Energy Transfer and Conservation in the Respiratory Chain 613 



Crossover Theorem 



A new approach to the locahzation of interaction sites is provided by the 

 crossover theorem (Chance and WiUiams, 1956a; Chance, Wilhams, Holmes, 

 and Higgins, 1955; Chance, Holmes, Higgins, and Connelly, 1958; Holmes, 

 1959) which is based on the simple observation that reducing equivalents 

 accumulate on the substrate side of an inhibition point and diminish on the 

 oxygen side. This is a — , + crossover for decreasing flux through the system, 

 the — sign denoting increased reduction, and the + sign denoting increased 

 oxidation. While the theorem appears to be trivial for a single interaction 

 site, it becomes sufficiently complicated for three interaction sites that both 

 Holton (1957, 1958) and Slater (1958) have questioned the generahty and 

 applicability of the theorem. Slater has discussed the case of two crossover 

 points and concluded that they can be explained by two sites of inhibition. 

 We should like to point out that three crossover points are needed for a direct 

 demonstration of three sites of inhibition, and such experiments have been 

 carried out (Chance and Williams, 1956b; Chance et aL, 1958). We have also 

 been concerned with the source of energy for the ~I compounds, particularly 

 in the case of DPNH, and have pointed out that the portion of the oxidation- 

 reduction cycle at which energy is conserved need not be the reduction phase 

 alone but could also be the oxidation phase (Chance et aL, 1955) ; both, in fact, 

 could be involved. However, crossover data clearly indicate that energy con- 

 servation and an inhibition have occurred between a pair of carriers. We have 

 never written an equation such as Slater's Scheme C (Slater, 1958, p. 235) in 

 which he has assigned the total energy requirement to the /9-OH -^ DPN 

 reaction. Also, no crossover point has yet been observed at the fp-b couple 

 (cf. Chance et aL, 1955; Chance and Williams, 1956b). Our views have been 

 expressed in the form of Fig. 7 since 1956 (Chance and Williams, 1956a, 

 pp. 96-7, Equations 13-15), and now we can amend Equation 15 of that 

 communication to replace c'" by c/" in view of Fig. 5 above. 



We first derived the theorem on the basis of physical argument; it has 

 more recently been possible to provide proofs for a variety of conditions by 

 means of an electronic analogue computer (Chance et aL, 1958) and by a 

 rigorous derivation (Holmes, 1959; see Note 7). The theorem is conveniently 

 expressed as follows. 



For interactions that cause decreases of flux, we can state: (1) an inter- 

 action site lies between a — to + change in the sequence from substrate to 

 oxygen ; (2) components between oxygen and the first site will always show 

 + changes, while those between substrate and the last site will always show 

 — changes ; (3) a crossover point near the oxygen end of the chain can be 

 shifted to the next site of interaction by a decrease of activity in the oxidase 

 portion of the chain and vice-versa; (4) a + to — change (reversed crossover) 

 does not identify an interaction site. 



