A Computational Model of Liver Iron Metabolism

Simon Mitchell1, Pedro Mendes1,2$\ast$

1 School of Computer Science and Manchester Institute of Biotechnology,
University of Manchester, Manchester, UK
2 Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, Virginia, USA

$\ast$ E-mail<EMAIL_ADDRESS>
## Abstract

Iron is essential for all known life due to its redox properties, however
these same properties can also lead to its toxicity in overload through the
production of reactive oxygen species. Robust systemic and cellular control
are required to maintain safe levels of iron and the liver seems to be where
this regulation is mainly located. Iron misregulation is implicated in many
diseases and as our understanding of iron metabolism improves the list of
iron-related disorders grows. Recent developments have resulted in greater
knowledge of the fate of iron in the body and have led to a detailed map of
its metabolism, however a quantitative understanding at the systems level of
how its components interact to produce tight regulation remains elusive.

A mechanistic computational model of human liver iron metabolism, which
includes the core regulatory components, is presented here. It was constructed
based on known mechanisms of regulation and on their kinetic properties,
obtained from several publications. The model was then quantitatively
validated by comparing its results with previously published physiological
data, and it is able to reproduce multiple experimental findings. A time
course simulation following an oral dose of iron was compared to a clinical
time course study and the simulation was found to recreate the dynamics and
time scale of the systems response to iron challenge. A disease state
simulation of haemochromatosis was created by altering a single reaction
parameter that mimics a human haemochromatosis gene (HFE) mutation. The
simulation provides a quantitative understanding of the liver iron overload
that arises in this disease.

This model supports and supplements understanding of the role of the liver as
an iron sensor and provides a framework for further modelling, including
simulations to identify valuable drug targets and design of experiments to
improve further our knowledge of this system.

## Author Summary

Iron is an essential nutrient required for healthy life but, in excess, is the
cause of debilitating and even fatal conditions. The most common genetic
disorder in humans caused by a mutation, haemochromatosis, results in an iron
overload in the liver. Indeed the liver plays a central role in the regulation
of iron. Recently, an increasing amount of detail has been discovered about
molecules related to iron metabolism, but an understanding of how they work
together and regulate iron levels (in healthy people) or fail to do it (in
disease) is still missing. We present a mathematical model of the regulation
of liver iron metabolism that provides explanations of its dynamics and allows
further hypotheses to be formulated and later tested in experiments.
Importantly, the model reproduces accurately the healthy liver iron
homeostasis and simulates haemochromatosis showing how the causative mutation
leads to iron overload. We investigate how best to control iron regulation and
identified reactions that can be targets of new medicines to treat iron
overload. The model provides a virtual laboratory for investigating iron
metabolism and improves understanding of the method by which the liver senses
and controls iron levels.

## Introduction

Iron is an essential element from archaea to complex eukaryotes and man [1],
and is required for many processes including oxygen transport, DNA synthesis
and respiration. Iron deficiency is the most common nutritional deficiency
affecting a large proportion of all humans [2]. The redox activity which
provides iron’s utility also means poorly regulated iron metabolism can lead
to highly toxic free radicals [3]. Maintaining the delicate balance of iron
requires robust cellular and systemic regulation since both iron deficiency
and overload can cause cell death [4]. Recent research has lead to a much
greater understanding of the mechanisms controlling iron metabolism and a
global view of the interactions between iron-related components is beginning
to emerge [5, 6].

The liver has been proposed to play a central role in the regulation of iron
homeostasis [7] through the action of the recently discovered hormone hepcidin
[8]. Hepcidin is expressed predominantly in the liver [9] and distributed in
the serum to control systemic iron metabolism. Hepcidin acts on ferroportin to
induce its degradation. Ferroportin is the sole iron exporting protein in
mammalian cells [10], therefore hepcidin expression reduces iron export into
the serum from enterocytes, and reduces iron export from the liver.
Intracellular iron metabolism is controlled by the action of iron response
proteins (IRPs) [11]. IRPs post-transcriptionally regulate mRNAs encoding
proteins involved in iron metabolism. IRPs combined with ferritin and the
transferrin receptors (TfR) make up the center of cellular iron regulation.
Ferritin is the iron-storage protein forming a hollow shell which counters the
toxic effects of free iron by storing iron atoms in a chemically less reactive
ferrihydrite [12]. Extracellular iron circulates bound to transferrin (Tf),
and is imported into the cell through the action of membrane bound proteins
transferrin receptors 1 and 2 (TfR1 and TfR2). Human haemochromatosis protein
(HFE) competes with transferrin bound iron for binding to TfR1 and TfR2 [13].

Systems Biology provides an excellent methodology for elucidating
understanding, through computational modelling, of the complex iron metabolic
network. A quantitative model of iron metabolism allows for a careful and
principled examination of the effect of the various components of the network.
Modelling allows one to do “what-if” experiments leading to new hypotheses
that can later be put to test experimentally. However, no comprehensive model
of liver iron metabolism exists to date. Models have been published that cover
specific molecular events only, such as the loading of iron in ferritin [14].
A qualitative map of mammalian iron metabolism provides a detailed overview of
the molecular interactions involved in iron metabolism, including in specific
cell types [6]. Similarly, a detailed model of iron metabolism and oxidative
stress was described but uses a Boolean approach and is specific for yeast
[15]. Quantitative models of the iron network have been recently described
[16, 17], yet these include only a few components of the iron network. The
model from Chifman et al. suggests that the dynamics of this iron network is
stable [16]. Large-scale models of the metabolism of the hepatocyte [18, 19]
and a generic human metabolism stoichiometric model [20] have also been
published, but these contain only four reactions relating to iron metabolism.
While they include iron transport, the receptors are not considered, and
regulatory details are absent altogether.

Existing models are therefore at two extremes of detail: very specific and
very generic — but to address questions about hepatic iron regulation, what is
desirable is a model that balances coverage and detail. This is the aim of the
present work. One of the problems of modelling iron metabolism quantitatively
and in detail arises from the lack of parameter values for many interactions.
Recently, several of those parameters have been described in the literature
(Table LABEL:tab:reaction_parameters), particularly using technologies like
surface plasmon resonance. This has enabled us to construct a detailed
mechanistic kinetic model of human hepatocyte iron metabolism. The model has
been validated by being able to reproduce data from several disease conditions
— importantly, these physiological data were not used in constructing the
model. This validation provides a sense of confidence that the model is indeed
appropriate for understanding liver iron regulation and for predicting the
response to various environmental perturbations.

## Results

Our model was constructed based on many published data on individual molecular
interactions (see Methods section), and is available in Systems Biology Markup
Language (SBML) and COPASI formats in supplementary data, as well as from
BioModels (http://identifiers.org/biomodels.db/MODEL1302260000) [21]. Figure 1
depicts a process diagram of the model, using the Systems Biology Graphical
Notation (SBGN) standard [22], where all the considered interactions are
shown. It is important to highlight that while results described below are
largely in agreement with observations, the model was not forced to replicate
them. The extent of agreement between model and physiological data provides
confidence that the model is accurate enough to carry out “what-if” type of
experiments that can provide quantitative explanation of iron regulation in
the liver.

