DETERMINATION OF THE RATE OF BEAT 167 



6. The Determination of the Rate of Beat of Cilia 



From a physical point of view, the rate of beat of a ciUum must 

 depend on its size, both as regards its length and its compound 

 nature; the width of single cilia is fairly uniform, and such 

 differences as are found probably make little difference to external 

 resistance to movement, although internal resistance may be 

 changed. Harris (1961) has put forward the idea that if one 

 assumes that the bending force that can be exerted by cilia is 

 constant, the duration of the effective stroke is proportional to 

 the cube of the cilium length (at constant amplitude), while the 

 duration of the recovery stroke is proportional to the cilium 

 length. If the cilia are compounded together, the duration of 

 the effective stroke is inversely proportional to the number of 

 component cilia, while that of the recovery stroke is unaltered. 



Any particular cilium may vary in its rate of beat because of 

 changes in the viscosity of the medium which change the external 

 resistance to movement of the cilium. It is possible that changes 

 in the internal resistance to ciliary bending may also take place. 

 The rate of propagation of the bending wave along a cilium may 

 also be influenced by the viscous resistance to flexure of the 

 cilium. Purely physical factors which affect the movement of a 

 cilium may thus influence the rate of beat, presumably by affecting 

 the rate at which it can contract. It is conceivable that in some 

 cases the rate of beat is limited by the availability of energy for 

 contraction. Some workers have found that the beating of cilia 

 may be accelerated by addition of ATP ; this may be acting as an 

 additional source of energy, or could conceivably facilitate ciliary 

 movements by a plasticizing action. 



Under most circumstances cilia seem to be subject to excitation, 

 either intrinsic or extrinsic, and the rate of excitation of cilia may 

 be the factor which normally determines their rate of beat. Most 

 cilia that have been studied may be made to beat faster by the 

 application of drugs like serotonin, adrenalin or veratrine, and in 

 all three cases the drug may act on the excitation of the cilia. 



The rate of beat may thus depend on either the rate of con- 

 traction or the rate of excitation, for it appears that either may be 

 limiting. It is not known for certain whether one beat of a 

 cilium must always be completed before the next one starts. It 



