A Mathematical Model of Folate Metabolism and DNA Methylation: Stability Analysis
Keywords:
Folate, DNA Methylation, Methionine, DNA Methyltransferase, S-Adenosyl Methionine
Abstract
In the mammalian genome, DNA methylation could be used to deduce health conditions associated with ageing and many other pathological conditions. In addition, folate is nutritionally vital for improving human health and growth. Folate is also essential in the activity of mammalian epigenetics, through its transfer of methyl groups for the DNA methylation reaction. Furthermore, folate, as part of the B12 vitamins, not only plays a key role in our diet, but is involved in the mechanism of DNA synthesis, maintenance of DNA methylation, and metabolism of the amino acids required for growth and cell division, especially during pregnancy and infancy. Investigations have shown that vitamin deficiency B12 has effects in all age groups, although to a higher degree among older people, infants, and pregnant women. Over the years, many mathematical models have been constructed, but none explicitly captured the complexity of the interdependent biochemical and molecular mechanisms of folate metabolism and DNA methylation. In this paper, we develop and assembled an all-inclusive model that connects folate metabolism and DNA methylation, and we investigated the stability of the system. We were also able to show that the system is stable, which is a basis for further analysis like bifurcation analysis and its applications.
References
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Braun, M., and Golubitsky, M. (1983). Differential equations and their applications (Vol. 4). New York: Springer.
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McGovern, A. P., Powell, B. E., and Chevassut, T. J. (2012). A dynamic multi-compartmental model of DNA methylation with demonstrable predictive value in hematological malignancies. Journal of Theoretical Biology, 310, 14-20.
Smith, Z. D., and Meissner, A. (2013). DNA methylation: roles in mammalian development. Nature Reviews Genetics, 14(3), 204-220.
Crider, K. S., Qi, Y. P., Yeung, L. F., Mai, C. T., Head Zauche, L., Wang, A., ... and Williams, J. L. (2022). Folic acid and the prevention of birth defects: 30 years of opportunity and controversies. Annual Review of Nutrition, 42, 423-452.
Hoffbrand, A. V., and Weir, D. G. (2001). The history of folic acid. British Journal of Haematology, 113(3).
Martinez, H., Benavides-Lara, A., Arynchyna-Smith, A., Ghotme, K. A., Arabi, M., and Arynchyna, A. (2023). Global strategies for the prevention of neural tube defects through the improvement of folate status in women of reproductive age. Child's Nervous System, 39(7), 1719-1736.
Lee, Y., Vousden, K. H., and Hennequart, M. (2024). Cycling back to folate metabolism in cancer. Nature Cancer, 5(5), 701-715.
Nijhout, H. F., Reed, M. C., Budu, P., and Ulrich, C. M. (2004). A mathematical model of the folate cycle: new insights into folate homeostasis. Journal of Biological Chemistry, 279(53), 55008-55016.
Bhalla, P., Rengaswamy, R., Karunagaran, D., Suraishkumar, G. K., and Sahoo, S. (2022). Metabolic modeling of host-microbe interactions for therapeutics in colorectal cancer. NPJ Systems Biology and Applications, 8(1), 1.
Sulistoyingrum, D. C., Sullivan, T. R., Skubisz, M., Palmer, D. J., Wood, S., Ueland, P. M., ... and Best, K. P. (2024). Maternal serum unmetabolized folic acid concentration following multivitamin and mineral supplementation with or without folic acid after 12 weeks gestation: A randomized controlled trial. Maternal and Child Nutrition, 20(4), e13668.
Piyathilake, C. J., Johanning, G. L., Macaluso, M., Whiteside, M., Oelschlager, D. K., Heimburger, D. C., and Grizzle, W. E. (2000). Localized folate and vitamin B-12 deficiency in squamous cell lung cancer is associated with global DNA hypomethylation. Nutrition and Cancer, 37(1), 99-107.
Kopp, Wolfgang. (2024). "Aging and "Age-related" Diseases- What is the Relation?". Aging and Disease 16, no. 3 : 1316.
Ly, L., Chan, D., Landry, M., Angle, C., Martel, J., and Trasler, J. (2020). Impact of mothers' early life exposure to low or high folate on progeny outcome and DNA methylation patterns. Environmental Epigenetics, 6(1), dwaa018.
Ebara, S. (2017). Nutritional role of folate. Congenital Anomalies, 57(5), 138-141.
Ford, A. H., and Almeida, O. P. (2019). Effect of vitamin B supplementation on cognitive function in the elderly: a systematic review and meta-analysis. Drugs and Aging, 36(5), 419-434.
