Abstract
For a number of reasons, receptor-mediated endocytosis provides an ideal system in which a biological process can be approached with mathematical modeling. Much progress has been made in the ability to define and measure individual steps in the complex multistep process of endocytosis, and the use of radiolabeled ligands makes quantitative kinetic data accessible to the modeler. In this chapter we briefly explore the role of mathematical modeling in interpreting experimental data and in elucidating details about the pathway of receptor-mediated endocytosis. We first discuss our current view of the endocytic pathway, emphasizing the kinetic and mechanistic possibilities for both ligand and receptor as they embark on their cellular journeys. We then review some of the published modeling of endocytosis; finally, we focus on the early steps in the binding and internalization of ligand and discuss in some detail the mathematics of these aspects of the process. Two particularly well-described systems are used to illustrate the endocytic pathway: the hepatic asialoglycoprotein (ASGP) receptor and the low-density lipoprotein (LDL) receptor.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, R. G. W., Goldstein, J. L., and Brown, M. S., 1976, Localization of low density lipoprotein receptors on plasma membrane of normal human fibroblasts and their absence in cells from a hypercholesterolemia homozygote, Proc. Natl. Acad. Sci. USA 73: 2434–2438.
Anderson, R. G. W., Brown, M. S., and Goldstein, J. L., 1977a, Role of the coated endocytic vesicle in the uptake of receptor-bound low density lipoprotein in human fibroblasts, Cell 10: 351–364.
Anderson, R. G. W., Goldstein, J. L., and Brown, M. S., 1977b, A mutation that impairs the ability of lipoprotein receptors to localize in coated pits on the cell surface of human fibroblasts, Nature 270: 695–699.
Barak, L. S., and Webb, W. W., 1982, Diffusion of low density lipoprotein-receptor complex on human fibroblasts, J. Cell Biol. 95: 846–852.
Berg, H. C., and Purcell, E. M., 1977, Physics of chemoreception, Biophys. J. 20: 193–219.
Berman, M., Shahn, E, and Weiss, M. F., 1962, The routein fitting of kinetic data to models: A mathematical formalism for digital computers, Biophys. J. 2: 275–290.
Bridges, K., Harford, J., Ashwell, G., and Klausner, R. D., 1982, Fate of receptor and ligand during endocytosis of asialoglycoproteins by isolated hepatocytes, Proc. Natl. Acad. Sci. USA 79: 350–354.
Brown, M. S., Anderson, R. G. W., and Goldstein, J. L., 1983, Recycling receptors: The round trip itinerary of migrant membrane proteins, Cell 32: 663–667.
Carpentier, J. L., Gordon, P., Goldstein, J. L., Anderson, R. G. W., Brown, M. S., and Orci, L., 1979, Binding and internalization of 125I-LDL in normal and mutant human fibroblasts, Exp. Cell Res 12: 131–142.
Davies, P. F., and Kuczera, L., 1981, Endocytic vesicles and surface invaginations in cultured vascular endothelium: A morphometric comparison, J. Histochem. Cytochem. 29: 1437–1441.
Fan, J. Y., Carpentier, J.-L., Gorden, P., Obberghen, E. V., Blackett, N. M., Grunfeld, C., and Orci, L., 1982, Receptor-mediated endocytosis of insulin: Role of microvilli, coated pits, and coated vesicles. Proc. Natl. Acad. Sci. USA 79: 7788–7791.
Gex-Fabry, M., and DeLisi, C., (in press), Receptor-mediated endocytosis: A model and its implications from experimental analysis, Am. J. Physiol.
Goldstein, B., Wofsy, C., and Bell, G., 1981, Interaction of low density lipoprotein receptors with coated pits on human fibroblasts: Estimate of the forward rate constant and comparison with the diffusion limit. Proc. Natl. Acad. Sci. USA 78: 5695–5698.
Goldstein, B., and Weigel, F. W., 1983, The effect of receptor clustering on diffusion-limited forward rate constants, Biophys. J. 43: 121–125.
Goldstein, B., Griego, R., and Wofsy, C. (in press), Diffusion limited forward rate constants in two dimensions: Application to the trapping of cell surface receptors by coated pits, Biophys. J.
Goldstein, J. L., Brown, M. S., and Stone, N. J., 1977, Genetics of the LDL receptor: Evidence that the mutations affecting binding and internalization are allelic, Cell 12: 629–641.
Harford, J., Bridges, K., Ashwell, G., and Klausner, R. D., 1983a, Intracellular dissociation of receptor-bound asialoglycoproteins in cultured hepatocytes: A pH-mediated nonlysosomal event, J. Biol. Chem. 258: 3191–3197.
Harford, J., Wolkoff, A. W., Ashwell, G., and Klausner, R. D., 1983b, Monensin inhibits intracellular dissociation of asialoglcyoproteins from their receptor. J. Cell Biol. 96: 1824–1828.
Helenius, A., Mellman, I., Wall, D., and Hubbard, A., 1983, Endosomes, Trends Biochem. Sci. 8: 245–250.
Innerarity, T. L., Pitas, R. E., and Mahley, R. W., 1980, Receptor binding of cholesterol-induced high-density lipoproteins containing predominantly apoprotein E to cultured fibroblasts with mutations at the low-density lipoprotein receptor locus, Biochemistry 19: 4359–4365.
Larkin, J. M., Brown, M. S., Goldstein, J. L., and Anderson, R. G. W., 1983, Depletion of intracellular potassium arrests coated pit formation and receptor-mediated endocytosis in fibroblasts, Cell 33: 273–285.
Maxfield, F. R., Willingham, M. C., Pastan, I., Dragsten, P., and Cheng, S.-Y., 1981, Binding and mobility of the cell surface receptors for 3,3’,5-triiodo-L-thyronine, Science 211: 63–65.
