timescale depend on the existence of geometrical constraints. At the lower activity of dynein, kinesins bundle and slide microtubules, organizing extensile microtubule bundles. In bulk extracts, the extensile bundles connected with each other and formed a random network, and vortex flows with a length scale comparable to the bundle length continually emerged and persisted for 1 min at multiple places. When the extracts were encapsulated in droplets, the extensile bundles pushed the droplet boundary. This pushing force initiated symmetry breaking of the randomly oriented bundle network, leading to bundles aligning into a rotating vortex structure. This vortex induced rotational cytoplasmic flows on the length scale and timescale that were 10- to 100-fold longer than the vortex flows emerging in bulk extracts. Our results suggest that microtubule systems use not only hydrodynamic interactions but also mechanical interactions to induce large-scale temporally stable cytoplasmic flow.

Processive Nanostepping of Formin mDia1 Loosely Coupled with Actin Polymerization.

Formins are actin-binding proteins that construct nanoscale machinery with the growing barbed end of actin filaments and serve as key regulators of actin polymerization and depolymerization. To maintain the regulation of actin dynamics, formins have been proposed to processively move at every association or dissociation of a single actin molecule toward newly formed barbed ends. However, the current models for the motile mechanisms were established without direct observation of the elementary processes of this movement. Here, using optical tweezers, we demonstrate that formin mDia1 moves stepwise, observed at a nanometer spatial resolution. The movement was composed of forward and backward steps with unitary step sizes of 2.8 and -2.4 nm, respectively, which nearly equaled the actin subunit length (∼2.7 nm), consistent with the generally accepted models. However, in addition to steps equivalent to the length of a single actin subunit, those equivalent to the length of two or three subunits were frequently observed. Our findings suggest that the coupling between mDia1 stepping and actin polymerization is not tight but loose, which may be achieved by the multiple binding states of mDia1, providing insights into the synergistic functions of biomolecules for the efficient construction and regulation of nanofilaments.

Biphasic Effect of Profilin Impacts the Formin mDia1 Force-Sensing Mechanism in Actin Polymerization.

Formins are force-sensing proteins that regulate actin polymerization dynamics. Here, we applied stretching tension to individual actin filaments under the regulation of formin mDia1 to investigate the mechanical responses in actin polymerization dynamics. We found that the elongation of an actin filament was accelerated to a greater degree by stretching tension for ADP-G-actin than that for ATP-G-actin. An apparent decrease in the critical concentration of G-actin was observed, especially in ADP-G-actin. These results on two types of G-actin were reproduced by a simple kinetic model, assuming the rapid equilibrium between pre- and posttranslocated states of the formin homology domain two dimer. In addition, profilin concentration dramatically altered the force-dependent acceleration of actin filament elongation, which ranged from twofold to an all-or-none response. Even under conditions in which actin depolymerization occurred, applications of a several-piconewton stretching tension triggered rapid actin filament elongation. This extremely high force-sensing mechanism of mDia1 and profilin could be explained by the force-dependent coordination of the biphasic effect of profilin; i.e., an acceleration effect masked by a depolymerization effect became dominant under stretching tension, negating the latter to rapidly enhance the elongation rate. Our findings demonstrate that the biphasic effect of profilin is controlled by mechanical force, thus expanding the function of mDia1 as a mechanosensitive regulator of actin polymerization.

Directional bleb formation in spherical cells under temperature gradient.

Living cells sense absolute temperature and temporal changes in temperature using biological thermosensors such as ion channels. Here, we reveal, to our knowledge, a novel mechanism of sensing spatial temperature gradients within single cells. Spherical mitotic cells form directional membrane extensions (polar blebs) under sharp temperature gradients (≥∼0.065°C µm(-1); 1.3°C temperature difference within a cell), which are created by local heating with a focused 1455-nm laser beam under an optical microscope. On the other hand, multiple nondirectional blebs are formed under gradual temperature gradients or uniform heating. During heating, the distribution of actomyosin complexes becomes inhomogeneous due to a break in the symmetry of its contractile force, highlighting the role of the actomyosin complex as a sensor of local temperature gradients.

Quantitative analysis of the lamellarity of giant liposomes prepared by the inverted emulsion method.

