Donnan equilibrium of ionic drugs in pH-dependent fixed charge membranes: theoretical modeling

We have studied theoretically the partition equilibrium of a cationic drug between an electrolyte solution and a membrane with pH-dependent fixed charges using an extended Donnan formalism. The aqueous solution within the fixed charge membrane is assumed to be in equilibrium with an external aqueous solution containing six ionic species: the cationic drug (DH(+)), the salt cations (Na(+) and Ca(2+)), the salt anion (Cl(-)), and the hydrogen and hydroxide ions. In addition to these mobile species, the membrane solution may also contain four fixed species attached to the membrane chains: strongly acid sulfonic groups (SO(3)(-)), weakly acid carboxylic groups in dissociated (COO(-)) and neutral (COOH) forms, and positively charged groups (COO...Ca(+)) resulting from Ca(2+) binding to dissociated weakly acid groups. The ionization state of the weak electrolyte groups attached to the membrane chains is analyzed as a function of the local pH, salt concentration, and drug concentration in the membrane solution, and particular attention is paid to the effects of the Ca(2+) binding to the negatively charged membrane fixed groups. The lipophilicity of the drug is simulated by the chemical partition coefficient between the membrane and external solutions giving the tendency of the drug to enter the membrane solution due to hydrophobic interactions. Comparison of the theoretical results with available experimental data allows us to explain qualitatively the effects that the pH, salt concentration, drug concentration, membrane fixed charge concentration, and Ca(2+) binding exert on the ionic drug equilibrium. The role of the interfacial (Donnan) electric potential difference between the membrane and the external solutions on this ionic drug equilibrium is emphasized throughout the paper.