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.