Hierarchical chirality of biofilament induced by its chiral microstructure

Abstract

Biological filaments with chirality are ubiquitous in biology, but the mechanism behind the chiral growth of these filaments is still unclear. To understand the formation mechanism of these chiral filaments, a hierarchical chiral model for plant tendrils is established in this work based on the Cosserat beam theory and the constitutive equation of chiral materials, which can be used to describe the deformation of chiral biological filaments. Based on this model, the bend–twist coupling chirality is considered, the chirality transfer of plant tendrils from the micro to the macro scale is derived, and the variation in the chirality coefficients with the axial strain is obtained. By introducing a pre-strain and a pre-twist deformation, a theoretical explanation for the swelling and deswelling of plant tendrils is provided as an example. Finally, based on the shooting method, the spatial configuration of plant tendrils under the action of an external force at the end load is obtained. It is found that plant tendrils can achieve regular chiral morphologies or even hierarchical chiral morphologies by adjusting their internal stresses and elastic properties. During this process, the bend–twist coupling is more critical than the stretch–twist coupling. In the presence of external loads, the chiral perversion of plant tendrils can be realized by adjusting the bend–twist coupling coefficient; however, it cannot be realized by adjusting the stretch–twist coupling coefficient. This work is of universal significance and can provide a theoretical guidance for the artificial design and performance optimization of chiral filament materials.