A rigorous theory of remote loading of drugs into liposomes

Abstract

Various gradients have been used to actively load molecules into preformed colloidal particles separated from a medium by a semipermeable membrane. Therapeutic applications of liposomes have predominantly utilized pH and ammonium sulfate gradient methods to load drug molecules, which are weak bases or acids, into preformed liposomes. Except for the influence of a few simple parameters in the case of the pH gradient loading, the influences of many variables, involving different mechanisms and processes affecting the loading, are not well understood. Here we present a rigorous theoretical treatment to explain these phenomena and simulate loading processes as a function of any given variable. Firstly, taking into account acid/base equilibria, we develop an Ansatz to calculate the pH of any solution as well as concentration of any species under given conditions. We use this concept to explain pH gradient loading and exchange gradient loading in the cases of simple or coupled redistribution of species across a semipermeable membrane in one or two directions. Finally we add the interaction of permeated species with the bilayer or with the liposome preencapsulated material and evaluate both concepts of loading for the case of drug binding to the membrane and formation of precipitate in the liposome. As a result, some examples of possible drug loading systems are simulated, discussed, and represented in the form of families of curves, showing the most significant parameters in the equilibrated liposome systems after loading. In general, the mathematical methodology presented in this article can be used to simulate physical and chemical processes which occur in any two compartment system separated by a semipermeable membrane.