We present here a mathematical model that accounts for the various proportions of plasma membrane constituents occurring in the lysosomal membrane of rat fibroblasts (Draye, J.-P., J. Quintart, P. J. Courtoy, and P. Baudhuin. 1987. Eur. J. Biochem. 170: 395-403; Draye, J.-P., P. J. Courtoy, J. Quintart, and P. Baudhuin. 1987. Eur. J. Biochem. 170:405-411). It is based on contents of plasma membrane markers in purified lysosomal preparations, evaluations of their half-life in lysosomes and measurements of areas of lysosomal and plasma membranes by morphometry. In rat fibroblasts, structures labeled by a 2-h uptake of horseradish peroxidase followed by a 16-h chase (i.e., lysosomes) occupy 3% of the cellular volume and their total membrane area corresponds to 30% of the pericellular membrane area. Based on the latter values, the model predicts the rate of inflow and outflow of plasma membrane constituents into lysosomal membrane, provided their rate of degradation is known. Of the bulk of polypeptides iodinated at the cell surface, only 4% reach the lysosomes every hour, where the major part (integral of 83%) is degraded with a half-life in lysosomes of integral to 0.8 h. For specific plasma membrane constituents, this model can further account for differences in the association to the lysosomal membrane by variations in the rate either of lysosomal degradation, of inflow along the pathway from the pericellular membrane to the lysosomes, or of lateral diffusion.

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