,156 



MOVEMENT OF CILIA AND FLAGELLA 



(except fibrils 5 and 6). The resulting graph, Fig. 42b, follows 

 a sine wave in which one complete cycle of flagellar bending 

 occurs in each cycle of fibrillar contraction, so that the model 

 would bend first to the right and then to the left before com- 

 pletion of the cycle. By this means Gray was able to explain the 

 symmetrical bending waves he found in some sea urchin sperm 

 tails. 



An explanation of asymmetrical bending waves using these 

 same assumptions is less easy unless one also assumes that the 

 ability to contract is greater on one side than the other. A small 

 modification of Gray's theory suggested by Sleigh (1960) may 

 provide a more satisfactory explanation of the various forms of 

 ciliary and flagellar beating. 



z 

 o 



w 



z 

 u 



TIME 



Fig. 43. Diagram of the course of contraction in a muscle fibre. 

 Values from this curve were used to calculate fibrillar tensions 



in the construction of Fig. 44. 



The contraction cycle in a muscle fibre normally follows an 

 asymmetrical course, as in Fig. 43. If we assume that the 

 contraction in each ciliary fibril follows a curve like this rather 

 than a sine curve, then a symmetrical bending cycle of the model 

 would still be produced when each fibril is J cycle out of phase 

 with its neighbours, as in Fig. 44a. If the phase difference 

 between adjacent fibrils is greater than one-sixth, the bending 

 cycle of the model will be asymmetrical or reduced in amplitude 

 or both. If the phase difference is reduced to -^ cycle, the 

 bending cycle is moderately asymmetrical (Fig. 44b), while if it 

 is 2^4 cycle, the bending cycle is very asymmetrical (Fig. 44c). 



