Stochastic Model for the Internal Transfer Kinetics of Cargo in Two-Compartment Carriers

Lipid vesicles and related nanocarriers often contain two compartments, such as the inner and outer leaflets of a bilayer membrane, between which amphipathic molecules can migrate. We develop a stochastic model for describing the transfer kinetics of cargo between the two compartments in an ensemble of carriers, neglecting inter-carrier exchange to focus exclusively on intra-carrier redistribution. Starting from a set of rate equations, we examine the Gaussian regime in the limit of low cargo occupation where Gaussian and Poissonian statistics overlap. We derive a Fokker–Planck equation that we solve analytically for any initial cargo distribution among the carriers. Moments of the predicted distributions and examples, including a comparison between numerical solutions of the rate equations and the analytic solutions of the Fokker–Planck equation, are presented and discussed, thereby establishing a theoretical foundation to study coupled intra- and inter-carrier transport processes in mobile nanocarrier systems.