A mathematical model of iron metabolism

A biomathematical model of human erythropoiesis and iron metabolism

Anaemia therapy or perisurgical support of erythropoiesis often require both, EPO and iron medication. However, excessive iron medication can result in iron overload and it is challenging to control haemoglobin levels in a desired range. To support this task, we develop a biomathematical model to simulate EPO- and iron medication in humans. We combine our previously established model of human erythropoiesis including comprehensive pharmacokinetic models of EPO applications with a newly developed model of iron metabolism including iron supplementation. Equations were derived by translating known biological mechanisms into ordinary differential equations. Qualitative model behaviour is studied in detail considering a variety of interventions such as bleeding, iron malnutrition and medication. The model can explain time courses of erythrocytes, reticulocytes, haemoglobin, haematocrit, red blood cells, EPO, serum iron, ferritin, transferrin saturation, and transferrin under a variety of scenarios including EPO and iron application into healthy volunteers or chemotherapy patients. Unknown model parameters were determined by fitting the predictions of the model to time series data from literature. We demonstrate how the model can be used to make predictions of untested therapy options such as cytotoxic chemotherapy supported by iron and EPO. Following our ultimate goal of establishing a model of anaemia treatment in chronic kidney disease, we aim at translating our model to this pathological condition in the near future.

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

Iron is essential for the normal development of cellular processes. This metal has a high redox potential that can damage cells and its overload or deficiency is related to several diseases, therefore it is crucial for its absorption to be highly regulated. A fast-response regulatory mechanism has been reported known as mucosal block, which allows to regulate iron absorption after an initial iron challenge. In this mechanism, the internalization of the DMT1 transporters in enterocytes would be a key factor. Two phenomenological models are proposed for the iron absorption process: DMT1's binary switching mechanism model and DMT1's swinging-mechanism model, which represent the absorption mechanism for iron uptake in intestinal cells. The first model considers mutually excluding processes for endocytosis and exocytosis of DMT1. The second model considers a Ball's oscillator to represent the oscillatory behavior of DMT1's internalization. Both models are capable of capturing the kinetics of iron absorption and represent empirical observations, but the DMT1's swinging-mechanism model exhibits a better correlation with experimental data and is able to capture the regulatory phenomenon of mucosal block. The DMT1 swinging-mechanism model is the first phenomenological model reported to effectively represent the complexity of the iron absorption process, as it can predict the behavior of iron absorption fluxes after challenging cells with an initial dose of iron, and the reduction in iron uptake observed as a result of mucosal block after a second iron dose.

Whole-body iron transport and metabolism: Mechanistic, multi-scale model to improve treatment of anemia in chronic kidney disease

Iron plays vital roles in the human body including enzymatic processes, oxygen-transport via hemoglobin and immune response. Iron metabolism is characterized by ~95% recycling and minor replenishment through diet. Anemia of chronic kidney disease (CKD) is characterized by a lack of synthesis of erythropoietin leading to reduced red blood cell (RBC) formation and aberrant iron recycling. Treatment of CKD anemia aims to normalize RBC count and serum hemoglobin. Clinically, the various fluxes of iron transport and accumulation are not measured so that changes during disease (e.g., CKD) and treatment are unknown. Unwanted iron accumulation in patients is known to lead to adverse effects. Current whole-body models lack the mechanistic details of iron transport related to RBC maturation, transferrin (Tf and TfR) dynamics and assume passive iron efflux from macrophages. Hence, they are not predictive of whole-body iron dynamics and cannot be used to design individualized patient treatment. For prediction, we developed a mechanistic, multi-scale computational model of whole-body iron metabolism incorporating four compartments containing major pools of iron and RBC generation process. The model accounts for multiple forms of iron in vivo, mechanisms involved in iron uptake and release and their regulation. Furthermore, the model is interfaced with drug pharmacokinetics to allow simulation of treatment dynamics. We calibrated our model with experimental and clinical data from peer-reviewed literature to reliably simulate CKD anemia and the effects of current treatment involving combination of epoietin-alpha and iron dextran. This in silico whole-body model of iron metabolism predicts that a year of treatment can potentially lead to 90% downregulation of ferroportin (FPN) levels, 15-fold increase in iron stores with only a 20% increase in iron flux from the reticulo-endothelial system (RES). Model simulations quantified unmeasured iron fluxes, previously unknown effects of treatment on FPN-level and iron stores in the RES. This mechanistic whole-body model can be the basis for future studies that incorporate iron metabolism together with related clinical experiments. Such an approach could pave the way for development of effective personalized treatment of CKD anemia.

