TABLE OF CONTENTS As described above, analyses based on free-energy relationships are meaningful only when the process under study is correctly identified as a single PT step. In acid-base catalysis this is often the case, but proton translocations in bioenergetics are likely to extend over several functional groups or molecules, including water. From a phe-nomenological view, this is similar to the situations investigated by Eigen and coworkers, working with proton donor and acceptor pairs in solution. [27], [99] Here, the proton-transfer reaction is preceded by the transient association of donor and acceptor in an encounter complex:
The symbol strictly implies only the solvent cage-induced association of the encounter complex, but for oxygen and nitrogen species it will almost certainly involve hydrogen bonding, too. For weak association, the concentration of complex will be very small and a steady-state analysis can be used, in which the total passage time is the sum of the component step times:
where K e = k elk ?e and K p = k plk ?p. Often, but not always, k e ? k ?d and k ?e ~ k d. Counter examples include products with different charges from reactants, such as AH + B vs. AH + BH +, or vice versa, and other sources of sticky products .
The free-energy relationships discussed above apply only to the actual PT process in the encounter...
