Skip to main content
SpringerLink
Log in

A mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance

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

Abstract

Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell a 2×2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.

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-Verlag.

    Google Scholar 

  • Butkovskiiy, A. G. 1982.Green's Functions and Transfer Functions Handbook. Chichester, U. K.: Ellis Harwood.

    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 

  • Curt, G. A., N. J. Clendeninn and B. A. Chabner. 1984. Drug resistance in cancer.Cancer Treat. Rep. 68, 87–99.

    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.Caner Res. 46, 3876–3885.

    Google Scholar 

  • Goldie, J. H. and A. J. Coldman. 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 G. A. Gudauskas. 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.Tr. Pharmacol. Sci. 9, 54–58.

    Article  Google Scholar 

  • Hamada, H. and T. Tsuruo. 1988. Characterization of the ATPase activity of the Mr 170,000 to 180,000 membrane glycoprotein (P-glycoprotein) associated with multidrug resistance in K562/ADM Cells.Cancer Res. 48, 4926–4932.

    Google Scholar 

  • Harris, A. L., 1984. Drug resistance to cancer chemotherapyDrugs of Today 20, 657–663.

    Google Scholar 

  • Horio, M., I. Pastan, M. Gottesman and J. Handler. 1990. Transpithelial transport of vinblastine by kidney-derived cell lines. Application of a new kinetic model to estimatein situ K m of the pump.Biochim. Biophys. Acta 1027, 116–122.

    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 of P388 leukemia.Cancer Res.,42, 4730–4733.

    Google Scholar 

  • Joshi, R. R. 1985. On control of the function of the sodium-potassium pump in malignant cells.Bull. math. Biol. 47, 551–564.

    Article  MATH  Google Scholar 

  • Juliano, R. L. and C. 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 

  • 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 

  • Marx, J. L. 1986. Drug resistance of cancer cells probed.Science 234, 818–820.

    Google Scholar 

  • Michelson, S. and D. Slate. 1989. Emergence of the drug-resistant phenotype in tumor subpopulations: a hybrid model.JNCI 81, 1392–1401.

    Google Scholar 

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

    Google Scholar 

  • Naito, M., H. Hamada and T. Tsuruo. 1988. ATP/Mg2+-dependent binding of vincristine to the plasma membrane of multidrug-resistant K562 cells.J. biol. Chem. 263, 11887–11891.

    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. 1992. Drug resistance reversal strategies: a comparison of experimental data with model predictions.JNCI, in press.

  • Stein, W. D. 1986.Transport and Diffusion Across Cell Membranes. San Diego, CA: Academic Press.

    Google Scholar 

  • Toko, K., M. Nosaka, T. Fujiyoshi, K. Yamafuji and K. Ogata. 1988. Periodic band patterns as a dissipative structure in ion transport systems with cylindrical shape.Bull. math. Biol. 50, 255–288.

    MATH  Google Scholar 

  • Tsuruo, T., H. Iida, S. Tsukagoshi and Y. Sakurai. 1982. Increased accumulation of vincristine and adriamycin in drug-resistant P388 tumor cells following incubation with calcium antagonists and calmodulin inhibitors.Cancer Res. 42, 4730–4733.

    Google Scholar 

  • Warr, J. R. and G. F. Atkinson. 1988. Genetic aspects of resistance to anticancer drugs.Physiol. Rev. 66, 1–26.

    Google Scholar 

  • Watanabe, T., M. Inaba and Y. Sugiyama. 1989. Saturable process involved in active efflux of vincristine as a mechanism of multidrug resistance in P388 leukemia cells.Pharm. Res. 6, 690–696.

    Article  Google Scholar 

  • Willingham, M. C., M. M. Cornwell, C. O. Cardarelli, M. M. Gottesman and I. Pastan. 1986. Single cell analysis of daunomycin uptake in multidrug resistant and sensitive KB cells: effects of verapamil and other drugs.Cancer Res. 46, 5941–5946.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Syntex Research, Institute of Research Data Management, 3401 Hillview Ave., M/S A4-100, 94303, Palo Alto, CA, U.S.A.

    Seth Michelson

  2. Syntex Research, Institute of Cancer and Developmental Biology, 3401 Hillview Ave., M/S S3-1, 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 of the P-glycoprotein pump as a mediator of multidrug resistance. Bltn Mathcal Biology 54, 1023–1038 (1992). https://doi.org/10.1007/BF02460664

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460664

Keywords

Search

Navigation