Computer simulation of flagellar movement. III. Models incorporating cross-bridge kinetics.

A computer simulation procedure is used to analyze the generation of propagated bending waves by flagellar models in which active sliding is generated by a cycle of cross-bridge activity. Two types of cross-bridge cycle have been examined in detail. In both cycles, cross-bridge attachment is followed immediately by a configurational change in the cross-bridge, which transfers energy to a stretched elastic element and generates a shearing force between the filaments. In the first model, which has cross-bridge behavior close to current ideas about cross-bridge behavior in muscle, cross-bridge attachment is proportional to curvature of the flagellum and detachment is an exponential decay process. The configurational change is equivalent to an angular deviation of pi/5 radians. In the second type of cross-bridge cycle, cross-bridge attachment occurs rapidly when a critical curvature is reached, and detachment occurs when a critical curvature in the opposite direction is reached. With this cycle, an unrealistically large angular deviation of the cross-bridges, equivalent to 3.0 radians, is required to obtain bending waves of normal amplitude. Both models generate bending wave patterns similar to those obtained in earlier work. However, the behavior of the second type of cross-bridge model more closely matches the actual behavior of flagella under experimental conditions: the chemical turnover rate per beat cycle remains constant as the viscosity is increased, and reduction in the number of active cross-bridges can cause a reduction in beat frequency, with little change in amplitude or wavelength.