The inverted emulsion method is used to prepare giant liposomes by pushing water-in-oil droplets through the oil/water interface into an aqueous medium. Due to the high encapsulation efficiency of proteins under physiological conditions and the simplicity of the protocol, it has been widely used to prepare various cell models. However, the lamellarity of liposomes prepared by this method has not been evaluated quantitatively. Here, we prepared liposomes that were partially stained with a fluorescent dye, and analyzed their fluorescence intensity under an epifluorescence microscope. The fluorescence intensities of the membranes of individual liposomes were plotted against their diameter. The plots showed discrete distributions, which were classified into several groups. The group with the lowest fluorescence intensity was determined to be unilamellar by monitoring the exchangeability of the inner and the outer solutions of the liposomes in the presence of the pore-forming toxin α-hemolysin. Increasing the lipid concentration dissolved in oil increased the number of liposomes ∼100 times. However, almost all the liposomes were unilamellar even at saturating lipid concentrations. We also investigated the effects of lipid composition and liposome content, such as highly concentrated actin filaments and Xenopus egg extracts, on the lamellarity of the liposomes. Remarkably, over 90% of the liposomes were unilamellar under all conditions examined. We conclude that the inverted emulsion method can be used to efficiently prepare giant unilamellar liposomes and is useful for designing cell models.

Go-and-Back method: effective estimation of the hidden motion of proteins from single-molecule time series.

We present an effective method for estimating the motion of proteins from the motion of attached probe particles in single-molecule experiments. The framework naturally incorporates Langevin dynamics to compute the most probable trajectory of the protein. By using a perturbation expansion technique, we achieve computational costs more than 3 orders of magnitude smaller than the conventional gradient descent method without loss of simplicity in the computation algorithm. We present illustrative applications of the method using simple models of single-molecule experiments and confirm that the proposed method yields reasonable and stable estimates of the hidden motion in a highly efficient manner.

Bayesian estimation of the internal structure of proteins from single-molecule measurements.

In single-molecule protein experiments, the observable variables are restricted within a small fraction of the entire degrees of freedom. Therefore, to investigate the physical nature of proteins in detail, we always need to estimate the hidden internal structure referring only to the accessible degrees of freedom. We formulate this problem on the basis of Bayesian inference, which can be applied to various complex systems. In the ideal case, we find that in general the framework actually works. Although careful numerical studies confirm that our method outperforms the conventional method by up to two orders of magnitude, we find a striking phenomenon: a loss-of-precision transition occurs abruptly when the design of the observation system is inappropriate. The basic features of the proposed method are illustrated using a simple but nontrivial model.

Tug-of-war between actomyosin-driven antagonistic forces determines the positioning symmetry in cell-sized confinement.

Symmetric or asymmetric positioning of intracellular structures including the nucleus and mitotic spindle steers various biological processes such as cell migration, division, and embryogenesis. In typical animal cells, both a sparse actomyosin meshwork in the cytoplasm and a dense actomyosin cortex underneath the cell membrane participate in the intracellular positioning. However, it remains unclear how these coexisting actomyosin structures regulate the positioning symmetry. To reveal the potential mechanism, we construct an in vitro model composed of cytoplasmic extracts and nucleus-like clusters confined in droplets. Here we find that periodic centripetal actomyosin waves contract from the droplet boundary push clusters to the center in large droplets, while network percolation of bulk actomyosin pulls clusters to the edge in small droplets. An active gel model quantitatively reproduces molecular perturbation experiments, which reveals that the tug-of-war between two distinct actomyosin networks with different maturation time-scales determines the positioning symmetry.

Cell-sized spherical confinement induces the spontaneous formation of contractile actomyosin rings in vitro.

During cell division, many animal cells transform into a spherical shape and assemble a contractile ring composed of actin filaments and myosin motors at the equator to separate the cell body into two. Although actomyosin regulatory proteins are spatio-temporally controlled during cytokinesis, the direct contribution of cell shape and actomyosin activity to the contractile ring assembly remains unclear. Here, we demonstrated in vitro that actin polymerization inside cell-sized spherical droplets induced the spontaneous formation of single ring-shaped actin bundles in the presence of bundling factors. Despite a lack of spatial regulatory signals, the rings always assembled at the equator to minimize the elastic energy of the bundles. Myosin promoted ring formation by the dynamic remodelling of actin networks, and an increase in the effective concentration of myosin triggered ring contraction. These results will help us understand how animal cells coordinate cell shape and actomyosin activities to direct cytokinesis.