Mitochondrial Iron-Sulfur Cluster Activity and Cytosolic Iron Regulate Iron Traffic in Saccharomyces cerevisiae*

Background: A mathematical model of iron trafficking and regulation in yeast cells was developed. Results: The model simulated experimental data from the literature fairly well. Conclusion: Both cytosolic iron and an exported product of mitochondrial iron-sulfur cluster activity appear to regulate iron traffic. Significance: The model has some predictive power that can be used to probe the mechanism of mitochondrial iron diseases. An ordinary differential equation-based mathematical model was developed to describe trafficking and regulation of iron in growing fermenting budding yeast. Accordingly, environmental iron enters the cytosol and moves into mitochondria and vacuoles. Dilution caused by increasing cell volume is included. Four sites are regulated, including those in which iron is imported into the cytosol, mitochondria, and vacuoles, and the site at which vacuolar FeII is oxidized to FeIII. The objective of this study was to determine whether cytosolic iron (Fecyt) and/or a putative sulfur-based product of iron-sulfur cluster (ISC) activity was/were being sensed in regulation. The model assumes that the matrix of healthy mitochondria is anaerobic, and that in ISC mutants, O2 diffuses into the matrix where it reacts with nonheme high spin FeII ions, oxidizing them to nanoparticles and generating reactive oxygen species. This reactivity causes a further decline in ISC/heme biosynthesis, which ultimately gives rise to the diseased state. The ordinary differential equations that define this model were numerically integrated, and concentrations of each component were plotted versus the concentration of iron in the growth medium and versus the rate of ISC/heme biosynthesis. Model parameters were optimized by fitting simulations to literature data. The model variant that assumed that both Fecyt and ISC biosynthesis activity were sensed in regulation mimicked observed behavior best. Such “dual sensing” probably arises in real cells because regulation involves assembly of an ISC on a cytosolic protein using Fecyt and a sulfur species generated in mitochondria during ISC biosynthesis and exported into the cytosol.

associated with respiratory complexes is reduced ϳ3-fold (implying a decline from ϳ600 to 200 M in iron). In contrast, the concentrations of nonheme high spin (NHHS) Fe II ions, NHHS Fe III ions, and Fe III phosphate oxyhydroxide nanoparticles are increased to ϳ130, 100, and 200 M, respectively. These latter three pools are probably related through redox and ligand exchange reactions.
Vacuoles are another iron traffic hub in yeast. These acidic organelles dynamically store and mobilize iron. They are devoid of iron under iron-deficient conditions. Vacuoles from cells grown on iron-sufficient medium contain high concentrations of a NHHS Fe III complex in which the coordinating ligands are closely related to polyphosphate (6). A NHHS Fe II species evident in Mössbauer spectra of adenine-deficient whole cells may also be located in vacuoles (7). Under adeninesufficient conditions in which the vacuolar iron importer Ccc1 is either absent or overproduced, high levels of Fe II are present (6).
Mössbauer spectra of whole yeast cells exhibit major contributions from both traffic hubs (8). In iron-sufficient WT cells, vacuolar iron exhibits a sextet that accounts for ϳ70% of spectral intensity. Much of the remaining intensity arises from mitochondrial iron, including a central quadrupole doublet that arises from [Fe 4 S 4 ] 2ϩ clusters and low spin Fe II hemes and quadrupole doublets that arise from high spin Fe II heme and NHHS Fe II ions. The intensity of the NHHS Fe II doublet in whole cell spectra is greater than can be accounted for by Fe II ions in mitochondria alone; Fe II cyt and vacuolar Fe II ions probably also contribute.
We define iron-deficient conditions as minimal medium supplemented with bathophenanthroline disulfonate and 1 M 57 Fe III citrate. We define iron-sufficient conditions as the same medium supplemented with 10 -40 M 57 Fe III citrate, and iron excess conditions as the medium supplemented with Ն100 M 57 Fe III citrate. Other researchers might use different media and supplement with Fe II rather than Fe III ions, making quantitative comparisons difficult.
