Probing Viscoelasticity of a Coiled Flagella System

The flow properties of a material are determined by the behavior of its microscopic constituents, whose shape dictates the entanglements that constrain the available modes of diffusion. More confined particles take longer to escape their cages, thereby generating a material that resists deformations on longer timescales. We aim to quantify the impact of filament geometry on bulk material properties using bacterial flagella, a micron-sized biological filament. Flagella assume several discrete helical conformational states. We focus on coiled flagella, the most flexible and tightly-wound helix. Microscopically, we observe that shorter coils form arcs that undergo an effective one-dimensional random walk about the long axis of the helix. Longer coils, on the other hand, are almost entirely caged on experimental time scales. Entangled suspensions of coiled flagella are elastic, indicating that strain response is determined by the system’s most heavily-confined filaments. Understanding the connection between the microscopic and macroscopic regime allows for the design of exotic materials with tunable viscoelastic properties.