ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be transferred between cells, which is the focus of this paper. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Durán et al. (Bull Math Biol 78(6):1218–1237, 2016) studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small lung cancer) cell lines. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this paper, we develop a new mathematical model for the transfer of drug resistance between cancer cells. Our model is based on incorporating a resistance phenotype into a model of cancer growth (Greene et al. in J Theor Biol 367:262–277, 2015). The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of Durán et al. (2016). The mathematical model shows a better fit when resistant cancer cells have a slower division rate than the sensitive cells.
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Ambudkar SV, Sauna ZE, Gottesman MM, Szakacs G (2005) A novel way to spread drug resistance in tumor cells: functional intercellular transfer of p-glycoprotein (abcb1). Trends Pharmacol Sci 26(8):385–387
Balaj L, Lessard R, Dai L, Cho YJ, Pomeroy SL, Breakefield XO, Skog J (2011) Tumour microvesicles contain retrotransposon elements and amplified oncogene sequences. Nat Commun 2:180
Borst P, Evers R, Kool M, Wijnholds J (2000) A family of drug transporters: the multidrug resistance-associated proteins. J Natl Cancer Inst 92(16):1295–1302
Breier A, Gibalova L, Seres M, Barancik M, Sulova Z (2013) New insight into p-glycoprotein as a drug target. Anti-Cancer Agents Med Chem 13(1):159–170
Brimacombe KR, Hall MD, Auld DS, Inglese J, Austin CP, Gottesman MM, Fung KL (2009) A dual-fluorescence high-throughput cell line system for probing multidrug resistance. Assay Drug Dev Technol 7(3):233–249
Cancer Facts and Figures 2016. https://www.cancer.org/research/cancer-facts-statistics/all-cancer-facts-figures/cancer-facts-figures-2016.html
Cordon-Cardo C, O’Brien J, Boccia J, Casals D, Bertino J, Melamed M (1990) Expression of the multidrug resistance gene product (p-glycoprotein) in human normal and tumor tissues. J Histochem Cytochem 38(9):1277–1287
Davidson AL, Dassa E, Orelle C, Chen J (2008) Structure, function, and evolution of bacterial atp-binding cassette systems. Microbiol Mol Biol Rev 72(2):317–364
Durán MR, Podolski-Renić A, Álvarez-Arenas A, Dinić J, Belmonte-Beitia J, Pešić M, Pérez-García VM (2016) Transfer of drug resistance characteristics between cancer cell subpopulations: a study using simple mathematical models. Bull Math Biol 78(6):1218–1237
Fodale V, Pierobon M, Liotta L, Petricoin E (2011) Mechanism of cell adaptation: when and how do cancer cells develop chemoresistance? Cancer J 17(2):89–95
Ford JM, Yang JM, Hait WN (1996) P-glycoprotein-mediated multidrug resistance: experimental and clinical strategies for its reversal. In: Drug resistance. Springer, pp 3–38
Geoffrey MC, Robert E et al (2000) The cell: a molecular approach. Boston University, Sunderland
Gillet JP, Gottesman MM (2010) Mechanisms of multidrug resistance in cancer. Methods Mol Biol 596:47–76
Greene JM, Levy D, Fung KL, Souza PS, Gottesman MM, Lavi O (2015) Modeling intrinsic heterogeneity and growth of cancer cells. J Theor Biol 367:262–277
Jackson TL, Byrne HM (2000) A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Math Biosci 164(1):17–38
Juranka P, Zastawny R, Ling V (1989) P-glycoprotein: multidrug-resistance and a superfamily of membrane-associated transport proteins. FASEB J 3(14):2583–2592
Lavi O, Gottesman MM, Levy D (2012) The dynamics of drug resistance: a mathematical perspective. Drug Resist Updates 15(1):90–97
Lavi O, Greene JM, Levy D, Gottesman MM (2013) The role of cell density and intratumoral heterogeneity in multidrug resistance. Cancer Res 73(24):7168–7175
Leonard GD, Fojo T, Bates SE (2003) The role of abc transporters in clinical practice. Oncologist 8(5):411–424
Levchenko A, Mehta BM, Niu X, Kang G, Villafania L, Way D, Polycarpe D, Sadelain M, Larson SM (2005) Intercellular transfer of p-glycoprotein mediates acquired multidrug resistance in tumor cells. Proc Nat Acad Sci USA 102(6):1933–1938
Lorz A, Lorenzi T, Hochberg ME, Clairambault J, Perthame B (2013) Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. ESAIM Math Model Numer Anal 47(2):377–399
Pasquier J, Galas L, Boulangé-Lecomte C, Rioult D, Bultelle F, Magal P, Webb G, Le Foll F (2012) Different modalities of intercellular membrane exchanges mediate cell-to-cell p-glycoprotein transfers in mcf-7 breast cancer cells. J Biol Chem 287(10):7374–7387
Pasquier J, Magal P, Boulangé-Lecomte C, Webb G, Le Foll F (2011) Consequences of cell-to-cell p-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model. Biol Direct 6(1):1
Thiebaut F, Tsuruo T, Hamada H, Gottesman MM, Pastan I, Willingham MC (1987) Cellular localization of the multidrug-resistance gene product p-glycoprotein in normal human tissues. Proc Nat Acad Sci 84(21):7735–7738
Ueda K, Clark D, Chen C, Roninson I, Gottesman M, Pastan I (1987) The human multidrug resistance (mdr1) gene. cdna cloning and transcription initiation. J Biol Chem 262(2):505–508
Weinberg R (2013) The biology of cancer. Garland Science, New York
The work of DL was supported in part by the NSF under Grant No. DMS-1713109, by the John Simon Guggenheim Memorial Foundation, by the Simons Foundation, and by the Jayne Koskinas Ted Giovanis Foundation.
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Becker, M., Levy, D. Modeling the Transfer of Drug Resistance in Solid Tumors. Bull Math Biol 79, 2394–2412 (2017). https://doi.org/10.1007/s11538-017-0334-x
- Multidrug resistance
- Integro-differential equations