A theoretical model of LDL-receptor trapping on a spherical cell

The kinetics of the trapping of LDL-receptor complexes by coated pits on the surface of fibroblasts is examined in this paper. We have recently developed a mathematical formalism to extend Keizer's non-linear, non-equilibrium fluctuation-dissipation theory to the kinetics of chemical systems constrained to a spherical surface. Keizer's theory is ideally suited to the study of open biological systems. In the past it has been used to investigate endocytosis on fibroblasts. However, these applications have modeled the cell membrane with an infinite plane. As such, the finite size of the cellular membrane, as well as its precise symmetry, could not be incorporated into the previous studies. Thus in this paper we use our recently developed methodology to reexamine the trapping step in endocytosis on spherical cells. For cell surface processes, the theoretical consideration of a spherical symmetry or an infinite plane, in model calculations, will depend on the experimental or in vivo conditions of the processes of interest. For a spherical symmetry, we find that the finite size of the cell surface does not significantly affect the rate of the trapping step given the empirically determined values for the relevant parametes on fibroblasts. This result supports the approximation used in the previous investigation. However, this and other analyses indicate that the finitie size of the biological surface probably is an important parameter for processes which occur on smaller biological surfaces such as those found on organelles.