Additivity and the physical basis of multivalency effects: a thermodynamic investigation of the calcium EDTA interaction.

To better understand the origin of multivalency effects in ligand binding, the binding of a series of mono-, bi-, tri- and tetravalent carboxylate ligands to Ca(II) was examined by isothermal titration calorimetry (ITC). The data are inconsistent with an entropic origin of enhanced affinity, but rather show that at least in this instance the multivalency effect is enthalpic in origin. Analysis of binding data using the Jencks model shows the addition of incremental carboxylate "ligands" produces an unfavorable interaction entropy that is more than offset by a strongly favorable interaction enthalpy. The most likely source of this interaction enthalpy is the relief of repulsive Coulombic interactions in the unbound state. The conformational entropy penalty arising from the restriction of flexible dihedrals is negligible, within experimental error. On the other hand, an enthalpic contribution from linker restriction contributes strongly to the overall thermodynamics of ligand binding. Together, these data suggest that enthalpic effects dominate ligand binding, and design strategies should seek to optimize these interactions. The incorporation of unfavorable interactions in the unbound ligand that are relieved during binding provides an important mechanism by which to enhance ligand affinities.