4 - Discussion

4.1 Mathematical Model of Iron Metabolism – General Structure

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The vital importance of iron for redox catalysis and oxygen handling and its strong toxic potential of its radical-forming capacity require a very carefully fine-tuned regulation of absorption, excretion and inter-tissue distribution as well as of cellular balance and intracellular deployment for biosynthesis and storage. A systems biological approach to understanding this complexity requires the application of a mathematical model which integrates the molecular and cell-biological detail in a way that makes the regulatory structure transparent. Ingenious interpreting work has so far been done on a qualitative level, but a full quantitative description of the cellular and organismal hierarchy is still missing. In the work presented here a first such model is presented for the iron metabolism of the mouse strain C57BL6. This is the most widespread and best characterized model animal for studying organismal status and transgenically constructed pathology of iron metabolism.

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From a technical point of view the model presented here follows a standard methodology of systems biology. We envisage the organism as an aggregate of organs and tissues, each of which represented as an idealized compartment, consisting of a given number (or volume) of cells. Transport into and out of a compartment and the interconversion of its elements is described as a network of metabolites and reactions, characterized by well-defined biochemical and biophysical status and interconversion descriptors. Metabolites are quantified by content (or “concentration”), and the dynamics of transfer of “substrate” into “product” is quantified by a reaction rate. The reaction rate is a function of the content in partaking metabolites and contains parameters of the catalysts and the signals (inhibitory or activatory) that influence the interconversion. The whole system´s dynamics is then described by a balance sheet of differential equations which usually are linear combinations of the reaction rates according to the stoichiometric matrix of the system.

This theory has envisaged metabolic systems as a kind of “well-stirred” biochemical reactor. It has been applied to holistic descriptions of E. coli, yeast cells and erythrocytes [86 ] [87-89 ]. For more complex eukaryotic cells the basic tenets of the theory, especially compartment and reactant homogeneity, are not given, and the description has to introduce subcompartments or has to integrate over the whole cell. In a cell with multiple subspaces embedded in a membranous structure filled with organelles and a certain content in macromolecules the description is bound to become phenomenological, assuming that a system can be quantitatively described in the conceptual framework of a cellular reactor, where the compartments, the variables and the parameter definitions and their numerical values are valid as a weighted average over the object considered.

Iron metabolism has some special properties that render such an idealized description applicable, and it has other features which introduce specific restrictions. The typical iron content of a cell, when expressed as if it were a homogenous water solution, is in the millimolar range (for instance 120 mg non-heme iron per kg liver, or, for that matter, 3 mg iron for 50 l water of a 70 kg human body [90 ]), but the cytosolic “concentration” of LIP (labile or transit iron pool) is in the micromolar range at most [26]. The bulk of iron is bound to specific protein carriers (below the micromolecular range), most of them containing per molecule only one or a few iron molecules (such as transferrin or myoglobin). Only ferritin and hemosiderin are able to corral up to 4500 iron atoms per macromolecule fold. It is evident that a kinetic description in classical terms does not apply in such situations, and only a phenomenological “quasi”-description is possible that has to justify itself by the criterion of “producing the global phenomena”.

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However, there are features that greatly simplify an adequate systemic description. One point in case is that fact that iron is inorganic and therefore alien in the ocean of bioorganic matter. So only few specific proteins or translocators of iron (and other metals) need to be considered. A second point is that iron is as Fe (II) or Fe(III) always in electrostatic coordination rather than in covalent bond, so the number of kinetically relevant biochemical states, although as prosthetic group present in multifarious protein entities (more than 100 species coded for in the whole genome [91 ], is limited in terms of metabolic turnover. Most of the states of iron bound to specific proteins are now well known and easily traceable by physical measurement. A further point is the residence time of most iron atoms in active cells is longer than the life-time of the carrier molecules (e.g. about 7 days vs. 1 day in liver), so one can assume that the binding/releasing cycle as well as the renewal of protein carriers is close to steady-state.

