MEASUREMENT OF SPERM MOTILITY 51 



INTERACTION OF SPERM CELLS 



Observations 



It has long been known that suspended microscopic particles (e.g., 

 erythrocytes, fat globules, bacteria) show a repulsive interaction 

 (Berkson et al., 1940; Van Kreveld, 1947). As a result, the standard 

 deviation of the number of particles present at regular time intervals 

 in a sample volume is found to be smaller than would be predicted 

 by a Poisson distribution. On the other hand, theoretical evidence has 

 been presented by Taylor (1952) for an attractive interaction between 

 microorganisms with undulatory fiagella, such as sperm cells. Taylor 

 found that two fiagella close together, having a synchronized tail 

 wave, dissipate less energy into the fluid than two independently mov- 

 ing fiagella. In undiluted semen, where sperm are close together, in- 

 teraction can be observed as "wave formation." Rothschild (1949) 

 based his "impedence change" method for evaluating motility of un- 

 diluted semen on this effect. 



Measurements of sperm interaction in diluted semen have been 

 performed in two ways, by using the cinematographic and the photo- 

 electric methods described above. From films, the number of motile 

 cells present on a slide in an area of 150 microns <f> was counted at 

 intervals of 2 sec. This interval is long enough to eliminate correla- 

 tion between successive events. The standard deviation a(n) of the 

 number of cells in the area, as illustrated in Fig. 19, is found to be 



a (n) = 0.93 \fn 

 By means of the photoelectric device, time intervals between the 

 beginning of passages of sperm were measured. If no interaction is 

 present, the distribution n(t) of interval lengths is exponential: 



n(t) = exp (-t/t ) 



where t is the average interval. The standard deviation o-(/) of the 

 distribution then is a(t) = t u . Actually measured distributions are 

 shown in Fig. 20; it is clear that the distribution is too low for the 

 small intervals. For twelve ejaculates, it Avas found that a(t) = (0.94 ± 

 0.2) X / (( , where t ranged from 1.8 to 4.7 sec. 



Discussion 



The results of both types of measurements reported in the previ- 

 ous section indicate a small repulsive interaction. If the very crude 



