Skip to main content

Advertisement

SpringerLink
Log in

Mathematical Modeling and Analysis of CD200–CD200R in Cancer Treatment

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200–CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200–CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200–CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.

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

  • Alapat D, Coviello-Malle J, Owens R, Qu P, Barlogie B, Shaughnessy JD, Lorsbach RB (2012) Diagnostic usefulness and prognostic impact of cd200 expression in lymphoid malignancies and plasma cell myeloma. Am J Clin Pathol 137:93–100

    Article  Google Scholar 

  • Alfaro C, Suarez N, Gonzalez A, Solano S, Erro L, Dubrot J et al (2009) Influence of bevacizumab, sunitinib and sorafenib as single agents or in combination on the inhibitory effects of vegf on human dendritic cell differentiation from monocytes. Br J Cancer 100(7):1111–1119

    Article  Google Scholar 

  • Almuallem N, Eftimie R (2020) A mathematical model for the role of macrophages in the persistence and elimination of oncolytic viruses. Math Appl Sci Eng 1(2):100–123

    Google Scholar 

  • Almuallem N, Trucu D, Eftimie R (2020) Oncolytic viral therapies and the delicate balance between virus-macrophage-tumour interactions: a mathematical approach. Math Biosci Eng 18:764–799

    Article  MathSciNet  MATH  Google Scholar 

  • Aminin D, Wang Y-M (2021) Macrophages as a weapon in anticancer cellular immunotherapy. Kaohsiung J Med Sci 37:749–758

    Article  Google Scholar 

  • Asadullah K, Sterry W, Volk HD (2003) Interleukin-10 therapy—review of a new approach. Pharmacol Rev 55:241–269

    Article  Google Scholar 

  • Barclay AN, Clark MJ, McCaughan GW (1986) Neuronal/lymphoid membrane glycoprotein MRC OX-2 is a member of the immunoglobulin superfamily with a light-chain-like structure. Biochem Soc Symp 51:149–157

    Google Scholar 

  • Barclay AN, Wright GJ, Brooke G, Brown MH (2003) Cd200 and membrane protein interactions in the control of myeloid cells. Trends Immunol 23:285–290

    Article  Google Scholar 

  • Biswas SK, Mantovani A (2010) Macrophage plasticity and interaction with lymphocyte subsets: cancer as a paradigm. Nat Immunol 11:889–896

    Article  Google Scholar 

  • Braunstein S, Karpisheva K, Pola J, Goldberg C, Hochman T, Yee H et al (2007) A hypoxia-controlled cap-dependent to cap-independent translation switch in breast cancer. Mol Cell 28(3):501–512

    Article  Google Scholar 

  • Breward CJW, Byrne HM, Lewis CE (2001) Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour. Eur J Appl Math 12:529–556

    Article  MathSciNet  MATH  Google Scholar 

  • Brewer G, Saccani S, Sarkar S, Lewis A, Pestka S (2003) Increased interleukin-10 mRNA stability in melanoma cells is associated with decreased levels of A + U-rich element binding factor AUF1. J Interf Cytok Res 23:553–564

    Article  Google Scholar 

  • Cao L, Che X, Qiu X, Li Z, Yang B, Wang S et al (2019) M2 macrophage infiltration into tumor islets leads to poor prognosis in non-small-cell lung cancer. Cancer Manag Res. 11:6125–6138

    Article  Google Scholar 

  • Chen D, Roda JM, Marsh CB, Eubank TD, Friedman A (2012) Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model. Bull Math Biol 74(11):2752–2777

    MathSciNet  MATH  Google Scholar 

  • Chen Z, Kapus A, Khatri I, Kos O, Zhu F, Gorczynski RM (2018) Cell membrane-bound cd200 signals both via an extra-cellular domain and following nuclear translocation of a cytoplasmic fragment. Leuk Res 69:72–80

