146 MOVEMENT OF CILIA AND FLAGELLA 



performance of these functions. The propagation of the wave 

 of contraction along the cilium must also be accounted for in any 

 theory of the mechanism of beat. 



The nine peripheral fibril doublets are placed in the ideal 

 position to act as the contractile structures of the cilium, since 

 they could bend the cilium simply by shortening. The peripheral 

 position of these fibrils permits some of them to exert a reasonably 

 large bending moment about an axis through the centre of the 

 ciUary shaft, and their distribution is such that bending moments 

 caused by equal contractions in all fibrils on the tw^o sides of any 

 axis through the centre of the shaft balance very closely. Nelson 

 (1958) has found that ATP-ase activity seems to be localised in 

 these peripheral fibrils of the cilium, so that the energy supply 

 is available there. 



What part of the cilium then can function as the compression 

 element to maintain ciUary rigidity ? The tw^o central fibrils are 

 absent from many non-motile cilia modified for sensory functions 

 (p. 32), so that it appears as if they may have a mechanical function. 

 Harris (1961) has recently calculated the bending couple necessary 

 to overcome the resistance of the medium in the effective stroke 

 of a cilium. On the basis that the rigidity of the cilium must 

 be able to resist this bending couple, he found that the central 

 fibrils would require a Young's modulus approximating to that 

 of steel wire if they were the only compression elements, and 

 they would therefore need to be much stronger than any known 

 biological material. As an alternative source of rigidity Harris 

 suggested that internal turgor pressure acting against the elastic 

 tension of the ciliary membrane might provide sufficient stiffness, 

 since no internal structures were likely to be strong enough. He 

 proceeded to show by calculation that both the turgor pressure 

 required and the Young's modulus of the membrane structure 

 necessary to resist the bending couple were within reasonable 

 limits for this sort of structure. 



In these calculations Harris assumed that the bending moment of 

 the effective stroke would be equivalent to half the couple exerted in 

 the rotation of an ellipsoid twice the length of the cilium. With some 

 minor approximations the bending couple can be expressed by 

 C = ^TrrjPo) (where C is the couple, rj is the viscosity, / is the cilium 

 length and co is the angular velocity). It will be seen that this is the 