4.2 Structural and Kinetic Hierarchy of the Model

The structure of the model is a set of peripheral organ and tissue compartments connected via a central compartment. The relative organ weight is the factor that integrates the compartments to a whole system. Each cell type is contains three levels of intertwined kinetic representation: material transfer of iron, synthesis and decay of the protein arsenal, and the regulatory superstructure (mainly IRP/IRE system). On the organismal scale there is the exchange flux into and out of the central compartment and the global absorption (via duodenum) and loss of iron (several organs), the turnover of the transferrin carrier and the regulatory superstructure (hepcidin for the iron household, and erythropoietin for the erythron). Hepcidin as a hormone has a similar function for global homeostasis of iron as has insulin for carbohydrate homeostasis. Both act as a feedback signal produced by a sensor cell reporting a high level (hepatocyte and pancreas ß-cell, respectively), and both exert their main effect via a membrane receptor in certain cell types (ferroportin vs. insulin receptor).

Compartment content and within- and inter-compartment transfers and fluxes are the main kinetic elements of the system. Simple linear kinetics has been installed for the turnover of the protein arsenal. The elementary kinetic formalism for material iron transfer is a rate law bilinear in iron content and in protein acceptor level for iron binding and a linear rate of iron release. Where regulatory signals have been experimentally demonstrated to be operative the basic rate law is multiplied by a simple signal expression (power law). Since the hormonal signals are triggered and exert their effect with a considerable gain we chose the exponent of the power law greater than unity. For the cellular IRP/IRE a value of unity was sufficient, since the experimental background was only qualitative. Anyway, the effect of a high exponent in a steady-state system is mainly the swiftness of concentration jump in order to trigger an effect. As is well known, high non-linearity introduced by steep signals in metabolic systems may produce alternative states or oscillations, but our system has only one potential positive feedback loop (i.e. back effect of hepcidin on the liver), but there is no indication so far that the system may run over a bifurcation surface (i.e. over a structure in the parameter space where the qualitative behaviour makes a sudden jump).

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The quantitative domain in which each cell metabolism is operating is set by the experimentally measurable content of the major iron fraction as well as the distribution of radioactive tracer into the organs and back into the central compartment. For the non-transferrin part of iron transport (haptoglobin- and haemopexin-borne) there were not enough quantitative data available, and it had to be modelled therefore only cursorily. The intracellular steady-state structure of most iron-related pathways, due to the nanomolar content level of the individual iron-carrying proteins, made it possible to apply the integrative assumptions, i.e. aggregation of kinetically similar reactions into one component (e.g. haemo- and myoglobin synthesis, mitochondrial iron uptake, iron-sulfur biogenesis), and normalization of contents and fluxes to a common reference state (adult healthy mouse on adequate iron food). Any further specification of the model must await corresponding quantitative determination as experimental input.

What can be expected and what cannot be achieved with a kinetic model as presented here?

The answer is:

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This can be done for the reference state of the normal mouse, but also for certain perturbational variations:

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This can be studied either by variation of the boundary conditions (e.g. acute loss from the RBC compartment) or of the parameter structure of the model. Parameters may be varied as a jump (as if by a gene knock-out) or by continuous variation that makes it possible to adapt the model structure to realistic measurements. The parameters of the models belong to three classes:

In what follows we discuss the results that we have obtained for establishing parameters from flux and content measurements in vivo, of physiological inferences that can be made from such estimates, and of computer experiments of acute and chronic changes of the model structure compared with explorative simple simulations.

4.3 Model Parameterization from Experimental Data: Iron Status and Fluxes

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From the viewpoint of systems analysis, iron metabolism of the body is an open black-box with input, internal processing and output. Absorption fluxes and losses are relatively slow compared to internal iron circulation [90 , 92]. The most relevant internal dynamic events occur within the first few days after tracer injection. They involve the plasma iron turnover and the turnover of the erythron. On this time scale the system is nearly closed, with input (absorption) and output (excretion, desquamation) being slow compared to the dominant rates of inner metabolism. Iron absorption from guts is in the range of 0.5 µg per day (calculated to whole-body scale from the data of Bahram et al. [93 ] and Lebeau et al. [35 ], whereas the rate of total plasma iron exchange with the body periphery, as shown in table 3.2, is in the range 20 – 30 µg per day. Such a system will approach an inner steady-state with slowly drifting concentrations and fluxes.

To study such a steady-state one can measure stationary content variables and inject a tiny dose of Fe59, preferentially bound to its transferrin carrier [94 ], into the central compartment of radioactive iron. In the initial hours after mixing of the injected iron, when the periphery does not appreciably return tracer, the flow of blood into the organs is proportional to the flow of tracer. This initiates distribution dynamics of the tracer in conformity with the pools and stationary rates of the unlabelled bulk of iron in the steady-state, which is not disturbed by the addition of trace amounts. The time course of the ensuing run-off of tracer distribution obeys a system of ordinary differential equations with constant coefficients.

4.4 Iron status of the adult mice on different dietary regimes

The experimental data which form the basis for the model calculations presented here are derived in adult mice that were on different dietary regimes during growth. The adult animal develops a steady-state which is maintained during its further adult life, i.e. for approximately 1-2 years. This assumption is prerequisite for the ferrokinetic model. The empirical background for the model consists of the static iron status and of tracer dynamic data.

4.5 Modelling iron fluxes by the Fe59 tracer method

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The literature contains numerous papers (e.g.[6 ,7, 10-12]) which measured the dynamics of iron metabolism on the intact organism with the help of the tracer Fe59. The basic rationale is that the tracer, while being always measurable as radioactivity, due to its tiny relative amount does not perturb appreciably the iron status of the body. Most of the mathematical models derived from such measurements were obtained for humans, dogs and rats. Only the paper by Vácha et al. [13 ] derived a whole-body model for the normal mouse , collected from measurements in blood, liver and spleen, without systematic control of dietary regime. The model was based on a number of ad-hoc assumptions of fluxes, which partly could not be substantiated by cellular mechanisms, and the parameters were in part estimated without a whole-model statistical fitting procedure (computer capacity-limited). We can confirm, with the experimental evidence now available, that their ingenious model, in spite of some speculative elements due to limited molecular knowledge, gives a remarkably adequate description of the global dynamic structure of murine iron metabolism

4.6 Iron status

This is defined as the iron content of the iron fractions in the different organs and tissues. It reflects the expression of protein carriers to which iron is bound (transferrin, ferritin, heme proteins etc.). We can assume that this status is stable during the ferrokinetic observation period.

4.7 Dynamic fluxes

The second data type is the time course of iron flow through body organs after administration of a radioactive tracer. The data base stems from partly published measurements of Prof. Schümann´s lab [27 ] and from studies done elsewhere under a comparable experimental design. The aim is to integrate the entire data set into an integrative model, thereby displaying the systemic structure which is not obvious from inspection of raw data.

4.8 Kinematic model of iron flux steady-state

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The crucial supposition for a representative model is that iron fluxes in the body are (approximately) balanced and cellular pools do not fluctuate violently during the experimental period. Tracer injection permits to collect data on internal fluxes without upsetting the steady-state. Analysis of the fate of tracer-Fe59 in the tissues in terms of a linear system of differential equations describing influx, outflux and internal metabolism of the system gives a picture of the prevailing “kinematics” of the system, i.e. it describes what happens, not the causes and controlling mechanisms. Such a phenomenology is the prerequisite for any in-depth systemic description.

4.9 Inhomogeneity of compartments

For some important tissues under consideration the assumption of homogeneity is not valid. This applies to liver, which consists of parenchymal cells (hepatocytes) and cells of the RES (Kupffer-cells). Both types have different iron regulation. Similarly, the murine spleen has subcompartments, of erythropoietic and of macrophage cells. Muscle tissue contains a large fraction of iron in myoglobin, the turnover of which is different from that of the macrophages in muscle. On the whole, the macrophages of RES are spread over a multiplicity of organs and change their distribution in inflammation. For the sake of model calculation, nevertheless, we treated these organs as compartments.

4.10 Numerical parameter estimation

Tracer motion in a steady-state system of homogenous pools (like fig. 2.1) can be modelled by ordinary linear differential equations. In theory, the concentration of tracer in these pools follows a time course described by superimposed exponentials. In the initially labelled central compartment (plasma) the tracer content falls monotonously. In all the other compartments, initially void of tracer, the concentration rises to a maximum and then turns into a monotonously decreasing phase of recycling into plasma together with outflux out of the body. The parameter values of the interconnected system can be obtained as “best fit” according to a suitable distance criterion. In practice this estimation process may run into two types of difficulty: statistical scatter and redundancy of the parameter space.

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The scatter of measured data in most biological systems is considerable and cannot be avoided. The reason is individual variation between subjects and the impossibility to exactly repeat the same experiment. A statistical model of this situation can, at best, be a close approximation to the measured data in the form of an idealized curve. We repeated the estimation procedure on sets of artificially generated data which keep the error structure of the observed data. The range of parameter variation was revealed in this way.

4.11 Interdependence (correlation) of parameter estimates

This is an unavoidable problem of complex biological models. It became clear from the ACE analysis (see methods) that our data contained two causes of parameter interdependence: insufficient resolution at very early time after tracer injection, and cases of double output of tracer back into plasma and out of the body. We overcame these problems by prescribing an approximate value of the total plasma clearance calculated from the data of Trinder et al. [33 ]. Furthermore, we replaced double outfluxes by a single lumped one, thus not specifying the precise fractional contribution of each pathway (see dotted outflux arrows in fig. 2.1). In this way we obtained parameter estimates with a reasonable range of scatter avoiding strong intercorrelation.

4.12 Further parameters of the model

The set of clearance- and rate-parameters resulting from the parameterization is given in table 3.1. The quality of the fit is satisfactory, as demonstrated in figs. 3.2-3.4. Table 3.1 contains the most compact representation of the information content of the empirical data. It can be used to calculate flux rates 3.3, pool sizes 3.4 and as well as a characteristic temporal structure of the system 3.5. Figures 3.5 and 3.6 visualize these quantitative estimates. These indirectly derived data indicate ranges (not precise values) of system-relevant parameters. Their totality is amenable to physiological interpretation of the static and dynamic state of the iron system in the mouse in the different “lifestyle” regimes studied. 

4.13 Physiological interpretation of the flux model

4.14 Systemic iron metabolism can be described as a closed compartment system.

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The quasi-closed state of the iron system together with the ensuing internal steady-state makes into possible to simplify the non-linear structure to a system of ordinary linear differential equations. The dynamics of tracer motion depicts the statics of the underlying stationary flux-and-pool network. We could build on a number of previous attempts to model iron metabolism in this way [9-12 , 95], reviews in [6 , 7]. The novel aspect here is the detailed reversible balance in a network of peripheral tissues that were previously combined ad hoc to black boxes.

4.15 Iron metabolism is organized as temporal hierarchy on five time scales

The importance of time structure has been emphasized by Klipp [96 ]. We adopted the simple time scale defined in eq. 4 (methods section). Analysis of the clearance parameters of our experiments (table 3.1, transformed into residence times – table 3.5) and of literature data [23 , 24, 33] lead to the following grouping of characteristic time periods:

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The time hierarchy does not change appreciably between different iron statuses in normal mice (confirming the conclusion in [33 ]).

4.16 Iron turnover in the plasma compartment depends on the iron status

The concentration of transferrin-bound plasma iron in plasma is in the range of 100 -200 μg/dL in the mouse. This is similar to other mammalian species (e.g. [19 , 58-61]). The iron concentration tends to lower values in iron-deficient and to higher values in iron-loaded mice. The iron clearance from plasma defines a half-time of renewal in the range of 1-2 hours, again similar for species otherwise as different as Mus musculus and Homo sapiens.  Rats [61 ] and dogs  [10 , 60] are also in the same range. In rats, however, iron deficiency does not lower the plasma concentration [61 ].

4.17 Iron distribution into body periphery is a three-level hierarchy of flux rates

The initial tracer concentration in plasma becomes rapidly cleared within a few hours after administration and stays at a low, but steady value afterwards. This coincides with the ascending tracer curves in the peripheral compartments (figs. 3.2-3.4). The initial distribution is complete at the first time of measurement (12 h). The position of the maximum fixes the time point when plasma tracer is nearly washed out and the periphery begins to return some of the previously accumulated tracer iron into the plasma. The continuous decrease of organ tracer content begins after 12-24 hours. It is an expression of the fact that “fresh” cellular iron is not only stored or channelled into biosynthesis, but also shows an appreciable back-flow into the plasma.

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The descending branch of the peripheral tracer curves show that all tissues return the radioactivity into the plasma, unless they lose it by desquamation, which is the case for intestine and integument. This characteristic pattern proves that iron flux into the periphery and reflux into plasma take place simultaneously.

The quantitative level of all the superimposed fluxes can result only from a deeper analysis of the corresponding mathematical model. This analysis yields a set of fractional clearance parameters (table 3.2). From these values and by application of the steady-state assumption all iron fluxes can be estimated when the iron content of the central compartment is available. Data by Trinder et al. [33 ] contribute an estimate of the total plasma turnover clearance rate (table 3.1).

Three clusters of flux rates may be distinguished (fig. 3.5):

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4.18 Share of flux into tissues mirrors transferrin receptor expression

The clearance time of plasma iron is in the range of 1 h, largely independent of the plasma iron content and hence the state of the animal’s iron supply. This linear kinetics suggests that the total population of TFR1 receptor molecules (responsible for most of the iron uptake) works far below its maximal capacity in all cells. The share of radioiron going into the body organs reflects this tissue-specific transferrin receptor expression. In contrast to the rather stable total clearance time the share of radioiron is dependent on the physiological state. In the states of iron depletion and of normal iron supply more than two thirds of the plasma iron turnover is directed to the erythropoietic bone marrow and is rapidly incorporated into hemoglobin. This is, again, similar to other species [6 , 20, 21, 65]. The corresponding fraction of tracer iron passes through the immature cells of the erythropoietic lineage until it reaches the erythrocyte compartment.

4.19 Tracer distribution iron-rich condition reflects the switch-over to the storage mode

The flux through the storage pathway into parenchymal organs increases from 25% to 49% of plasma turnover (table 3.2; visualized in figures 3.1 and 3.5). Stores are filled up in liver, kidney, spleen/RES, to a lesser extent also heart and skeletal muscle, but not integument and brain.

4.20 Tissue cells equilibrate influx and reflux of iron to maintain the iron pool

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An adult mouse does not grow much during its life-time of ~2 years (if not killed before). Iron is taken up by cells with a time characteristic of a few days and must, therefore, be balanced by corresponding iron-release. Muscle, fat, heart, lungs, brain and testicles excrete iron into plasma or extravascular fluid. The influx of tracer is mediated by transferrin receptor. It is not clear from tracer data whether the export is mediated only by the ferroportin channel [18 ], or also via catabolism of heme-bound iron. Ferroportin is dominantly expressed in liver, duodenum, and macrophages, and to a lesser extent also in other tissues [97 ]. Ferroportin is not involved in the case of catabolism of whole cells (erythrocytes, intestine, and integument). The tracer data as used here cannot distinguish between export of iron and loss of whole cells. They yield only an estimate of the total flux out of the compartment.

4.21 Intracellular residence time of iron is longer than the life time of its protein “carriers"

The life-time of the iron-storage proteins (such as apoferritin/holoferritin) is in the range of one day in the liver [98 ]. Up to 4500 iron ions can be stored in one ferritin molecule [69 ], and become released on proteolytic ferritin degradation. The residence time of iron in the liver cell, however, is much longer - in the range of 1-2 weeks (table 3.5). This shows that iron released into the very small labile iron pool does not leave the cell, but is re-utilized. This slow export conforms to well-known data showing how slowly iron is mobilized from ferritin stores to replace iron losses, e.g. after phlebotomy (in men: [66 , 99]). Intracellular iron stores are no inert long-term reserves, but are continuously turned over within the cell and may therefore be directed, in accordance with changing requirements, into the three competing pathways (biosynthesis, storage, export).

4.22 Readily accessible tissue iron pools are a fraction of the non-heme iron

These iron pools are stored in different subcompartments, mainly in non-heme form. The iron-loaded liver stores ferritin in the hepatocytes and a less mobilizable (hemosiderin?) form in the Kupffer cell [100-102 ]. The labelled and unlabelled iron data from whole organs do not permit to differentiate quantitatively between parenchymal and macrophage iron in such mixed cases. Tracer dynamics identifies iron pools that become quickly labelled. Their pool sizes have been estimated from the fractional plasma iron turnover and the tissue clearance rates (table 3.1 and 3.2). Three groups may be distinguished. Red blood cells contain as hemoglobin the largest readily labelled iron pool (~ 300 µg Fe per mouse, about 50% of total haemoglobin-iron, see calculation in table 3.1). There is a second cluster of pools (integument, liver, bone marrow, skeletal muscles, skin), each containing about 20-40μg Fe. In particular the hepatic iron pool is expandable in iron overload to reach a kinetic pool level of ~ 100μg Fe, presumably in ferritin form. A still larger store can possibly accumulate on a longer time scale, which is not covered here. There are additional pools with an iron content (lungs, kidneys, intestine, heart, and spleen) of about 3µg Fe, which can moderately expand up to 4-14µg. Other organs, such as fat, testicles or brain, are not able to store more iron in overload. Table 3.7 shows that in some tissues the readily accessible pools are only a fraction (6 to 40%) of cellular non-heme iron.

