Skip to main content

Advertisement

SpringerLink
Log in

A Mathematical Model for the Glucose-Lactate Metabolism of in Vitro Cancer Cells

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

Abstract

We propose a mathematical model of tumor cell nutrient uptake governed by the presence of two key biomolecular fuels: glucose and lactate. The model allows us to describe, in a remarkably simple way, different in vitro scenarios previously reported in experiments of tumor cell metabolism using distinct energy sources. The predictions of our model show good agreement with all the examined tumor cell lines (cervix, colon, and glioma) and provide a first step toward the development of more comprehensive frameworks accounting for in vivo cancer dynamics under complex spatial heterogeneities.

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

Similar content being viewed by others

References

  • Baumann, F., Leukel, P., Doerfelt, A., Beier, C. P., Dettmer, K., Oefner, P. J., Kastenberger, M., Kreutz, M., Nickl-Jockschat, T., Bogdahn, U., Bosserhoff, A.-K., & Hau, P. (2009). Lactate promotes glioma migration by TGF-β2 dependent regulation of matrix metalloproteinase-2. Neuro-oncology, 11(4), 368–380.

    Article  Google Scholar 

  • Bertuzzi, A., Fasano, A., Gandolfi, A., & Sinisgalli, C. (2010). Necrotic core in EMT6/Ro tumour spheroids: Is it caused by an ATP deficit? J. Theor. Biol., 262, 142–150.

    Article  Google Scholar 

  • Bonnet, S., Archer, S. L., Allalunis-Turner, J., Haromy, A., Beaulieu, C., Thompson, R., Lee, C. T., Lopaschuk, G. D., Puttagunta, L., Bonnet, S., Harry, G., Hashimoto, K., Porter, C. J., Andrade, M. A., Thebaud, B., & Michelakis, E. D. (2007). A mitochondria-K+ channel axis is suppressed in cancer and its normalization promotes apoptosis and inhibits cancer growth. Cancer Cell, 11, 37–51.

    Article  Google Scholar 

  • Bonuccelli, G., Tsirigos, A., Whitaker-Menezes, D., Pavlides, S., Pestell, R. G., Chiavarina, B., Frank, P. G., Flomenberg, N., Howell, A., Martinez-Outschoorn, U. E., Sotgia, F., & Lisanti, M. P. (2010). Ketones and lactate “fuel” tumor growth and metastasis. Evidence that epithelial cancer cells use oxidative mitochondrial metabolism. Cell Cycle, 9, 3514–3596.

    Google Scholar 

  • Bouzier, A.-K., Goodwin, R., de Gannes, F. M., Valeins, H., Voisin, P., Canioni, P., & Merle, M. (1998). Compartmentation of lactate and glucose metabolism in C6 glioma cells. A 13c and 1H NMR study. J. Biol. Chem., 273, 27162–27169.

    Article  Google Scholar 

  • Bouzier-Sore, A. K., Canioni, P., & Merle, M. (2001). Effect of exogenous lactate on rat glioma metabolism. J. Neurosci. Res., 65, 543–548.

    Article  Google Scholar 

  • Brahimi-Horn, M. C., Chiche, J., & Pouyssegur, J. (2007). Hypoxia signalling controls metabolic demand. Curr. Opin. Cell Biol., 19, 223–229.

    Article  Google Scholar 

  • Bristow, R. G., & Hill, R. P. (2008). Hypoxia and metabolism: Hypoxia, DNA repair and genetic instability. Nat. Rev., 8, 180–192.

    Article  Google Scholar 

  • Buckingham, S. C., Campbell, S. L., Haas, B. R., Montana, V., Robel, S., Ogunrinu, T., & Sontheimer, H. (2011). Glutamate release by primary brain tumors induces epileptic activity. Nat. Med., 17, 1269–1274.

    Article  Google Scholar 

  • Cairns, R. A., Harris, I. S., & Mak, T. W. (2011). Regulation of cancer cell metabolism. Nat. Rev., Cancer, 11, 85–95.

    Article  Google Scholar 

  • Chiche, J., Brahimi-Horn, M. C., & Pouysségur, J. (2010). Tumour hypoxia induces a metabolic shift causing acidosis: a common feature in cancer. J. Cell. Mol. Med., 14, 771–794.

    Article  Google Scholar 

  • De Berardinis, R. J., Mancuso, A., Daikhin, E., Nissim, I., Yudkoff, M., Wehrli, S., & Thompson, C. B. (2007). Beyond aerobic glycolysis: transformed cells can engage in glutamine metabolism that exceeds the requirement for protein and nucleotide synthesis. Proc. Natl. Acad. Sci. USA, 104, 19345–19350.

