Shape control and compartmentalization in active colloidal cells

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core–shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble–crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non–momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier–Stokes equation.Active matter describes particulate systems with the characteristic that each “particle” (agent) converts energy into motion (1, 2). Active matter covers a range of length scales that include molecular motors in the cytoskeleton (3–5), swimming bacteria (6–8), driven colloids (9, 10), flocks of birds and fish (11–14), and people and vehicles in motion (15). Over the last decade, studies of active matter have demonstrated behavior not seen in equilibrium systems, including giant number fluctuations (16, 17), emergent attraction and superdiffusion (18–20), clustering (21, 22), swarming (23–27), and self-assembled motifs (28, 29). These systems provide interesting theoretical and engineering challenges as well as opportunities to explore and target novel behaviors that proceed outside of thermodynamic equilibrium.Of particular interest are systems found in nature or inspired by natural phenomena. Biological systems usually operate in confined regions of space––think of intracellular space, interfaces and membranes, and the crowding of cells near surfaces. The role of hydrodynamics in confinement has been studied for biological swimmers, such as bacteria and sperm, showing accumulation at the walls (30–32) and upstream swimming along surfaces (33) or in a spiral vortex (34–36). Attraction to walls has also been reported in the absence of hydrodynamics for disks (37, 38), spheres (39), and dumbbell swimmers (40). But, whereas these examples study the behavior under the influence of hard boundaries, biological swimmers typically interact with soft boundaries, such as membranes and biofilms. Another design variable is the possibility that the boundary itself is active, as in the surface of a bacterium covered with flagellae or, as demonstrated recently, active nematic vesicles (41).In this work, we propose and investigate an active matter system under flexible, active confinement. We call this system an active colloidal cell. Our realization of an active colloidal cell consists of independent particles, called spinners (42), that translate and rotate in two dimensions and are constrained within a finite area by a flexible boundary that is also built from spinners. Each spinner has a gear-like geometry, which consists of a large central disk and four smaller satellite disks (Fig. 1A). Similar gear-shaped rigid aggregates of self-propelled particles have been formed experimentally (43). Spinners are freely mobile in the cell interior. On the cellular boundary, spinners are connected to one another by a flexible chain of beads attached by finitely extensible springs. Both the interior and the boundary spinners can be subject to a clockwise or counterclockwise driving torque, which makes them active.Open in a separate windowFig. 1.Schematic of the confined spinner models. (A) The active colloidal cell is made up of spinners driven counterclockwise (blue) or clockwise (yellow). Boundary spinners are connected by a flexible bead–spring chain (gray). We compare the behavior of a continuum model (B) to a microscopic model (C). The compartmentalization of interior spinners is visualized by coloring the Voronoi tessellation in the microscopic model.Rotationally driven particles can synchronize and self-organize (44, 45) in the absence (42) and in the presence (46–48) of hydrodynamic interactions. Crystallization has recently been observed in rotating magnetic Janus colloids (49) and fast-moving bacteria (50). Spinners in the interior of the cell resemble molecular motors that push themselves forward on their neighbors and, thus, sustain convective dynamics. The effect of the boundary spinners is similar to that found in the cilia of living tissues, which stir nearby fluid. Our results demonstrate that a natural consequence of the activity present in the colloidal cell is control over both its external shape and internal structure. We report compartmentalization into regions of clockwise and counterclockwise spinners––a behavior which is affected by, and can be controlled via, properties of the enclosing boundary configuration as previously suggested (51). Transitions in the internal structure of the colloidal cell occur as its radius increases, and as the composition of the interior spinners and the patterning of the boundary are varied.A previous study of spinners in bulk (42) showed phase separation into clockwise- and counterclockwise domains. Cates and collaborators (6, 52, 53) have suggested that phase separation is a generic consequence of local energy input in an otherwise equilibrium system. Here and in the study of bulk spinners we demonstrate phase separation due to local rotational, rather than translational, energy input. We obtain our results using a particulate, microscopic model (Fig. 1C) as well as a continuum model (Fig. 1B). This allows us to conclude that the phenomena we observe are robust with respect to details of the model.In this study we use two models to study the behavior of an active colloidal cell, illustrated in Fig. 1. The microscopic model describes spinners as individual particles and simulates their motion using Langevin dynamics. It resolves the behavior of individual spinners but does not include hydrodynamic effects. In contrast, the continuum model describes the spinner system as a viscous binary fluid, which is governed by an incompressible Navier–Stokes equation coupled to a Cahn–Hilliard equation. Both models are described in detail in Materials and Methods below. Note that the microscopic model was introduced in earlier work using Brownian dynamics (42) and is extended here to include boundaries.