4.23 There are two kinetically distinct major iron pools in the mouse body

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The total tracer-accessible iron amounts to ~400 µg table 3.6. The residence time in the main compartments excluding intestine (table 3.5) is between 5 and 25 days. This comprises about 20% of the total iron (i.e. of ~2 mg per 25 g body [24 ]). The reminder is not readily accessible. The residence time of molecules here is ~200 days [23 , 24 ].

4.24 Iron turnover occurs at similar rate in intestine and skin, but assignment to iron loss vs. iron reflux is only indirectly estimable

Physiologically iron enters the body via duodenal and (less) small-intestinal absorption in a tightly controlled way. It leaves the body by desquamation, exfoliation of epithelial cells, by blood losses, and to a lesser extent via bile and urine [103 ]. The relative amount leaving the murine body is, according to literature references, 2 to 5 times larger than in other animals and man [24 , 34, 58, 73, 74, 103]. A consequence of this higher excretion is that heavy iron-load is sometimes difficult to attain in mouse models.

Net iron losses cannot be measured by the tracer method as applied here. However, the fractional clearance rates (table 3.2) yield indirect information on iron fluxes through intestine and integument (table 3.3). Iron clearance of the epidermis integument is about 5% per day and that of the stomach-intestinal epithelium ca. 36% per day (calculated from table 3.2). From the fractional uptake from plasma one can calculate influx rates of ~1.7 µg per day into epidermis, and a sum of ~1.5 µg per day into intestine plus stomach (all for iron-adequate mouse, see table 3.3). These values are about 39% lower and higher in iron deficient and iron-load regimes, respectively. The data do not support a calculation of the rate of net iron loss through these compartments, because there may be a fraction that is recycled into plasma. The iron residence times for intestine are similar to the known exfoliation times of epithelium (both 3-5 days), which suggests that the main fraction goes into loss. For skin integument (iron residence about 40 days) such external information was not available.

4.25 Murine erythrocyte iron turnover has a random elimination component together with a lifespan-determined removal component

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During one month after administration 60% of the tracer (40% in iron-loaded state) accumulates in the red blood cell compartment (figs. 3.2-3.4). The first quick uptake of Fe59 reflects passage through bone marrow and incorporation into hemoglobin at a steady rate. The uptake reaches a saturation phase which is clearly visible in the RBC curve of figs. 3.2 to 3.4. This behaviour proves the existence of a reflux caused by a random component of erythrocyte catabolism independent of the cell age. Without reflux iron would be further incorporated even at a very low plasma radioactivity. The erythron cycle transports (table 3.3) 15;19;14 µg Fe/d into bone marrow in iron-deficient, -adequate, and -loaded animals, respectively, of which 12;17;12 µg Fe/d pass through the RBC compartment back via into RES into plasma. This turnover rate is quantitatively analogous to ~ 25 mg Fe/d per 70 kg in iron-adequate humans [87].

The life span of mouse erythrocytes has been studied in mathematical detail by Horký et al. [67 ]. They also formulated an age-independent linear elimination component acting simultaneously with a lifespan-determined senescence process. Our elimination rate (between 0.03 and 0.06 d-1) is somewhat higher than obtained in [67 ] (0.012d-1). However, our estimates are not very reliable, as they stem from an indirect deduction. This applies also to the size of the “readily accessible” iron pool in red blood cells (300 µg instead of the 568 µg calculated from the hemoglobin pool of the mouse, see table 3.1).

4.26 The spleen is a mixed indicator of erythropoiesis and RES activity

The murine spleen is an erythropoietic organ [64 ]. Therefore, one subcompartment of iron in the spleen is expected to behave similar to iron in the bone marrow. Figs. 3.2 - 3.4 show a quick uptake phase in both bone marrow and spleen. The ratio of tracer iron content between both organs after 12 h is about 50 to 60 in adequate and iron-rich mice, and 20 in iron-deficient animals. Thus, the quantitative contribution of the spleen to total murine erythropoiesis is not high. Furthermore, the iron-deficient spleen loses iron as quickly as the bone marrow, reflecting the rapid flow into “iron-deficient” erythropoiesis. In contrast to the bone marrow, the iron-adequate, and even more so the iron-loaded spleen retains Fe59 for long periods. This reflects a storage behaviour which is similar to that of RES cells in the liver and elsewhere. The spleen contains 5% and the liver 16% of the whole population of macrophages [30 ]. The RES system serves as scavenger to remove senescent erythrocytes together with their hemoglobin and colloidal iron from the circulation [9 ,68]. Part of this RES iron is rapidly recirculated into plasma, thereby completing the iron-recirculation back to the erythrocyte pool. Except in iron deficiency, another part of the RES iron is stored as ferritin or hemosiderin [69 ].

