Sequestered Water and Binding Energy are Coupled in Complexes of λ Cro Repressor with Non-consensus Binding Sequences

We use the osmotic pressure dependence of dissociation rates and relative binding constants to infer differences in sequestered water among complexes of λ Cro repressor with varied DNA recognition sequences. For over a 1000-fold change in association constant, the number of water molecules sequestered by non-cognate complexes varies linearly with binding free energy. One extra bound water molecule is coupled with the loss of ∼ 150 cal/mol complex in binding free energy. Equivalently, every tenfold decrease in binding constant at constant salt and temperature is associated with eight to nine additional water molecules sequestered in the non-cognate complex. The relative insensitivity of the difference in water molecules to the nature of the osmolyte used to probe the reaction suggests that the water is sterically sequestered. If the previously measured changes in heat capacity for λ Cro binding to different non-cognate sequences are attributed solely to this change in water, then the heat capacity change per incorporated water is almost the same as the difference between ice and water. The associated changes in enthalpies and entropies, however, indicate that the change in complex structure involves more than a simple incorporation of fixed water molecules that act as adaptors between non-complementary surfaces.