No Access

A PROGNOSTIC IMMUNOTHERAPY MODEL FOR 4T1 BREAST CANCER WITH COMBINED CYCLOPHOSPHAMIDE AND TLR AGONIST

DANHUA HE

Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, P. R. China

Search for more papers by this author

WEINAN XU

NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 119077, Singapore

Search for more papers by this author

XUEFANG LI

School of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China

Guangdong Provincial Key Laboratory of Intelligent Transportation System, School of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China

E-mail Address: lixuef25@mail.sysu.edu.cn

Corresponding author.

Search for more papers by this author

, and

JIAN-XIN XU

Department of Electrical and Computer Engineering, National University of Singapore, 117576, Singapore

Search for more papers by this author

https://doi.org/10.1142/S0218339020500035Cited by:0 (Source: Crossref)

Abstract

Based on experimental results of a mouse model provided in the literature, we develop a mathematical model by using system biology approach, aiming to investigate immunotherapy for 4T1 breast cancer. It is worth to mention that only 4 types of cells (tumor cells, CD8 $^{+}$ T cells, regular T cells (Tregs), and tumoricidal myeloid CD11b $+$ Gr1dim cells) are quantitatively measured in experiments, which make the immunotherapy modelling more difficult since only limited system knowledge is available. To overcome the difficulty, the mathematical model is proposed by employing Evolutionary Computation to optimize the system parameters. Furthermore, with the mathematical model, analysis can be conducted to capture the inherent properties of the model, such as the number and stability of equilibria, and parameter sensitivity analysis, which disclose the nature of 4T1 breast cancer from a system biological perspective. Not limited to replication of experimental results, we further show that the mathematical model is in fact a prognostic immunotherapy model that can predict treatment outcomes of various cases; for instance, different combinations of drug delivery schedules. By virtue of computational convenience, it is relatively easy to intensively investigate most of the treatments that are impossible for animal models or clinical trials. In other words, a mathematical model based on system biology can provide meaningful reference when exploiting more effective treatment protocols.

Keywords:

