The concept of a coupled reaction system

The stability constant K of a host/guest (1 1) complex is defined by the equilibrium (1), 

In this scheme, H, G and HG in normal or subscript positions represent the host, guest and complex species respectively subscripts ox and red indicate that the corresponding symbols or parameters refer to molecules in oxidized and reduced states E° is the formal potential of the electron transfer reaction and K is the stability constant. According to thermodynamics, there are four relationships linking the concentrations of the four molecules at the four corners of the square. These are two Nernst equations for the upper (2) and lower (3) electron transfer reactions, 

The two complexation equilibrium equations for the left and right complexation/decomplexation equilibria are (4) and (5) respectively. 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and Kied of a complex in different oxidation states with experimentally measurable redox potentials EH and HG. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if KIed is known or vice versa. 

Ideally the electrochemical molecular recognition process should result in a large shift of the redox potential of the host species. The minimum magnitude of a potential shift is gauged by experimental error. For most voltammetric techniques, this error is about 5 mV. According to (6), the potential shift is determined by the ratio KoxIKied. This ratio reflects the influence of the redox reaction upon complexation, in other words, the RCE. So far, the coupling has 

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