    Article  Google Scholar 

  • Chen Y, Song Y, Du W, Gong L, Chang H, Zou Z (2019) Tumor-associated macrophages: an accomplice in solid tumor progression. J Biomed Sci 26:78

    Article  Google Scholar 

  • Choueiry F, Torok M, Shakya R, Agrawal K, Deems A, Benner B et al (2019) Cd200 promotes immunosuppression in the pancreatic tumor microenvironment. J Immunother Cancer 8:e000189

    Article  Google Scholar 

  • Clark DA, Dhesy-Thind S, Ellis P, Ramsay J (2014) The cd200-tolerance signaling molecule associated with pregnancy success is present in patients with early-stage breast cancer but does not favor nodal metastasis. Am J Reprod Immunol 72:435–439

    Article  Google Scholar 

  • Coles SJ, Wang ECY, Man S, Hills RK, Burnett AK, Tonks A, Darley RL (2011) Cd200 expression suppresses natural killer cell function and directly inhibits patient anti-tumor response in acute myeloid leukemia. Leukemia 25:792–799

    Article  Google Scholar 

  • D’Andrea A, Aste-Amezaga M, Valiante NM, Ma X, Kubin M, Trinchieri G (1993) Interleukin 10 (IL-1) inhibits humman lymphocyte interferon \(\gamma \)-production by suppressing natural killer cell stimulatory factor/IL-12 synthesis in accessory cells. J Exp Med 178:1041–1048

    Google Scholar 

  • D’Arena G, Valvano L, Vitale C, Coscia M, Statuto T, Bellesi S et al (2019) Cd200 and prognosis in chronic lymphocytic leukemia: conflicting results. Leuk Res 83:106169

    Article  Google Scholar 

  • Day J, Friedman A, Schlesinger LS (2008) Modeling the immune rheostat of macrophages in the lung in response to infection. PNAS 106:11246–11251

    Article  Google Scholar 

  • den Breems NY, Eftimie R (2016) The re-polarisation of M2 and M1 macrophages and its role on cancer outcomes. J Theor Biol 390:23–39

    Article  MathSciNet  MATH  Google Scholar 

  • Di Raimondo F, Azzaro MP, Palumbo GA, Bagnato S, Stagno F, Giustolisi GM et al (2001) Elevated vascular endothelial growth factor (VEGF) serum levels in idiopathic myelofibrosis. Leukemia 15:976–980

    Article  Google Scholar 

  • Eftimie R, Eftimie G (2018) Tumour-associated macrophages and oncolytic virotherapies: a mathematical investigation into a complex dynamics. Lett Biomath 5(2):6–35

    Article  MathSciNet  Google Scholar 

  • Eftimie R, Eftimie G (2019) Investigating macrophages plasticity following tumour–immune interactions during oncolytic therapies. Acta Biotheor 67:321–359

    Article  Google Scholar 

  • Eftimie R, Gibelli L (2020) A kinetic theory approach for modelling tumour and macrophages heterogeneity and plasticity during cancer progression. Math Models Methods Appl Sci 30(4):659–683

    Article  MathSciNet  MATH  Google Scholar 

  • Erin N, Podnos A, Tanriover G, Duymuş Ö, Cote E, Khatri I, Gorczynski RM (2015) Bidirectional effect of cd200 on breast cancer development and metastasis, with ultimate outcome determined by tumor aggressiveness and a cancer-induced inflammatory response. Oncogene 34:3860–3870

    Article  Google Scholar 

  • Eubank TD, Roberts RD, Khan M, Curry JM, Nuovo GJ, Kuppusamy P, Marsh CB (2009) Granulocyte macrophage colony-stimulating factor inhibits breats growth and metastasis by invoking an anti-angiogenic program in tumor-educated macrophages. Cancer Res 69:2133–2140

    Article  Google Scholar 

  • Evans R, Philips GS, Marsh CB, Eubank TD, Roda JM, Summer LA (2011) Hypoxiainducible factor-2\(\alpha \) regulates GM-CSF-derived soluble vascular endothelial growth factor receptor 1 production from macrophages and inhibits tumor growth and angiogenesis. J Immunol 187:1970–1976