Naderi, N., and House, J. D. (2018). Recent developments in folate nutrition. Advances in Food and Nutrition Research, 83, 195-213.
Panetta, J. C., Paugh, S. W., and Evans, W. E. (2013). Mathematical modeling of folate metabolism. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 5(5), 603-613.
Massaro, E., and Rogers, J. (2002). Folate and human development. Scandinavian Journal of Nutrition, 46(3), 148-150.
Wagner, C. (2001). Biochemical role of folate in cellular metabolism. Clinical Research and Regulatory Affairs, 18(3), 161-180.
Urey, C. L., Liu, L., Andrews, L. G., and Tollefsbol, T. O. (2005). The impact of metabolism on DNA methylation. Human Molecular Genetics, 14(suppl_1), R139-R147.
Wu, G., Lupton, J. R., Turner, N. D., Fang, Y. Z., and Yang, S. (2004). Glutathione metabolism and its implications for health. The Journal of Nutrition, 134(3), 489-492.
Vargason, T., Howsmon, D. P., Melnyk, S., James, S. J., and Hahn, J. (2017). Mathematical modeling of the methionine cycle and transsulfuration pathway in individuals with autism spectrum disorder. Journal of Theoretical Biology, 416, 28-37.
Stead, L. M., Jacobs, R. L., Brosnan, M. E., and Brosnan, J. T. (2004). Methylation demand and homocysteine metabolism. Advances in Enzyme Regulation, 44(1), 321-333.
Purohit, V., Abdelmalek, M. F., Barve, S., Benevenga, N. J., Halsted, C. H., Kaplowitz, N., ... and Zakhari, S. (2007). Role of S-adenosylmethionine, folate, and betaine in the treatment of alcoholic liver disease: summary of a symposium. The American Journal of Clinical Nutrition, 86(1), 14-24.
Morgan, A. E., Salcedo-Sora, J. E., and Mc Auley, M. T. (2024). A new mathematical model of folate homeostasis in E. coli highlights the potential importance of the folinic acid futile cycle in cell growth. BioSystems, 235, 105088.
Reed, M. C., Nijhout, H. F., Sparks, R., and Ulrich, C. M. (2004). A mathematical model of the methionine cycle. Journal of Theoretical Biology, 226(1), 33-43.
Dale, R., and Mosher, R. (2024). Mathematical model of RNA-directed DNA methylation predicts tuning of negative feedback required for stable maintenance. Open Biology, 14(11).
Latham, T., Gilbert, N., and Ramsahoye, B. (2008). DNA methylation in mouse embryonic stem cells and development. Cell and Tissue Research, 331(1), 31-55.
Danbaba, U. A., Aloko, M. D., and Ayinde, A. M. (2024). Mathematical modeling of mosquito borne diseases with vertical transmissions as applied to Dengue. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), 31-56.
Isah, N., Ibrahim, M. O., Isah, B. Y., and Magaji, B. A. (2024). Bifurcation Analysis of an Age Structured Malaria Model. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), 106-132.
Zagkos, L., Mc Auley, M., Roberts, J., and Kavallaris, N. I. (2019). Mathematical models of DNA methylation dynamics: Implications for health and ageing. Journal of Theoretical Biology, 462, 184-193.
Braun, M., and Golubitsky, M. (1983). Differential equations and their applications (Vol. 4). New York: Springer.
Nagle, R., Saff, E., and Snider, A. (2014). Fundamentals of Differential Equations. Evaluation, 3, 4.
Nijhout, H. F., Reed, M. C., Lam, S. L., Shane, B., Gregory III, J. F., and Ulrich, C. M. (2006). In silico experimentation with a model of hepatic mitochondrial folate metabolism. Theoretical Biology and Medical Modelling, 3(1), 40.
Nwanaji-Enwerem, J. C., Colicino, E., Gao, X., Wang, C., Vokonas, P., Boyer, E. W., ... and Schwartz, J. (2021). Associations of plasma folate and vitamin B6 with blood DNA methylation age: an analysis of one-carbon metabolites in the VA normative aging study. The Journals of Gerontology: Series A, 76(5), 760-769.
McGovern, A. P., Powell, B. E., and Chevassut, T. J. (2012). A dynamic multi-compartmental model of DNA methylation with demonstrable predictive value in hematological malignancies. Journal of Theoretical Biology, 310, 14-20.
Published
2026-03-15
How to Cite
Aku, M. (2026). A Mathematical Model of Folate Metabolism and DNA Methylation: Stability Analysis. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 12(1), 11 - 31. https://doi.org/10.5281/zenodo.20384219
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