Physical model relating diffusional transport and concurrent metabolism of peptides in metabolically active cell sheets.

The physical model developed describes the complex interplay of diffusion and saturable metabolism in metabolically active cell sheets under reflection kinetics in contact with a bulk solution containing a substrate. A prominent implication of this work is the enzymatic cleavage of drugs in the viable epidermis, which represents the major metabolic barrier of the skin. The mathematical solution is based on steady-state Fickian diffusion and nonlinear Michaelis-Menten kinetics. Both substrate concentration gradients in the cell sheets and metabolic rates versus substrate concentration profiles were generated by mathematical simulation. The effects of various parameter estimates on the overall kinetics were studied (i.e., cell sheet thickness, effective diffusion coefficient, cell sheet/bulk solution partition coefficient, and maximum metabolic rate). By variation of the parameters, shifts between metabolism control and diffusion control are predicted. As an example, metabolism-controlled substrate turnover in thin cell sheets transforms into diffusion control in thick cell sheets, as diffusion of fresh substrate into cell sheets of increasing thickness becomes rate limiting. Close approximation of experimental data concerning Ala-4-methoxy-2-naphthylamide and Leuenkephalin metabolism in cell culture sheet was achieved by independent simulations. The model may thus help to evaluate the potential of metabolically labile drugs (e.g., peptides) to penetrate the metabolic barrier of the viable epidermis.