    Article  Google Scholar 

  • Elstrom, R. L., Bauer, D. E., Buzzai, M., Karnauskas, R., Harris, M. H., Plas, D. R., Zhuang, H., Cinalli, R. M., Alavi, A., Rudin, C. M., & Thompson, C. B. (2004). Akt stimulates aerobic glycolysis in cancer cells. Cancer Res., 64, 3892–3899.

    Article  Google Scholar 

  • Fang, J., Quinones, Q. J., Holman, T. L., Morowitz, M. J., Wang, Q., Zhao, H., Sivo, F., Maris, J. M., & Wahl, M. L. (2006). The H+-linked monocarboxylate transporter (MCT1/SLC16A1): A potential therapeutic target for high-risk neuroblastoma. Mol. Pharmacol., 70, 2108–2115.

    Article  Google Scholar 

  • Froberg, M. K., Gerhart, D. Z., Enerson, B. E., Manivel, C., Guzman-Paz, M., Seacotte, N., & Drewes, L. R. (2001). Expression of monocarboxylate transporter MCT1 in normal and neoplastic human CNS tissues. Membr. Cell. Biophys. Bioch., 12, 0959.

    Google Scholar 

  • Funes, J. M., Quintero, M., Henderson, S., Martinez, D., Qureshi, U., Westwood, C., Clements, M. O., Bourboulia, D., Pedley, R. B., Moncada, S., & Boshoff, C. (2007). Transformation of human mesenchymal stem cells increases their dependency on oxidative phosphorylation for energy production. Proc. Natl. Acad. Sci. USA, 104, 6223–6228.

    Article  Google Scholar 

  • Gatenby, R. A., & Gillies, R. J. (2004). Why do cancers have high aerobic glycolysis? Nat. Rev., Cancer, 4, 891–899.

    Article  Google Scholar 

  • Grillon, E., Farion, R., Fablet, K., De Waard, M., Tse, C. M., Donowitz, M., Remy, C., & Coles, J. A. (2011). The spatial organization of proton and lactate transport in a rat brain tumor. PLOS One, 6, e17316.

    Article  Google Scholar 

  • Halestrap, A. P., & Price, N. T. (1999). The proton-linked monocarboxylate transporter (MCT) family: structure, function and regulation. Biochem. J., 343, 281–299.

    Article  Google Scholar 

  • Hanahan, D., & Weinberg, R. A. (2011). Hallmarks of cancer: the next generation. Cell, 144, 646–674.

    Article  Google Scholar 

  • Izumi, H., Takahashi, M., Uramoto, H., Nakayama, Y., Oyama, T., Wang, K.-Y., Sasaguri, Y., Nishizawa, S., & Kohno, K. (2010). Monocarboxylate transporters 1 and 4 are involved in the invasion activity of human lung cancer cells. Cancer Sci., 105, 1007–1013.

    Google Scholar 

  • Kennedy, K. M., & Dewhrist, M. W. (2010). Tumor metabolism of lactate: the influence and therapeutic potential for MCT and CD147 regulation. Future Oncol., 6, 127–148.

    Article  Google Scholar 

  • Koppenol, W. H., Bounds, P. L., & Dang, C. V. (2011). Otto Warburg’s contributions to current concepts of cancer metabolism. Nat. Rev., Cancer, 11, 325–337.

    Article  Google Scholar 

  • Kroemer, G., & Pouyssegur, J. (2008). Tumor cell metabolism: cancer’s achilles’ heel. Cancer Cell, 13, 472–482.

    Article  Google Scholar 

  • Mankoff, D. A., Eary, J. F., Link, J. M., Muzi, M., Rajendran, J. G., Spence, A. M., & Krohn, K. A. (2007). Tumor-specific positron emission tomography imaging in patients: [18F] fluorodeoxyglucose and beyond. Clin. Cancer Res., 13, 3460–3469.

    Article  Google Scholar 

  • Mathupala, S. P., Parajuli, P., & Sloan, A. E. (2004). Silencing of monocarboxylate transporters via siRNA inhibits glycolysis and induces cell death in malignant glioma: An in vitro study. Neurosurgery, 55, 1410–1419.

    Article  Google Scholar 

  • Mathupala, S. P., Colen, C. B., Parajuli, P., & Sloan, A. E. (2007). Lactate and malignant tumors: A therapeutic target at the end stage of glycolysis. J. Bioenerg. Biomembr., 39, 73–77.

    Article  Google Scholar 

  • Mathupala, S., Ko, Y. H., & Pedersen, P. L. (2010). The pivotal roles of mitochondria in cancer: Warburg and beyond and encouraging prospects for effective therapies. Biochim. Biophys. Acta, 1797, 1225–1230.

