article: A major process of iron homeostasis in whole-body iron metabolism is the release of iron from the macrophages of the reticuloendothelial system. Macrophages recognize and phagocytose senescent or damaged erythrocytes. Then, they process the heme iron, which is returned to the circulation for reutilization by red blood cell precursors during erythropoiesis. The amount of iron released, compared to the amount shunted for storage as ferritin, is greater during iron deficiency. A currently accepted model of iron release assumes a passive-gradient with free diffusion of intracellular labile iron (Fe2+) through ferroportin (FPN), the transporter on the plasma membrane. Outside the cell, a multi-copper ferroxidase, ceruloplasmin (Cp), oxidizes ferrous to ferric ion. Apo-transferrin (Tf), the primary carrier of soluble iron in the plasma, binds ferric ion to form mono-ferric and di-ferric transferrin. According to the passive-gradient model, the removal of ferrous ion from the site of release sustains the gradient that maintains the iron release. Subcellular localization of FPN, however, indicates that the role of FPN may be more complex. By experiments and mathematical modeling, we have investigated the detailed mechanism of iron release from macrophages focusing on the roles of the Cp, FPN and apo-Tf. The passive-gradient model is quantitatively analyzed using a mathematical model for the first time. A comparison of experimental data with model simulations shows that the passive-gradient model cannot explain macrophage iron release. However, a facilitated-transport model associated with FPN can explain the iron release mechanism. According to the facilitated-transport model, intracellular FPN carries labile iron to the macrophage membrane. Extracellular Cp accelerates the oxidation of ferrous ion bound to FPN. Apo-Tf in the extracellular environment binds to the oxidized ferrous ion, completing the release process. Facilitated-transport model can correctly predict cellular iron efflux and is essential for physiologically relevant whole-body model of iron metabolism.
  The body maintains strict control of iron levels to avoid both iron deficiency and excess. One of the major processes of iron homeostasis in whole-body iron metabolism is the release of iron from the macrophages of the reticuloendothelial system. In adult men, iron absorption in the small intestine is about 1 mg/day, iron loss is about 1 mg/day, and iron recycling from macrophages into plasma and then into erythrocytes is about 25 mg/day [1]. Iron efflux is tightly controlled by the plasma iron requirement. In several pathological states including chronic inflammation and renal failure, macrophages accumulate iron because of an apparent inability to release iron normally. From a study of intestinal iron absorption in perfused rat liver, data were consistent with the concept of passive iron efflux across the intestinal epithelium [2]. A negative iron gradient across the serosal wall of the epithelial cells was presumed to cause an iron efflux. Intracellular iron is readily available for release from the labile iron pool (LIP), which is mostly in the ferrous state [3], and from the sequestered iron in the ferric state. Ferrous iron in the labile iron pool is either sequestered to iron storage in ferritin (in ferric form) or transported across the cell membrane (in ferrous form) into plasma [4]. At the cell membrane, the ferrous form becomes oxidized to ferric. According to this passive-gradient mechanism, iron is transported across the cell membrane in the ferrous form, which is a more usable (labile) form in cells. To maintain the iron gradient, apo-transferrin (Tf), the primary carrier of soluble iron in the plasma, binds and removes iron from the site of efflux. A key protein involved in macrophage iron efflux is ceruloplasmin (Cp). This plasma protein Cp has ferroxidase activity, which is critical in iron efflux as shown by Osaki and Johnson [5]. They hypothesized that Cp accelerates oxidation and binding of iron to apo-Tf. Consequently, the negative iron gradient is increased across the cellular membrane that produces an iron efflux. Cp protein level is known to be regulated by a cis-regulatory GAIT (interferon-gamma activated inhibitor of translation complex) element [6]. Binding to GAIT complex leads to translational silencing of Cp transcript to some minimal basal level [7]. The in vivo role of Cp in iron homeostasis is evident from iron overload in patients with aceruloplasminemia (i. e. , hereditary Cp deficiency) [8]. The effect of Cp as a plasma ferroxidase in iron release depends on other factors. Young et al. [9] reported a 40% stimulation of iron release from human hepatocarcinoma HepG2 cells by Cp in the presence of