Electrostatic and specific binding to macromolecular ligands: A general analytical expression for the Donnan volume

The dependence of the apparent acid dissociation constant of charged polyacids on the ionic strength and on the degree of dissociation is analysed in terms of the Donnan model. We introduce a new approximate analytical expression for the Donnan volume which depends on the ionic strength and on the degree of dissociation with only one adjustable parameter. This expression stems from analytical solutions of the non-linear Poisson–Boltzmann equation (NLPB) under different geometries. Two kinds of polyelectrolytes are studied: polyacrylic acid (PAA), as a model of homogeneous ligand, and Aldrich humic acid (HA), a heterogeneous ligand which exhibits a pKa dependent on the pH, even when the polyelectrolytic correction is applied. The new approximate Donnan volume expression allows to justify the empirical dependence of previous expressions found in the literature on the ionic strength, gives rise to master curves well behaved in all the range of macromolecular charges and can fit experimental results in good agreement with classical treatments like NLPB, used as a reference, involving a greatly simplified numerical treatment. Three different complexation isotherms are independently used to account for the specific binding. The robustness of the results is evidenced by the fact that similar central moments of the affinity distribution underlying each isotherm and of the adjustable parameter of the Donnan volume are obtained in each case.