Emergence of periodic circumferential actin cables from the anisotropic fusion of actin nanoclusters during tubulogenesis.

The periodic circumferential cytoskeleton supports various tubular tissues. Radial expansion of the tube lumen causes anisotropic tensile stress, which can be exploited as a geometric cue. However, the molecular machinery linking anisotropy to robust circumferential patterning is poorly understood. Here, we aim to reveal the emergent process of circumferential actin cable formation in a Drosophila tracheal tube. During luminal expansion, sporadic actin nanoclusters emerge and exhibit circumferentially biased motion and fusion. RNAi screening reveals the formin family protein, DAAM, as an essential component responding to tissue anisotropy, and non-muscle myosin II as a component required for nanocluster fusion. An agent-based model simulation suggests that crosslinkers play a crucial role in nanocluster formation and cluster-to-cable transition occurs in response to mechanical anisotropy. Altogether, we propose that an actin nanocluster is an organizational unit that responds to stress in the cortical membrane and builds a higher-order cable structure.

Mechanochemical subcellular-element model of crawling cells.

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Swinging motion of active deformable particles in Poiseuille flow.

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Tunable dynamic response of magnetic gels: impact of structural properties and magnetic fields.

Ferrogels and magnetic elastomers feature mechanical properties that can be reversibly tuned from outside through magnetic fields. Here we concentrate on the question of how their dynamic response can be adjusted. The influence of three factors on the dynamic behavior is demonstrated using appropriate minimal models: first, the orientational memory imprinted into one class of the materials during their synthesis; second, the structural arrangement of the magnetic particles in the materials; and third, the strength of an external magnetic field. To illustrate the latter point, structural data are extracted from a real experimental sample and analyzed. Understanding how internal structural properties and external influences impact the dominant dynamical properties helps to design materials that optimize the requested behavior.

Deformable microswimmer in a swirl: capturing and scattering dynamics.

Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.

Dynamics of a deformable active particle under shear flow.

The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, we propose coupled nonlinear dynamical equations for the particle position, velocity, deformation, and rotation. In our model, both, passive rotations induced by the shear flow as well as active spinning motions, are taken into account. Our equations reduce to known models in the two limits of vanishing shear flow and vanishing particle deformability. For varied shear rate and particle propulsion speed, we solve the equations numerically in two spatial dimensions and obtain a manifold of different dynamical modes including active straight motion, periodic motions, motions on undulated cycloids, winding motions, as well as quasi-periodic and chaotic motions induced at high shear rates. The types of motion are distinguished by different characteristics in the real-space trajectories and in the dynamical behavior of the particle orientation and its deformation. Our predictions can be verified in experiments on self-propelled droplets exposed to a linear shear flow.

Oscillatory motions of an active deformable particle.

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of n- and 2n-mode deformations for n=1, and those for n=2. We show that an oscillatory bifurcation occurs for n=2, which corresponds mathematically to the bifurcation for n=1 where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

Spinning motion of a deformable self-propelled particle in two dimensions.

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

Breathing instability versus drift instability in a two-component reaction-diffusion system.

We investigate the stability of an excited domain in a two-component reaction-diffusion system in two dimensions and correct the previous results obtained by one of the authors [L. M. Pismen, Patterns and Interfaces in Dissipative Dynamics (Springer, Berlin, 2006); L. M. Pismen, Phys. Rev. Lett. 86, 548 (2001)].