apo-Tf. Also, they reported that low oxygen concentration stimulated iron release by Cp. Furthermore, Cp stimulated iron release from macrophages in the presence of apo-Tf and hypoxia with a large LIP [10]. In a dose-dependent manner, Cp enhanced iron release in HepG2 cells compared to bovine serum albumin (BSA) control [11]. Another factor that affects macrophage iron release is ferroportin (FPN), an iron transporter [12], [13]. FPN is essential for intestinal iron absorption as shown by knock-out mice studies [13]. The role of FPN in iron release has been demonstrated in several cell types [14], [15]. The specific role of FPN in up-regulation of iron release from macrophages after erythrophagocytosis has been examined [16]. The passive-gradient mechanism assumes that FPN allows free diffusion of iron across the plasma membrane. In macrophages, however, FPN is apparently distributed throughout the cell and not predominantly on the plasma membrane [17], which raises uncertainty about its proposed role in passive-gradient mechanism of iron release. Another study has shown that ferroxidases such as Cp can maintain cellular iron efflux by stabilizing FPN on cell membrane [18]. The passive-gradient mechanism has been a dominant concept in macrophage iron release, but it has not been quantitatively analyzed by a mathematical model that includes detailed kinetic processes. Although FPN is associated with the iron release process, the molecular mechanism for iron transport from macrophages via FPN has not been established [8]. In this study, we hypothesized that iron efflux involves a facilitated-transport process in which FPN binds the ferrous iron and carries it to the cellular membrane for iron release. To distinguish the effects of passive and facilitated-transport mechanisms, we compare simulations of mathematical models to experimental data. These mechanisms are represented in the cartoons shown in Fig. 1. The models that describe the detailed transport and kinetic processes of iron release are based on dynamic mass balances for each of the molecular species in intracellular, membrane, and extracellular domains. The computational outputs of these models are compared to experimental data from studies of iron kinetics in solution and from in vitro studies of iron release from macrophages. Consequently, the validity of the passive and facilitated-transport hypotheses can be quantitatively ascertained. The new facilitated-transport model could accurately reproduce the iron release process and describe for the first time the detailed molecular mechanism associated with iron transport via FPN.
  In this section, we develop mathematical models of iron kinetics and transport to quantify mechanisms associated with iron release from macrophages. The major issue is whether a passive-gradient or facilitated-transport mechanism is most likely. The simplest model with the passive-gradient mechanism assumes spatially uniform (or lumped) solute concentrations. To represent the in vitro experiments with a macrophage culture, a model must incorporate an extracellular (EC) domain with spatially distributed solute concentrations. Such a spatially distributed domain is included in passive-gradient (spatially distributed form) and facilitated-transport models. The passive-gradient models assume that FPN produces selective permeability of ferrous form of iron so that ferrous ion can diffuse from the cell. According to this model, high intracellular concentration of ferrous ion across the cell produces a concentration gradient that causes passive diffusion of ferrous ion. In the facilitated-transport model, ferrous ion must be bound to FPN in order to be transported out of the cell. In this model, FPN species kinetics must be included because FPN does not merely act as a passive channel. Regardless of the model used to describe iron transport and kinetics in cell culture, some basic aspects of iron kinetics can be analyzed from studies in solution. This information is applicable for analysis of iron kinetics in the EC domain of the cell culture. In the passive-gradient and facilitated-transport models, some common mathematical aspects are presented before examining the distinctions between these models. To analyze data from the experiments in solution and cell culture, we applied computational models to simulate the experimental measurements under a variety of conditions with the same minimal set of parameter values. The initial conditions for these experiments are shown in Table 4 (for iron kinetics in solution) and Table 5 (for iron release in cell culture). The details related to the implementation of computational models to perform simulations depicting various experimental conditions are described in the methods section.
