The effect of diffusion on the binding of membrane-bound receptors to coated pits

We have formulated a kinetic model for the primary steps that occur at the cell membrane during receptor-mediated endocytosis. This model includes the diffusion of receptor molecules, the binding of receptors to coated pits, the loss of coated pits by invagination, and random reinsertion of receptors and coated pits. Using the mechanistic statistical theory of nonequilibrium thermodynamics, we employ this mechanism to calculate the two-dimensional radial distribution of receptors around coated pits at steady state. From this we obtain an equation that describes the effect of receptor diffusion on the rate of binding to coated pits. Our equation does not assume that ligand binding is instantaneous and can be used to assess the effect of diffusion on the binding rate. Using experimental data for low density lipoprotein receptors on fibroblast cells, we conclude that the effect of diffusion on the binding of these receptors to coated pits is no more than 84% diffusion controlled. This corresponds to a dissociation rate constant for receptors on coated pits (k-) that is much less than the rate constant for invagination of the pits (lambda = 3.3 X 10(-3)/s) and a correlation length for the radial distribution function of six times the radius of a coated pit. Although the existing experimental data are compatible with any value of k-, we obtain a lower bound for the value of the binding constant (k+) of 2.3 X 10(-2)(micron)2/s. Comparison of the predicted radial distributions with experiment should provide a clear indication of the effect of diffusion on k+.