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

Giancarlo Cicconofri; Giovanni Noselli; Antonio DeSimone

The shear of axonemal MTs determines the orientation of the PFR cross sections. In Figure 5 (middle pictures) we show an example of this kinematic interplay. The Ax is again bent in an arc of a circle on the plane d 1 − d 3 , with U 1 (s) = 0, U 2 (s) = K, γ 1 (s) = Ks, and γ 2 (s) = 0. PFR and Ax centerlines run parallel to each other, indeed from (9) we have that ∂ s r a ≈ ∂ s r p for every deformation. The linking bonds impose a rotation of the cross sections of the PFR as we progress from the proximal to the distal end of the flagellum, generating shear strain V 2 (s) = − sin φ p γ 1 (s) = − sin φ p Ks on the PFR. This mechanical interplay leads to non-planarity of the euglenid flagellar beat. This mechanism is controlled by the offset between the PFR-Ax joining line and the local spontaneous bending plane of the Ax, as further discussed in the Results Section.