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Kinetics of passive transport in water/membrane/water system. A mathematical description.

Passive transport across the lipid region of the membrane is considered to be one of the main mechanisms by which many solutes, especially xenobiotics, enter the cell (Stein 1981). Although the problem of mathematical description of the process has been intensively treated, it continues to be a subject of controversy. Some approaches do not take into account the solute accumulation in the membrane (Stein 1981), while others consider only equal volumes of individual phases (Kubinyi 1976; van de Waterbeemd et al. 1978; Hyde and Lord 1979; Cooper et al. 1981; Aarons et al. 1982). However, apparently any of the approximations mentioned above does not fully correspond to the real situation. In this communication usefully simplified equations for general description of the time course of solute accumulation in both aqueous compartments as well as in the membrane are presented. The kinetics of the solute partitioning in a 3-compartment system (Fig. 1) can be described by a set of linear differential equations (1)—(3) using the real assumption of practically instantaneous homogeneous concentration in the bulks of individual phases, owing to their small volumes (Baláž et al. 1984) or to appropriate stirring: