Emergent Structures in an Active Polar Fluid: Dynamics of Shape, Scattering, and Merger

Spatially localized defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar “actin” filaments and “myosin” motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile—we derive effective equations of motion for these “extended particles” and analyze their shape, kinetics, interactions, and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger. Our results are relevant for the dynamics of actomyosin-dense structures at the cell cortex, reconstituted actomyosin complexes, and 2D active colloidal gels.

Figure 1

(a) Typology of spatially compact single-defect structures in the $K$—$\zeta$ plane for a fixed concentration of filaments $c_0$, together with snapshots of the textures formed by the filament orientation $\mathbf{n}$—the heat map represents $c$ and the arrows represent $c\mathbf{n}$. All snapshots are equally sized. (b) Myosin (red) and actin (black) concentration profiles within a moving virtual aster, along directions (i) longitudinal and (ii) transverse to the direction of motion (dashed arrow). Insets: semilog scale.

Figure 2

(a) Left: several representative trajectories from the numerics with varying $v_0$ and fixed $b=5.5$ (merger is depicted by the $\times$). Right: The outcome as a function of impact parameter $b$ and self-advection $v_0$. (b) Left: The scattering geometry (green: $c$, arrows: $\mathbf{n}$, red: $\rho$). (c) The phase portrait of the scattering dynamical system, Eqs. (10), generated using the software pplane [41]. The black dot is the saddle point whose unstable separatrix (red dashed line) separates the merge region from the scattering region. Plotted in green is the stable separatrix. In blue are two example trajectories. The shaded region is the distance at which the merger will occur.

Figure 3

A schematic of the sequence of events in merger, namely, (a) approach of the clusters, followed by (b) neck formation, which (c) grows to form an elliptic domain that (d) relaxes exponentially to a radially symmetric domain. (e) Time evolution of the ratio of the neck width $a$ to the single domain radius $R$ (red diamonds) as well as the shape factor $\epsilon =d_{\text{maj}}/d_{\min }-1$ (black squares), where $d_{\text{maj}}$, $d_{\min }$ are the lengths of the major and minor axes of the ellipse enclosing the merging domain area. The blue line is an exponential fit.