Skip to main content
SpringerLink
Log in

A mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

An extension of an earlier model of the p170 glycoprotein pump is presented. In an earlier work (Michelson and Slate,Bull. math. Biol. 54, 1023–1038, 1992), the pump was modeled using an energy-dependent model of facilitated diffusion. In this paper we add an inhibitor to the model. New equations are derived which represent either competitive or non-competitive inhibition in the pumping action of the glycoprotein. Numerical simulations were run which provide a response surface (initial loading concentration of inhibitor and its ability to compete with an ideal anti-cancer drug vs a summary measure of cytoplasmic exposure) for each scenario. The importance of the exposure profile, how it is related to ultimate tumor cell survival, and the binding requirements for developing multidrug resistance inhibitors are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Barman, T. E. 1969.Enzyme Handbook, Vols I and II. Berlin: Springer.

    Google Scholar 

  • Beck, W. T. and X.-D. Qian. 1992. Photoaffinity substrate for P-glycoprotein.Biochem. Pharmac. 43, 89–93.

    Article  Google Scholar 

  • Bruggemann, E. P., S. J. Currier, M. M. Gottesman and I. Pastan. 1992. Characterization of the azidopine and vinblastine binding site of P-glycoprotein.J. biol. Chem. 267, 21,010–21,026.

    Google Scholar 

  • Coldman, A. J. and J. H. Goldie, 1983. A model for the resistance of tumor cells to cancer chemotherapeutic agents.Math. Biosci. 65, 291–307.

    Article  MATH  Google Scholar 

  • Coldman, A. J., J. H. Goldie and V. Ng. 1985. The effects of cellular differentiation on the development of permanent drug resistance.Math. Biosci. 74, 177–198.

    Article  MATH  Google Scholar 

  • Croop, J. M., P. Gros and D. E. Housman. 1988. Genetics of multidrug resistance.J. clin. Invest. 81, 1303–1309.

    Article  Google Scholar 

  • Currier, S. J., S. E. Kane, M. C. Willingham, C. D. Cardarelli, I. Pastan and M. M. Gottesman. 1992. Identification of residues in the first cytoplasmic loop of P-glycoprotein involved in the function of the chimeric human MDR1-MDR2 transporters.J. biol. Chem. 267, 25,153–25,159.

    Google Scholar 

  • Day, R. S. 1986a. A branching process model for heterogeneous cell populations.Math. Biosci. 78, 73–90.

    Article  MATH  MathSciNet  Google Scholar 

  • Day, R. S. 1986b. Treatment sequencing, asymmetry, and uncertainty: protocol strategies for combination chemotherapy.Cancer Res. 46, 3876–3885.

    Google Scholar 

  • Devine, S. E., V. Ling and P. W. Malera. 1992. Amino acid substitutions in the sixth transmembrane domain of P-glycoprotein alter multidrug resistance.Proc. natn. Acad. Sci. U.S.A. 89, 4564–4568.

    Article  Google Scholar 

  • Doige, C.A., X. Yu and F. J. Sharom. 1992.ATPase activity of partially purified P-glycocprotein from multidrug-resistant Chinese hamster ovary cells.Biochim. biophys. Acta 1109, 149–160.

    Article  Google Scholar 

  • Ferry, D. R., M. A. Russell and M. H. Cullen. 1992. P-glycoprotein possesses a 1,4-dihydropyridine-selective drug acceptor site which is allosterically coupled to a vinca alkaloid-selective binding site.Biochem. biophys. Res. Commun. 188, 440–445.

    Article  Google Scholar 

  • Ford, J. M. and W. N. Hait. 1990. Pharmacology of drugs that alter multidrug resistance in cancer.Pharmac. Rev. 42, 155–199.

    Google Scholar 

  • Goldie, J. H. and Coldman, A. J. 1979. A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate.Cancer Treat. Rep. 63, 1727–1733.

    Google Scholar 

  • Goldie, J. H. and A. J. Coldman. 1984. The genetic origin of drug resistance in neoplasms: implications for systemic therapy.Cancer Treat. Rep. 67, 923–931.

    Google Scholar 

  • Goldie, J. H., A. J. Coldman and Gudauskas, G. A. 1982. Rationale for the use of alternating non-cross-resistant chemotherapy.Cancer Treat. Rep. 66, 439–449.

    Google Scholar 

  • Gottesman, M. and I. Pastan. 1988. Resistance to multiple chemotherapeutic agents in human cancer cells.Trends Pharmac. Sci. 9, 54–58.

    Article  Google Scholar 

  • Greenberger, L. M., C. J. Lisanti, J. T. Silva and S. B. Horowitz. 1991. Domain mapping of the photoaffinity drug-binding sites in P-glyprotein encoded by mousemdr1b.J. biol. Chem. 266, 20,744–20,751.

    Google Scholar 

  • Hamada, H. and T. Tsuruo. 1988. Characterization of theATPase activity of the Mr 170,000 to 180,000 membrane glycoprotein (P-glycoprotein) associated with multidrug resistance inK562/ADM cells.Cancer Res. 48, 4926–4932.

