Bend propagation in flagella. II. Incorporation of dynein cross-bridge kinetics into the equations of motion.

The cross-bridge formalism of T. Hill has been incorporated into the nonlinear differential equations describing planar flagellar motion in an external viscous medium. A stable numerical procedure for solution of these equations is presented. A self-consistent two-state diagram with curvature-dependent rate functions is sufficient to generate stable propagating waves with frequencies and amplitudes typical of sperm flagella. For a particular choice of attachment and detachment rate functions, reasonable variation of frequency and wave speed with increasing viscosity is also obtained. The method can easily be extended to study more realistic state diagrams.