Skip to main content
SpringerLink
Log in

Mathematical modeling to distinguish cell cycle arrest and cell killing in chemotherapeutic concentration response curves

  • Published:
Journal of Pharmacokinetics and Pharmacodynamics Aims and scope Submit manuscript

Abstract

Concentration response experiments are utilized widely to characterize the response of tumor cell lines to chemotherapeutic drugs, but the assay methods are non-standardized and their analysis based on phenomenological equations. To provide a framework for better interpretation of these experiments, we have developed a mathematical model in which progression through the tumor cell cycle is inhibited by drug treatment via either cell cycle arrest or entrance into cell death pathways. By fitting concentration response data, preferably over a dynamic range, the contributions of these mechanisms can be delineated. The model was shown to fit well experimental data for three glioma cell lines treated with either carmustine or etoposide. In each cell line, the major mechanism of tumor cell inhibition was cell death for carmustine in contrast to cell cycle arrest for etoposide. The model also provides a possible interpretation for the acquired in vitro resistance of U87 cells to carmustine as an accelerated desensitization to cell killing effects. This approach will aid in understanding better the action of chemotherapeutic agents on tumor cells.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Basse B, Baguley BC, Marshall ES, Joseph WR, van Brunt B, Wake G, Wall DJ (2004) Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel. J Math Biol 49:329–357

    Article  PubMed  Google Scholar 

  2. Kozusko F, Chen P, Grant SG, Day BW, Panetta JC (2001) A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A. Math Biosci 170:1–16

    Article  PubMed  CAS  Google Scholar 

  3. Panetta JC, Evans WE, Cheok MH (2006) Mechanistic mathematical modelling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukaemia cells. Br J Cancer 94:93–100

    Article  PubMed  CAS  Google Scholar 

  4. Xu GW, Nutt CL, Zlatescu MC, Keeney M, Chin-Yee I, Cairncross JG (2001) Inactivation of p53 sensitizes U87MG glioma cells to 1,3-bis(2-chloroethyl)-1-nitrosourea. Cancer Res 61:4155–4159

    PubMed  CAS  Google Scholar 

  5. Batista LF, Roos WP, Christmann M, Menck CF, Kaina B (2007) Differential sensitivity of malignant glioma cells to methylating and chloroethylating anticancer drugs: p53 determines the switch by regulating xpc, ddb2, and DNA double-strand breaks. Cancer Res 67:11886–11895

    Article  PubMed  CAS  Google Scholar 

  6. Yan L, Donze JR, Liu L (2005) Inactivated MGMT by O6-benzylguanine is associated with prolonged G2/M arrest in cancer cells treated with BCNU. Oncogene 24:2175–2183

    Article  PubMed  CAS  Google Scholar 

  7. Das CM, Aguilera D, Vasquez H, Prasad P, Zhang M, Wolff JE, Gopalakrishnan V (2007) Valproic acid induces p21 and topoisomerase-II (alpha/beta) expression and synergistically enhances etoposide cytotoxicity in human glioblastoma cell lines. J Neurooncol 85:159–170

    Article  PubMed  CAS  Google Scholar 

  8. Branzeiand D, Foiani M (2008) Regulation of DNA repair throughout the cell cycle. Nat Rev Mol Cell Biol 9:297–308

    Article  Google Scholar 

  9. Chiu CC, Li CH, Ung MW, Fuh TS, Chen WL, Fang K (2005) Etoposide (VP-16) elicits apoptosis following prolonged G2–M cell arrest in p53-mutated human non-small cell lung cancer cells. Cancer Lett 223:249–258

    Article  PubMed  CAS  Google Scholar 

  10. Mayo LD, Dixon JE, Durden DL, Tonks NK, Donner DB (2002) PTEN protects p53 from Mdm2 and sensitizes cancer cells to chemotherapy. J Biol Chem 277:5484–5489

    Article  PubMed  CAS  Google Scholar 

  11. Xu GW, Mymryk JS, Cairncross JG (2005) Inactivation of p53 sensitizes astrocytic glioma cells to BCNU and temozolomide, but not cisplatin. J Neurooncol 74:141–149

    Article  PubMed  CAS  Google Scholar 

  12. Yin D, Tamaki N, Kokunai T (2000) Wild-type p53-dependent etoposide-induced apoptosis mediated by caspase-3 activation in human glioma cells. J Neurosurg 93:289–297

    Article  PubMed  CAS  Google Scholar 

  13. Florian JA Jr, Eiseman JL, Parker RS (2005) Accounting for quiescent cells in tumour growth and cancer treatment. Syst Biol (Stevenage) 152:185–192

    CAS  Google Scholar 

  14. Sherer E, Hannemann RE, Rundell A, Ramkrishna D (2006) Analysis of resonance chemotherapy in leukemia treatment via multi-staged population balance models. J Theor Biol 240:648–661

    Article  PubMed  CAS  Google Scholar 

  15. Ribba B, Colin T, Schnell S (2006) A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor Biol Med Model 3:7

    Article  PubMed  Google Scholar 

  16. Venkatasubramanian R, Henson MA, Forbes NS (2008) Integrating cell-cycle progression, drug penetration and energy metabolism to identify improved cancer therapeutic strategies. J Theor Biol 253:98–117