    Google Scholar 

  • Freeman BJ, Roberts MS, Vogler CA, Nicholes A, Hofling AA, Sands MS (1999) Behavior and therapeutic efficacy of \(\beta \)-glucuronidase-positive mononuclear phagocytes in murine model of mucopolysaccharidosis type vii. Blood 94:2142–2150

    Article  Google Scholar 

  • Friedman A, Lai X (2018) Combination therapy for cancer with oncolytic virus and checkpoint inhibitor: a mathematical model. PLoS ONE 13:e0192449

    Article  Google Scholar 

  • Friedman A, Turner J, Szomolay B (2008) A model on the influence of age on immunity to infection with mycobacterium tuberculosi. Exp Gerontol 43:275–285

    Article  Google Scholar 

  • Gabrilovich DI, Chen HL, Girgis KR, Cunningham HT, Meny GM, Nadaf S et al (1996) Production of vascular endothelial growth factor by human tumors inhibits the functional maturation of dendritic cells. Nat Med 2(10):1096–1103

  • Gabrilovich DI, Rosenberg SO, Bronte V (2012) Coordinated regulation of myeloid cells by tumors. Nat Rev Immunol 12:253–268

    Article  Google Scholar 

  • Huizinga TWJ, Keijsers V, Yanni G, Hall M, Ramage W, Lanchbury J et al (2000) Are differences in interleukin 10 production associated with joint damage? Rheumatology 39:1180–1188

    Article  Google Scholar 

  • Janco JMT, Lamichhane P, Karyampudi L, Knutson KL (2015) Tumor-infiltrating dendritic cells in cancer pathogenesis. J Immunol 194:2985–2991

    Article  Google Scholar 

  • Kallio R, Surcel HM, Bloigu A, Syrjälä H (2001) Balance between interleukin-10 and interleukin-12 in adult cancer patients with or without infections. Eur J Cancer 37:857–861

    Article  Google Scholar 

  • Keane J, Balcewicz-Sablinska MK, Remold HG, Chupp GL, Meek BB, Fenton MJ, Kornfeld H (1997) Infection by mycobacterium tuberculosis promotes human alveolar macrophage apoptosis. Infect Immun 65:298–304

    Article  Google Scholar 

  • Kendall MD (1998) Dying to live: how our bodies fight disease. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Koshikawa N, Iyozumi A, Gassmann M, Takenaga K (2003) Constitutive upregulation of hypoxiainducible factor 1\(\alpha \) MRNA occurring in highly metastatic lung carcinoma cells leads to vascular endothelial growth factor over-expression upon hypoxic exposure. Oncogene 22:6717–6724

    Article  Google Scholar 

  • Kut C, Mac Gabhann F, Popel AS (2007) Where is VEGF in the body? A meta-analysis of VEGF distribution in cancer. Br J Cancer 97:978–985

    Article  Google Scholar 

  • Lai X, Friedman A (2017) Combination therapy for melanoma with BRAF/MEK inhibitor and immune checkpoint inhibitor: a mathematical model. BMC Syst Biol 11(1):70

    Article  Google Scholar 

  • Lai X, Friedman A (2019) Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs. J Theor Biol 462:490–498

    Article  MathSciNet  MATH  Google Scholar 

  • Lai X, Stiff A, Duggan M, Wesolowski R, Carson WE, Friedman A (2018) Modeling combination therapy for breast cancer with bet and immune checkpoint inhibitors. PNAS 115(21):5534–5539

    Article  Google Scholar 

  • Li X, Jolly MK, George JT, Pienta KJ, Levine H (2018) Computational modeling of the crosstalk between macrophage polarization and tumor cell plasticity in the tumor microenvironment. Front Oncol 9:10

    Article  Google Scholar 

  • Liao K-L, Bai X-F, Friedman A (2013) The role of cd200–cd200r in tumor immune evasion. J Theor Biol 328:65–76

