Mathematical models of iron metabolism: structure and functions

   Mathematical models represent a powerful theoretical tool for studying complex biological systems. They provide an opportunity to track non-obvious interactions and conduct in silico experiments to address practical problems. Iron plays a key role in oxygen transport in the mammals. However, a high concentration of this microelement can damage cellular structures through the production of reactive oxygen species and can also lead to ferroptosis (programmed cell death associated with iron-dependent lipid peroxidation). The immune system contributes greatly to the regulation of iron metabolism – hypoferritinemia (decreased ferritin concentration in the blood) during infection – which is a result of the innate immune response. In the study of iron metabolism, many aspects of regulation remain insufficiently studied and require a deeper understanding of the structural-functional organization and dynamics of all components of this complex process in both normal and pathological conditions.

   Consequently, mathematical modeling becomes an important tool to identify key regulatory interactions and predict the behavior of the iron metabolism regulatory system in the human body under various conditions.

   This article presents a review of iron metabolism models applicable to humans presented in chronological order of their development to illustrate the evolution and priorities in modeling iron metabolism. We focused on the formulation of numerical problems in the analyzed models, their structure and reproducibility, thereby highlighting their advantages and drawbacks. Advanced models can numerically simulate various experimental scenarios: blood transfusion, signaling pathway disruption, mutation in the ferroportin gene, and chronic inflammation. However, existing mathematical models of iron metabolism are difficult to scale and do not account for the functioning of other organs and systems, which severely limits their applicability. Therefore, to enhance the utility of computational models in solving practical problems related to iron metabolism in the human body, it is necessary to develop a scalable and verifiable mathematical model of iron metabolism that considers interactions with other functional human systems (e. g., the immune system) and state-of-the-art standards for representing mathematical models of biological systems.

1. Ahmed M.H., Ghatge M.S., Safo M.K. Hemoglobin: structure, function and allostery. In: Hoeger U., Harris J. (Eds) Vertebrate and Invertebrate Respiratory Proteins, Lipoproteins and other Body Fluid Proteins. Subcellular Biochemistry. Vol. 94. Springer, 2020;345-382. doi: 10.1007/978-3-030-41769-7_14

2. Carmona U., Li L., Zhang L., Knez M. Ferritin light-chain sub-units: key elements for the electron transfer across the protein cage. Chem Commun. 2014;50:15358-15361. doi: 10.1039/C4CC07996E

3. Chua A.C.G., Delima R.D., Morgan E.H., Herbison C.E., Tirnitz-Parker J.E.E., Graham R.M., Fleming R.E., Britton R.S., Bacon B.R., Olynyk J.K., Trinder D. Iron uptake from plasma transferrin by a transferrin receptor 2 mutant mouse model of haemochromatosis. J Hepatol. 2010;52(3):425-431. doi: 10.1016/j.jhep.2009.12.010

4. Enculescu M., Metzendorf C., Sparla R., Hahnel M., Bode J., Muckenthaler M.U., Legewie S. Modelling systemic iron regulation during dietary iron overload and acute inflammation: role of hepcidin-independent mechanisms. PLoS Comput Biol. 2017;13(1):e1005322. doi: 10.1371/journal.pcbi.1005322

5. Franzone P.C., Paganuzzi A., Stefanelli M. A mathematical model of iron metabolism. J Math Biol. 1982;15(2):173-201. doi: 10.1007/BF00275072

6. Harrison P.M., Hoy T.G., Macara I.G., Hoare R.J. Ferritin iron uptake and release. Structure–function relationships. Biochem J. 1974; 143(2):445-451. doi: 10.1042/bj1430445

7. Hoops S., Sahle S., Gauges R., Lee C., Pahle J., Simus N., Singhal M., Xu L., Mendes P., Kummer U. COPASI – a COmplex PAthway SImulator. Bioinformatics. 2006;22(24):3067-3074. doi: 10.1093/bioinformatics/btl485

8. Killick S.B., Bown N., Cavenagh J., Dokal I., Foukaneli T., Hill A., Hillmen P., Ireland R., Kulasekararaj A., Mufti G., Snowden J.A., Samarasinghe S., Wood A., Marsh J.C.W. Guidelines for the diagnosis and management of adult aplastic anaemia. Br J Haematol. 2016;172(2):187-207. doi: 10.1111/bjh.13853

9. Kiss J.E., Brambilla D., Glynn S.A., Mast A.E., Spencer B.R., Stone M., Kleinman S.H., Cable R.G.; National Heart, Lung, and Blood Institute (NHLBI) Recipient Epidemiology and Donor Evaluation Study-III (REDS-III). Oral iron supplementation after blood donation: a randomized clinical trial. JAMA. 2015;313(6):575-583. doi: 10.1001/jama.2015.119

10. Kolpakov F., Akberdin I., Kiselev I., Kolmykov S., Kondrakhin Y., Kulyashov M., Kutumova E., Pintus S., Ryabova A., Sharipov R., Yevshin I., Zhatchenko S., Kel A. BioUML – towards a universal research platform. Nucleic Acids Res. 2022;50(W1):W124-W131. doi: 10.1093/nar/gkac286

