Coupling between axial stretch and bending/twisting deformation of actin filaments caused by a mismatched centroid from the center axis

A cytoskeletal actin filament with a spirally arranged centroid (a biopolymer with a double helical structure) exhibits mechanically interesting phenomena, such as tensile-twisting coupling behavior involved in the binding of actin-related proteins. To describe this mechanical behavior of the actin filament, we propose a Cosserat continuum model by focusing on the mismatch between the centroid and the center axis. We derive the equations of motion based on the variational principle and discuss the coupling behavior caused by the mismatch, which is responsible for interesting couplings between axial stretch and bending/twisting deformation. The proposed model can express the mechanical behavior of actin filaments with a spirally arranged centroid mismatched from its center axis, through which we can explore the fundamental filament-level mechanism of an actin cytoskeleton in relation to the mechanical regulation of biological functions.