    Article  MATH  Google Scholar 

  • Liu JQ, Hu A, Zhu J, Yu J, Talebian F, Bai XF (2020) Cd200–cd200r pathway in the regulation of tumor immune microenvironment and immunotherapy. Adv Exp Med Biol 1223:155–165

    Article  Google Scholar 

  • Louzoun Y, Xue C, Lesinski GB, Friedman A (2014) A mathematical model for pancreatic cancer growth and treatments. J Theor Biol 351:74–82

    Article  MathSciNet  MATH  Google Scholar 

  • Love JE, Thompson K, Kilgore MR, Westerhoff M, Murphy CE, Papanicolau-Sengos A et al (2017) Cd200 expression in neuroendocrine neoplasms. Am J Clin Pathol 148:236–242

    Article  Google Scholar 

  • Łukaszewicz-Zajac M, Mroczko B, Kozłowski M, Nikliński J, Laudański J, Szmitkowski M (2010) Clinical significance of serum macrophage-colony stimulating factor (M-CSF) in esophageal cancer patients and its comparison with classical tumor markers. Clin Chem Lab Med 48:1467–1473

    Article  Google Scholar 

  • Ma Y, Shurin GV, Peiyuan Z, Shurin MR (2013) Dendritic cells in the cancer microenvironment. J Cancer 4(1):36–44

    Article  Google Scholar 

  • Marino S, Kirschner DE (2004) The human immune response to mycobacterium tuberculosis in lung and lymph node. J Theor Biol 227:463–486

    Article  MATH  Google Scholar 

  • Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254:178–196

    Article  MathSciNet  MATH  Google Scholar 

  • Morales V, Soto-Ortiz L (2018) Modeling macrophage polarization and its effect on cancer treatment success. OJI 8(2):36–80

    Article  Google Scholar 

  • Moreaux J, Hose D, Reme T, Jourdan E, Hundemer M, Legouffe E et al (2006) Cd200 is a new prognostic factor in multiple myeloma. Blood 108:4194–9197

    Article  Google Scholar 

  • Moreaux J, Veyrune JL, Reme T, De Vos J, Klein B (2008) Cd200: a putative therapeutic target in cancer. Biochem Biophys Res Commun 366:117–122

    Article  Google Scholar 

  • Nickaeen N, Ghaisari J, Heiner M, Moein S, Gheisari Y (2019) Agent-based modeling and bifurcation analysis reveal mechanisms of macrophage polarization and phenotype pattern distribution. Sci Rep 9:12764

    Article  Google Scholar 

  • Öwen H, Duman N, Abacioglu H, Özkan H, Irken G (2001) Association between serum macrophage colony-stimulating factor levels and monocyte and thrombocyte counts in healthy, hypoxic, and septic term neonates. Pediatrics 108:329–332

    Article  Google Scholar 

  • Palucka J, Banchereau J (2012) Cancer immunotherapy via dendritic cells. Nat Rev Cancer 12:265–277

    Article  Google Scholar 

  • Pan Y, Yu Y, Wang X, Zhang T (2020) Tumor-associated macrophages in tumor immunity. Front Immunol 11:583084

    Article  Google Scholar 

  • Petermann KB, Rozenberg GI, Zedek D, Groben P, McKinnon K, Buehler C et al (2007) Cd200 is induced by ERK and is a potential therapeutic target in melanoma. J Clin Invest 117:3922–3929

    Google Scholar 

  • Plank MJ, Sleeman BD, Jones PF (2004) A mathematical model of tumor anglogenesis, regulated by vascular endothelial growth factor and the angiopoietins. J Theore Biol 229:435–454

    Article  MATH  Google Scholar 

  • Qian B, Deng Y, Hong Im J, Muschel RJ, Zou Y, Li J, Lang RA, Pollard JW (2009) A distinct macrophage population mediated metastatic breast cancer cell extravasation, establishment and growth. PLoS ONE 4:e6563

