Nonlinear modeling of 3-d flagellar dynamics

We develop exact equations formulas for the sliding between arbitrary filament pairs in a bundle subjected to a general 3‐d deformation. We introduce a classification of deformations, and we study particular examples for bending, twisting, helical and toroidal shapes. We prove that simultaneous combination of twisting and bending can produce a drastically drop in the sliding. These results can relate the geometry of shapes and motions with the distribution of molecular motors activity.