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A mathematical model of chromosome recombination-induced drug resistance in cancer therapy

1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021,China
2 Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084, China

Special Issues: Mathematical modelling and analysis of tumour growth, evolution and therapy

Cytotoxic chemotherapeutics are common treatment methods of many cancers, and patients are often dosed at maximum tolerated dose (MTD), which is trying to eliminate cancer cells as much as possible. However, highly doses chemotherapy may induce unexpected gene mutations or DNA recombinations, which in turn result in unpredictable outcomes and drug resistance. In this study, we focus on the occurrence of DNA recombinations, and present a mathematical model for the influence of genomic disorder due to chemotherapy, and investigate how it may lead to drug resistance. We show that there is an optimal dose so that the tumor cells number is minimum at the steady state, which suggests the existence of an optimal dose of chemotherapy below the MTD. Model simulations show that when the dose is either low or high, the tumor cancer cells number may maintain a higher level steady state, or even sustained oscillations when the dose is too high, which are clinically inappropriate. Our results provide a theoretical study on the dose control of chemotherapy in cancer therapy.
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Keywords delay differential equation; genomic disorder; non-clonal chromosome aberrations; chemotherapy; drug resistance

Citation: Hongli Yang, Jinzhi Lei. A mathematical model of chromosome recombination-induced drug resistance in cancer therapy. Mathematical Biosciences and Engineering, 2019, 16(6): 7098-7111. doi: 10.3934/mbe.2019356