### Steady State

Initial validation of the model was performed by assessing the ability to
recreate experimentally-observed steady-state concentrations of metabolites
and rates of reactions. Simulations were run to steady state using the
parameters and initial conditions from Tables 1 and
LABEL:tab:reaction_parameters. Table 3 compares steady-state concentrations of
metabolites and reaction rates with experimental observations.

Chua et al. [23] injected radio-labeled transferrin bound iron into the serum
of mice and measured the total uptake of the liver after 120 minutes. The
uptake rate, when expressed as mol/s, was close to that found at steady state
by the computational model (Table 3).

A technical aspect of note in this steady state solution, is that it is very
stiff. This originates because one section of the model is orders or magnitude
faster than the rest: the cycle composed of iron binding to ferritin,
internalization and release. Arguably this could be resolved by simplifying
the model, but the model was left intact because this cycling is an important
aspect of iron metabolism and allows the representation of ferritin
saturation. Even though the stiffness is high, our software is able to cope by
using an appropriate numerical method.

### Response to Iron Challenge

An oral dose of iron creates a fluctuation in serum transferrin saturation of
approximately 10% [24]. The fixed serum iron concentration in the simulation
was replaced by a transient increase in concentration equivalent to a 10%
increase in transferrin saturation as a simulation of oral iron dosage on
hepatocytes. The simulated hepcidin response (Figure 2A) is consistent with
the hepcidin response measured by Girelli et al. [24] (Figure 2B & C). The
time scale and dynamics of the hepcidin response to iron challenge has been
accurately replicated in the simulation presented here. Although the exact
dynamics of the simulated response is not validated by either experimental
technique (mass spectrometry or ELISA) the simulation appears to present an
approximation of the two experimental techniques reaching a peak between 4 and
8 hours and returning to around basal levels within 24 hours.

### Cellular Iron Regulation

The computational model supports the proposed role of HFE and TFR2 as sensors
of systemic iron. Figure 3B shows that as the concentration of HFE bound to
TfR2 (HFE-TfR2) increases with serum transferrin-bound iron (Tf-Fe_intercell),
at the same time the abundance of HFE bound to TfR1 (HFE-TfR1) decreases. The
increase in HFE-TfR2 complex, even though of small magnitude, promotes
increased expression of hepcidin (Figure 3A). It is through this mechanism
that liver cells sense serum iron levels and control whole body iron
metabolism through the action of hepcidin. Although the labile iron pool
increases with serum transferrin-bound iron in this simulation, this is only
because the model does not include the action of hepcidin in reducing duodenal
export of iron. Expression and secretion of hepcidin will have a global effect
of reducing the labile iron pool.

### Hereditary Haemochromatosis Simulation

Hereditary haemochromatosis is the most common hereditary disorder with a
prevalence higher than 1 in 500 [25]. Type 1 haemochromatosis is the most
common and is caused by a mutation in the HFE gene leading to a misregulation
of hepcidin and consequent systemic iron overload.

A virtual HFE knockdown was performed by reducing 100-fold the rate constant
for HFE synthesis in the model, to create a simulation of type 1 hereditary
haemochromatosis. The simulation was run to steady state and results were
compared with experimental findings.

Qualitative validation showed the in silico HFE knockdown could reproduce
multiple experimental findings as shown in Table 4. Quantitatively the model
was unable to reproduce accurately the finding that Hfe -/- mice have 3 times
higher hepatic iron levels [26]. This was due to the fixed intercellular
transferrin bound iron concentration in the model, unlike in Hfe -/- mice
where there is an increase in transferrin saturation as a result of increased
intestinal iron absorption [26]. Despite fixed extracellular conditions the
model predicted an intracellular hepatocyte iron overload which would be
further compounded by the systemic effects of the misregulation of hepcidin.
The simulation recreated increased ferroportin levels despite the expression
of ferroportin remaining the same as wild type which was consistent with mRNA
measurements from Ludwiczek et al.  [27]. mRNA based experiments can be used
to validate expression rates and protein assays are able to validate steady
state protein concentrations as both expression rates and steady state protein
concentrations are available as results from the computational model. The
model of haemochromatosis was also able to replicate the dynamics of
experimental responses to changing dietary iron conditions. An approximate
2-fold increase in hepatic ferroportin expression is caused by increased
dietary iron in both haemochromatosis and healthy mice [27]. The model
presented here recreated this increase with increasing intercellular iron as
can be seen in Figure 4.

HFE knockout has been shown to impair the induction of hepcidin by iron in
mouse [27], and human [28] hepatocytes and this was seen in the computational
model as increasing transferrin bound iron did not induce hepcidin as strongly
in HFE knockdown.

Although an increase in transferrin receptor 2 was observed in the model
($1.77\mu M$ healthy; $2.80\mu M$ type 1 haemochromatosis), the up-regulation
was slightly smaller than the change observed in vivo [29]. This is due to the
model having fixed extracellular transferrin bound iron concentration, in
contrast to haemochromatosis where this concentration increases due to higher
absorption in the intestine.

Type 3 haemochromatosis results in similar phenotype as type 1
haemochromatosis, however the mutation is found in the TfR2 gene as opposed to
HFE. A virtual TfR2 knockdown mutation was performed by decreasing 100-fold
the rate constant of synthesis of TfR2 from the model. Model results were then
compared with the findings of Chua et al. [23]. The simulation showed a steady
state decrease of liver TfR1 from $0.29\mu M$ to $0.19\mu M$ with TfR2
knockdown. This is supported by an approximate halving of TfR1 levels in TfR2
mutant mice [23]. An increase in hepcidin and consequent decrease in
ferroportin as seen in mice was matched by the simulation.

An iron overload phenotype with increased intracellular iron is not recreated
by the model of the TfR2 mutant. This is, again, due to the fixed serum
transferrin-bound iron concentration, while in the whole body there would be
increased iron absorption from the diet through the effect of hepcidin.

#### Metabolic Control Analysis

Metabolic control analysis (MCA) is a standard technique to identify the
reactions that have the largest influence on metabolite concentrations or
reaction fluxes in a steady state [30, 31]. MCA is a special type of
sensitivity analysis and thus is used to quantify the distributed control of
the biochemical network. A control coefficient measures the relative change of
the variable of interest caused by a small change in the reaction rate (e.g. a
control coefficient can be interpreted as the percentage change of the
variable given a 1% change in the reaction rate).

The control over the concentration of the labile iron pool by each of the
model reactions can be seen in Table 5. The synthesis and degradation of TfR2,
TfR1, HFE and the formation of their complexes were found to have the highest
control over the labile iron pool. Synthesis and degradation of IRP was also
found to have some degree of control, but synthesis and degradation of
hepcidin have surprisingly a very small effect on the labile iron pool.

The control over the hepcidin concentration was also measured (Table 6), as
the ability to control hepatic hepcidin levels could provide therapeutic
opportunities to control whole system iron metabolism, due to its action on
other tissues. Interestingly, in addition to the expression and degradation of
hepcidin itself, the expression of HFE and degradation of HFETfR2 complex have
almost as much control over hepcidin. The expression of TfR2 has a
considerably lower effect, though still significant.

Flux control coefficients were also determined which indicate the control that
reactions have on a chosen reaction flux. The flux control coefficients for
the ferroportin mediated iron export reaction are given in Table 7. This
reaction is of particular interest as it is the only method of iron export,
therefore controlling this reaction rate could be important in treating
various iron disorders including haemochromatosis and anemia. The reactions of
synthesis and degradation of TfR1, TfR2 and HFE were found to have high
control, despite not having direct interactions with ferroportin. TfR1 and
TfR2 may show consistently high control due to having dual roles as iron
importers and iron sensors which control hepcidin expression.

A drawback of MCA, and any other local sensitivity analysis, is that it is
only predictive for small changes of reaction rates. However, the changes that
result in disease states are usually large, and experimental parameter
estimation can result in large uncertainty. Thus a global sensitivity analysis
was also performed following the method described in [32]. This calculates the
maximal and minimal values of the sensitivity coefficients within a large
space of parameter values. This technique is useful, for example, if there is
uncertainty about the values of the model parameters as it reveals the
possible range of control of each one given the uncertainty. All parameters
were allowed to vary within $\pm$ 10% and the maximal and minimal control
coefficients were measured (Tables 5, 6 and 7).

In terms of the control of the labile iron pool (Table 5), the reactions with
highest control in the reference steady state are still the ones with highest
control in the global case (i.e. when all parameters have an uncertainty of
$\pm 10\%$). However TfR1 expression, TfR1 binding, TfR1 degradation, IRP
expression and IRP degradation, which all have significant (but not the
highest) control in the reference state, could have very low control in the
global sense. On the other hand HFETfR2 degradation, hepcidin expression,
hepcidin degradation and TfR2 binding 2, have low control in the reference
steady state, but could have significant control in the global sense. All
other reactions have low control in any situation.

In the case of the control of hepcidin concentration (Table 6) the differences
between the reference state and the global are much smaller overall, and one
could only identify a few reactions that have moderate control in the
reference, but could have a bit less in the global sense (TfR2 expression,
TfR2 binding, and TfR2 iron internalisation).

In the case of the control of the flux of iron export (Table 7), we find some
reactions with high control in the reference that could have low control in
the global sense: TfR1 expression, TfR1 biding, TfR1 degradation, IRP
expression and IRP degradation. Hepcidin expression, hepcidin degradation, and
HFETfR2 degradation have almost no control in the reference, but in the global
sense they could exert considerable control. This is very similar to the
situation of the control of the labile iron pool.

Chifman et al. [16] analysed the parameter space of their core model of iron
metabolism in breast epithelial cells and concluded the system behavior is far
more dependent on the network structure than the exact parameters used. The
analysis presented here lends some support to that finding, since only a few
reactions could have different effect on the system if the parameters are
wrong. A further scan of initial conditions for metabolites found that varying
initial concentrations over 2 orders of magnitude had no affect on the steady
state achieved (Table 3), indicating that the steady state found in these
simulations is unique.

### Receptor Properties

It is known that the iron sensing by the transferrin receptors is responsive
over a wide range of intercellular iron concentrations [33]. The present model
reproduces this well (Figure 6A, $1\times$ turnover line). Becker et al.
argued that a linear response of a receptor to its signal over a wide range
could be achieved through a combination of: high receptor abundance, increased
expression when required, recycling to the surface of internalised receptors
and high receptor turnover [34]. This was illustrated with the behaviour of
the erythropoietin (EPO) receptor [34]. Since the present model contains
essentially the same type of reactions that can lead to such a behaviour,
simulations were carried out to investigate to what extent this linearity of
response is present here. In this case it is the response of the total amount
of all forms of TfR1 and TfR2 bound to Tf-Fe against the amount of Tf-
Fe_intercell that is important. A variable was created in the model to reflect
the total receptor response (see Material and Methods), and this variable was
followed in a time course response to an iron pulse (Figure 5A). The response
to the iron pulse is remarkably similar to the response of the EPO receptor to
EPO [34].

Becker et al. [34] reported that the linearity of EPO-R response, i.e. the
integral of the response curve, is increased by increasing turnover rate of
the receptor and this property was also observed in the simulation of TfR1
response (Figure 6). The range in which the iron response is linear is smaller
than that found for EPO (Figure 6). As TfR1’s half life in the model matches
the experimentally determined value [35] the non-linear receptor response seen
in the simulation is expected to be accurate. This suggests that TfR1 is a
poor sensor for high levels of intercellular iron. On the other hand TfR2 is
more abundant than TfR1 [35] and accordingly shows an increased linearity for
a greater range of intercellular iron concentrations (Figure 7). This suggests
the two transferrin receptors play different roles in sensing intercellular
iron levels with TfR2 providing a wide range of sensing and TfR1 sensing
smaller perturbations. The activation of TfR2 directly influences the
expression of hepcidin and therefore it is desirable for it to sense large
systemic imbalances. TfR1 does not modulate hepcidin expression itself instead
it plays a primary role as an iron transporter .

## Discussion

Iron is an essential element of life, in humans it is involved in oxygen
transport, respiration, biosynthesis, detoxification, and other processes.
Iron regulation is essential because iron deficiency results in debilitating
anemia, while iron excess leads to free radical generation and is involved in
many diseases [3]. It is clear that healthy life depends on tight regulation
of iron in the body. The mechanisms involved in iron absortion, transport,
storage and regulation form a complex biochemical network [6]. The liver has a
central role in the regulation of systemic iron metabolism through secretion
of the peptide hormone hepcidin.

Here we analysed the hepatic biochemical network involved in iron sensing and
regulation through a mathematical model and computer simulation. The model was
constructed mostly based on in vitro biochemical data, such as protein complex
dissociation constants. The model was then validated by comparison with
experimental data from multiple physiological studies at both steady state and
during dynamic responses. Where quantitative data were available the model
matched these well and also qualitatively recreated many findings from
clinical and experimental investigations. The simulation accurately modelled
the highly prevalent iron disorder haemochromatosis. The disease state was
simulated through altering a single parameter of the model and showed
quantitatively how an iron overload phenotype occurs in patients with a HFE
mutation.

Due to the limited availability of quantitative clinical data on human iron
metabolism, various other data sources, particularly from in vitro experiments
and animal models, were integrated for the parameterisation of this model.
This computational modelling effort constitutes a clinical translational
approach, enabling data from multiple sources to improve our understanding of
human iron metabolism. Several arguments could be raised to cast doubt on this
approach, such as the the failure of in vitro conditions to mimic those in
vivo or the difference between animal models and humans. This means that this
type of data integration must be carefully monitored in terms of establishing
the validity of the resulting model. Examining the behaviour of the model by
simulating it at different values of initial conditions or other parameters
(parameter scans) is important to establish the limits of utility of the
model. Global sensitivity analysis is another approach that determines the
boundaries of parameter variation that the model tolerates before it becomes
too distant from the actual system behaviour. Model validation is an essential
step in modelling. Validation should be carried out by enquiring if the model
is able to match experimental observations that were not used to calibrate it.
Here the model was validated by the simulation of haemochromatosis disease,
where the model behaviour matched the clinical data (Table 4).