    Article  PubMed  CAS  Google Scholar 

  17. Damia G, Broggini M (2004) Improving the selectivity of cancer treatments by interfering with cell response pathways. Eur J Cancer 40:2550–2559

    Article  PubMed  CAS  Google Scholar 

  18. Senderowicz AM (2004) Targeting cell cycle and apoptosis for the treatment of human malignancies. Curr Opin Cell Biol 16:670–678

    Article  PubMed  CAS  Google Scholar 

  19. Gardner SN (2000) A mechanistic, predictive model of dose-response curves for cell cycle phase-specific and -nonspecific drugs. Cancer Res 60:1417–1425

    PubMed  CAS  Google Scholar 

  20. Khoshyomn S, Nathan D, Manske GC, Osler TM, Penar PL (2002) Synergistic effect of genistein and BCNU on growth inhibition and cytotoxicity of glioblastoma cells. J Neurooncol 57:193–200

    Article  PubMed  Google Scholar 

  21. Sarkaria JN, Kitange GJ, James CD, Plummer R, Calvert H, Weller M, Wick W (2008) Mechanisms of chemoresistance to alkylating agents in malignant glioma. Clin Cancer Res 14:2900–2908

    Article  PubMed  CAS  Google Scholar 

  22. Law ME, Templeton KL, Kitange G, Smith J, Misra A, Feuerstein BG, Jenkins RB (2005) Molecular cytogenetic analysis of chromosomes 1 and 19 in glioma cell lines. Cancer Genet Cytogenet 160:1–14

    Article  PubMed  CAS  Google Scholar 

  23. Bar EE, Chaudhry A, Lin A, Fan X, Schreck K, Matsui W, Piccirillo S, Vescovi AL, DiMeco F, Olivi A, Eberhart CG (2007) Cyclopamine-mediated hedgehog pathway inhibition depletes stem-like cancer cells in glioblastoma. Stem Cells 25:2524–2533

    Article  PubMed  CAS  Google Scholar 

  24. Iwadate Y, Fujimoto S, Namba H, Yamaura A (2003) Promising survival for patients with glioblastoma multiforme treated with individualised chemotherapy based on in vitro drug sensitivity testing. Br J Cancer 89:1896–1900

    Article  PubMed  CAS  Google Scholar 

  25. Camphausen K, Purow B, Sproull M, Scott T, Ozawa T, Deen DF, Tofilon PJ (2005) Influence of in vivo growth on human glioma cell line gene expression: convergent profiles under orthotopic conditions. Proc Natl Acad Sci USA 102:8287–8292

    Article  PubMed  CAS  Google Scholar 

  26. Ogunnaike BA (2006) Elucidating the digital control mechanism for DNA damage repair with the p53-Mdm2 system: single cell data analysis and ensemble modelling. J R Soc Interface 3:175–184

    Article  PubMed  CAS  Google Scholar 

  27. Gurkan E, Schupp JE, Aziz MA, Kinsella TJ, Loparo KA (2007) Probabilistic modeling of DNA mismatch repair effects on cell cycle dynamics and iododeoxyuridine-DNA incorporation. Cancer Res 67:10993–11000

    Article  PubMed  CAS  Google Scholar 

  28. Haberichter T, Madge B, Christopher RA, Yoshioka N, Dhiman A, Miller R, Gendelman R, Aksenov SV, Khalil IG, Dowdy SF (2007) A systems biology dynamical model of mammalian G1 cell cycle progression. Mol Syst Biol 3:84

    Article  PubMed  Google Scholar 

  29. Ma L, Wagner J, Rice JJ, Hu W, Levine AJ, Stolovitzky GA (2005) A plausible model for the digital response of p53 to DNA damage. Proc Natl Acad Sci USA 102:14266–14271

    Article  PubMed  CAS  Google Scholar 

  30. Toettcher JE, Loewer A, Ostheimer GJ, Yaffe MB, Tidor B, Lahav G (2009) Distinct mechanisms act in concert to mediate cell cycle arrest. Proc Natl Acad Sci USA 106:785–790

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

Funding support was provided by the Charles and Johanna Busch Memorial Fund and an NSF IGERT Fellowship (DGE 0333196) to SH. We thank Debrabata Banerjee for advice on generating resistance and Ioannis Androulakis for a discussion on parameter estimation. We thank Theresa Choi at the Flow Cytometry Lab at EOHSI for help with ModFit for cell cycle phase quantitation.

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Rutgers, The State University of New Jersey, 599 Taylor Road, Piscataway, NJ, 08854, USA

    Salaheldin S. Hamed & Charles M. Roth

  2. Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA

    Charles M. Roth

Authors
  1. Salaheldin S. Hamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles M. Roth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Charles M. Roth.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hamed, S.S., Roth, C.M. Mathematical modeling to distinguish cell cycle arrest and cell killing in chemotherapeutic concentration response curves. J Pharmacokinet Pharmacodyn 38, 385–403 (2011). https://doi.org/10.1007/s10928-011-9199-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10928-011-9199-z

Keywords

Search

Navigation