158 MOVEMENT OF CILIA AND FLAGELLA 



in the same way both as regards its contraction and the propaga- 

 tion of the contraction, could produce both the flagellar and ciliary 

 beating patterns. 



It is assumed in this hypothesis that the cycle of beat starts 

 with a contraction in fibril 1, and that contraction of the other 

 fibrils follows in the order indicated by the arrows in Fig. 41b. 

 This is in accordance with the finding by Afzelius that the eft'ective 

 stroke is norm Hay towards fibril 1 in Mnemiopis cilia (p. 17), but 

 in Anodonta cilia Gibbons has neatly shown that the effective 

 stroke is towards fibrils 5 and 6. It is interesting that Mnemiopsis 

 comb -plates are capable of reversal, and may therefore start their 

 beat towards either fibril 1 or fibrils 5 and 6. Cilia of Opalina 

 may beat in any direction, and presumably any fibril, or pair of 

 fibrils, may be the first to contract. 



If curves similar to those in Fig. 44 are constructed on the 

 assumption that contractions in fibrils 5 and 6 start the beat, then 

 results very close to those shown are obtained, being almost 

 identical for the symmetrical beat (a), and showing slightly 

 increased asymmetry in graphs b and c. Valuable evidence for 

 the theory is provided by the findings of Afzelius (1959) and 

 Gibbons (1961b) that a permanent bridge structure connects 

 fibrils 5 and 6 in sea urchin sperm and Anodonta cilia; this 

 suggests that these two fibrils always move together. Similar 

 links are not found between other fibrils in the main part of the 

 shaft. 



According to the theory outHned above, the various beating 

 patterns found in cilia and flagella differ primarily in the timing 

 of the contractions in the component fibrils. That is, the ratio : 



Interval between the excitation of neighbouring fibrils 

 Interval between successive excitations of the same fibril 



(which is equivalent to the phase difference between adjacent 

 fibrils) determines the form of beat. If the phase difference is 

 greater than one-sixth, the resultant bending moments are 

 reduced since contractions on the two sides will always oppose 

 one another, e.g. at a phase difference of one-fifth the maximum 

 bending moment is little more than half that at one-sixth, although 

 the bending cycle is reasonably symmetrical. If the phase 

 difference is less than one-sixth, the bending cycle is asymmetrical 



