Peripheral doublet microtubules and wave generation in eukaryotic flagella

The shape and propagation of waves produced by eukaryotic flagella depend on the three-dimensional arrangement and physical-chemical properties of peripheral substructures. The modeling analysis presented here, which assumes force-moment equilibrium and neglects the viscous resistances of the medium, shows how substructural arrangements characteristic of 9+0, 9+1, and 9+2 axonemes can yield their characteristic wave patterns. When flexural stiffnesses are equal along all axonemal radii, any non-uniform doublet shearing pattern propagated distally at constant rate, with successive pairs 1 9 cycle out of phase, should generate helical waves. When stiffnesses differ greatly on different radii, but the stiffness pattern is the same for all cross-sections, any such shearing pattern should yield planar waves resembling sine-generated curves. Propagated axonemal bending results from the active bending moment produced by local shearing of doublet pairs. Uniformly twisting the doublets about the axonemal axis cannot directly alter the magnitude of the active bending moment. If dynein cross-bridges are activated by shear displacement between peripheral doublets, then the resulting distribution of the active bending moment will be appropriate for balancing the elastic moment in a propagated bending wave.