Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

Abstract

Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex systems.

Mathematical modeling of the relocation of the divalent metal transporter DMT1 in the intestinal iron absorption process

“…Uptake was considered as the total radioactivity in the cells plus the basolateral medium after incubation. Fe–ascorbate was used to avoid a possible interference of Dcytb ferrireductase with the uptake process [49].…”

“…Experimental data for the second challenge were used for phenomenologically validating the proposed model. We presented a detailed description of the application of the Jackknife method in [49]. It has been shown that the coefficient of determination R 2 is an inadequate measure for the goodness of fit in non-linear models, since differences in model quality rarely affect its value more than in the third to fifth decimal place [78].…”

“…To study the short-term effect of iron exposure in iron absorption fluxes we proposed a method for developing mathematical models for complex systems, based on a genetic algorithm (genetic programming). Even though Michaelis–Menten and Hill kinetics are the simplest way to characterize saturable uptake of nutrients in cell culture for single substrate—single product settings [47, 48], we showed in a previous work that these classic models cannot capture the key characteristics of the iron absorption process as they cannot represent more complex mechanisms that take place in this system [49]. The model developed by Colins et al was able to capture the complex non-linear dynamics observed experimentally using a genetic algorithm methodology [49].…”

“…Even though Michaelis–Menten and Hill kinetics are the simplest way to characterize saturable uptake of nutrients in cell culture for single substrate—single product settings [47, 48], we showed in a previous work that these classic models cannot capture the key characteristics of the iron absorption process as they cannot represent more complex mechanisms that take place in this system [49]. The model developed by Colins et al was able to capture the complex non-linear dynamics observed experimentally using a genetic algorithm methodology [49]. However, it is difficult to provide a biological interpretation for this specific model in terms of the relevant phenomena involved in iron absorption and its regulation.…”

Iron metabolism and its contribution to cancer (Review)

“…In the cytosol, iron is neutralized by ferritin (a multimeric iron-storage protein) (Table I) and weakly bound together to form a pool of iron termed the cytoplasmic labile iron pool (cLIP) (20). The cLIP supplies iron to a number of cytoplasmic enzymes, in addition to mitochondria for heme and iron sulfur cluster synthesis.…”