The precise regulatory mechanism behind transferrin receptors and HFE
controlling hepcidin expression remains to be validated experimentally,
however the model presented here supports current understanding that the
interaction of TfR2 and HFE form the signal transduction pathway that leads to
the induction of hepcidin expression [36].

The global metabolic control analysis results support the identification of
the transferrin receptors, particularly TfR2, and HFE as potential therapeutic
targets; a result that is robust even to inaccuracies in parameter values.
Although hepcidin would be an intuitive point of high control of this system
(and therefore a good therapeutic target), in the present model this is not
the case. It seems that targeting the promoters of hepcidin expression may be
more desirable. However this conclusion has to be expressed with some
reservation that stems from the fact that the global sensitivity analysis
identified the hepcidin synthesis and degradation reactions in the group of
those with the largest uncertainty. By changing parameter values by no more
than 10% it would be possible to have the hepcidin expression and degradation
show higher control. So it seems important that the expression of hepcidin be
studied in more detail. We also predict that the control of hepcidin over the
system would be higher if the model had included the regulation of intestinal
ferroportin by hepatic ferroportin.

The global sensitivity analysis, however, allows taking strong conclusions
about the reactions for which the reference steady state is not much different
from the maximal and minimal values. It turns out that these are the reactions
that have the largest and the smallest control over the system variables. For
example, the reactions with greatest control on the labile iron pool and iron
export are those of the HFE-TfR2 system. But the reactions of the HFE-TfR1
system have always low control. These two conclusions are valid under a wide
range of parameter values.

Construction of this model required several assumptions to be made due to lack
of measured parameter values, as described in Material and Methods. These
assumptions may or may not have a large impact on the model behaviour, and it
is important to identify those that have a large impact, as their measurement
will improve our knowledge the most. Of all the assumptions made, the rates of
expression and degradation of ferroportin are those that have a significant
impact on the labile iron pool in the model (see Table 5). This means that if
the values assumed for these rate parameters were to be significantly
different the model prediction for labile iron pool behaviour would also be
different. The model is therefore also useful by suggesting experiments that
will optimally improve our knowledge about this system.

Limitations on the predictive power of the model occur due to the scope of the
system chosen. Fixed serum iron conditions, which were used as boundary
conditions in the model, do not successfully recreate the amplifying feedbacks
that occur as a result of hepcidin expression controlling enterocyte iron
export. To relieve this limitation, a more advanced model should include
dietary iron uptake and the action of hepcidin on that process.

The model predicts a quasi-linear response to increasing pulses of serum iron,
similar to what has been predicted for the erythropoietin system [34]. Our
simulations display response of the transferrin receptors to pulses of
extracellular transferrin-bound iron that is similar to the EPO-R response to
EPO (Figure 6). The integral of this response versus the iron sensed deviates
very little from linearity in the range of physiological iron (Figure 5).

Computational models are research tools whose function is to allow for
reasoning in a complex nonlinear system. The present model can be useful in
terms of predicting properties of the liver iron system. These predictions
form hypotheses that lead to new experiments. Their outcome will undoubtedly
improve our knowledge and will also either confirm the accuracy of the model
or refute it (in which case it then needs to be corrected). The present model
and its results identified a number of predictions about liver iron regulation
that should be investigated further:

  * •

changes in activity of the hepcidin gene in the liver have little effect on
the size of the labile iron pool,

  * •

the rate of expression of HFE has a high control over the steady state level
of hepcidin,

  * •

the strong effect of HFE is due to its interaction with TfR2 rather than TfR1,

  * •

the rate of liver iron export by ferroportin has a strong dependence on the
expression of TfR1, TfR2 and HFE,

  * •

the rate of expression of hepcidin is approximately linear with the
concentration of plasma iron within the physiological range.

The present model is the most detailed quantitative mechanistic model of
cellular iron metabolism to date, allowing for a comprehensive description of
its regulation. It can be used to elucidate the link from genotype to
phenotype, as demonstrated here with hereditary haemochromatosis. The model
provides the ability to investigate scenarios for which there are currently no
experimental data available — thus making predictions about the system and
aiding in experimental design.

## Materials and Methods

The model is constructed using ordinary differential equations (ODEs) to
represent the rate of change of each chemical species. COPASI [37] was used as
the software framework for model construction, simulation and analysis. Cell
Designer [38] was used for construction of a SBGN process diagram (Figure 1).

The model consists of 2 compartments representing the serum and the liver.
Concentrations of haeme and transferrin bound iron in the serum were fixed to
represent constant extracellular conditions. Fixed metabolites simulate a
constant influx of iron through the diet as any iron absorbed by the liver is
effectively replenished. A labile iron pool (LIP) consumption reaction is
added to represent various uses of iron and create a flow through the system.
Some of the LIP consumption reaction would be attributed to heme biosynthesis
however this process was not considered explicitly in this study to avoid
unnecessary complexity and because the bone marrow is the major site of heme
biosynthesis [39].

Initial concentrations for metabolites were set to appropriate concentrations
based on a literature survey (Table 1). All metabolites formed through complex
binding were set to zero initial concentrations (Table 1). The concentration
of a chemical species at a time point in the simulation is determined by
integrating the system of ODEs. For some proteins a half-life was available in
the literature, but sources could not be found for their synthesis rates
(translation). In this occurrence, estimated steady-state concentrations were
used from the literature and a synthesis rate was chosen such that at steady
state the concentration of the protein would be approximately accurate,
following Equation 1:

$\frac{d[\textrm{P]}}{dt}=+k-d[\textrm{P}]=0.$ (1)

This is solved for $k$ where $[\textrm{P}]$ is the steady-state concentration
of the protein and $d$ is the degradation rate obtained from the half-life
($\lambda$) using:

$d=\frac{\ln{2}}{\lambda}.$ (2)

Complex formation reactions, such as binding of TfR1 to Tf-Fe for iron uptake,
are modelled using the on and off binding constants as a forward and reverse
mass action reaction. For example:

$\textrm{TfR1}+\textrm{Tf-Fe}\rightleftharpoons\textrm{Tf-Fe-TfR1}$ (3)

is modelled using two reactions:

$\textrm{TfR1}+\textrm{Tf-Fe}\stackrel{{\scriptstyle
k_{a}}}{{\rightarrow}}\textrm{Tf-Fe-TfR1}$ (4)

$\textrm{Tf-Fe-TfR1}\stackrel{{\scriptstyle
k_{d}}}{{\rightarrow}}\textrm{TfR1}+\textrm{Tf-Fe}$ (5)

There is one ODE per each chemical species. The two reactions 4 and 5 add the
following terms to the set of ODEs:

$\begin{split}\frac{d[\textrm{TfR1}]}{dt}=&-k_{a}[\textrm{TfR1}][\textrm{TF-
Fe}]+k_{d}[\textrm{Tf-Fe-TfR1}]\ldots\\\ \frac{d[\textrm{Tf-
Fe}]}{dt}=&-k_{a}[\textrm{TfR1}][\textrm{TF-Fe}]+k_{d}[\textrm{Tf-Fe-
TfR1}]\ldots\\\ \frac{d[\textrm{Tf-Fe-
TfR1}]}{dt}=&+k_{a}[\textrm{TfR1}][\textrm{TF-Fe}]-k_{d}[\textrm{Tf-Fe-
TfR1}]\ldots\end{split}$ (6)

Intracellular haeme levels are controlled by a balance between uptake, export
and oxygenation. haeme import through the action of haeme carrier protein 1
(HCP1), export by ATP-binding cassette sub-family G member 2 (ABCG2) and
oxygenation by haeme oxygenase-1 (HO-1) follow Michaelis-Menten kinetics. HO-1
expression is promoted by haeme through by a Hill function (Equation (7)).

