Crossover theorem

The sites of action of some of the commonly used inhibitors of the electron-transport chain are shown in Fig. 14-3. These sites have been established by application of the crossover theorem (Chap. 10). For example, the fungus-derived antibiotic antimycin A causes an increase in the level of reduced cytochrome b and a decrease in the level of reduced cytochrome C] (i.e., an increase in the level of oxidized cytochrome c() thus, it is inferred that antimycin A interacts with complex III. 

The absence of ADP is acting, in effect, as an inhibitor of electron transport, for reasons discussed in Prob. 14.6 below. Hence, by application of the crossover theorem (Chap. 10), there are large differences in the reduction of sites of the electron-transport-chain between NAD and coenzyme Q, between cytochrome b and cytochrome c, and between cytochrome c and cytochrome a. Therefore, the absence of ADP must be inhibiting electron transport at these points in fact, these are the sites of proton extrusion leading to ATP synthesis during electron transport. 

Apply the crossover theorem, with reference to the figure in Example 14.5. The proportions of the iron-sulfur proteins in complexes I, II, and III with iron atoms in the Fe3+ and Fe2+ states can, in principle, be estimated from the electron spin resonance signals of the preparation of mitochondria. In the case of mitochondria oxidizing NADH in the presence of rotenone, application of the crossover theorem reveals that the iron atoms in the iron-sulfur proteins in complex I will become more reduced, while those in complex III will become more oxidized, in comparison to their states in the absence of rotenone. In the case of KCN-treated mitochondria, both sets of iron-sulfur proteins will become more... 

Heinrich, R. Rapoport, T.A. (1974) Eur J Biochem 42, 97-105. A linear steady-state treatment of enzymatic chains Critique of the crossover theorem and a general procedure to identify interaction sites with an effector. 

The above approaches identify reactions in a pathway which might exercise a regulatory function. Proof of the actual site of rate control under specified conditions is, however, only possible when measurements are made on a pathway whose flux has been perturbed by an activator or inhibitor. Such an approach characterizes the crossover theorem of Chance et al. (1958) and was originally applied to studies of electron-transport chain. According to this theorem, one may define the... 

Figure 2 Flow diagram of the DHT with N=8, P=3. Broken lines represent transfer factors -1 while full lines represent unity transfer factor. The crossover boxes perform the sign reversal called for by the shift theorem which also requires the sine and cosine factors Sn, Cn.

This basic difference equation - known as the Schema Theorem [holl92] - expresses the fact that the sample representation of schemas whose average fitness remains above average relative to the whole population increases exponentially over time. As it stands, however, this equation addresses only the reproduction operator, and ignores effects of both crossover and mutation. 

Finally, in order to also take into account the mutation operator, we note that the probability that a schema S survives under mutation is given by pu S) = (1 — Pm) where pm is the single-bit mutation probability and 0( S) is the number of fixed-bits (i.e. the order) or S. With this we can now express the Schema Theorem that (partially) respects the operations of reproduction, crossover and mutation ... 

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