    Article  Google Scholar 

  • Rapella A, Negrioli A, Melillo G, Pastorino S, Varesio L, Bosco M (2002) Flavopirisol inhibits vascular endothelial growth factor production induced by hypoxia or picolinic acid in human neuroblastoma. Int J Cancer 99:658–664

    Article  Google Scholar 

  • Rexin P, Tauchert A, Hanze J, Heers H, Schmidt A, Hofmann R, Hegele A (2018) The immune checkpoint molecule cd200 is associated with tumor grading and metastasis in bladder cancer. Anticancer Res 38:2749–2754

    Google Scholar 

  • Robertson MJ, Ritz J (1996) Interleukin 12: basic biology and potential applications in cancer treatment. Oncologist 1:88–97

    Article  Google Scholar 

  • Robertson MJ, Cameron C, Atkins MB, Gordon MS, Lotze MT, Sherman ML, Ritz J (1999) Immunological effects of interleukin 12 administered by bolus intravenous injection to patients with cancer. Clin Cancer Res 5:9–16

    Google Scholar 

  • Rygiel TR, Meyaard L (2012) Cd200r signalling in tumomr tolerance and inflammation: a tricky balance. Curr Opin Immunol 24:233–238

    Article  Google Scholar 

  • Rygiel TP, Karnam G, Goverse G, van der Marel AP, Greuter MJ, van Schaarenburg RA et al (2011) Cd200–cd200r signaling suppresses anti-tumor responses independently of cd200 expression on the tumor. Oncogene 24:2979–2988

    Google Scholar 

  • Saenz R, Futalan D, Leutenez L, Eekhout F, Fecteau JF, Sundelius S et al (2014) TLR4-dependent activation of dendritic cells by an HMGB1-derived peptide adjuvant. J Transl Med 12:1–11

    Article  Google Scholar 

  • Sánchez-Hernández C, Gutiérrez-Ortega A, Aguilar-León D, Hernández-Pando R, Gómez-Lim M, Gómez-García B (2010) In vivo activity of plant-based interleukin-12 in the lung of Balb/c mouse. BMC Res Notes 3:151

    Article  Google Scholar 

  • Shang Z, Li Z, Li J (2006) VEGF is up-regulated by hypoxic stimulation and related to tumor angiogenesis and severity of disease in oral squamous cell carcinoma: in vitro and in vivo studies. Int J Oral Maxillofac Surg 35:533–538

    Article  Google Scholar 

  • Sickert D, Aust DE, Langer S, Baretton GB, Dieter P (2007) Characterization of macrophage subpopulations and microvessel density in carcinomas of the gastrointestinal tract. Anticancer Res 27:1693–1700

    Google Scholar 

  • Sims GP, Rowe DC, Rietdijk ST, Herbst R, Coyle AJ (2010) HMGB1 and RAGE in inflammation and cancer. Annu Rev Immunol 28:367–388

    Article  Google Scholar 

  • Solinas G, Germano G, Mantovani A, Allavena P (2009) Tumor-associated macrophages (TAM) as major players of the cancer-related inflammation. J Leukoc Biol 86:1065–1073

    Article  Google Scholar 

  • Sud D, Bigbee C, Flynn JL, Kirschner DE (2006) Contribution of cd8\(^+\) t cells to control of mycobacterium tuberculosis infection. J Immunol 176:4296–4314

    Article  Google Scholar 

  • Szomolay B, Eubank TD, Roberts RD, Marsh CB, Friedman A (2012) Modeling the inhibition of breast cancer growth by GM-CSF. J Theoret Biol 303:141–151

    Article  MathSciNet  MATH  Google Scholar 

  • Talebian F, Liu JQ, Liu Z, Khattabi M, He Y, Ganju R, Bai X-F (2012) Melanoma cell expression of cd200 inhibits tumor formation and lung metastasis via inhibition of myeloid cell functions. PLoS ONE 7:e31442

