Tuning mechanical properties of an elastic network by controlling the filament length and shape*

The connection between the macroscopic properties of an elastic network and the structure of its constituent filaments is not fully understood. We assemble a colloidal gel comprised of bacterial flagella, a rigid biological colloid, to explore this relationship. The length and shape of flagella are tunable. By controlling the number of constituent protein, we can assemble flagella of arbitrary length. By modifying the protein structure with point mutations, we can control the flagella's shape, choosing between several discrete structures ranging from a straight rod to a helix. Cross-linking a dense suspension of flagella generates a soft gel whose macroscopic rheology is directly informed by the length and shape of its constituent filaments. We quantify this relationship by measuring the elastic properties of these gels in a rheometer. Helical filaments generate a soft elastic gel. Straight filaments, contrastingly, generate an order-of-magnitude more rigid gel. We attribute this difference to the ability of helical flagella to entangle with neighbors, thereby creating a network that distributes stress in a distinct manner compared to a gel consisting of straight flagella. This relationship between the properties of individual colloids and the bulk properties of the cross-linked network provides a new means for designing novel gels with specified rheological properties.