Modeling the dynamics of mouse iron body distribution: hepcidin is necessary but not sufficient

BACKGROUND

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.

RESULTS

A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.

CONCLUSIONS

These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important.

Serum ferritin is an important inflammatory disease marker, as it is mainly a leakage product from damaged cells

"Serum ferritin" presents a paradox, as the iron storage protein ferritin is not synthesised in serum yet is to be found there. Serum ferritin is also a well known inflammatory marker, but it is unclear whether serum ferritin reflects or causes inflammation, or whether it is involved in an inflammatory cycle. We argue here that serum ferritin arises from damaged cells, and is thus a marker of cellular damage. The protein in serum ferritin is considered benign, but it has lost (i.e. dumped) most of its normal complement of iron which when unliganded is highly toxic. The facts that serum ferritin levels can correlate with both disease and with body iron stores are thus expected on simple chemical kinetic grounds. Serum ferritin levels also correlate with other phenotypic readouts such as erythrocyte morphology. Overall, this systems approach serves to explain a number of apparent paradoxes of serum ferritin, including (i) why it correlates with biomarkers of cell damage, (ii) why it correlates with biomarkers of hydroxyl radical formation (and oxidative stress) and (iii) therefore why it correlates with the presence and/or severity of numerous diseases. This leads to suggestions for how one might exploit the corollaries of the recognition that serum ferritin levels mainly represent a consequence of cell stress and damage.

Iron dosing in kidney disease: inconsistency of evidence and clinical practice

The management of anemia in patients with chronic kidney disease (CKD) is difficult. The availability of erythropoiesis-stimulating agents (ESAs) has increased treatment options for previously transfusion-requiring patients, but the recent evidence of ESA side effects has prompted the search for complementary or alternative approaches. Next to ESA, parenteral iron supplementation is the second main form of anemia treatment. However, as of now, no systematic approach has been proposed to balance the concurrent administration of both agents according to individual patient's needs. Furthermore, the potential risks of excessive iron dosing remain a topic of controversy. How, when and whether to monitor CKD patients for potential iron overload remain to be elucidated. This review addresses the question of risk and benefit of iron administration in CKD, highlights the evidence supporting current practice, provides an overview of standard and potential new markers of iron status and outlines a new pharmacometric approach to physiologically compatible individualized dosing of ESA and iron in CKD patients.

The effects of resistance exercise and post-exercise meal timing on the iron status in iron-deficient rats

Resistance exercise increases heme synthesis in the bone marrow and the hemoglobin in iron-deficient rats. Post-exercise early nutrient provision facilitates skeletal muscle protein synthesis compared to late provision. However, the effects of post-exercise nutrition timing on hemoglobin synthesis are unclear. The current study investigated the effect of post-exercise meal timing on the activity of the key enzyme involved in hemoglobin synthesis, δ-aminolevulinic acid dehydratase (ALAD), in the bone marrow and examined the hemoglobin concentration in iron-deficient rats. Male 4-week-old Sprague-Dawley rats were fed an iron-deficient diet containing 12 mg iron/kg and performed climbing exercise (5 min × 6 sets/day, 3 days/week) for 3 weeks. The rats were divided into a group fed a post-exercise meal early after exercise (E) or a group fed the meal 4 h after exercise (L). A single bout of exercise performed after the 3-week training period increased the bone marrow ALAD activity, plasma iron concentration, and transferrin saturation. Although the plasma iron concentration and transferrin saturation were lower in the E group than the L group after a single bout of exercise, the basal hematocrit, hemoglobin, and TIBC after 3 weeks did not differ between the groups. Therefore, resistance exercise increases the bone marrow ALAD activity, while the post-exercise meal timing has no effect on the hemoglobin concentration in iron-deficient rats.

