December  2011, 4(6): 1465-1498. doi: 10.3934/dcdss.2011.4.1465

An enzyme kinetics model of tumor dormancy, regulation of secondary metastases

1. 

Department of Mathematics & Statistics, University of Michigan, Dearborn, MI 48128, United States

2. 

Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011

Received  March 2009 Revised  November 2009 Published  December 2010

In this paper we study 1 dimensional (1D) and 2D extended version of a two compartment model for tumor dormancy suggested by Boushaba et al. [3]. The model is based on the idea that the vascularization of a secondary tumor can be suppressed by inhibitor originating from a larger primary tumor. It has been observed emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites five to seven centimeters from the primary site within a period of one month after the excision of the primary site. 1D and 2D simulations show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumors while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumors, even after it is removed. The sensitivity analysis was carried out for the 1D model. It has been long observed that surgery should be followed by other treatment options such as chemotherapy. 2D simulation suggests a possible treatment options with different dosage schedule after a surgery in order to achieve better clinical outcome.
Citation: Yangjin Kim, Khalid Boushaba. An enzyme kinetics model of tumor dormancy, regulation of secondary metastases. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1465-1498. doi: 10.3934/dcdss.2011.4.1465
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show all references

References:
[1]

S. G. Anderson, R. H. Buckingham and C. G. Kurland, Does codon composition influence ribosome function?, EMBO, 3 (1983), 91-94.

[2]

L. S. Beck, W. P. L. DeGuzman, Y. X. Lee, M. W. Siegel and E. P. Amento, One systemic administration of transforming growth factor-beta 1 reverses age- or glucocorticoid-impaired wound healing, J. Clin. Invest., 92 (1993), 2841-2849. doi: 10.1172/JCI116904.

[3]

K. Boushaba, H. A. Levine and M. Nilsen-Hamilton, A mathematical model for the regulation of tumor dormancy based on enzyme kinetics, Bull Math. Biol., 68 (2006), 1495-1526. doi: 10.1007/s11538-005-9042-z.

[4]

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[5]

F. Brivio, P. Lissoni, G. Alderi, S. Barni, F. Lavorato and L. Fumagalli, Preoperative interleukin-2 subcutaneous immunotherapy may prolong the survival time in advanced colorectal cancer patients, Oncology, 53 (1996), 263-268. doi: 10.1159/000227571.

[6]

F. Brivio, P. Lissoni, M. S. Perego, A. Lissoni and L. Fumagalli, Abrogation of surgery-induced IL-6 hypersecretion by presurgical immunotherapy with IL-2 and its importance in the prevention of postoperative complications, J. Biol. Regul. Homeost Agents, 15 (2001), 370-374.

[7]

Y. Cao, M. S. O'Reilly, B. Marshall, E. Flynn, R. W. Ji and J. Folkman, Expression of angiostatin cDNA in a murine fibrosarcoma suppresses primary tumor growth and produces long-term dormancy of metastases, J. Clin. Invest., 101 (1998), 1055-1063. doi: 10.1172/JCI1558.

[8]

R. Castello, A. Estelles, C. Vazquez, C. Falco, F. Espana, S. M. Almenar, C. Fuster and J. Aznar, Quantitative real-time reverse transcription-pcr assay for urokinase plasminogen activator, plasminogen activator inhibitor type 1, and tissue metalloproteinase inhibitor type 1 gene expressions in primary breast cancer, Clin. Chem., 48 (2002), 1288-1295.

[9]

W. L. Chandler, M. C. Alessi, M. F. Aillaud, P. Vague and I. Juhan-Vague, Formation, inhibition and clearance of plasmin in vivo, Haemostasis, 30 (2002), 204-218.

[10]

J. Cheng and L. Weiner, Tumors and their microenvironments: tilling the soil commentary re: A. m. scott et al., a phase i dose-escalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation protein-positive cancer, Clin Cancer Res, 9 (2003), 1590-1595.

[11]

J. C. Coffey, M. Doyle, L. O'Mahony et al., Probiotics confer protection against perioperative metastatic tumour growth, Annals of Surg. Oncol., 85 (2001), 273-278.

[12]

J. C. Coffey, J. H. Wang, T. G. Cotter and H. P. Redmond, Cytoreductive surgery enhances tumorogenicityby downregulating mitochondrial apoptosis, Ann Surg Oncol, 10 (2003), S24.

[13]

J. C. Coffey, J. H. Wang, M. J. Smith, D. Bouchier-Hayes, T. G. Cotter and H. P. Redmond, Excisional surgery for cancer cure: Therapy at a cost, Lancet Oncol., 4 (2003), 760-768. doi: 10.1016/S1470-2045(03)01282-8.

[14]

M. L. Costa and H. P. Redmond and D. J. Bouchier-Hayes, Taurolidine improves survival by abrogating the accelerated development and proliferation of solid tumors and development of organ metastases from circulating tumor cells released, J. Surg. Res., 101 (2001), 111-119. doi: 10.1006/jsre.2001.6250.

[15]

B. Davis, Reinforced random walks, Probal. Theory Related Fields, 84 (1990), 203-229. doi: 10.1007/BF01197845.

[16]

G. De Crescenzo, S. Grothe, J. Zwangstra, M. Tsang and M. D.O'Connor-McCourt, Real-time monitoring of the interactions of transforming growth factor- (TGF- ) isoforms with latency-associated protein and the ectodomains of the TGF- type II and III receptors reveals different kinetic models and stoichiometries of binding, J. Biol. Chem., 276 (2001), 29632-29643. doi: 10.1074/jbc.M009765200.

[17]

G. De Crescenzo, P. L. Pham, Y. Durocher and M. D.O'Connor-McCourt, Transforming growth factor-beta(tgf-$\beta$ binding to the extracellular domain of the type ii (tgf-$\beta$ receptor: Receptor capture on a biosensor surface using a new coiled-coil capture system demonstrates that avidity contributes significantly to high affinity binding, J. Mol. Biol., 328 (2003), 1173-1183. doi: 10.1016/S0022-2836(03)00360-7.

[18]

V. De Giorgi, D. Massai, G. Gerlini, F. Mannone, E. Quercioli and P. Carli, Immediate local and regional recurrence after the excision of a polypoid melanoma: tumor dormancy or tumor activation?, Derm. Surgery, 29 (2003), 664-667. doi: 10.1046/j.1524-4725.2003.29163.x.

[19]

R. Demicheli, P. Valagussa and G. Bonadonna, Does surgery modify growth kinetics of breast cancer micrometastases?, Br. J. Cancer, 85 (2001), 490-492. doi: 10.1054/bjoc.2001.1969.

[20]

R. Demicheli, Tumour dormancy: findings and hypotheses from clinical research on breast cancer, Semin. Cancer Biol., 11 (2001), 297-306. doi: 10.1006/scbi.2001.0385.

[21]

E. R. Edelman, N. M. A. and M. J. Karnovsky, Perivascular and intravenous administration of basic fibroblast growth factor: Vascular and solid organ deposition, Proc. Natl. Acad. Sci., 90 (1993), 1513-1517. doi: 10.1073/pnas.90.4.1513.

[22]

S. Eikenberry, C. Thalhauser and Y. Kuang, Tumor-immune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma, PLoS Comput. Biol., 5 (2009) e1000362. doi: 10.1371/journal.pcbi.1000362.

[23]

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