In our studies, the overall concentration of iron in cells grown on iron-deficient, iron-sufficient, and iron excess conditions is ϳ 200, 400, and 600 M iron, respectively. Iron-deficient cells are largely devoid of vacuolar iron; their Mössbauer spectra are dominated by the central doublet and an unusually strong NHHS Fe II doublet (5). Mitochondria isolated from iron-deficient cells contain less iron than do mitochondria from iron-sufficient or iron-excess ones (ϳ400 M versus 700 -800 M), but they contain similar levels of respiration-related ISCs and heme centers. This has ramifications for the mechanism of iron regulation.
Fe cyt is trafficked into the mitochondria via two paralogous inner membrane transporters, namely Mrs3 and Mrs4 (Mrs3/4) (9,10). Imported mitochondrial NHHS Fe II ions are primarily used for heme and ISC biosynthesis. At higher [Fe med ], Fe cyt is also trafficked into vacuoles through the Ccc1 importer (11,12). These are the major iron traffic patterns in a yeast cell (Fig. 1). There are other secondary import and trafficking pathways but they will be ignored here.
The best studied mechanism of iron regulation in S. cerevisiae involves Aft1 and Aft2 (13)(14)(15)(16). These transcriptional acti-vators control expression of 20 -30 genes known as the "iron regulon," including, but not limited to genes FET3, FTR1, FET5, FTH1, SMF3, ISU1, GRX4, MRS4, and CTH2. Aft1 and Aft2 have slightly different functions (13,17), but these differences will be ignored here. In iron-deficient cells, Aft1/2 monomers are located in the nucleus (18) where they are bound to promotor sites and serve to activate the iron regulon. Under ironsufficient and iron-excess conditions, Aft1/2 release from these sites, exit the nucleus, and dimerize, thereby deactivating the iron regulon. Aft1/2 dimers bind a Fe 2 S 2 cluster that bridges the two subunits (19). These events are part of a signal transduction regulatory pathway that originates in mitochondria (Fig. 2).
The form of iron sensed by Aft1/2 has been considered since the mid 1990s, when Yamaguchi-Iwai et al. (13,14) monitored Aft1 activity using Fet3 expression as a reporter. Fet3 expression increases under iron-deficient conditions relative to ironsufficient ones (supplemental Table S1 and Ref. 46). The Aft1/ 2-dependent regulatory system was initially assumed to sense Fe cyt (11)(12)(13)(14), but the situation changed starting in circa 2004 when Kaplan, Winge, and co-workers (3) determined that Aft1/ 2-dependent iron regulation was sensitive to ISC biosynthesis in the matrix of mitochondria rather than to Fe cyt .
Deleting proteins that are involved in mitochondrial ISC biosynthesis, such as Yfh1, Atm1, and Yah1, affords an unusual phenotype that has been characterized extensively and has been used to probe the mechanism of Aft1/2-based regulation (20 -22). The so-called ISC mutant phenotype includes the (a) increase of cytosolic and mitochondrial iron import rates, (b) accumulation of Fe III phosphate oxyhydroxide nanoparticles in mitochondria, (c) decline of both ISCs and hemes in mitochondria, (d) increase of ROS damage in mitochondria, (e) absence of vacuolar iron in cells grown on iron-sufficient media, and (f) increase of cytosolic iron levels.
These effects are absent when ISC mutant cells are grown anaerobically (21,22). The iron regulon is active in such mutant cells, even when grown on high [Fe med ]. The discovery that FIGURE 1. Chemical model of iron trafficking and regulation in S. cerevisiae. Nutrient Fe III citrate (N) becomes cytosolic Fe II (C) as it enters the cell. C moves into the vacuole forming F2 (Fe II ), which oxidizes to Fe III (F3) and converts into nanoparticles (VP). C also moves into mitochondria, forming FM (Fe II ), which is used to generate FS. This component symbolizes ISCs and heme centers. FS is inserted into respiratory complexes, which function to maintain an O 2 -free environment in healthy mitochondria. Some O 2 that diffuses into the matrix reacts with FM to generate mitochondrial nanoparticles and ROS. Red dots indicate the four regulated sites.
[Fe cyt ] is not low in ISC mutant cells (23) raised the possibility that Fe cyt may not be sensed in cellular iron regulation.
An elaborate scenario has developed to explain how a signal originating in mitochondria can be relayed to Aft1/2 in the nucleus (Fig. 2). Atm1, an ATP-binding cassette half-transporter on the inner membrane of mitochondria, is thought to export a sulfur-containing by-product of ISC assembly called "X-S" (24,25). The identity of X-S is unknown, but it is thought to pass through a cavity sized for a small metabolite such as glutathione persulfide (26). X-S provides the sulfur required for cytosolic ISC biosynthesis and indirectly controls Aft1/2 activity and the iron regulon. The sulfur is probably used to build the Fe 2 S 2 cluster that bridges a homodimer of Grx3/4 in the cytosol (27). These monothiol glutaredoxins are critical for Aft1/2-dependent regulation. The absence of Grx3/4 activates the iron regulon (28) as this disrupts the signal transduction pathway. Fra2 reacts with the Grx⅐Fe 2 S 2 ⅐Grx homodimer to generate a Grx⅐Fe 2 S 2 ⅐Fra2 heterodimer (19,28,29). This heterodimer donates its Fe 2 S 2 cluster to two Aft1/2 monomers to generate the Aft⅐Fe 2 S 2 ⅐Aft homodimer, titrating away apo-Aft1/2 monomers that would otherwise bind tightly to iron regulon promotor sites on DNA. In this way, ISC biosynthesis in mitochondria controls the activity of the iron-regulon in the nucleus.
Iron traffic into and out of vacuoles is also highly regulated, with Yap5 playing the dominant role (30). This iron-sensitive transcription factor is constitutively expressed in the nucleus where it is bound to the promoters of CCC1 (and other genes) to regulate expression (Fig. 2). Earlier studies suggested that Yap5 senses Fe cyt (31), but a later study (4) found that it senses mitochondrial ISC synthesis activity. When ISC synthesis is blocked, Yap5 transcription levels decline, and vacuoles no longer fill with iron (31). However, Yap5 is not controlled by Aft1/2, and the Yap5 signaling pathway does not involve Grx proteins. Yap5 contains seven cysteine residues that are used in iron sensing. Under high iron conditions, Yap5 uses them to bind two Fe 2 S 2 clusters (32). This alters the conformation of the protein such that it binds DNA and promotes CCC1 expression.
Fet5 and Fth1, respective homologs of Fet3 and Ftr1, are also involved in regulating vacuolar iron. The Fet5⅐Fth1 complex on the vacuolar membrane exports iron to the cytosol. Expression levels of FET5 and FTH1 increase under iron-deficient conditions because they are part of the iron regulon (33). SMF3 is another iron exporter on the vacuolar membrane and is also part of the Aft1/2 system (15). Aft1/2-dependent activation under extreme iron-deficient conditions increases expression of CTH2 (31). Cth2 binds to and destabilizes CCC1 mRNA transcripts (34) preventing vacuoles from importing Fe cyt .
Iron traffic into mitochondria is also regulated. Deleting MRS3/4 affords mitochondria with reduced ISC and heme activities and lower iron concentrations (9,10). Although the exact species imported by Mrs3/4 is/are unknown, members of this family transport small metabolites and cofactors (35). ⌬MRS3/4 cells acquire more than normal amounts of iron because the Aft1/2-dependent iron regulon is activated due to low ISC activity (9,10). Mrs4 expression in ⌬YFH1 cells is higher than in WT cells, indicating an up-regulation of mitochondrial iron import under ISC mutant conditions. Activating Aft1/2 under iron-deficient conditions also enhances MRS4 expression (17).
Cells lacking Ccc1 are sensitive to high iron levels in the medium because Fe cyt , which most likely engages in ROS-generating chemistry, is probably present at higher than normal concentrations. Overexpressing Mrs3/4 suppresses that sensitivity probably because it imports more Fe cyt into mitochondria (36). Cells lacking Mrs3/4 up-regulate Ccc1 activity-evidence of what Kaplan calls a "mitochondrial vacuolar" signaling pathway (36).

Materials and Methods
A chemical model was developed to describe trafficking and regulation of iron in yeast cells (Fig. 1); reactions and rate expressions are listed in Table 1. Relevant data were obtained from WT and ISC mutant cells grown in batch culture under iron-deficient, iron-sufficient, and iron excess conditions (supplemental Tables S1 and S2). Cells in these studies were generally harvested during exponential phase.
The concentrations of iron-containing components in exponentially growing cells should be invariant with time. In an expanding steady state, the increase in cellular iron caused by iron influx is counterbalanced by the dilution of cellular iron caused by increasing cell volume. The exponential growth rate of the cell, defined as ␣ ϭ (1/V) ϫ (dV/dt), is an essential aspect FIGURE 2. Iron regulation pathways in S. cerevisiae. ISC assembly in mitochondria is thought to generate a sulfur-based species called X-S that is exported from the organelle, possibly through Atm1. X-S and Fe cyt combine in the cytosol to generate a Fe 2 S 2 cluster bridged between two glutaredoxin monomers (red star). This reaction is proposed to be the origin of Dual regulation. In the Aft1/2 signaling pathway (purple symbols) and under iron-sufficient conditions, the cluster is passed to Aft1/2 (via Fra2), which prevents activation of the iron regulon in the nucleus. Under iron-deficient conditions, cluster-free monomeric Aft1/2 activates the iron regulon including the Fet3/ Ftr1 importer on the plasma membrane. Cth2, Fet5, and Smf3 are also regulated to control vacuole iron levels. Less is known about Yap signaling pathway (red symbols). An ISC is likely built on an unknown protein and transferred eventually to Yap5. Cluster-bound Yap5 activates Ccc1, which imports cytosolic iron into the vacuoles. of our model. When cells grow exponentially, ␣ is constant which makes it particularly easy to evaluate. Assuming that the optical density of cells is proportional to cell volume, ␣ equals the slope of the straight line that results when the natural logarithm of A 600 is plotted versus time (lnOD t ϭ lnOD 0 ϩ ␣t).
Modeling homeostatic regulatory systems that control cytosolic, mitochondrial, and vacuolar iron import on the molecular level is currently not feasible because many critical details remain unknown. Our goal was merely to explore essential aspects of the regulation at four key traffic sites. To do this, we used surrogate mathematical expressions-called "Reg functions"-to mimic regulatory behavior (6,37). Reg functions can be viewed as valves that dynamically adjust between closed and fully opened to smoothly regulate traffic flow through a site. These functions are characterized by the iron species that they sense (S), the set point concentration at which the valve is halfopened ([S] sp ), and the sensitivity of the response (sen). There are two types of Reg functions, called Reg ϪS and Reg ϩS , defined as follows. In addition to including regulation at the site of iron import into the cytosol, and at the two sites through which iron moves into mitochondria and vacuoles, the model includes a fourth regulatory site in which vacuolar Fe II (called F2) is oxidized to Fe III (F3). There are a number of conditions and genetic strains (iron-deficient, adenine-deficient, ⌬CCC1, and CCC1 overexpression) in which F3 levels are low and F2 levels are high relative to iron-sufficient adenine-sufficient WT conditions (Refs. 5-7 and supplemental Table S1). The model regulates the rate of this oxidation to recreate the effect.
We wanted to evaluate whether Fe cyt (called C in our model) or mitochondrial ISC activity (proportional to the concentration of FS in our model) was sensed in regulation. To do this, three model variants were considered. The C-Reg variant assumes that all four regulatory valves exclusively sense C. For rates associated with importing iron into the cytosol (R cyt ) and into mitochondria (R mit ), Reg ϪC functions shut down import when [C] is too high. For rates associated with importing C into vacuoles (R vac ) or oxidizing F2 to F3 (R 23 ), Reg ϩC functions are needed.
The FS-Reg variant exclusively senses the activity of ISC assembly in the mitochondria, which in our model generates FS (a substitute for X-S). Reg ϪFS functions regulate R cyt and R mit , whereas Reg ϩFS functions regulate R vac and R 23 . The Dual-Reg variant assumes that both C and FS are sensed at all four regulation sites. To control the rates of R cyt and R mit , we used the product of two Reg ϪS functions (see supplemental information for a derivation). A similar {Reg ϩC ⅐Reg ϩFS } product function was used to control R vac and R 23 .
Inferring the appropriate Reg functions to describe the regulation of vacuolar iron requires some consideration. At the transcriptional level, CCC1 expression is regulated by Yap5 activity. The response to high [C] and/or [FS] is to increase flow into vacuoles, implying that Reg ϩC and Reg ϩFS functions should be used. At the translational level, Ccc1 mRNA is degraded by Cth2 which is regulated, in turn, by Aft1/2. The cell response to low [C] and/or [FS] is to decrease flow through Ccc1 (via increasing Cth2-associated Ccc1 degradation). This  (36); thus Mrs3/4 can be viewed as inhibiting Ccc1-analogous to the overall effect of Cth2again implying use of Reg ϩ functions. Finally, Smf3 and Fet5 export vacuolar iron into the cytosol, and an increase in either protein (which are both controlled by the Aft1/2-dependent iron regulon and thus are up-regulated under iron-deficient conditions) causes loss of vacuolar iron. This has the same net effect as inhibiting CCC1 expression. In summary, although Yap5, Cth2, Mrs3/4, Smf3, and Fet5 regulate vacuolar iron by different mechanisms, their effects can be collectively simulated using Reg ϩ functions.
The model presumes a cell encapsulated by a semipermeable membrane surrounded by an environment containing Fe III citrate (N) and molecular oxygen (RO2). The in silico cell is composed exclusively of cytosol, mitochondria, and vacuoles such that V cell ϭ V cyt ϩ V vac ϩ V mit . The model involves seven chemical components that contain iron and four that do not (Fig. 1). In addition to F2 and F3, vacuoles contain nanoparticles (VP). In addition to FS, mitochondria contain FM (NHHS Fe II ) and MP (mitochondrial nanoparticles). Other non-iron species include O 2 and ROS in the mitochondrial matrix. Mass balance of iron requires that where f vac , f mit , and f cyt are fractional volume ratios (volume of the designated compartment divided by the volume of the cell). The ordinary differential equations that define the Dual-Reg variant of the model are given by the following equations.
Ϫ Ordinary differential equations for the C-Reg and FS-Reg variants were identical except that they lacked FS-sensed and C-sensed Reg functions, respectively. The model included 30 floating and 9 fixed parameters (Table 1 and supplemental  Table S3). The exponential growth rate for cells that were transitioning smoothly from healthy to diseased state, for any point i along that transition, was calculated by solving for ␣ current using the FS concentration from the previous point in the transition. Connecting growth rate to [FS] makes sense because FS represents mitochondrial respiratory complexes and hemes. These complexes control cellular energy and perhaps growth rate. The overall change in cellular iron is given by the following equation (see supplemental information for derivation).