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The quantitative contribution of both spleen compartments to whole body iron turnover is low. The spleen is therefore an indicator, but not the main quantitative locus of the total erythropoietic and macrophage activity. In iron-deficiency splenic iron clearance is very rapid (15 % d-1, see table 3.2), while it is distinctly slower (down to 1.9 % d-1) in iron loaded mice. This may reflect distinct differences in the role of the spleen depending on the state of iron-repletion. A precise quantitative partition of splenic iron fluxes into a RES- and an erythron-fraction would require separation of the cells.

4.27 Experimental design for characterizing the iron status and the dynamic turnover of the C57BL6 mouse strain.

The C57BL6 mouse is a widely used strain for genetic modifications to address the regulatory networks of iron metabolism. Any such transgenic strain needs a characterization of its iron kinetics (examples in [104-105 ]). This includes a survey of static and dynamic characteristics of iron metabolism under the limitations set by thrifty experimental expense. The turnover model developed here permits to derive diagnostic requirements for healthy or diseased mice, after a steady-state has been established and maintained for the time of at least one red blood cell turnover. The following data should be scaled up to the total body level:

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The biochemical parameters yield a survey of the static of iron metabolism and its steady-state level. Ferrokinetics yields the fluxes. This full programme can be reduced, if in a particular situation preliminary analysis of data and their comparison with the mathematical model indicate that certain features of the iron status are not changed or are negligible.

4.28 Simulated Experiments – Perturbation and Transgenic Reconstruction

Given knowledge on the stoichiometric network structure, the most important regulatory signal (IRP/IRE system), hepcidin and erythropoetin) and the flux parameters estimated from the distribution dynamics of radioactive iron in the mouse body, it is possible to draft a kinetic model of cellular metabolism integrated to the whole organism. The important parameters of this system have been chosen as to reproduce the flux pattern into and out of the periphery of the body. The intracellular parameters that are not available have been set at normalized standard values, relative to the normal state of the adult mouse.

We have done simulation runs on the resulting system of balance equations. Extracts of calibration experiments in silico have been presented and discussed in the “results” section. Studies are at present under way to built a specified model version that takes into account the results of ongoing transgenic cpmstructions in the labos of Profs. Hentze, Muckenthaler and Schümann.

4.29 Conclusion and Outlook

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This mathematical model presented a comprehensive physiological picture of mice under three different diets with varying iron contents. We could assess which parameters will change under dietary perturbations and study in quantitative terms when those changes take place. We have devised a simulation model of the iron metabolism of the mouse that integrates the various tissues and cell types in the form of a system of differential equations. We chose the parameters of this model, partly by fitting to ferrokinetic tracer data, partly by adopting biochemical data, and partly by formulating black boxes of kinetic behavior and of regulatory signals, using the established general theory of metabolism as source of first principles. This is a different from the recent review paper of Hower et al. [106 ] where they explained many known molecular mechanisms of iron metabolism and finished offering a SBML layout, but without equations or simulations.The kinetic model of the reference state reproduces in a semi-quantitative way the main features of the iron status of the mouse in several conditions, including transgenic constructs.

Future studies could profit from the model and the results presented here. One idea would be to perform the same type of ferrokinetic studies in genetically constructed mice, either knock-out, knock-in or conditional knock-out mice. Adapting the parameter structure of our model to these artificial conditions and carrying out biochemical measurements of the iron status of these animals one will obtain a still more precise quantitative description of the system.

An obvious extension of the work would be an attempt to transform the model to the human organism. This can of course not been a simple up-scaling everything by a factor of 3000 or so. There is ample literature data on the iron metabolism of man and its physiological and pathological perturbations. There is hope that such a quantified global computer model could be of great help in the diagnostics and therapy planning of iron disorders.


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