Modelling Approach to Enzymatic pH Oscillators in Giant Lipid Vesicles

The urease-catalyzed hydrolysis of urea can display feedback driven by base production (NH 3 ) resulting in a switch from acidic to basic pH under non-buffered conditions. Thus, this enzymatic reaction is a good candidate for investigation of chemical oscillations or bistability. In order to determine the best conditions for oscillations, a two-variable model was initially derived in which acid and urea were supplied at rates k H and k S from an external medium to an enzyme-containing compartment. Oscillations were theoretically observed providing the necessary condition that k H > k S was met. To apply this model, we devised an experimental system able to ensure the fast transport of acid compared to that of urea. In particular, by means of the droplet transfer method, we encapsulated the enzyme, together with a proper pH probe, in 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) based liposomes, where differential diffusion of H + and urea is ensured by the different permeability (P m ) of the membrane to the two species. Here we present an improved theoretical model that accounts for the products transport and for the probe hydrolysis, to obtain a better guidance for the experiments.