$\displaystyle v=[\textrm{S}]\cdot a\cdot$
$\displaystyle\left(\frac{[\textrm{M}]^{n_{H}}}{K^{n_{H}}+[\textrm{M}]^{n_{H}}}\right),$
(7) $\displaystyle v=[\textrm{S}]\cdot a\cdot$
$\displaystyle\left(1-\frac{[\textrm{M}]^{n_{H}}}{K^{n_{H}}+[\textrm{M}]^{n_{H}}}\right).$
(8)

Where $S$ is the substrate, $M$ is the modifier, $a$ is the turnover number,
$K$ is the ligand concentration which produces half occupancy of the binding
sites of the enzyme, and $n_{H}$ is the Hill coefficient. Values of $n_{H}$
larger than $1$ produce positive cooperativity (i.e. a sigmoidal response);
when $n_{H}=1$ the response is the same as Michaelis-Menten kinetics. A Hill
coefficient of $n_{H}=1$ was assumed unless there is literature evidence for a
different value. Where $K$ is not known it has been estimated to be of the
order of magnitude of experimentally observed concentrations for the ligand.

IRP/Iron-responsive elements (IRE) regulation is represented by Hill kinetics
using Equation (7) to simulate the 3’ binding of IRP promoting the translation
rate, and Equation (8) to represent the 5’ binding of IRP reducing the
translation rate. Ferroportin degradation is modelled using 2 reactions: one
representing the standard half-life and the other representing the hepcidin-
induced degradation. A Hill equation (Equation 7) is used to simulate the
hepcidin-induced degradation of ferroportin.

Hepcidin expression is the only reaction modelled using a Hill coefficient
greater than 1. Due to the small dynamic range of HFE-TfR2 concentrations a
Hill coefficient of 5 was chosen to provide the sensitivity required to
produce the expected range of hepcidin concentrations. The mechanism by which
HFE-TfR2 interactions induce hepcidin expression is not well understood, but
is thought to involve the mitogen-activated protein kinase (MAPK) signalling
pathway [40]. The stimulus/response curve of the MAPK cascade has been found
to be equivalent to a cooperative enzyme with a Hill coefficient of 4-5 [41],
making the steep Hill function appropriate to model hepcidin expression.

Ferritin modelling follows the work of Salgado et al. [14]. Iron from the LIP
binds to, and is internalised in, ferritin with mass action kinetics.
Internalised iron release from ferritin occurs through 2 reactions (intact
ferritin release and release due to ferritin degradation). The average amount
of iron internalised per ferritin affects the iron release rate and this is
modelled using Equation 9 (adapted from [14]):

$v=[\textrm{S}]\cdot
k_{\textrm{loss}}\cdot\left(1+\frac{0.048\cdot\frac{[\textrm{FT1}]}{[\textrm{FT}]}}{1+\frac{[\textrm{FT1}]}{[\textrm{FT}]}}\right).$
(9)

Where $S$ is internalised iron, $k_{\textrm{loss}}$ is the rate constant and
$[\textrm{FT1}]/[\textrm{FT}]$ is the ratio of iron internalised in ferritin
to total ferritin available. The value 0.0048 was obtained by dividing the
value given in Salgado et al. [14] by 50 as that simulation was scaled for 50
iron atom packages.

Iron is also released from ferritin when the entire ferritin cage is degraded.
The kinetics of ferritin degradation are mass action, however the amount of
iron released when a ferritin cage is degraded is an average based on ferritin
levels and total iron internalised in ferritin. Incorporating mass action and
ferritin saturation ratio gives the following rate law for
$\textrm{FT1}~{}\rightarrow~{}\textrm{LIP}$:

$v=[\textrm{S}]\cdot k\cdot\frac{[\textrm{FT1}]}{[\textrm{FT}]}.$ (10)

Iron export rate was modelled using Equation 7 with ferroportin as the
modifier and a Hill coefficient of 1. $K$ was assumed to be around the steady
state concentration of IRP ($1\mu M$). A rate (V) of
$40\textrm{pm}\cdot(10^{6}cells\cdot 5\textrm{min})^{-1}$ was used from Sarkar
et al. [42] and these values were substituted into the equation and solved for
$a$.

Ferroportin expression rates and degradation rates are poorly understood.
Ferroportin abundance data [43] lead to an estimate of ferroportin
concentration around $0.16\mu M$. The hepcidin induced degradation of
ferroportin is represented in the model by a rate law in the form of Equation
7 with a Hill coefficient $n_{H}=5$ (see above) and a $K^{n_{H}}$ equal to the
measured concentration of hepcidin [44] (see Table 1). We then assume a
maximal rate of degradation to be 1 $nMs^{-1}$, and using the steady state
concentration of ferroportin, the rate constant can be estimated as 0.0002315
$s^{-1}$. The ferroportin synthesis rate was then calculated to produce the
required steady-state concentration of ferroportin at the nominal hepcidin
concentration.

The HFE-TfR2 binding and dissociation constants were also not available and so
it was assumed that they were the same as those of TfR1-HFE. Finally, the HFE-
TfR and HFE-TfR2 degradation rates are also not known; we used a value that is
an order of magnitude lower than the half life for unbound TfR (i.e. we assume
the complex to be more stable than the free form of TfR).

Although DMT1 may contribute towards transferrin bound iron uptake in
hepatocytes this contribution has been found to be minor and DMT1 knockout has
little affect on iron metabolism [45], therefore DMT1 was not included in the
model.

The two iron response proteins (IRP1 and IRP2) which are responsible for
cellular iron regulation were modelled as a single metabolite in this study as
the mechanistic differences in their regulatory roles is poorly understood.
Equivalent regulation by both IRPs has been found in multiple studies [46, 47,
48].

Global sensitivity analysis was performed using the method proposed by Sahle
et al. [32], where all parameter values were allowed to vary within $\pm 10\%$
of their nominal value in the model and we search for the maximum and minimum
value that concentration- or flux-control coefficients of interest are able to
reach within that parameter space. The searches were carried out with the
particle swarm optimisation algorithm [49]. In order to process these
optimisations in a reasonable time a HTCondor [50] distributed computing
system was used, managed through the Condor-COPASI package [51].