    Article  Google Scholar 

  • McCarthy, N. (2009). Metabolism: room to breathe. Nat. Rev., Cancer, 9, 13.

    Article  Google Scholar 

  • Michelakis, E. D., Sutendra, G., Dromparis, P., Webster, L., Haromy, A., Niven, E., Maguire, C., Gammer, T.-L., Mackey, J. R., Fulton, D., Abdulkarim, B., McMurtry, M. S., & Petruk, K. C. (2010). Metabolic modulation of glioblastoma with dichloroacetate. Sci. Transl. Med., 2(31), 31ra34.

    Article  Google Scholar 

  • Moreno-Sánchez, R., Rodríguez-Enríquez, S., Marín-Hernández, A., & Saavedra, E. (2007). Energy metabolism in tumor cells. FEBS J., 274, 1393–1418.

    Article  Google Scholar 

  • Morris, M. E., & Felmlee, M. A. (2008). Overview of the proton-coupled MCT family of transporters. AAPS J., 10, 311–321.

    Article  Google Scholar 

  • Pavlides, S., Whitaker-Menezes, D., Castello-Cros, R., Flomenberg, N., Witkiewicz, A. K., Frank, P. G., Casimiro, M. C., Wang, C., Fortina, P., Addya, S., Pestell, R. G., Martinez-Outschoorn, U. E., Sotgia, F., & Lisanti, M. P. (2009). The reverse Warburg effect: Aerobic glycolysis in cancer associated fibroblasts and the tumor stroma. Cell Cycle, 8, 3984–4001.

    Article  Google Scholar 

  • Pavlides, S., Tsirigos, A., Vera, I., Flomenberg, N., Frank, P. G., Casimiro, M. C., Wang, C., Pestell, R. G., Martinez-Outschoorn, U. E., Howell, A., Sotgia, F., & Lisanti, M. P. (2010). Transcriptional evidence for the “Reverse Warburg Effect” in human breast cancer tumor stroma and metastasis: similarities with oxidative stress, inflammation, Alzheimer’s disease, and “Neuron-Glia Metabolic Coupling”. Aging, 2, 185–199.

    Google Scholar 

  • Pérez-García, V. M., Calvo, G. F., Belmonte-Beitia, J., Diego, D., & Pérez-Romasanta, L. (2011). Bright solitary waves in malignant gliomas. Phys. Rev. E, 84, 021921.

    Article  Google Scholar 

  • Pinheiro, C., Longatto-Filho, A., Scapulatempo, C., Ferreira, L., Martins, S., Pellerin, L., Rodrigues, M., Alves, V. A. F., Schmitt, F., & Baltazar, F. (2008). Increased expression of monocarboxylate transporters 1, 2, and 4 in colorectal carcinomas. Virchows Arch., 452, 139–146.

    Article  Google Scholar 

  • Pinheiro, C., Albergaria, A., Paredes, J., Sousa, B., Dufloth, R., Vieira, D., Schmitt, F., & Baltazar, F. (2010a). Monocarboxylate transporter 1 is up-regulated in basal-like breast carcinoma. Histopathology, 56, 860–867.

    Article  Google Scholar 

  • Pinheiro, C., Reis, R. M., Ricardo, S., Longatto-Filho, A., Schmitt, F., & Baltazar, F. (2010b). Expression of monocarboxylate transporters 1, 2, and 4 in human tumours and their association with CD147 and CD44. J. Biomed. Biotechnol., 2010, 427694.

    Article  Google Scholar 

  • Rossignol, R., Gilkerson, R., Aggeler, R., Yamagata, K., Remington, S. J., & Capaldi, R. A. (2004). Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells. Cancer Res., 64, 985–993.

    Article  Google Scholar 

  • Sauer, L. A., Stayman, J. W., & Dauchy, R. T. (1987). Amino acid, glucose, and lactic acid utilization in vivo by rat tumors. Cancer Res., 42, 4090–4097.

    Google Scholar 

  • Simpson, I. A., Carruthers, A., & Vannucci, S. J. (2007). Supply and demand in cerebral energy metabolism: The role of nutrient transporters. J. Cereb. Blood Flow Metab., 27, 1766–1791.

    Article  Google Scholar 

  • Smallbone, K., Gatenby, R. A., & Maini, P. K. (2008). Mathematical modelling of tumour acidity. J. Theor. Biol., 255, 106–112.

