Salt effects on polyelectrolyte-ligand binding: comparison of Poisson-Boltzmann, and limiting law/counterion binding models.
The theory for salt dependence of the free energy, entropy, and enthalpy of a polyelectrolyte in the PB (PB) model is extended to treat the nonspecific salt dependence of polyelectrolyte-ligand binding reactions. The salt dependence of the binding constant (K) is given by the difference in osmotic pressure terms between the reactants and products. For simple 1-1 salts it is shown that this treatment is equivalent to the general preferential interaction model for the salt dependence of binding [C. Anderson and M. Record (1993) Journal of Physical Chemistry, Vol. 97, pp. 7116-7126]. The salt dependence, entropy, and enthalpy are compared for the PB model and one specific form of the preferential interaction coefficient model that uses counterion condensation/limiting law (LL) behavior. The PB and LL models are applied to three ligand-polyelectrolyte systems with the same net ligand charge: a model sphere-cylinder binding reaction, a drug-DNA binding reaction, and a protein-DNA binding reaction. For the small ligands both the PB and limiting law models give (In K vs. In[salt]) slopes close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the predominant ion cratic (release) entropy in the limiting law model. The relative contributions of these three terms in the PB model depends on the ligand: For the protein, ion release entropy is the smallest contribution to the salt dependence of binding. The effect of three approximations made in the LL model is examined: These approximations are (1) the ligand behaves ideally, (2) the preferential interaction coefficient of the polyelectrolyte is unchanged upon ligand binding, and (3) the polyelectrolyte preferential interaction coefficient is given by the limiting law/counterion-condensation value. Analysis of the PB model shows that assumptions 2 and 3 break down at finite salt concentrations. For the small ligands the effects on the slope cancel, however, giving net slopes that are similar in the PB and LL models, but with a different entropy/enthalpy breakdown. For the protein ligand the errors from assumptions 2 and 3 in the LL models do not cancel.