11. Le Novère N., Hucka M., Mi H., Moodie S., Schreiber F., Sorokin A., Demir E., … Sander C., Sauro H., Snoep J.L., Kohn K., Kitano H. The systems biology graphical notation. Nat Biotechnol. 2009; 27(8):735-741. doi: 10.1038/nbt.1558

12. Liedén G., Höglund S., Ehn L. Changes in certain iron metabolism variables after a single blood donation. Acta Med Scand. 1975; 197(1-2):27-30. doi: 10.1111/j.0954-6820.1975.tb04873.x

13. Masison J., Mendes P. Modeling the iron storage protein ferritin reveals how residual ferrihydrite iron determines initial ferritin iron sequestration kinetics. PLoS One. 2023;18(2):e0281401. doi: 10.1371/journal.pone.0281401

14. Mitchell S., Mendes P. A computational model of liver iron metabolism. PLoS Comput Biol. 2013;9(11):e1003299. doi: 10.1371/journal.pcbi.1003299

15. Nemeth E., Ganz T. Hepcidin and iron in health and disease. Annu Rev Med. 2023;74:261-277. doi: 10.1146/annurev-med-043021-032816

16. Pantopoulos K., Porwal S.K., Tartakoff A., Devireddy L. Mechanisms of mammalian iron homeostasis. Biochemistry. 2012;51(29):5705-5724. doi: 10.1021/bi300752r

17. Pfreundschuh M., Trümper L., Kloess M., Schmits R., Feller A.C., Rübe C., Rudolph C., Reiser M., Hossfeld D.K., Eimermacher H., Hasenclever D., Schmitz N., Loeffler M.; German High-Grade Non-Hodgkin’s Lymphoma Study Group. Two-weekly or 3-weekly CHOP chemotherapy with or without etoposide for the treatment of elderly patients with aggressive lymphomas: results of the NHL-B2 trial of the DSHNHL. Blood. 2004;104(3):634-641. doi: 10.1182/blood-2003-06-2095

18. Phan J., Mazloom A., Medeiros L.J., Zreik T.G., Wogan C., Shihadeh F., Rodriguez M.A., Fayad L., Fowler N., Reed V., Horace P., Dabaja B.S. Benefit of consolidative radiation therapy in patients with diffuse large B-cell lymphoma treated with R-CHOP chemotherapy. J Clin Oncol. 2010;28(27):4170-4176. doi: 10.1200/JCO.2009.27.3441

19. Rutherford C.J., Schneider T.J., Dempsey H., Kirn D.H., Brugnara C., Goldberg M.A. Efficacy of different dosing regimens for recombinant human erythropoietin in a simulated perisurgical setting: the importance of iron availability in optimizing response. Am J Med. 1994;96(2):139-145. doi: 10.1016/0002-9343(94)90134-1

20. Schirm S., Scholz M. A biomathematical model of human erythropoiesis and iron metabolism. Sci Rep. 2020;10(1):8602. doi: 10.1038/s41598-020-65313-5

21. Schirm S., Engel C., Loeffler M., Scholz M. A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration. PLoS One. 2013;8(6):e65630. doi: 10.1371/journal.pone.0065630

22. Souillard A., Audran M., Bressolle F., Gareau R., Duvallet A., Chanal J.L. Pharmacokinetics and pharmacodynamics of recombinant human erythropoietin in athletes. Blood sampling and doping control. Br J Clin Pharmacol. 1996;42(3):355-364. doi: 10.1046/j.1365-2125.1996.41911.x

23. Tavernini L. Linear multistep methods for the numerical solution of Volterra functional differential equations. Appl Anal. 1973;3(2): 169-185. doi: 10.1080/00036817308839063

24. Vogt A.-C.S., Arsiwala T., Mohsen M., Vogel M., Manolova V., Bachmann M.F. On iron metabolism and its regulation. Int J Mol Sci. 2021;22(9):4591. doi: 10.3390/ijms22094591

25. Wadsworth G.R. Recovery from acute haemorrhage in normal men and women. J Physiol. 1955;129(3):583-593. doi: 10.1113/jphysiol.1955.sp005380

26. Weinberg E.D. Iron availability and infection. Biochim Biophys Acta. 2009;1790(7):600-605. doi: 10.1016/j.bbagen.2008.07.002

27. Xie Y., Hou W., Song X., Yu Y., Huang J., Sun X., Kang R., Tang D. Ferroptosis: process and function. Cell Death Differ. 2016;23(3): 369-379. doi: 10.1038/cdd.2015.158

28. Xu Y., Alfaro-Magallanes V.M., Babitt J.L. Physiological and pathophysiological mechanisms of hepcidin regulation: clinical implications for iron disorders. Br J Haematol. 2021;193(5):882-893. doi: 10.1111/bjh.17252

29. Ziegler A.K., Grand J., Stangerup I., Nielsen H.J., Dela F., Magnussen K., Helge J.W. Time course for the recovery of physical performance, blood hemoglobin, and ferritin content after blood donation. Transfusion. 2015;55(4):898-905. doi: 10.1111/trf.12926