Kinetic studies of the flagellar movement of sea-urchin spermatozoa.

In previous papers (Holwill & Silvester, 1965, 1967) results have been presented which support the hypothesis that the frequency of beating of a flagellum (hereinafter referred to simply as 'frequency') is identical with, or at least proportional to, a rate constant of the first-order chemical reaction which limits the frequency. If, as seems probable (e.g. Bishop, 1962; Brokaw, 1962) adenosine triphosphate (ATP) is directly involved in the supply of energy to an active organelle, then the experimental evidence indicates that the rate-limiting reaction is the breakdown of an ATP-ATPase complex. It has been found possible to treat certain flagella with solutions containing glycerol in such a way that these appendages can be reactivated by the addition of ATP, the frequency being controlled by the ATP concentration (e.g. Hoffmann-Berling, 1955; Brokaw, 1961, 1967). Earlier workers (e.g. Bishop, 1958; Bishop & Hoffmann-Berling, 1959) reported that the re-activated appendages exhibited only local oscillations but more recently Brokaw (1962, 1963) and Gibbons (1965c) have prepared 'models' in which all the features of normal wave propagation are preserved. The relation between frequency and ATP concentration is found to be similar in form to the MichaelisMenten law of enzyme kinetics (Brokaw, 1967; Brokaw & Holwill, 1967). The glycerinated models appear to provide an externally controllable system in which all the machinery for wave propagation is preserved and are potentially suitable for further studies of the thermodynamic aspects of flagellar movement. In this paper the reactions of sea-urchin spermatozoa are investigated in an attempt to characterize further the enzymatic reactions which underly flagellar motility.