Oka, J. A., and Weigel, P. H., 1983, Recycling of asialoglycoprotein receptor in isolated rat hepatocytes: Dissociation of internalized ligand from receptor occurs in two kinetically and thermally distinguishable compartments, J. Biol. Chem. 258: 10253–10262.
Orci, L., Carpentier, J.-L., Perrelet, A., Anderson, R. G. W., Goldstein, J. L., and Brown, M. S., 1978, Occurrence of low density lipoprotein receptors with large pits on the surface of human fibroblasts as demonstrated by freeze-etching, Exp. Cell Res. 113: 1–13.
Pastan, I. H., and Willingham, M. C., 1981, Receptor-mediated endocytosis in cultured cells, Annu. Rev. Physiol. 42: 239–250.
Pastan, I. H., and Willingham, M. C., 1983, Receptor-mediated endocytosis: Coated pits, receptosomes, and the Golgi, Trends Biochem. Sci. 8: 250–254.
Petersen, O. W., and van Vuers, B., 1983, Serial-section analysis of coated pits and vesicles involved in adsorptive pinocytosis in cultured fibroblasts, J. Cell Biol. 96: 277–281.
Pitas, R. E., Innerarity, T. L., Arnold, K. S., and Mahley, R. W., 1979, Rate and equilibrium constants for binding of apo-E HDLG (a cholesterol-induced lipoprotein) and low density lipoproteins to human fibroblasts: Evidence for multiple receptor binding of apo-E HDLG, Proc. Natl. Acad. Sci. USA 76: 2311–2315.
Robenck, H., and Hesz, A., 1983, Dynamics of low-density lipoprotein receptors in the plasma membrane of cultured human skin fibroblasts as visualized by colloidal gold in conjunction with surface replicas, Eur. J. Cell Biol. 31: 275–282.
Rodbard, D., 1979, Negative cooperativity: Positive finding? Am. J. Physiol. 237: E203–E205. Scatchard, G., 1949, The attractions of proteins for small molecules and ions, Ann. N.Y. Acad. Sci. 51: 660–672.
Schlessinger, J., Shechter, Y., Cuatrecasas, P., Willingham, M. C., and Pastan, I., 1978, Quantitative determination of the lateral diffusion coefficients of the hormone-receptor complexes of insulin and epidermal growth factor on the plasma membrane of cultured fibroblasts, Proc. Natl. Acad. Sci. USA 75: 5353–5357.
Schwartz, A. L., Fridovich, S. E., and Lodish, H. F., 1982, Kinetics of internalization and recycling of the asialoglycoprotein receptor in a hepatoma cell line, J. Biol. Chem. 257: 4230–4237.
Tycko, B., Keith, C. H., and Maxfield, F. R., 1983, Rapid acidification of endocytic vesicles containing asialoglycoprotein in cells of a human hepatoma line, J. Cell Biol. 97: 1762–1776.
Wall, D. A., Wilson, G., and Hubbard, A. L., 1980, The galactose-specific recognition system of mammalian liver: Route of ligand internalization in rat hepatocytes, Cell 21: 79–93.
Wall, D. A., and Hubbard, A. L., 1981, Galactose-specific recognition system of mammalian liver: Receptor distribution on the hepatocyte cell surface, J. Cell Biol. 90: 687–696.
Wiley, H. S., and Cunningham, D. D., 1981, A steady state model for analyzing the cellular binding, internalization and degradation of polypeptide ligands, Cell 25: 433–440.
Wiley, H. S., and Cunningham, D. D., 1982, The endocytotic rate constant. A cellular parameter for quantitating receptor-mediated endocytosis. J. Biol. Chem. 257: 4222–4229.
Wiley, H. S. (in press), Receptors as models for the mechanisms of membrane protein turnover and dynamics, in: Current Topics in Membranes and Transport, Volume 20: Membrane Protein Biosynthesis and Turnover (P. A. Knaut and J. S. Cook, eds.), Academic Press, New York.
Willingham, M. C., and Pastan, I., 1980, The receptosome: An intermediate organelle of receptor-mediated endocytosis in cultured fibroblasts, Cell 21: 67–77.
Willingham, M. C., Rutherford, A. V., Gallo, M. G., Wehland, J., Dickson, R. B., Schlegel, R., and Pastan, I. H., 1981, Receptor-mediated endocytosis in cultured fibroblasts: Cryptic coated pits and the formation of receptosomes, J. Histochem. Cytochem. 29: 1003–1013.
Willingham, M C, and Pastan, I. H., 1983, Formation of receptosomes from plasma membrane coated pits during endocytosis: Analysis by serial section with improved membrane labeling and preservation techniques, Proc. Natl. Acad. Sci. USA 80: 5617–5621.
Wofsy, C., and Goldstein, B., (in press). Coated pit and low density lipoprotein recycling, in: Cell Surface Dynamics: Concepts and Models (A. Perelson, C. DeLisi, and F. Weigel, eds.), Marcel Dekker, New York.
Wolkoff, A. W., Klausner, R. D., Ashwell, G., and Harford, J., 1984, Intracellular segregation of aisaloglycoproteins and their receptor: A prelysosomal event subsequent to dissociation of the ligand-receptor complex, J. Cell Biol. 98: 375–381.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Plenum Press, New York
About this chapter
Cite this chapter
Klausner, R., Van Renswoude, J., Harford, J., Wofsy, C., Goldstein, B. (1985). Mathematical Modeling of Receptor-Mediated Endocytosis. In: Pastan, I., Willingham, M.C. (eds) Endocytosis. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6904-6_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-6904-6_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-6906-0
Online ISBN: 978-1-4615-6904-6
eBook Packages: Springer Book Archive