References

1. Ghochikyan A, Davtyan A, Hovakimyan A, Davtyan H, Poghosyan A, Bagaev A, Ataullakhanov RI, Nelson EL, Agadjanyan MG, Primary 4T1 tumor resection provides critical window of opportunity for immunotherapy, Clin Exp Metastasis 31 :185–198, 2014. Crossref, Web of Science, Google Scholar
2. Aslakson CJ, Miller FR, Selective events in the metastatic process defined by analysis of the sequential dissemination of subpopulations of a mouse mammary tumor, Cancer Res 52(6) :1399–1405, 1992. Web of Science, Google Scholar
3. Heppner GH, Miller FR, Shekhar PM, Nontransgenic models of breast cancer, Breast Cancer Res 2(5) :331–334, 2000. Crossref, Web of Science, Google Scholar
4. Pulaski BA, Terman DS, Khan S, Muller E, Ostrand-Rosenberg S, Cooperativity of Staphylococcal aureus enterotoxin B superantigen, major histocompatibility complex class II, and CD80 for immunotherapy of advanced spontaneous metastases in a clinically relevant postoperative mouse breast cancer model, Cancer Res 60(10) :2710–2715. 2000. Web of Science, Google Scholar
5. Pulaski BA, Ostrand-Rosenberg S, Reduction of established spontaneous mammary carcinoma metastases following immunotherapy with major histocompatibility complex class II and B7.1 cell-based tumor vaccines, Cancer Res 58(7) :1486–1493, 1998. Web of Science, Google Scholar
6. Manrique SZ, Dominguez Ana L, Mirza N, Spencer CD, Bradley JM, Finke JH, Lee JJ, Pease LR, Gendler SJ, Cohen PA, Definitive activation of endogenous antitumor immunity by repetitive cycles of cyclophosphamide with interspersed toll-like receptor agonists, Oncotarget 7(28) :42919–42942, 2016. Crossref, Google Scholar
7. Miyara SS, Natural regulatory T cells: Mechanisms of suppression, Trends Mol Med 13(3) :108–116, 2007. Crossref, Web of Science, Google Scholar
8. Shevach E, From vanilla to 28 flavors: Multiple varieties of T regulatory cells, Immunity 25(2) :195–201, 2006. Crossref, Web of Science, Google Scholar
9. Tang Q, Adams JY, Tooley AJ, Bi M, Fife BT, Serra P, Santamaria P, Locksley RM, Krummel MF, Bluestone JA, Visualizing regulatory T cell control of autoimmune responses in nonobese diabetic mice, Nat Immunol 7(1) :83–92, 2006. Crossref, Web of Science, Google Scholar
10. von Boehmer H, Mechanisms of suppression by suppressor T cells, Nat Immunol 6(4) :338–344, 2005. Crossref, Web of Science, Google Scholar
11. Gabrilovich DI, Nagaraj S, Myeloid-derived suppressor cells as regulators of the immune system, Nat Rev Immunol 9 :162–174, 2009. Crossref, Web of Science, Google Scholar
12. Peranzoni ES, Zilio , Marigo I, Dolcetti L, Zanovello P, Mandruzzato S, Bronte V, Myeloid-derived suppressor cell heterogeneity and subset definition, Curr Opin Immunol 22 :238–244, 2010. Crossref, Web of Science, Google Scholar
13. Sergey Ryzhov, Sergey V Novitskiy, Anna E Goldstein, Asel Biktasova, Michael R Blackburn, Italo Biaggioni, Mikhail M Dikov, Igor Feoktistov, Adenosinergic regulation of the expansion and immunosuppressive activity of CD11b+Gr1+ Cells, J Immunol 187 :6120–6129, 2011. Crossref, Web of Science, Google Scholar
14. Kim J, Myung H, Evolutionary programming techniques for constrained optimization problems, IEEE Trans Evol Comput 1(2) :129–140, 1997. Crossref, Google Scholar
15. Runarsson T, Yao X, Stochastic ranking for constrained evolutionary optimization, IEEE Trans Evol Comput 4 :344–354, 2000. Crossref, Web of Science, Google Scholar
16. Wang Y, Cai Z, Xhau Y, Zeng W, An adaptive tradeoff model for constrained evolutionary computation, IEEE Trans Evol Comput 12(1) :80–92, 2008. Crossref, Web of Science, Google Scholar
17. Li XF, Xu JX, A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy, J Theor Biol 406 :42–51, 2016. Crossref, Web of Science, Google Scholar
18. de Pillis LG, Fister KR, Gu W, Head T, Maples K, Neal T, Murugan A, Kozai K, Optimal control of mixed immunotherapy and chemotherapy of tumors, J Biol Syst 16(1) :51–80, 2008. Link, Web of Science, Google Scholar
19. Kyewski B, Suri-Payer E, CD4+CD25+ Regulatory T Cells: Origin, Function and Therapeutic Potential, Springer-Verlag, Berlin Heidelberg, 2005. Google Scholar
20. Kuznetsov VA, Makalkin IA, Taylor MA, Perelson AS, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull Math Biol 56(2) :295–321, 1994. Crossref, Web of Science, Google Scholar
21. Castiglione F, Piccoli B, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bull Math Biol 68(2) :255–274, 2006. Crossref, Web of Science, Google Scholar
22. Li XF, Xu JX, A mathematical model of immune response to tumor invasion incorporated with danger model, J Biol Syst 23(3) :505–526, 2015. Link, Web of Science, Google Scholar
23. Sakaguchi S, Yamaguchi T, Nomura T, Ono M, Regulatory T cells and immune tolerance, Cell 133(5) :775–787, 2008. Crossref, Web of Science, Google Scholar
24. Beyer M, Kochanek M, Darabi K et al., Reduced frequencies and suppressive function of CD4 $^{+}$ CD25 high regulatory T cells in patients with chronic lymphocytic leukemia after therapy with fludarabine, Blood 106 :2018–2025, 2005. Crossref, Web of Science, Google Scholar
25. Ghiringhelli F, Larmonier N, Schmitt E et al., CD4 $^{+}$ CD25 $^{+}$ regulatory T cells suppress tumor immunity but are sensitive to cyclophosphamide which allows immunotherapy of established tumors to be curative, Eur J Immunol 34 :336–344, 2004. Crossref, Web of Science, Google Scholar
26. Ikezawa Y, Nakazawa M, Tamura C, Takahashi K, Minami M, Ikezawa Z, Cyclophosphamide decreases the number, percentage and the function of CD25 $^{+}$ CD4 $^{+}$ regulatory T cells, which suppress induction of contact hypersensitivity, J Dermatol Sci 39 :105–112, 2005. Crossref, Web of Science, Google Scholar
27. Lutsiak ME, Semnani RT, De Pascalis R, Kashmiri SV, Schlom J, Sabzevari H, Inhibition of CD4 $^{+}$ 25 $^{+}$ T regulatory cell function implicated in enhanced immune response by low-dose cyclophosphamide, Blood 105 :2862–2868, 2005. Crossref, Web of Science, Google Scholar
28. Kopans DB, Breast Imaging, Lippincott-Raven Publishers, Philadelphia, 1997. Google Scholar
29. Thomas Bk, Schwefel H-P, An overview of evolutionary algorithms for parameter optimization, Evol Comput 1(1) :1–23, 1993. Crossref, Web of Science, Google Scholar
30. Takahama T, Sakai S, Iwane N, Solving nonlinear constrained optimization problems by the constrained differential evolution, IEEE Int Conf Syst Man Cybernet, 2006. Crossref, Google Scholar
31. Deb, K et al., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans Evol Comput 6(2) :182–197, 2002. Crossref, Web of Science, Google Scholar