Thermodynamics of the Binding of Lysozyme to a Dendritic Polyelectrolyte: Electrostatics Versus Hydration

The interaction between dendritic polyglycerol sulfate (dPGS) of the second generation and lysozyme was studied by isothermal titration calorimetry (ITC) at different temperatures and salt concentrations. Analysis by ITC showed that 2-3 lysozyme molecules were bound to each dPGS. The resulting binding constant K _b and the Gibbs free energy ΔG ^o decreased markedly with increasing salt concentration but were nearly independent of temperature. The salt dependence of K _b led to the conclusion that ca. 3 counterions bound to dPGS were released upon complex formation. The gain in entropy ΔG _ci by this counterion-release scales logarithmically with salt concentration and is the main driving force for binding. The temperature dependence of ΔG ^o was analyzed by the nonlinear van't Hoff plot, taking into account a finite heat capacity change ΔC . This evaluation led to the binding enthalpy ΔH _vH and the binding entropy ΔS _vH. Both quantities varied strongly with temperature and even changed sign, but they compensated each other throughout the entire range of temperature. Coarse-grained computer simulations with explicit salt and implicit water were used to obtain the binding free energies that agreed with ITC results. Thus, electrostatic factors were the driving forces for binding whereas all hydration contributions leading to the strongly varying ΔH _vH and ΔS _vH canceled out. The calorimetric enthalpy ΔH _ITC measured directly by ITC differed largely from ΔH _vH. ITC measurements done in two buffer systems with different ionization enthalpies revealed that binding was linked to buffer ionization and a partial protonation of the protein.