To perform analysis of receptor response in a similar manner to the EPO system
studied by Becker et al. [34] initial conditions were adjusted to recreate a
similar virtual experiment. Haeme concentration was fixed at zero to isolate
transferrin bound iron uptake. The rate constant of the labile iron pool
depletion reaction was reduced to balance the reduced iron uptake (which
results in iron having a similar half-life to EPO in [34]). Initial
concentrations for all metabolites were set to steady-state concentrations
with the exception of the labile iron pool and iron bound to all receptors
which were set to zero. Extracellular transferrin bound iron was allowed to
vary and set at increasing concentrations to determine receptor response. Time
courses were calculated for Tf-Fe-TfR1, 2(Tf-Fe)-TfR1, Tf-Fe-TfR2 and 2(Tf-
Fe)-TfR2 as iron binds its two receptors in a two-staged process. Two new
variables were defined in COPASI which integrated the results of the time
courses corresponding to the two receptors (in their different ligand states):

$\textrm{Int\\_TfR1\\_binding}=\int[\textrm{Tf\\-Fe\\-TfR1}]\cdot
dt+\int[\textrm{2(Tf\\-Fe)\\-TfR1}]\cdot dt,$ (11)

$\textrm{Int\\_TfR2\\_binding}=\int[\textrm{Tf\\-Fe\\-TfR2}]\cdot
dt+\int[\textrm{2(Tf\\-Fe)\\-TfR2}]\cdot dt.$ (12)

## Acknowledgments

We thank Steve Ackman, Douglas Kell, Reinhard Laubenbacher, Frank Torti and
Suzy Torti for many discussions. We thank Ed Kent and the EPS IT Research
Services staff for help with running the HTCondor pool. We also thank Anthony
West for sharing binding data for HFE, TfR1 and TfR2. SM is grateful to the
Virginia Bioinformatics Institute and the Wake Forest University Department of
Cancer Biology for hosting visits.

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## Figure Legends

Figure 1:  SBGN process diagram of human liver iron metabolism model. The
compartment with yellow boundary represents the hepatocyte, while the
compartment with pink boundary represents plasma. Species overlayed on the
compartment boundaries represent membrane-associated species. Abbreviations:
Fe: iron, FPN1: ferroportin, FT: ferritin, HAMP: hepcidin, haeme:
intracellular haeme, haeme_intercell: plasma haeme, HFE: human
haemochromatosis protein, HO-1: haeme oxygenase 1, IRP: iron response protein,
LIP: labile iron pool, Tf-Fe_intercell: plasma transferrin-bound iron, TfR1:
transferrin receptor 1, TfR2: transferrin receptor 2. Complexes are
represented in boxes with the component species. In the special case of the
ferritin-iron complex symbol, the amounts of each species are not in
stoichiometric amounts (since there are thousands of iron ions per ferritin).
Figure 2:  Simulated time course concentrations of hepcidin in response to
changing serum transferrin-bound iron levels. The model shows similar dynamics
to time course samples from patients measured by mass spectrometry and ELISA
by Girelli et al., 2011 [24]. Hereditary haemochromatosis simulations show
reduced hepcidin levels and peak response compared to WT (Wild Type). Figure
3:  Simulated steady state concentrations of metabolites in response to
increasing serum Tf-Fe. Increasing HFE-TfR2 complex as a result of HFE-TfR1
reduction induces increased hepcidin.  Figure 4:  Ferroportin expression rate
in the model doubles in response to changing serum iron concentrations as
verified experimentally. HFE knock-down (HH) simulations and WT simulation of
Fe-Tf against ferroportin (Fpn) expression.  Figure 5:  Iron and Epo receptors
show a similar response following an impulse of ligand. Ligand receptor
binding for iron shows a distinctive curve which closely resembles EPO
receptor binding studied by Becker et al. 2010 [34] (their Fig. 2B). Figure 6:
Increasing receptor turnover increases the linearity of the response for
transferrin receptor 1. The range of linear response for the transferrin
receptor depends on its half-life. This effect was first demonstrated in the
EPO receptor by Becker et al. 2010 [34] who found similar behavior (their Fig.
4D). Figure 7:  TfR2 response versus intercellular transferrin-bound iron. The
response is approximately linear over a wide range of intercellular iron
concentrations.

## Tables

Table 1:  Initial Conditions. Initial concentrations of all metabolites and the source for their value. Parameter | Initial Concentration (mol/l) | Source
---|---|---
LIP | 1.3E-6 | [52]
FPN1 | 1E-9 |
IRP | 1.16E-06 | [53]
HAMP | 5E-9 | [44]
haeme | 1E-9 |
2(Tf-Fe)-TfR1_Internal | 0 |
2(Tf-Fe)-TfR2_Internal | 0 |
Tf-Fe-TfR2_Internal | 0 |
Tf-Fe-TfR1_Internal | 0 |
Tf-TfR1_Internal | 0 |
Tf-TfR2_Internal | 0 |
Fe-FT | 0 |
FT | 1.66E-10 | [54]
HO-1 | 3.56E-11 | [55]
FT1 | 0 |
Tf-Fe_intercell | 5E-6 | fixed, [56]
TfR | 4E-7 | [35]
Tf-Fe-TfR1 | 0 |
HFE | 2e-07 | [35]
HFE-TfR | 0 |
HFE-TfR2 | 0 |
Tf-Fe-TfR2 | 0 |
2(Tf-Fe)-TfR1 | 0 |
2HFE-TfR | 0 |
2HFE-TfR2 | 0 |
2(Tf-Fe)-TfR2 | 0 |
TfR2 | 3E-6 | [35]
haeme_intercell | 1e-07 | [57]

