276 C. J. BROKAW 



lates. These properties can be duplicated by a simple electronic ana- 

 log. The mechanism of oscillation can also be expressed by saying 

 that the active tension exerted by the muscle varies in such a way 

 that there is a constant time delay of about 7 msec between maximum 

 length and maximum tension (Machin and Pringle, 1960). 



The extension of these ideas to flagella implies that the contrac- 

 tion of muscle-like elements distributed through the flagellum is 

 triggered by their extension by passive elasticity and the active con- 

 traction of antagonistic elements. There must be a time delay be- 

 tween length changes and changes in active tension. The result will 

 be a steady oscillation of each contractile element through a cycle of 

 relative deactivation, allowing extension, followed automatically by 

 relative activation leading to shortening. Twenty years ago the pro- 

 posal of a model of this complexity would have sounded wildly 

 speculative. Today it sounds considerably more reasonable, because 

 we have seen such spontaneous oscillations in insect flight muscle and 

 in some muscle model systems, because we have found some bio- 

 chemical similarities between flagella and muscle, and because we 

 have finally discarded the idea that the flagellum is a passive filament 

 waved by contractile elements situated in the basal granule. The 

 above model not only explains oscillation but also eliminates the 

 need for a separate mechanism, above the level of the contractile 

 elements, to produce a uniform propagated wave. The apparent co- 

 ordination can be explained simply by the sensitivity of individual 

 contractile elements to elongation by movement of other parts of 

 the flagellum. 



The analogy between insect flight muscle and flagella cannot be 

 carried very far, since it has been generally accepted that the inertia! 

 forces acting on a flagellum are negligible compared to the elastic 

 and viscous forces (Taylor, 1952; Gray, 1955; Machin, 1958). The 

 frequency and waveform of flagellar oscillation must be determined 

 by something other than the interaction between the mass and elas- 

 ticity of the system. The effect of increased viscosity on frequency 

 rather than on amplitude of flagellar oscillation also cannot be ex- 

 plained with reference to a typical mechanical oscillator. In flagella, 

 oscillation must involve some more intimate interaction between the 

 biochemistry of the contractile elements and the mechanical parame- 

 ters of the flagellum. Correspondingly, a much more complicated 