    Article  Google Scholar 

  • Sonveaux, P., Végran, F., Schroeder, T., Wergin, M. C., Verrax, J., Rabbani, Z. N., De Saedeleer, C. J., Kennedy, K. M., Diepart, C., Jordan, B. F., Kelley, M. J., Gallez, B., Wahl, M. L., Feron, O., & Dewhirst, M. W. (2008). Targeting lactate-fueled respiration selectively kills hypoxic tumor cells in mice. J. Clin. Invest., 118, 3930–3942.

    Google Scholar 

  • Sun, R. C., Fadia, M., Dahlstrom, J. E., Parish, C.R., Board, P.G., & Blackburn, A.C. (2009). Reversal of the glycolytic phenotype by dichloroacetate inhibits metastatic breast cancer cell growth in vitro and in vivo. Breast Cancer Res. Treat., 120, 253–260.

    Article  Google Scholar 

  • Tennant, D. A., Durán, R. V., & Gottlieb, E. (2010). Targeting metabolic transformation for cancer therapy. Nat. Rev., Cancer, 10, 267–277.

    Article  Google Scholar 

  • Terpstra, M., Gruetter, R., High, W. B., Mescher, M., DelaBarre, L., Merkle, M., & Garwood, M. (1998). Magnetic resonance spectroscopy lactate turnover in rat glioma measured by in vivo nuclear magnetic resonance spectroscopy. Cancer Res., 58, 5083–5088.

    Google Scholar 

  • Vander Heiden, M. G., Cantley, L. C., & Thompson, C. B. (2009). Understanding the Warburg effect: the metabolic requirements of cell proliferation. Science, 324, 1029–1033.

    Article  Google Scholar 

  • Vaupel, P., Thews, O., & Hoeckel, M. (2001). Treatment resistance of solid tumors role of hypoxia and anemia. Rev. Med. Oncol., 18(4), 243–259.

    Article  Google Scholar 

  • Végran, F., Boidot, R., Michiels, C., Sonveaux, P., & Feron, O. (2011). Lactate influx through the endothelial cell monocarboxylate transporter MCT1 supports an NF-kappaB/IL-8 pathway that drives tumor angiogenesis. Cancer Res., 71, 2550–2560.

    Article  Google Scholar 

  • Venkatasubramanian, R., Henson, M. A., & Forbes, N. S. (2006). Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J. Theor. Biol., 242, 440–453.

    Article  MathSciNet  Google Scholar 

  • Voisin, P., Bouchaud, V., Merle, M., Diolez, P., Duffy, L., Flint, K., Franconi, J.-M., & Bouzier-Sore, A.-K. (2010). Microglia in close vicinity of glioma cells: correlation between phenotype and metabolic alterations. Front. Neuroenerg., 2, 131.

    Article  Google Scholar 

  • Walenta, S., & Mueller-Klieser, W. F. (2004). Lactate: mirror and motor of tumor malignancy. Semin. Radiat. Oncol., 14, 267–274.

    Article  Google Scholar 

  • Warburg, O., Posener, K., & Negelein, E. (1924). Über den Stoffwechsel der Tumoren. Biochem. Z., 152, 319–344.

    Google Scholar 

  • Weissleder, R., & Pittet, M. J. (2008). Imaging in the era of molecular oncology. Nature, 452, 580–589.

    Article  Google Scholar 

  • Wolf, A., Agnihotri, S., Micallef, J., Mukherjee, J., Sabha, N., Cairns, R., Hawkins, C., & Guha, A. (2011). Hexokinase 2 is a key mediator of aerobic glycolysis and promotes tumor growth in human glioblastoma multiforme. J. Exp. Med., 208, 313–326.

    Article  Google Scholar 

Download references

Acknowledgements

We wish to thank P. Melgar and R. Sánchez-Prieto (CRIB, UCLM), and L. Pérez-Romasanta (HGCR) for fruitful discussions. This work has been supported by grants MTM2009-13832 (Ministerio de Ciencia e Innovación, Spain), PEII11-0178-4092 (Junta de Comunidades de Castilla-La Mancha, Spain) and the James S. McDonnell Foundation.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, E. T. S. I. Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain

    Berta Mendoza-Juez, Alicia Martínez-González & Víctor M. Pérez-García

  2. Departamento de Matemáticas, E. T. S. I. Caminos, Canales y Puertos and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain

    Gabriel F. Calvo

Authors
  1. Berta Mendoza-Juez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alicia Martínez-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gabriel F. Calvo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Víctor M. Pérez-García
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Berta Mendoza-Juez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mendoza-Juez, B., Martínez-González, A., Calvo, G.F. et al. A Mathematical Model for the Glucose-Lactate Metabolism of in Vitro Cancer Cells. Bull Math Biol 74, 1125–1142 (2012). https://doi.org/10.1007/s11538-011-9711-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-011-9711-z

Keywords

Search

Navigation