Abstract
Surface-bound molecular motors can drive the collective motion of cytoskeletal filaments in the form of nematic bands and polar flocks in reconstituted gliding assays. Although these "swarming transitions" are an emergent property of active filament collisions, they can be controlled and guided by tuning the surface chemistry or topography of the substrate. To date, the impact of surface topography on collective motion in active nematics is only partially understood, with most experimental studies focusing on the escape of a single filament from etched channels. Since the late 1990s, significant progress has been made to utilize the nonequilibrium properties of active filaments and create a range of functional nanodevices relevant to biosensing and parallel computation; however, the complexity of these swarming transitions presents a challenge when attempting to increase filament surface concentrations. In this work, we etch shallow, linear trenches into glass substrates to induce the formation of swarming nematic bands and investigate the mechanisms by which surface topography regulates the two-dimensional (2D) collective motion of driven filamentous actin (F-actin). We demonstrate that nematic swarms only appear at intermediate trench spacings and vanish if the trenches are made too narrow, wide, or tortuous. To rationalize these results, we simulate the F-actin as self-propelled, semiflexible chains subject to a soft, spatially modulated potential that encodes the energetic cost of bending a filament along the edge of a trench. In our model, we hypothesize that an individual filament experiences a penalty when its projected end-to-end distance is smaller than the trench spacing ("bending and turning"). However, chains that span the channel width glide above the trenches in a force- and torque-free manner ("crowd-surfing"). Our simulations demonstrate that collections of filaments form nematic bands only at intermediate trench spacings, consistent with our experimental findings.