Pattern-induced local symmetry breaking in active-matter systems

Abstract

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.

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

“…Stopping also plays a role in the accumulation of filaments in the presence of obstacles and, thus, in their polarity sorting. This allows breaking the microscopic nematic symmetry and is at the base of the formation of polar streams and vortices, which are different from those observed for driven actin filaments on hard substrates ( 7 – 9 ) and reminiscent of microtubules systems with slightly stronger steric interactions ( 10 – 12 , 57 ). Simulations of flexible filaments with volume exclusion ( 26 , 29 , 30 , 47 , 58 ) also result in similar vortexes and stream-like structures, as observed here.…”

“…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 ).…”

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization

“…This regime is followed by a wide range of collision angles i ∈ [50 • , 150 • ] where the final separation angle is almost constant around f 50 • , therefore corresponding to a partial alignment regime. Note that, unlike alignment mechanisms in other active systems with an intrinsic asymmetry [41], here the alignment seems bounded: it kicks in only at high-enough angle, and aligns to within a minimum angle. Note also that this partial alignment tends to disappear for smaller values of M − M c where the chemical cloud asymmetry is weaker; in this case the collision remains closer to specular throughout the first two regimes.…”

Active nematic order and dynamic lane formation of microtubules driven by membrane-bound diffusing motors

“…At high enough concentrations, global nematic order can emerge in the MT or actin layer, purely due to lateral steric interactions and activity, creating an active nematic system of self-propelled filaments (23)(24)(25). These experimental results have recently been explored theoretically with agent-based simulations producing polar and apolar nematics and motile polar clusters (26)(27)(28)(29).…”