Pattern formation and polarity sorting of driven actin filaments on lipid membranes

Collective motion of active matter is ubiquitously observed, ranging from propelled colloids to flocks of bird, and often features the formation of complex structures composed of agents moving coherently. However, it remains extremely challenging to predict emergent patterns from the binary interaction between agents, especially as only a limited number of interaction regimes have been experimentally observed so far. Here, we introduce an actin gliding assay coupled to a supported lipid bilayer, whose fluidity forces the interaction between self-propelled filaments to be dominated by steric repulsion. This results in filaments stopping upon binary collisions and eventually aligning nematically. Such a binary interaction rule results at high densities in the emergence of dynamic collectively moving structures including clusters, vortices, and streams of filaments. Despite the microscopic interaction having a nematic symmetry, the emergent structures are found to be polar, with filaments collectively moving in the same direction. This is due to polar biases introduced by the stopping upon collision, both on the individual filaments scale as well as on the scale of collective structures. In this context, positive half-charged topological defects turn out to be a most efficient trapping and polarity sorting conformation.

Collective motion of active matter is ubiquitous, with observations ranging from flocks of birds (1) and schools of fish (2) to propelled colloids (3). The interactions between agents in such systems lead to the formation of complex structures including clusters, swirls, or lanes of agents moving coherently (4). The structure of the emerging patterns strongly depends on both the agents’ shape and their velocity alignment mechanism. A particular case is that of elongated microscopic particles that translate along their major axis in a quasi-two-dimensional environment and only interact upon collision (5, 6). In the context of cytoskeletal systems, gliding actin filaments or microtubules propelled by molecular motors are found to be able to readily crawl over each other and only retain a weak level of alignment upon binary collisions, which eventually leads at high densities to a diverse set of patterns (7). Such resulting patterns are found to be strongly dependent on this weak microscopic alignment interaction, and therefore, even slightly tuning it causes the system to switch between polar and nematic phases, separated by a coexistence regime (8, 9). Observed structures in cytoskeletal systems with weak to moderate interactions include nematic lanes, polar waves, and vortices (10–12). Conversely, pattern formation in systems of elongated bacteria or granular matter is often based on hard interactions with a strong steric component (13–18). In this repulsion-dominated regime, particles are unable to crawl over each other and must stop upon collision. In the limiting case of spherical self-propelled particles, this kind of steric interaction can lead to a stable phase separation between stuck and moving particles, the so-called motility induced phase separation (MIPS) (19). On the other hand, in the case of elongated particles, steric effects can still act as velocity aligning mechanisms. As orientation mismatches are unstable, particles end up aligning and this leads to flocking behavior rather than to phase separation (5, 20–25). This latter case, in which strong steric constraints dominate binary interactions but alignment is still present, is poorly understood, and how modeling has to be extended to account for the emergent collective behavior of elongated, flexible agents with volume exclusion also remains still under debate (26–30). This is partly due to the lack of microscopic experimental systems allowing to explore this regime. Semiflexible cytoskeletal filaments would be the best candidate, but their volume exclusion is usually too weak. However, having them propelled by motors immobilized on a fluid membrane would be a promising route to bridge this experimental gap (31).Here, we enforce a steric repulsion-dominated interaction, leading to alignment between actin filaments by coupling myosin motors to a fluid-supported lipid bilayer. Because of the slippage of the motors on the membrane, the force propelling the filaments is too weak to enable filaments to crawl over each other and thus effectively implements a repulsion-dominated regime, with filaments stopping upon collisions. Eventually, however, because of the thermal fluctuations of their tips, filaments can align and resume motion. The experimental realization of such a microscopic binary interaction, based on volume exclusion, enables us to observe and quantify the resulting pattern formation process in a system of active semiflexible filaments. We then first characterize the interaction at the single filament scale, showing that it leads to nematic alignment. As the filaments’ density is increased, patterns of collective motion emerge, ranging from clusters to thick streams and vortices. Despite the nematic collision rule, we find the emerging structures to be locally polar. The repulsion-dominated interaction indeed introduces a polar bias not only due to the tendency of active filaments or clusters to keep moving together after a polar collision but also by forcing filaments with similar orientation to stop and accumulate when encountering an obstacle. In particular, at high densities, such an interaction leads to the formation of transient local +1/2 topological defects, which act as wedges and, therefore, effectively trap and polarity-sort motile filaments. We interpret this trapping mechanism as an analog of MIPS for elongated self-propelled particles.