Release of cationic polymer-DNA complexes from the endosome: A theoretical investigation of the proton sponge hypothesis

Polyplexes are complexes composed of DNA and cationic polymers; they are promising transport vehicles for nonviral gene delivery. Cationic polymers that contain protonatable groups, such as polyethylenimine, have been suggested to trigger endosomal escape of polyplexes according to the proton sponge hypothesis. Here, osmotic swelling is induced by a decrease in the endosomal pH value, leading to an accumulation of polymer charge accompanied by the influx of Cl(-) ions to maintain overall electroneutrality. We study a theoretical model of the proton sponge mechanism. The model is based on the familiar Poisson-Boltzmann approach, modified so as to account for the presence of ionizable polyelectrolytes within self-consistent field theory with assumed ground state dominance. We consider polyplexes, composed of fixed amounts of DNA and cationic polymer, to coexist with uncomplexed cationic polymer in an enclosing vesicle of fixed volume. For such a system, we calculate the increase in osmotic pressure upon moderately decreasing the pH value and relate that pressure to the rupture tension of the enclosing membrane. Our model predicts membrane rupture upon pH decrease only within a certain range of free polymer content in the vesicle. That range narrows with increasing amount of DNA. Consequently, there exists a maximal amount of DNA that can be incorporated into a vesicle while maintaining the ability of content release through the proton sponge mechanism.