The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena

Giancarlo Cicconofri; Giovanni Noselli; Antonio DeSimone

are the target bending strains generated by the dynein forces. The use of this terminology is clear from (22). The effect of dynein actuation at equilibrium (when the energy is minimized) is to bring the bending strains U 1 and U 2 as close as possible to U * 1 and U * 2 , respectively. The emerging bending strains and the target bending strains might not match due to the interference by the PFR component of the energy (D p = 0). From the formulas for the target bending strains in (22) we can infer the importance of the concentrated shear forces H 1 and H 2 . Without these forces, admissible spontaneous configurations of the Ax would be ruled out. If the concentrated shear forces are null, for example, the Ax cannot spontaneously bend into a circular arc. Indeed, for a circular arc of radius 1/K on the plane d 1 -d 3 we must have U * 2 = 0 and U * 2 = K. In this case, from (22) we have that −H 1 /B a = ∂ s U * 2 = 0, which implies H 1 = 0 and H 1 = −B a K, so the concentrated forces must be non zero.