introduction: flagellar propulsion 9 



its length when treated with adenosine triphosphate (ATP) while 

 remembering that the total degree of shortening involved by bending 

 a very thin filament may be very small. 



That a radial arrangement of contractile elements should produce 

 bending in one plane is not restricted to flagella or cilia; it occurs in 

 a large number of other undulating organisms and involves no great 

 mechanical difficulty provided there is a suitable difference in phase 

 between each of the contractile elements (Bradfield, 1953; Gray, 

 1955). All elements could execute the same cycle of changes in 

 length and tension and each contribute to the energy required for 

 uniplanar bending (Gray, 1955, p. 798). But why there should always 

 be nine radial elements remains a mystery. 



A more amenable problem concerns the mechanism which con- 

 trols the phase difference between adjacent regions of the filament. 

 How far is this maintained by an intrinsic timing mechanism and 

 how far by forces exerted against the filament by the external me- 

 dium? Or as Brokaw (this symposium) has put it, how far is the ef- 

 fort of contractile units exercised against internal as opposed to ex- 

 ternal resistances? The frequency of the waves is undoubtedly af 

 fected by changes in the viscosity and other physical properties of 

 the medium, but until we know the precise changes, if any, which 

 such factors exercise on the amplitude and length of the waves, the 

 situation will remain rather obscure. On the other hand, facts rela- 

 tive to the nature of the timing mechanism may be available from 

 other sources. 



The spermatozoa of a sea urchin (Psammechinus) exhibit two in- 

 teresting features: (1) the tail is motionless when isolated from the 

 "middle piece," and (2) a wave cannot pass beyond an element which 

 is mechanically prevented from moving (Gray, 1955, Fig. 12e). If 

 these two facts are of general application, there seems no need to 

 postulate internal structures specifically concerned with the main- 

 tenance of phase differences between adjacent segments. As shown by 

 Machin (1958) the form and rate of movement of the waves can be 

 visualized partly in terms of passive conduction along an elastic fila- 

 ment and partly in terms of energy being fed into the system- when 

 elements undergo passive changes in length or tension. On this basis, 

 uniplanar bending of an element near the proximal end of the tail 

 would induce a wave traveling in the same plane, whereas if the proxi- 



