Relationships between apparent binding energies measured in site-directed mutagenesis experiments and energetics of binding and catalysis

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Abstract
The use of binding energy in molecular recognition and enzyme catalysis is currently being probed by experiments on engineered proteins. The interaction energy of an individual side chain with a substrate may be quantified by comparing the binding and rate constants for wild-type enzyme with those for a mutant in which the side chain has been truncated. An apparent binding energy .DELTA.Gapp is obtained. The physical significance of .DELTA.Gapp is analyzed with particular reference to hydrogen bonding where one partner in the bond is deleted by mutagenesis. The following conclusions have been drawn for situations where mutagenesis does not unduly perturb the structure of the protein. .DELTA.Gapp is always a measurement of specificity of binding and catalysis. But, it does not generally measure the incremental binding energy of the hydrogen bond .DELTA.Gbind. This discrepancy between .DELTA.Gapp and .DELTA.Gbind is especially large when mutation leaves a charged donor or acceptor unpaired. Here, .DELTA.Gapp overestimates .DELTA.Gbind by possibly several kilocalories per mole. On the other hand, changes in .DELTA.Gapp (.DELTA..DELTA.Gapp) as a reaction proceeds through its intermediates and transition states are particularly amenable to simple analysis. It is shown that .DELTA..DELTA.Gapp can measure changes in .DELTA.Gbind (.DELTA..DELTA.Gbind). For example, if there is a change in the energy of an individual bond on going from one state to the next, then .DELTA..DELTA.Gapp = .DELTA..DELTA.Gbind. This rule breaks down, however, when the particular step analyzed involves the relevant groups on the enzyme and substrate binding to water in one state but to each other in the next state. In this situation, .DELTA..DELTA.Gapp does not equal .DELTA..DELTA.Gbind and can seriously overestimate it when there is an unpaired charged donor or acceptor.