  Iron release from macrophages, which is one of the most important processes involved in control of iron homeostasis, has been assumed to follow a passive-diffusion model. The “gradient hypothesis” associated with this passive-diffusion model was developed for gut iron absorption by Saltman [2] and supported by Osaki [5], [20], but not analyzed mathematically. In this study, we developed and compared passive-gradient and facilitated-transport models to explain iron release from macrophages. The presence of Cp, the multi-copper ferroxidase, catalyzes the oxidation of ferrous ion, which is consistent with model simulations. The consumption of apo-Tf for ferric iron incorporation is also accelerated in the presence of Cp (Fig. 6B). These observations confirm the catalyzing ability of Cp. Our studies indicate that the passive-gradient hypothesis [5] proposed to describe the stimulation of iron release by Cp from the gut cannot explain the iron efflux mechanism from macrophages (Fig. 9B). Although some experimental observations might suggest the efflux mechanism conforms to the gradient hypothesis, mathematical analysis and simulations of data with passive-gradient models do not support this hypothesis. Theoretically, ferrous ions as they diffuse to the cell membrane are quickly oxidized making the concentration of ferrous iron just outside the cell membrane negligible. Addition of Cp or apo-Tf or both cannot significantly reduce the already negligible ferrous ion concentration. No change in the flux of iron occurs in simulations of the passive-gradient model under these experimental conditions (Fig. 8A). Consequently, the passive-gradient model cannot explain the stimulation of iron release from macrophages. The facilitated-transport model with a single, optimal set of parameter values simulated all the iron-release data (Fig. 9B). The parameter values obtained initially from in vitro kinetics in solution did not change significantly from the values found from cellular experiments. Based on simulations, the facilitated-transport model indicates that Cp acts as a ferroxidase to increase iron release from macrophages in the presence of apo-Tf under physiological conditions of O2. Experimentally, maximal iron release from macrophages was observed under hypoxia in the presence of apo-Tf and Cp together. Simulations with the facilitated-transport model indicate that decreased Cp concentration results in decreased iron release from macrophage cells leading to possible iron retention in cells (Fig. 9C). With the facilitated-transport model, it is evident that Cp deficiency can cause iron overload diseases through retention of iron in macrophage cells. The main difference between the passive-gradient models (SL and SD) and the facilitated-transport model is the effect of FPN-mediated facilitated-transport of iron to the plasma membrane (Fig. 1). Instead of a passive channel, FPN plays an active role in iron efflux in the facilitated-transport mechanism. While there have been reports of iron transport being a facilitated-transport process [21], this mechanism had not been quantitatively tested using a mathematical model. Simulations using mathematical model based on facilitated-transport reveal that iron release is sensitive to the reaction rate coefficient for binding FPN and ferrous ion in all the four experimental conditions of extracellular medium. Furthermore, the facilitated-transport of iron by FPN to the plasma membrane provides a mechanism of stimulated iron release by Cp, apo-Tf, or apo-Tf + Cp. Because of unavailability of data regarding concentration of FPN molecules in the intracellular domain, we assumed its concentration to be at least twice the concentration of ferrous iron. Although FPN is assumed to be in excess of ferrous ion to facilitate its transport across the cell, this assumption does not affect model outcomes. It is known that FPN is expressed in intracellular vesicles and can get transported to plasma membrane of macrophages [22]. This information was incorporated into the model. The FPN in the membrane compartment is internalized and transported back to the cell as soon as ferric-FPN dissociates. The diffusion parameters for the transport of FPN between the IC and the membrane domains (and) were assumed to be identical. Inside a cell, the processes of vesicular trafficking to the plasma membrane and endocytosis are quite separate and the kinetics may differ. This distinction could be made if there were experimental data on the kinetics of the exocytosis and endocytosis of FPN. Although the iron binding sites of apo-Tf may differ to some extent, the model assumes them to be identical. Analysis of the solution kinetic model shows that this assumption does not limit the ability of the model to predict the experimental results. Furthermore, this assumption would not significantly alter simulations of the cellular processes by the facilitated-transport model. In the experimental studies in which apo-Tf was added to the EC domain, we assume that the consequent mono-ferric and di-ferric Tf species remain in the EC fluid. However, both apo- and holo-Tf could be taken up by the cells through Tf receptor endocytosis. Hence, the facilitated transport model in its current form may not correctly predict iron release at longer release interval in hours. The facilitated-transport model can be the basis for developing other physiologically relevant models of iron release that incorporate important proteins such as hepcidin [23]. Although iron release from macrophages is very tightly controlled through control of FPN expression, this is not addressed in the current model. This aspect could be incorporated by considering the change of gene expression of FPN as well as protein degradation through interaction with hepcidin. From a systems perspective of the control of iron release from macrophages, control loops and interactions can be added to the present model. Furthermore, the facilitated-transport model iron release mechanism can be included in a whole-body model of iron metabolism to predict more accurate iron status in body. This would be important for devising patient-specific treatments in chronic kidney disease.