    Google Scholar 

  • Higgins, C. F. 1992.ABC transporters: from micro-organisms to man.A. Rev. Cell Biol. 8, 67–113.

    Google Scholar 

  • Higgins, C. F. and M. M. Gottesman. 1992. Is the multidrug transporter a flippase?Trends biochem. Sci. 17, 18–21.

    Article  Google Scholar 

  • Horio, M., E. Lovelace, I. Pastan and M. M. Gottesman. 1991. Agents which reverse multidrug-resistance are inhibitors of [3H]vinblastine transport by isolated vesicles.Biochim. biophys. Acta 1061, 106–110.

    Article  Google Scholar 

  • Inaba, M., H. Kobayashi, Y. Sakurai and R. K. Johnson, 1979. Active efflux of daunorubicin and adriamycin in sensitive and resistant sublines ofP388 leukemia.Cancer Res. 42, 4730–4733.

    Google Scholar 

  • Juliano, R. L. and V. Ling. 1976. Cell surface P-glycoprotein modulating drug permeability in Chinese hamster ovary cell mutants.Biochim. biophys. Acta. 455, 152–162.

    Article  Google Scholar 

  • Kartner, N., J. R. Riordan and V. Ling. 1983. Cell surface P-glycoprotein associated with multidrug resistance in mammalian cell lines.Science 221, 1285–1288.

    Google Scholar 

  • Lehnert, M., W. S. Dalton, D. Roe, S. Emerson and S. Salmon. 1991. Synergistic inhibition by verapamil and guinine ofP-glycoprotein-mediated multidrug resistance in a human myeloma cell line model.Blood 77, 348–354.

    Google Scholar 

  • Ling, V. and L. H. Thompson. 1974. Reduced permeability in CHO cells as a mechanism of resistance to colchicine.J. Cell Physiol. 83, 103–116.

    Article  Google Scholar 

  • Michelson, S. and D. L. Slate. 1989. Emergence of the drug-resistant phenotype in tumor subpopulations. A hybrid model.J. Nat. Cancer Inst. 81, 1392–1401.

    Google Scholar 

  • Michelson, S. and D. L. Slate. 1992. A mathematical model of the multidrug resistant P-glycoprotein pump.Bull. math. Biol. 54, 1023–1038.

    Article  MATH  Google Scholar 

  • Moscow, J. A. and K. H. Cowan. 1988. Multidrug resistance.J. Nat. Cancer Inst. 80, 14–20.

    Google Scholar 

  • Pastan, I. and M. Gottesman. 1987. Multiple drug resistance in human cancer.New Engl. J. Med. 316, 1388–1393.

    Article  Google Scholar 

  • Schimke, R. T. 1984. Gene amplification, drug resistance, and cancer.Cancer Res. 44, 1735–1742.

    Google Scholar 

  • Slate, D. L. and S. Michelson. 1991. Drug resistance reversal strategies: a comparison of experimental data with model predictions.J. Nat. Cancer Inst. 83, 1574–1580.

    Google Scholar 

  • Spoelstra, E. C., H. V. Westerhoff and J. Lankelma. 1992. Kinetics of daunorubicine transport by P-glycoprotein of intact cancer cells.Eur. J. Biochem. 207, 567–579.

    Article  Google Scholar 

  • Tamai, I. and A. R. Safa. 1991. Azidopine noncompetitively interacts with vinblastine and cyclosporinA binding to P-glycoprotein in multidrug resistant cells.J. biol. Chem. 226, 16,796–16,800.

    Google Scholar 

  • Tsuruo, T., H. Iida, S. Tsukagoshi and Y. Sakurai. 1982. Increased accumulation of vincristine and adriamycin in drug-resistantP388 tumor cells following incubation with calcium antagonists and calmodulin inhibitors.Cancer Res. 42, 4730–4733.

    Google Scholar 

  • Watanabe, T., M. Inaba and Y. Sugiyama. 1989. Saturable process involved in active efflux of vincristine as a mechanism of multidrug resistance inP388 leukemia cells.Pharm. Res. 6, 690–696.

    Article  Google Scholar 

  • White, A., P. Handler, E. L. Smith, R. L. Hill and I. R. Lehman. 1979.Principles of Biochemistry. Sixth Edn. New York: McGraw-Hill.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomathematics, Syntex Drug Discovery Research, M/S S3-1B, 3401 Hillview Ave., 94303, Palo Alto, CA, U.S.A.

    Seth Michelson

  2. Syntex Research, Institute of Biochemistry and Cell Biology, M/S S3-1, 3401 Hillview Ave., 94303, Palo Alto, CA, U.S.A.

    Doris Slate

Authors
  1. Seth Michelson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Doris Slate
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Michelson, S., Slate, D. A mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump. Bltn Mathcal Biology 56, 207–223 (1994). https://doi.org/10.1007/BF02460640

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460640

Keywords

Search

Navigation