Linear free energy relationships in enzyme binding interactions studied by protein engineering.

Experiments on mutants of tyrosyl-tRNA synthetase have shown that there can be linear free energy relationships (LFERs) between changes in activation free energies and changes in binding energies when groups are deleted that bind to non-reacting parts of the substrate (Fersht et al., 1986, 1987). It has now been proposed (Straub and Karplus, 1990) that such LFERs can occur for the mutation of hydrogen bonding groups only for the limiting examples of Brønsted beta of 0, 1 or infinity, and that fractional values of beta are not permissible. The reasoning behind this is that the energy of a hydrogen bond is not linear with distance and the (false) premise that an LFER requires that there is a linear relationship between bond energy and distance. We show from a simple model how LFERs can arise for binding interactions and how they can give fractional values of beta, in accord with experimental evidence. An LFER occurs between binding and catalysis when a set of interactions exists in which each member contributes to the binding energy of the transition state the same fraction of the binding energy it contributes to the products (both relative to the ground state).