  The model parameters belong to the following categories: reaction rate coefficients, transport coefficients and initial concentrations (associated with each experimental condition). For the spatially distributed models, the spatial derivatives were discretized (i. e. , method of lines [28]) so that in all cases, the models had the form of a set of ordinary, first-order differential equations. These models expressed as initial-value problems were solved numerically with a stiff integrator, ‘ode15s’ (MATLAB, MathWorks Inc.). The values of some parameters are known by direct measurements and others were obtained from the literature. Most parameter values (viz. , reaction rate and transport coefficients) were estimated by least-squares fitting of model simulated outputs to experimental data at many time points (ti: i = 1,2, …n). This was accomplished by non-linear optimization with constraints implemented using ‘lsqcurvefit’ (MATLAB, MathWorks Inc.). The estimation procedure was repeated with different initial parameter values to show convergence to global optimal values. A sequential process was followed. First, data from the experiments in solution were simulated using the corresponding iron kinetics model. Then, the passive-gradient and facilitated-transport models were tested to determine if these could simulate data from cell culture experiments with optimal parameter estimates. We rejected a model if it could not simulate all the data satisfactorily with the same parameter values. We used lsqcurvefit, which is a gradient-based algorithm that incorporates constraints as lower and upper bounds on the parameter values. This greatly improves its efficiency in minimizing the least-squares objective function. We used lsqcurvefit for optimal estimation because it is faster than other optimization algorithms such as genetic algorithm. This algorithm has been routinely used by scientific community [29], [30]. With the experimental data available, model parameters can be estimated more efficiently in a step-wise process. First, we estimated parameters with a subset model that describes solution kinetics. The parameter values from this model were applied in estimating parameters of the more complex passive and facilitated- transport models. With this procedure, fewer parameters with no prior knowledge are estimated on each step to provide better precision and accuracy of the estimates. This step-wise approach has been used previously with demonstrated success in even more challenging applications [31]. For each of the four models (solution kinetics, passive-gradient SL, passive-gradient SD and facilitated-transport), we estimated parameter values that provided the best fit of the model output to the experimental data in the following sequence: first, iron release in the medium only (control), then in the presence of apo-Tf alone, Cp alone, and both Cp and apo-Tf. The iron release models were simulated by starting with a reduced model that did not consist of any species related to Cp or apo-Tf and devoid of any processes related to those species. The reduced model with iron release in the medium alone does not contain reaction process represented by equations K. 2, K. 3, K. 4, K. 5, K. 9, K. 11, K. 12, K. 13, K. 14 and K. 15 (that is, involving either Cp and apo-Tf). The reduced model with iron release in the presence of apo-Tf alone excluded any reaction process involving Cp, while the one with iron release in the presence of Cp alone excluded reaction processes involving apo-Tf. We have specified each chemical species (j) involved in a given reduced version of model during stage-wise parameter estimation. We recreated the model process diagrams in SBGN graphical notation (made in Cell Designer) and have provided them as supplementary figures along with the MATLAB codes (Data S1) used to implement each model. We wrote custom MATLAB codes to run the models instead of using ordinary differential equation (ODE) solver in SBML software (Cell Designer). This is easier for use with the method of lines that converts partial differential equations in some of our models to ODEs. Electronic formats of our models (MATLAB codes) along with experimental data used to fit the models are supplied as supplementary information (Data S1).
summary: Iron metabolism is an important physiological phenomenon essential for sustaining life. There is a tight regulation of iron levels in humans and both deficiency and overload can lead to disorders such as anemia and hemochromatosis. Recycling of iron in human body via macrophage iron release is crucial to maintain healthy iron levels. However, a computational model is needed to quantitatively analyze the mechanism underlying a key process in iron homeostasis, which is the release of iron from the macrophages. Using mechanistic, mathematical models to simulate experimental data, we found a novel mechanism by which macrophages release iron. A comparison of experimental data with model simulations shows that a currently accepted passive-gradient mechanism cannot represent the iron-release process from macrophages. However, our model with a facilitated-transport mechanism associated with ferroportin (only known protein for iron export) accurately reproduces the iron release process. This model quantifies for the first time the detailed molecular mechanism associated with iron transport via ferroportin. This quantitative predictive model of cellular iron efflux is essential for physiologically relevant simulation of whole-body model of iron metabolism in healthy and disease states.
keywords: biotechnology
  blood cells
  medicine and health sciences
  chronic kidney disease
  engineering and technology
  applied mathematics
  anemia
  mathematics
  red blood cells
  bioengineering
  animal cells
  biophysics
  hematology
  systems biology
  cell biology
  calculus
  biology and life sciences
  cellular types
  chemical engineering
  computational biology
  physical sciences
  nephrology
  biophysical simulations
title: Computational Modeling and Analysis of Iron Release from Macrophages