STUDIES ON ISOLATED FLAGELLA 277 



electronic analog appears to be required to simulate the behavior of 

 the flagellar oscillator. 



We might also suggest that in the case of flagella, where beat fre- 

 quency is not completely determined by mechanical parameters, 

 there is a more direct relationship between the frequency and the 

 time lag between length and active tension. The time delay might 

 originate in a biochemical process which is sensitive to ATP con- 

 centration and other chemical factors. For effective beating, the peak 

 tension exerted by the contractile elements should come in phase 

 with the sum of the elastic and viscous resistive forces. The phase 

 angle of this sum will vary with viscosity. If the viscosity is low 

 enough, the resistance will be primarily elastic and will be maximal 

 at 180° past maximum elongation. In high viscosity, the maximum 

 resistance will occur 90° past maximum elongation (Machin, 1958). 



This analysis implies that if there is a constant time delay between 

 length and tension, and if this delay determines the frequency, then 

 it would not be possible for the frequency to be varied by more than 

 a factor of 2 by changing the viscosity of the medium, so long as the 

 amplitude and waveform remain constant. This conclusion is cer- 

 tainly not supported by the film Lord Rothschild has shown us of 

 bull spermatozoa swimming in a medium of high viscosity, but pre- 

 liminary observations on isolated Polytoma flagella do give some in- 

 dication of aberrant movement at very high viscosities. This point 

 requires further examination; these experiments may provide some 

 basis for comparing the behavior of flagella with that of the insect 

 flight muscle system. The conclusion which begins to emerge from 

 these preliminary experiments is that the basic idea that flagella con- 

 tain contractile elements sensitive to elongation may be valid, but 

 that the details of the feedback between length and tension may be 

 peculiar to flagella, with little carry-over from investigations of in- 

 sect fibrillar muscle. 



In discussing these models, a number of problems have been ig- 

 nored, such as: Why are contractile waves propagated in only one 

 direction? Do the isolated flagella retain any morphologically differ- 

 entiated region at their basal ends which may play a part in their 

 motility? Why is the wavelength of flagellar beating independent 

 of viscosity and ATP concentration but strongly correlated with the 

 length of the flagellum? How does ATP reach the isolated flagella? 