Table 2: Reactions, rate laws and kinetic constant values. Name |  Reaction |  Rate law |  Parameters | Source
---|---|---|---|---
Fpn Export |  LIP $\to$ Tf-Fe_intercell; FPN1 |  Hill Function $\to$ |  a=15 mol s-1, $n_{H}=1$, k=1E-6 mol | [42]
TfR1 expression |  $\to$ TfR; IRP |  Hill Function $\to$ |  a=6e-12 s-1, $n_{H}=1$, k=1e-6 mol | [35]
TfR1 degradation |  TfR $\to$ |  Mass action |  k=8.37e-06 s-1 | [56]
Ferroportin Expression |  $\to$ FPN1; IRP |  Hill Function -$|$ |  a=4e-9 s-1, $n_{H}=1$, $K=$1e-6 mol |
IRP expression |  $\to$ IRP; LIP |  Hill Function -$|$ |  a=4e-11 s-1, $n_{H}=1$, K=1e-6 mol | [58]
IRP degradation |  IRP $\to$ |  Mass action |  k = 1.59e-5 s-1 | [58]
Fpn degradation Hepc |  FPN1 $\to$ ; HAMP |  Hill Function $\to$ |  a=2.315E-5 s-1, $n_{H}=1$, K=1e-9 mol |
HFE degradation |  HFE $\to$ |  Mass action |  k = 6.418e-5 s-2 | [59]
HFE expression |  $\to$ HFE |  Constant flux |  v = 2.3469e-11 mol (l $\cdot$ s)-1 | [59]
TfR2 expression |  $\to$ TfR2 |  Constant flux |  v = 2e-11 mol (l $\cdot$ s)-1 | [35]
TfR2 degradation |  TfR2 $\to$ ; Tf-Fe_intercell |  Hill Function -$|$ |  a=3.2e-05 s-1, $n_{H}=1$, K=2.5e9 mol | [35]
Hepcidin expression |  $\to$ HAMP; 2HFE-TfR2 2(Tf-Fe)-TfR2 |  Hill Function $\to$ |  a=5e-12 s-1, $n_{H}=5$, K=1.35e-07 mol, a=5e-12 mol s-1, K=6e-7 mol | [44]
Hepcidin degradation |  HAMP $\to$ |  Mass action |  k = 9.63e-05 s-1 | [60]
Heme oxygenation |  Heme $\to$ LIP; HO-1 |  Henri-Michaelis-Menten |  kcat=17777.7 s-1, Km=2e-6 mol l-1 | [61]
HFE TfR1 binding |  HFE + TfR $\to$ HFE-TfR |  Mass action |  k = 1.102e+06 l (mol $\cdot$ s)-1 | [62]
HFE TfR1 release |  HFE-TfR $\to$ HFE + TfR |  Mass action |  k = 0.08 s-1 | [62]
TfR1 binding |  Tf-Fe_intercell + TfR $\to$ Tf-Fe-TfR1 |  Mass action |  k = 837400 l (mol $\cdot$ s)-1 | [62]
TfR1 release |  Tf-Fe-TfR1 $\to$ Tf-Fe_intercell + TfR |  Mass action |  k = 9.142e-4 s-1 | [62]
HFE TfR2 binding |  $2*$HFE + TfR2 $\to$ 2HFE-TfR2 |  Mass action |  k = 3.9438e+11 l2 (mol2 $\cdot$ s)-1 |
HFE TfR2 release |  2HFE-TfR2 $\to$ 2 * HFE + TfR2 |  Mass action |  k = 0.0018 s-1 |
TfR2 binding |  Tf-Fe_intercell + TfR2 $\to$ Tf-Fe-TfR2 |  Mass action |  k = 222390 l (mol $\cdot$ s)-1 | [62]
TfR2 release |  Tf-Fe-TfR2 $\to$ Tf-Fe_intercell + TfR2 |  Mass action |  k = 0.0061 s-1 | [62]
TfR1 binding 2 |  Tf-Fe-TfR1 + Tf-Fe_intercell $\to$ 2(Tf-Fe)-TfR1 |  Mass action |  k = 121400 l (mol $\cdot$ s)-1 | [62]
TfR1 release 2 |  2(Tf-Fe)-TfR1 $\to$ Tf-Fe-TfR1 + Tf-Fe_intercell |  Mass action |  k = 0.003535 s-1 | [62]
HFE TfR1 binding 2 |  HFE-TfR + HFE $\to$ 2HFE-TfR |  Mass action |  k = 1.102e+06 l (mol $\cdot$ s)-1 | [62]
HFE TfR1 release 2 |  2HFE-TfR $\to$ HFE-TfR + HFE |  Mass action |  k = 0.08 s-1 | [62]
TfR2 binding 2 |  Tf-Fe-TfR2 + Tf-Fe_intercell $\to$ 2(Tf-Fe)-TfR2 |  Mass action |  k= 69600 l (mol $\cdot$ s)-1 | [62]
TfR2 release 2 |  2(Tf-Fe)-TfR2 $\to$ Tf-Fe-TfR2 + Tf-Fe_intercell |  Mass action |  k = 0.024 s-1 | [62]
TfR1 iron internalisation |  2(Tf-Fe)-TfR1 $\to$ 4(LIP) + TfR |  Mass action |  k = 0.8333 l$\cdot$s-1 | [63]
TfR2 iron internalisation |  2(Tf-Fe)-TfR2 $\to$ 4(LIP)-TfR2 |  Mass action |  k = 0.8333 l$\cdot$s-1 | [63]
outFlow |  LIP $\to$ |  Mass action (irreversible) |  k = 4e-04 s-1 |
Ferritin Iron binding |  LIP + FT $\to$ Fe-FT |  Mass action |  k = 4.71e+10 l (mol $\cdot$ s)-1 | [14]
Ferritin Iron release |  Fe-FT $\to$ LIP + FT |  Mass action |  k = 22922 s-1 | [14]
Ferritin Iron internalisation |  Fe-FT $\to$ FT1 + FT |  Mass action |  k = 108000 s-1 | [14]
Ferritin internalised iron release |  FT1 $\to$ LIP; FT1 FT |  Kloss Hill |  kloss = 13.112 s-1 | [14]
ferritin expression |  $\to$ FT; IRP |  Hill Function -$|$ |  a=2.312e-13 s-1, $n_{H}=1$, K=1e-06 mol | [54]
HO1 Degradation |  HO-1 $\to$ |  Mass action |  k= 3.209e-05 s-1 | [64]
HO1 Expression |  $\to$ HO-1; Heme |  Hill Function $\to$ |  a=2.1432e-15 s-1, K=1e-9 mol | [65]
Ferritin Degradation Full |  FT $\to$ |  Mass action |  k = 1.203e-05 s-1 | [14]
Heme uptake |  Heme_intercell $\to$ Heme |  Henri-Michaelis-Menten |  Km=1.25e-4 mol, v=1.034e-5 mol s-1 | [66]
Heme export |  Heme $\to$ Heme_intercell |  Henri-Michaelis-Menten |  Km=1.78e-05 mol, v=2.18e-5 mol s-1 | [67]
Ferritin Degradation Full Iron Release |  FT1 $\to$ LIP; FT1 FT |  Mass Action Ferritin |  k=1.203e-05 s-1 | [14]
HFE-TfR degradation |  2HFE-TfR $\to$ |  Mass action |  k=8.37e-07 s-1 |
HFE-TfR2 degradation |  2HFE-TfR2 $\to$ |  Mass action |  k=8.37e-07 s-1 |
Continued on next page
Table 3:  Steady State Validation — Comparison between model and experimental observations. IRP, Ferritin and TfR are expressed in particles per cell assuming a cellular volume of $10^{-12}$ l. Iron per Ferritin is a ratio.  Metabolite | Model | Experimental | Reference
---|---|---|---
Labile Iron Pool | $0.804\mu M$ | $0.2-1.5\mu M$ | [52]
Iron Response Protein |  $836000$ cell-1 |  $\sim 700000$ cell-1 | [68]
Ferritin |  $4845$ cell-1 |  $3000-6000$ cell-1 (mRNA), $2.5-54600$ cell-1(protein) |  [68], [69]
TfR |  $1.74\times 10^{5}$ cell-1 |  $1.6-2\times 10^{5}$ cell-1 | [70]
TfR2 | $4.63\times\left[\textrm{TfR1}\right]$ | $4.5-6.1\times\left[\textrm{TfR1}\right]$ | [35]
Iron per Ferritin | 2272 average |  2400 | [71]
