ENERGY RELATIONSHIPS 165 



dehydrogenase was present in sperm tails to regenerate some 20 

 times the ATP required for this (bull sperm may use the citric 

 acid cycle to provide free energy). 



It is not so easy to study cilia in this way, but both practical 

 and theoretical figures are available. According to Jensen (1893) 

 each cilium of Paramecium is able to exert a force on the water 

 of about 4-5 X 10~^ mg. If this force is exerted in each effective 

 stroke, then the rate of doing work in the effective stroke is of 

 the order of 1 x 10~' erg/cilium/sec, and the average rate of energy 

 consumption throughout the cycle is probably rather less than this. 



The result of calculations based on the figures used by Harris 

 (1961) for Paramecium may be compared with this. If the cilium 

 of Paramecium exerts a bending couple of 5 x 10~^^ dyn cm in 

 order to overcome viscous resistance in the effective stroke, and 

 the cilium moves through an angle of rather more than 90° in 

 this phase of beat in a time of about 0-008 sec, work is done at a 

 rate of about 1 -25 x 10"'' erg/cilium/sec in the effective stroke. 

 Here again, the average rate of doing work is likely to be rather 

 less than that found for the effective stroke alone. The figure 

 obtained in this calculation agrees well with that obtained from 

 Jensen's data, and tolerably well with the figures for the utilization 

 of energy by sperm calculated by Rothschild. 



Compound cilia may be treated in much the same way. Thus, 

 the bending couple calculated for a membranelle of Stentor at 

 about 20°C (see p. 147) is about 3 x 10"^ dyn cm, and the 

 membranelles move through about 140° in the effective stroke, 

 so that the work done in the effective stroke is about 7 x 10~* 

 erg/cilium/beat. These compound cilia beat at about 30 beats/sec 

 and each effective stroke occupies about a quarter of the beat, 

 which means that the rate of doing work in the effective stroke 

 is about 8-4 X 10~^ erg/cilium/sec. Since 60 to 75 cilia are 

 present in each membranelle, each component cilium uses energy 

 at a rate of 1-1 to 1*4 x 10"'^ erg/sec in overcoming external 

 resistance in the effective stroke. 



A direct measurement of the force exerted on a needle which 

 arrests an abfrontal cilium of Mytilus has been made by Yoneda 

 (1960). Very fine glass microneedles were prepared, and the 

 force required to displace the tip of each needle by 1 /x was 

 measured. These needles were used to arrest the cilia near the 



