THE FORM OF BEAT OF FLAGELLA 131 



mid-point, and consequently the sperm will tend to move in 

 a circle. In addition, however, all sea urchin sperm seem to 

 roll, and a combination of yawing and rolling results in a spiral 

 movement of the sperm about a straight line, which is the axis 

 of progression. The greater the yaw, the larger the diameter 

 of the spiral, and the faster the roll, the smaller the diameter of 

 the spiral, if the rate of forward movement is constant. Pitching 

 movements seem to occur rarely and are probably of lesser 

 importance. 



The presence of a yaw component in the movement of a sperm 

 is easily accounted for by an asymmetry of bending, but a rolling 

 component requires more explanation. It appears that the 

 majority of sea urchin sperm roll in an anticlockwise direction 

 (looking along the axis of progression), and earlier observers 

 attributed this to an asymmetry of the head, but both Gray (1958) 

 and Bishop (1958b) believe that rolling of sperm (of bull and 

 squid respectively) takes place because the beating of the terminal 

 part of the tail is not in quite the same plane as that of the main 

 part of the tail. A slight twist in the plane of beating of the 

 tail of a moving sperm could easily cause such a roll, but Bishop 

 found that the rolling movement occurred in stationary squid 

 sperm that were motionless except for oscillations of the distal 

 end of the tail. A sea urchin sperm whose tail is beating with a 

 frequency of 30 or 40 c/s may roll with a frequency of -5 to 3-0 

 per sec, so that a relatively small motion of the tail may be 

 sufficient for rolling. 



It seems well established, both from observations on sea 

 urchin sperm by Gray (1955) and the calculations of Machin 

 (1958), that the bending movements of sperm tails are not the 

 result of waves propagated along a passive structure from a 

 driving system at the attached end, but that active contractile 

 elements are situated along the length of the flagellum and energy 

 for bending is contributed throughout this length. The most 

 probable site for contraction is the ring of nine peripheral fibrils ; 

 bending of the flagellum could be caused by a localized shortening 

 of some of these fibrils (see p. 146). The asymmetrical waves of 

 bending evidently result from unequal contractions on the two 

 sides of the tail, and this in turn may result from an asymmetry 

 of the timing of contractions on the two sides. 



K 