Hepcidin |  $5.32$nM |  $3.5-8.3$nM | [72]
Reaction | Model | Experimental | Reference
TBI import rate |  $2.67\mu M$ s-1 |  $2.08\mu M$ s-1 | [23]
Table 4:  HFE Knockout Validation — The simulation of type-1 hereditary haemochromatosis closely matches experimental findings at steady state. Metabolite | Model | Experiment | Reference
---|---|---|---
IRP | - | - | [73]
LIP | + | + | [73]
HAMP | - | - | [74]
TfR2 | + | + | [29]
Reaction | Model | Experimental | Reference
TfR1/2 iron import | + | + | [73]
FT expression | + | + | [73]
TfR expression | - | - | [73]
FPN expression | $\approx$ | = | [27]
Table 5:  Metabolic Control Analysis — Concentration control coefficients for the labile iron pool. Reaction | Local | Global
---|---|---
Minimum | Maximum
TfR2 expression | 0.894573 | 0.515971 | 1.41255
Fpn Export | -0.825483 | -0.924 | -0.698754
TfR2 binding | 0.569815 | 0.298433 | 0.901285
TfR2 degradation | -0.563132 | -0.898362 | -0.293111
Fpn degradation | 0.351397 | 0.186176 | 0.50289
Ferroportin Expression | -0.351397 | -0.502317 | -0.176245
HFE expression | -0.313525 | -0.623067 | 0.346532
TfR1 expression | 0.259758 | 0.0652 | 0.496352
TfR1 binding | 0.259436 | 0.06577 | 0.497636
TfR1 degradation | -0.258004 | -0.503067 | -0.0657364
IRP expresion | 0.209893 | 0.0748546 | 0.300039
IRP degradation | -0.209893 | -0.347477 | -0.0753367
HFE-TfR2 degradation | -0.0341692 | -0.684936 | 0.000229851
Hepcidin expression | 0.0283652 | 0.0004375 | 0.6553120
Hepcidin degradation | -0.0283652 | -0.791216 | -0.000576136
HFE degradation | 0.0162284 | -0.0259426 | 0.0386967
TfR2 binding 2 | 0.0100938 | 0.298433 | 0.901285
TfR2 release | -0.0100938 | -0.0194113 | -0.00434313
HFE TfR2 binding | -0.00668253 | -0.0187053 | 0.0218869
HFE TfR2 release | 0.0063856 | -0.0205303 | 0.018034
TfR2 iron internalisation | -0.00335169 | -0.156882 | 0.000557494
HFE TfR1 binding | -0.00143167 | -0.0120993 | 0.0000742
HFE TfR1 release | 0.00143166 | 0.0000760 | 0.0121124
HFE TfR1 binding 2 | -0.00143166 | -0.0121238 | -0.0000739
HFE TfR1 release 2 | 0.00143165 | 0.0000738 | 0.0121135
HFE-TfR degradation | -0.00143165 | -0.0121249 | -0.0000737
Table 6:  Metabolic Control Analysis — Concentration control coefficients for hepcidin. Reaction | Local | Global
---|---|---
Minimum | Maximum
Hepcidin expression | 1.00002 | 0.512257 | 1.487664
Hepcidin degradation | -1.00002 | -1.00027 | -0.999001
HFE-TfR2 degradation | -0.956041 | -1.3943 | -0.380497
HFE expression | 0.9131 | 0.274035 | 1.30051
TfR2 expression | 0.243052 | 0.0984356 | 0.486305
TfR2 degradation | -0.153001 | -0.293528 | -0.0638787
TfR2 binding | 0.128436 | 0.0558287 | 0.273304
TfR2 iron internalisation | -0.128062 | -0.272967 | -0.0557919
HFE degradation | -0.047263 | -0.102578 | -0.0122656
HFE TfR2 binding | 0.0245645 | 0.00630724 | 0.0573883
HFE TfR2 release | -0.023473 | -0.0557905 | -0.00602681
TfR2 binding 2 | 0.00227514 | 0.000811688 | 0.00589495
TfR2 release | -0.00227514 | -0.00589437 | -0.000812498
HFE TfR1 binding | -0.00093303 | -0.00728765 | -5.22895e-05
HFE TfR1 release | 0.000933028 | 4.84169e-05 | 0.00697082
HFE TfR1 binding 2 | -0.000933028 | -0.0073373 | -5.31758e-05
HFE TfR1 release 2 | 0.000933018 | 5.3417e-05 | 0.00731269
HFE-TfR degradation | -0.000933018 | -0.00733725 | -5.69006e-05
TfR1 expression | -0.000796332 | -0.00607511 | -4.36181e-05
TfR1 degradation | 0.000790955 | 4.53395e-05 | 0.00623214
IRP expresion | -0.000544238 | -0.00281211 | -4.71681e-05
IRP degradation | 0.000544238 | 4.16666e-05 | 0.00351147
Fpn export | -0.00045206 | -0.00277642 | -4.33404e-05
Fpn degradation | 0.000192436 | 1.47897e-05 | 0.00153538
Ferroportin expression | -0.000192436 | -0.00153463 | -1.41905e-05
TfR1 binding | 0.000142075 | 3.78713e-06 | 0.00137383
TfR2 release 2 | -6.36921e-05 | -0.000176906 | -2.18216e-05
Table 7:  Metabolic Control Analysis — Flux-control coefficients for the iron export out of the liver compartment. Reaction | Local | Global
---|---|---
Minimum | Maximum
TfR2 expression | 0.910944 | 0.449405 | 1.38521
TfR2 binding | 0.581149 | 0.285737 | 0.867434
TfR2 degradation | -0.573438 | -0.858215 | -0.278218
HFE expression | -0.353566 | -0.669513 | -0.187987
TfR1 expression | 0.266964 | 0.0676606 | 0.510467
TfR1 binding | 0.266601 | 0.0675083 | 0.51963
TfR1 degradation | -0.265162 | -0.51689 | -0.0669265
IRP expresion | 0.182446 | 0.063823 | 0.310888
IRP degradation | -0.182446 | -0.313848 | -0.0656558
Fpn Export | 0.151719 | 0.0626056 | 0.271594
Ferroportin Expression | 0.0645849 | 0.0189112 | 0.149717
Fpn degradation | -0.0645849 | -0.149993 | -0.0189094
HFE degradation | 0.0183009 | 0.00812358 | 0.0401559
TfR2 release | -0.0102946 | -0.018781 | -0.00414945
TfR2 binding 2 | 0.0102946 | 0.00414543 | 0.0187846
HFE TfR2 binding | -0.0077113 | -0.0191638 | 0.00292511
HFE TfR2 release | 0.00736866 | -0.00282598 | 0.0186586
Hepcidin expression | -0.00521336 | -0.1785377 | -0.0000387334
Hepcidin degradation | 0.00521336 | 5.77312e-05 | 0.224586
HFE-TfR2 degradation | -0.00226218 | -0.0183295 | 0.19571
HFE TfR1 binding | -0.00143917 | -0.0119501 | -7.50839e-05
HFE TfR1 release | 0.00143917 | 7.49065e-05 | 0.0119095
HFE TfR1 binding 2 | -0.00143917 | -0.0114124 | -7.49686e-05
HFE TfR1 release 2 | 0.00143915 | 7.49046e-05 | 0.0116242