References

  • 1. N. Beerenwinkel, C. D. Greenman, and J. Lagergren, Computational Cancer Biology: An Evolutionary Perspectiv, PLoS Comput. Biol., 12 (2016), e1004717.
  • 2. N. Beerenwinkel, R. F. Schwarz, M. Gerstung, et al., Cancer evolution: Mathematical models and computational inference, Syst. Biol., 64 (2015), e1–e25.
  • 3. S. Blum, F. Martins and M. Lübbert, Immunotherapy in adult acute leukemia, Leuk. Res., 60 (2017), 63–73.
  • 4. C. H. June, R. S. O'Connor, O. U. Kawalekar, et al., CAR T cell immunotherapy for human cancer, Science, 359 (2018), 1361–1365.
  • 5. L. Labanieh, R. G. Majzner and C. L. Mackall, Programming CAR-T cells to kill cancer, Nat. Biomed. Eng., 2 (2018), 377–391.
  • 6. M. H. Abdul-Aziz, J. Lipman, J. W. Mouton, et al., Applying pharmacokinetic/pharmacodynamic principles in critically ill patients: Optimizing efficacy and reducing resistance development, Semin. Respir. Crit. Care Med., 36 (2015), 136–153.
  • 7. W. J. Aston, D. E. Hope, A. K. Nowak, et al., A systematic investigation of the maximum tolerated dose of cytotoxic chemotherapy with and without supportive care in mice, BMC Cancer, 17 (2017), 684.
  • 8. C. Hudis and C. Danq, The development of dose-dense adjuvant chemotherapy, Breast J., 21 (2015), 42–51.
  • 9. A. Matikas, T. Foukakis and J. Berqh, Dose intense, dose dense and tailored dose adjuvant chemotherapy for early breast cancer: An evolution of concepts, Acta Oncol., 56 (2017), 1143–1151.
  • 10. T. Prasanna, J. Beith, S. Kao, et al., Dose modifications in adjuvant chemotherapy for solid organ malignancies: A systematic review of clinical trials, Asia Pac. J. Clin. Oncol., 14 (2018), 125–133.
  • 11. J. A. Roberts, P. Kruger, D. L. Paterson, et al., Antibiotic resistance: What's dosing got to do with it? Crit. Care Med., 36 (2008), 2433–2440.
  • 12. C. L. Tourneau, J. J. Lee and L. L. Siu, Dose escalation methods in phase I cancer clinical trials, J. Natl. Cancer Inst., 101 (2009), 708–720.
  • 13. J. Y. Lin, H. M. He, Y. Yang, et al., Comparison of two different treatment regimens for curative effect and recurrence rate in patients with extranodal nasal type NK/T cell lymphoma, Chin. J. Clin. Res., 29 (2016), 1042–1045.
  • 14. Y. Yang, Y. Wen, C. Bedi, et al., The relationship between cancer patient's fear of recurrence and chemotherapy: A systematic review and meta-analysis, J. Psychosomatic Res., 98 (2017), 55–63.
  • 15. Y. A. Luqmani, Mechanisms of drug resistance in cancer chemotherapy, Med. Princ. Pract., 14 (2005), 35–48.
  • 16. M. Moschovi, E. Critselis, O. Cen, et al., Drugs acting on homeostasis: Challenging cancer cell adaptation, Expert Rev. Anticancer Ther., 15 (2015), 1405–1417.
  • 17. J. Zhang, J. J. Cunningham, J. S. Brown, et al., Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer, Nat. Commun., 8 (2017), 1816.
  • 18. H. Easwaran, H. C. Tsai and S. B. Baylin, Cancer epigenetics: Tumor heterogeneity, plasticity of stem-like states, and drug resistance, Mol. Cell, 54 (2014), 716–727.
  • 19. C. E. Meacham and S. J. Morrison, Tumour heterogeneity and cancer cell plasticity, Nature, 501 (2013), 328–337.
  • 20. C. Kim, R. Gao, E. Sei, et al., Chemoresistance evolution in triple-negative breast cancer delineated by single-cell sequencing, Cell, 173 (2018), 879–893.
  • 21. Y. Su, W. Wei, L. Robert, et al., Single-cell analysis resolves the cell state transition and signaling dynamics associated with melanoma drug-induced resistance, Proc. Natl. Acad. Sci. USA, 114 (2017), 13679–13684.
  • 22. H. Sakahira, M. Enari and S. Nagata, Cleavage of CAD inhibitor in CAD activation and DNA degradation during apoptosis, Nature, 391 (1998), 96–99.
  • 23. G. Liu, J. B. Stevens, S. D. Horne, et al., Genome chaos: Survival strategy during crisis, Cell Cycle, 13 (2014), 528–537.
  • 24. J. B. Stevens, B. Y. Abdallah, G. Liu, et al., Diverse system stresses: Common mechanisms of chromosome fragmentation, Cell Death Dis., 2 (2011), e178.
  • 25. C. Gao, Y. Su, J. Koeman, et al., Chromosome instability drives phenotypic switching to metastasis Proc. Natl. Acad. Sci. USA, 113 (2016), 14793–14798.
  • 26. H. H. Heng and J. B. Stevens, Patterns of genome of dynamics and cancer evolution, Cell. Oncol., 30 (2008), 513–514.
