General Thermodynamics of Binding

Equations 4.1-4.4 explicitly ignore the solvent, even though the discussion in the last chapter indicates that the solvent can have a dramatic influence on the magnitude of binding forces. We do not need the solvent explicitly written as part of these equations because AG for the association reflects the stability of solvated H and G relative to solvated H G and released solvent. As such, binding constants and related thermodynamic quantities should always be tabulated as being measured in a particular solvent, as well as at a particular temperature. 

In Section 3.1.5 we explored the thermodynamics of a simple reaction involving a single reactant A going to a single product B. The ratio of A and B at equilibrium reflects their intrinsic stabilities at their standard states. The intrinsic stabilities are expressed as AG° values, which are indicative of the energy it would take to convert one mole of A to B if A started at its standard state and B ended at its standard state. The ratio of A to B at equilibrium is constant for any initial concentration of the reactant ([A]o). For example, for a reaction with an equilibrium constant K of 10 and an initial concentration [A]o of 11 mM, at equilibrium there will be lOmMB and 1 mM A, because 10/1 = 10. If the initial concentration of A was 2.2 xM, then at equilbrium there will be 2 )jlM B and 0.2 xM A, because 2/0.2 = 10. We now explore how a reaction such as that given in Eq. 4.1 differs. 

For a reaction as in Eq. 4.1, the ratios of [H], [G], and [FI G] are not constant for different initial concentrations of H and G. This is because the numerator of Eq. 4.2 is a concentration to the first power, but the denominator is related to concentration squared, and vice versa for Eq. 4.3. Let s examine some scenarios of various concentrations to delineate the trends. In our analysis we use an association constant of 10 M , reflecting an exergonic reaction. However, for the sake of the following argument, let s assume that the reaction is also exothermic, a fact that we would not know unless we measured AH°. 

A normal reaction coordinate diagram for an exergonic binding process. 

Given the definition of from Eq. 4.2, we find that the binding constant has units of M Other equilibria can have different units. Putting units on values is the most common convention used by chemists. Yet, we must remember that all equilibrium constants are really defined by ratios of activities, which are dimensionless values (see Section 3.1.5). True binding constants are therefore dimensionless. This should not come as a surprise, because the 

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