(27) Hence, a measurement of ω1 and ω2 could be used to obtain the two model parameters (K and G). Figure 6 displays a plot of MdO(t), MdI(t), MaO(t), MaI(t), Ma(t), Md(t), calculated for G/K = 1/10 and Na/N = Nd/N = 0.5. All drug CHIR-258 concentration molecules are initially distributed equally among the two leaflets of the donor liposomes. Release of drug molecules from the outer leaf of the donor liposomes is fast (K = 10G), the slow process is the flip-flop of drug molecules between the Inhibitors,research,lifescience,medical two leaflets of the liposomes. Hence, at intermediate times, say at t = 3/K, the

outer leaflets have almost reached their equilibrium values whereas the inner layers remain still fairly close to their initial values. After reaching thermal equilibrium (t → ∞), half of all drug molecules Inhibitors,research,lifescience,medical have migrated to the acceptor

liposomes. Clearly, the presence of the two different rate constants (K and G) leads to the biexponential behavior of Md and Ma in Figure 6. Figure 6 Fractions of drug molecules in inner and outer leaflets of donor and acceptor liposomes. Inhibitors,research,lifescience,medical The quantities MdO(t), MdI(t), MaO(t), and MaI(t) are plotted according to (26) for G/K = 1/10 and Na/N = Nd/N = 0.5. The broken lines show the biexponential behaviors … We briefly discuss two limiting cases for (26). First, for G = 0 the flip-flop of drug molecules between the inner and outer leaves is infinitely slow, implying MdI(t) = M/2, MaI(t) = 0, MaO(t) = M/2 − MdO(t) = (1 − e−Kt)(MNa)/(2N). In this case, we recover the kinetics of (8), yet with only M/2 (instead of M) Inhibitors,research,lifescience,medical drug molecules participating in the transfer and identical donor and acceptor liposomes (k = 0). Second, for G → ∞ flip-flop becomes infinitely fast and (26) read MaI(t) = MaO(t) = M/2 − MdI(t) = M/2 − MdO(t) = (1 − e−Kt/2)(MNa)/(2N). Because 50% of the drug molecules reside in the inner leaflets, they do not contribute to the outer-leaflet-concentration-differences

that drive the transfer kinetics. Hence, the apparent rate constant is reduced from K to K/2. 4. Conclusions In Inhibitors,research,lifescience,medical this work, we have presented a detailed model for the transfer kinetics of poorly water-soluble drug molecules many between liposomal carrier systems. Apart from liposomes, the scope of the model includes other types of small and mobile pharmaceutical nanocarriers, such as micelles, colloids, and nanoparticles. Starting from a microscopic distribution function of drug molecules among donor and acceptor liposomes, we have specified the conditions that lead to an apparent first-order kinetic behavior. These include low drug loading of the liposomes, strict proportionality of all rate constants to drug concentrations, no aggregation phenomena of drugs within liposomes, and no overlap of the intraliposomal flip-flop kinetics. Systems that do not fulfill these conditions do not, generally, exhibit an apparent first-order kinetics. Instead the behavior may become biexponential or sigmoidal.