  • 27. J. B. Stevens, S. D. Horne, B. Y. Abdallah, et al., Chromosomal instability and transcriptome dynamics in cancer, Cancer Metastasis Rev., 32 (2013), 391–402.
  • 28. J. B. Stevens, G. Liu, B. Y. Abdallah, et al., Unstable genomes elevate transcriptome dynamics, Int J. Cancer, 134 (2014), 2074–2087.
  • 29. P. M. Altrock, L. L. Liu and F. Michor, The mathematics of cancer: Integrating quantitative models, Nat. Rev. Cancer, 15 (2015), 730–745.
  • 30. F. S. Borges, K. C. Iarosz, H. P. Ren, et al., Model for tumour growth with treatment by continuous and pulsed chemotherapy, BioSystems, 116 (2014), 43–48.
  • 31. H. Cho and D. Levy, Modeling the dynamics of heterogeneity of solid tumors in response to chemotherapy, Bull. Math. Biol., 79 (2017), 2986–3012.
  • 32. K. C. Larosz, F. S. Borges, A. M. Batista, et al., Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment, J. Theor. Biol., 368 (2015), 113–121.
  • 33. Á.G. López, K.C. Larosz, A.M. Batista, et al., Nonlinear cancer chemotherapy: Modelling the Norton-Simon hypothesis, Commun. Nonlinear Sci. Numer Simul., 70 (2019), 307–317.
  • 34. F. Michor, Mathematical models of cancer stem cells, J. Clin. Oncol., 26 (2008), 2854–2861.
  • 35. H. H. Heng, S. M. Regan, G. Liu, et al., Why it is crucial to analyze non clonal chromosome aberrations of NCCAs? Mol. Cytogenet., 9 (2016), 15.
  • 36. C. Colijin and M. C. Mackey, A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia, J. Theor. Biol, 237 (2005), 117–132.
  • 37. C. Colijin and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia, J. Theor. Biol., 237 (2005), 133–146.
  • 38. A. C. Fowler and M. C. Mackey, Relaxation oscillations in a class of delay differential equations, SIAM J. Appl. Math., 63 (2002), 299–323.
  • 39. L. Pujo-Menjouet, S. Bernard and M. C. Mackey, Long period oscillations in a model of hematopoietic stem cells, SIAM J. Appl. Dyn. Syst., 4 (2005), 312–332.
  • 40. F. Burns and I. Tannock, On the existence of a G 0 phase in the cell cycle, Cell Tissue Kinet., 3 (1970), 321–334.
  • 41. M. C. Mackey and P. Dormer, Continuous maturation of proliferating erythroid precursor, Cell Tissue Kinet., 15 (1982), 381–392.
  • 42. M. C. Mackey and J. G. Milto, Dynamical disease, Ann. New York Acad. Sci., 504 (1987), 16–32.
  • 43. D. C. Dale and M. C. Mackey, Understanding, treating and avoiding hematological disease: Better medicine through mathematics? Bull. Math. Biol., 77 (2015), 739–757.
  • 44. J. Lei and M. C. Mackey, Multisability in an age-structured model of hematopoiesis: Cyclical neutropenia, J. Theor. Biol., 270 (2011), 143–153.
  • 45. M. C. Mackey, Cell kinetic status of haematopoietic stem cells, Cell Prolif., 34 (2001), 71–83.
  • 46. C. Zhuge, M. C. Mackey and J. Lei, Origins of oscillation patterns in cyclical thrombocytopenia, J. Theor. Biol., 462 (2019), 432–445.
  • 47. G. Brooks, G. Provencher, J. Lei, et al., Neutrophil dynamics after chemotherapy and G-CSF: The role of pharmacokinetics in shaping the response, J. Theor. Biol., 315 (2012), 97–109.
  • 48. C. Zhuge, J. Lei and M. C. Mackey, Neutrophil dynamics in response to chemotherapy and G-CSF, J. Theor. Biol., 293 (2012), 111–120.
  • 49. Y. Hannun, Apoptosis and dilemma of cancer chemotherapy, Blood, 89 (1997), 1845–1853.
  • 50. S. Bernard, J. Belair and M. C. Mackey, Oscillations in cyclical neutropenia: New evidence based in mathematical modeling, J. Theor. Biol., 223 (2003), 283–298.
  • 51. D. Hanahan and R.A. Weinberg, Hallmarks of cancer: The next generation, Cell, 144 (2011), 646–674.
  • 52. J. Abkowitz, R. Holly and W. P. Hammond, Cyclic hematopoiesis in dogs: Studies of erythroid burst forming cells confirm and early stem cell defect, Exp. Hematol., 16 (1988), 941–945.
  • 53. C. Foley and M. C. Mackey, Dynamic hematological disease: A review, J. Math. Biol., 58 (2009), 285–322.
  • 54. T. B. Gaspar, J. Henriques, L. Marconato, et al., The use of low-dose metronomic chemotherapy in dogs-insight into a modern caner field, Vet. Comp. Oncol., 16 (2018), 2–11.
  • 55. A. Safarishahribijari and A. Gaffari, Parameter identification of hematopoiesis mathematical model – periodic chronic myelogenous leukemia, Contemp. Oncol(Pozn)., 17 (2013), 73–77.

 

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