    Article  Google Scholar 

  • Talty R, Olino K (2021) Metabolism of innate immune cells in cancer. Cancers (Basel) 13(4):904

    Article  Google Scholar 

  • Tang S, Liu H, Chen G, Rao Q, Geng Y, Zheng G, Zheng D, Wu K (2000) Internalization and half-life of membrane-bound macrophage colony-simulating factor. Chinese Sc Bull 45:1697–1703

    Article  Google Scholar 

  • Tonks A, Hills R, White P, Rosie B, Mills KI, Burnett AK, Darley RL (2007) Cd200 as a prognostic factor in acute myeloid leukaemia. Leukemia 21:566–568

    Article  Google Scholar 

  • Utting JC, Flanagan AM, Brandao-Burch A, Orriss IR, Aenett TR (2010) Hypoxia stimulates osteoclast formation from human peripheral blood. Cell Biochem Funct 28:374–380

    Article  Google Scholar 

  • Vathiotis IA, MacNeil T, Zugazagoitia J, Syrigos KN, Aung TN, Gruver AM et al (2021) Quantitative assessment of cd200 and cd200r expression in lung cancer. Cancers (Basel) 13(5):1024

    Article  Google Scholar 

  • Vaupel P, Mayer A, Briest S, Höckel M (2003) Oxygenation gain factor: a novel parameter characterizing the association between hemoglobin level and the oxygenation status of breast cancers. Cancer Res 63:7634–7637

    Google Scholar 

  • Vesosky B, Flaherty DK, Turner J (2006) Th1 cytokines facilitate CD8-t-cell-mediated early resistance to infection with Mycibacterium tuberculosis in old mice. Infect Immun 74:3314–3324

    Article  Google Scholar 

  • Wang L, Liu JQ, Talebian F, Ei-Omrani HY, Khattabi M, Yu L, Bai X-F (2010) Tumor expression of cd200 inhibits IL-10 production by tumor-associated myeloid cells and prevents tumor immune evasion of CTL therapy. Eur J Immunol 40:2569–2579

    Article  Google Scholar 

  • Wang H, Yung MMH, Ngan HYS, Chan KKL, Chan DW (2021) The impact of the tumor microenvironment on macrophage polarization in cancer metastatic progression. Int J Mol Sci 22(12):6560

    Article  Google Scholar 

  • Winslow GM, Roberts AD, Blackman MA, Woodland DL (2003) Persistence and turnover of antigen-specific CD4 t cells during chronic tuberculosis infection in the mouse. J Immunol 170:2046–2052

    Article  Google Scholar 

  • Wright GJ, Cherwinski H, Foster-Cuevas M, Brooke G, Puklavec MJ, Bigler M et al (2003) Characterization of the cd200 receptor family in mice and humans and their interactions with cd200. J Immunol 171:3034–3046

    Article  Google Scholar 

  • Zhang S, Cherwinski H, Sedgwick JD, Phillips JH (2004) Molecular mechanisms of cd200 inhibition of mast cell activation. J Immunol 173:6786–6793

    Article  Google Scholar 

  • Zhou L, Nazarian AA, Smale ST (2004) Interleukin-10 inhibits interleukin-12 p40 gene transcription by targeting a late event in the activation pathway. Mol Cell Biol 24:2385–2396

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the Discovery Grant from the Natural Sciences and Engineering Research Council of Canada [grant number RGPIN-2020-07097 for Kang-Ling Liao].

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    Kang-Ling Liao & Kenton D. Watt

Authors
  1. Kang-Ling Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kenton D. Watt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kang-Ling Liao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 2475 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, KL., Watt, K.D. Mathematical Modeling and Analysis of CD200–CD200R in Cancer Treatment. Bull Math Biol 84, 82 (2022). https://doi.org/10.1007/s11538-022-01039-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11538-022-01039-x

Keywords

Mathematics Subject Classification

Search

Navigation