Rule-based modelling of iron homeostasis in tuberculosis

To establish itself within the host system, Mycobacterium tuberculosis (Mtb) has formulated various means of attacking the host system. One such crucial strategy is the exploitation of the iron resources of the host system. Obtaining and maintaining the required concentration of iron becomes a matter of contest between the host and the pathogen, both trying to achieve this through complex molecular networks. The extent of complexity makes it important to obtain a systems perspective of the interplay between the host and the pathogen with respect to iron homeostasis. We have reconstructed a systems model comprising 92 components and 85 protein-protein or protein-metabolite interactions, which have been captured as a set of 194 rules. Apart from the interactions, these rules also account for protein synthesis and decay, RBC circulation and bacterial production and death rates. We have used a rule-based modelling approach, Kappa, to simulate the system separately under infection and non-infection conditions. Various perturbations including knock-outs and dual perturbation were also carried out to monitor the behavioral change of important proteins and metabolites. From this, key components as well as the required controlling factors in the model that are critical for maintaining iron homeostasis were identified. The model is able to re-establish the importance of iron-dependent regulator (ideR) in Mtb and transferrin (Tf) in the host. Perturbations, where iron storage is increased, appear to enhance nutritional immunity and the analysis indicates how they can be harmful for the host. Instead, decreasing the rate of iron uptake by Tf may prove to be helpful. Simulation and perturbation studies help in identifying Tf as a possible drug target. Regulating the mycobactin (myB) concentration was also identified as a possible strategy to control bacterial growth. The simulations thus provide significant insight into iron homeostasis and also for identifying possible drug targets for tuberculosis.

Pharmacokinetic modeling of manganese. II. Hepatic processing after ingestion and inhalation

Current concerns regarding inhalation exposure to Mn, a component from oxidation of the gasoline antiknock agent MMT, have stimulated interest in developing kinetic tools for describing the inhalation and combined inhalation/oral route kinetics of Mn. Kinetic approaches were integrated kinetic for (1) bulk tissue Mn kinetics and (2) hepato-intestinal control of oral-route Mn uptake into a integrated model structure connecting systemic and oral Mn. Linkages were developed between the hepato-intestinal and systemic tissues in order to evaluate differences in hepatic processing of orally absorbed Mn and systemic Mn. The integrated, unified model described the uptake, net absorption, and elimination of ingested Mn and the elimination kinetics of i.v. administered (systemic) Mn by treating Mn arriving at the liver from systemic versus portal blood differently. Hepatic extraction of orally absorbed Mn in rats predicted through simulation of the oral uptake data was 19, 54, and 78% at dietary exposures of 1.5, 11.2, and 100 ppm, respectively. In contrast, hepatic extraction of systemic Mn predicted through simulation of elimination kinetics i.v. tracer Mn was much less, 0.004, 0.005, or 0.009% at dietary levels of 2, 10, and 100 ppm, respectively. These differences in hepatic processing of blood Mn derived from different dose routes need to be accounted for in more complete PK models for Mn that are intended to support human health risk assessments.

A compartmental model of iron regulation in the mouse

A simple compartmental model is developed for investigating the mechanism of iron homeostasis. In contrast to previous mathematical models of iron metabolism, the liver is included as a key site of iron regulation. Compartments for free iron in blood, diferric transferrin (Tf) in blood, hepatocytes, red blood cells, and macrophages are included, and their roles in iron regulation are explored. The function of hepcidin in regulating iron absorption is modeled through an inverse relationship between hepatocyte transferrin receptor 2 (TfR2) levels and the rate of iron export processes mediated by ferroportin (Fpn). Simulations of anemia and erythropoiesis stimulation support the idea that the iron demands of the erythroid compartment can be communicated through diferric Tf. The iron-responsive element of Fpn is found to be important for stabilizing intracellular iron stores in response to changing iron demands and allowing proper iron regulation through diferric Tf. The contribution of iron dysregulation to the pathogenesis of iron overload disorders is also investigated. It is shown that the characteristics of HFE hemochromatosis can be reproduced by increasing the setpoint of iron absorption in the duodenum to a level where the system cannot downregulate iron absorption to meet the iron excretion rate.

A model of intestinal iron absorption and plasma iron kinetics: optimal parameter estimates for normal dogs

A multicompartment model describing the physiological processes of intestinal iron absorption has been developed. The model accounts for uptake by the intestinal mucosa of iron in the lumen, followed by either iron incorporation into a mucosal storage pool (presumably ferritin) or direct iron transfer to the plasma. To enable analysis of iron absorption from noninvasive measurements, plasma iron kinetics were also analyzed. The model was validated in studies of three beagle dogs given oral 59Fe-citrate and intravenous 55Fe-transferrin simultaneously. Model parameters were estimated from the best (least-squares) fit of the model outputs to the tracer iron activity in venous blood samples and in the whole body. The parameter values show that both incorporation of iron into the mucosal storage pool and transfer of iron from the mucosa to the plasma occur at rates approximately 100 times greater than mucosal uptake of iron from the gut lumen. Further, release of iron from mucosal storage, while measurable, occurs at a slow rate. The study demonstrates the practicality of this noninvasive approach for the simultaneous study of iron absorption and plasma iron kinetics.