. The biology of cilia and flagella. Cilia and ciliary motion; Flagella (Microbiology). 130 MOVEMENT OF CILIA AND FLAGELLA The movements of the sea urchin sperm have been shown by Gray and Hancock (1955) to approach closely to the ideal theoretical pattern. They derived an equation expressing the rate of forw^ard movement of sea urchin sperm in terms of the ampHtude and wavelength of the bending waves, the number of waves in the tail length, the frequency of waves, the radius of the tail and the radius of the head. Substitution of measured values of these parameters in the equation gave a calc
. The biology of cilia and flagella. Cilia and ciliary motion; Flagella (Microbiology). 130 MOVEMENT OF CILIA AND FLAGELLA The movements of the sea urchin sperm have been shown by Gray and Hancock (1955) to approach closely to the ideal theoretical pattern. They derived an equation expressing the rate of forw^ard movement of sea urchin sperm in terms of the ampHtude and wavelength of the bending waves, the number of waves in the tail length, the frequency of waves, the radius of the tail and the radius of the head. Substitution of measured values of these parameters in the equation gave a calculated speed of movement of 191 /x sec, while the average observed speed was 191 '4 /u,/sec. The simpHcity of the pure sine wave pattern, even in sea urchin tails with a symmetrical beat, is usually complicated by an increase in both wavelength and amplitude as the bend passes L~. Fig. 32. Diagram of a sperm to show the three axes mentioned in the text. The oscillations of the tail take place in plane T-T\ the axis P-P is at right angles to both T-T and the longitudinal axis L-L. down the tail. The beat is further complicated in the majority of sperm tails by an inequality of bending on the two sides, so that the wave pattern is asymmetrical, one side showing a larger amplitude and longer half-wave than the other as in Fig. 31. Such an asymmetry of bending will have important effects on the movement of the sperm. Three axes of the sperm may be defined as in Fig. 32 by L-L, T-T and P-Py the last being perpendicular to both the transverse and longitudinal axes of the sperm (the waves of bending are here assumed to be in the transverse plane). Movements about these three axes are designated as follows: movements about L-L constitute a roll, about T-T 2^ pitch, and about P-P a yaw. Where bending of the sperm tail is asymmetrical, the sperm will persistently yaw towards one side or the other because the transverse forces acting on the tail will not balance about its. Please note tha
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