The iron importers that contribute to the import rate R cyt were viewed as a single collective Michaelis-Menten enzyme acting on substrate N. For cells in an expanding steady state, For R cyt , f cyt , N, ␣, K cyt , Reg ϪC , and Reg ϪFS values of 410 M/h, 0.65, 40 M, 0.2 h Ϫ1 , 14 M (Table 1), 1, and 0.4, respectively, the concentration of cellular iron would be ϳ400 M.
Oxygen plays a major role in the ISC mutant phenotype, but how it acts on the molecular level remains uncertain. We hypothesize that the matrix of healthy mitochondria is nearly anaerobic and that [O 2 ] in the matrix is higher in ISC mutants. Because of the activity of cytochrome c oxidase on the inner membrane, the concentration of O 2 in the matrix of healthy mitochondria must be lower than in the cytosol (38). However, the magnitude of this difference is uncertain, and [O 2 ] in the matrix has not been measured. ISC assembly assays require anaerobic conditions (39), as do a number of enzymes in the matrix, including aconitase (40), biotin synthase (41), and lipoic acid synthase (42), supporting our hypothesis.
Our model implies that anaerobic conditions arise in healthy mitochondria because most of the O 2 that diffuses across the IM is rapidly reduced by the respiratory complexes. ISC mutants contain fewer functional respiratory complexes such that more O 2 diffuses into the matrix. Once in the matrix, O 2 reacts with a pool of NHHS Fe II (FM) that is used as feedstock for ISC biosynthesis (8,43). Reaction of O 2 with FM not only depletes a reagent needed for ISC biosynthesis; it also generates nanoparticles and ROS. The O 2 -dependent loss of FM reduces [FS] further, which causes more O 2 to penetrate the mitochondrial inner membrane. A "disease spiral" results, transforming healthy mitochondria into the ISC mutant diseased state. All of these events are choreographed by our model. This disease spiral would occur regardless of the particular role served by the deleted protein in ISC biosynthesis; the only requirement is that loss of the protein leads to a decline in ISC activity. This situation is indeed observed in that the losses of various proteins, each with different functions in ISC biosynthesis, exhibit the same iron accumulation phenotype.
Ordinary differential Equations 3-11 were coded into Mathematica 9 (Wolfram, Champaign, IL) and numerically integrated using the NDSolve routine and the parameters listed in Table 1. The large number of parameters precluded a rigorously systematic optimization of parameter space. Moreover, the data used in fitting (supplemental Tables S1 and S2) were sparse and had large uncertainties. Thus, parameters were initially adjusted at will to achieve the following desired qualitative behavior.  Table 1. To evaluate sensitivities, RMSDs obtained when a given parameter was 10% greater (RMSD ϩ ) and 10% lesser (RMSD Ϫ ) than its optimal value were averaged and divided by RMSD min (supplemental Table S3). Once the Dual-Reg variant was optimized, the C-reg and FS-reg versions were generated by removing the appropriate Reg functions.

Results
The optimized Dual-Reg variant simulated iron import and trafficking in exponentially growing fermenting WT cells with relatively high fidelity; RMSD min was 0.33, nearly half of that obtained using the FS-Reg variant (RMSD min ϭ 0.54) and four times less than obtained using the C-Reg variant (RMSD min ϭ  To simulate the ISC phenotype, we incrementally reduced the rate of ISC synthesis (R isu ) from 250 M/h, the rate for healthy cells, to 15 M/h. The concentration plots of all species changed significantly at 30 Ͻ R isu Ͻ 100 M/h (Fig. 4). In this regime [FS] declined and [FM] increased more dramatically than at higher R isu rates. These changes are easily rationalized, because R isu is the rate by which FM converts to FS. Other observed changes are secondary effects caused by shifts in reg-ulation due to declining [FS]. These include a decline in vacuolar iron levels and increases in the rates of iron import into the cytosol and into mitochondria.
At R isu Ͻ 30 M/h, even more dramatic changes occurred, all associated with the ISC disease spiral. The primary event causing these changes was a decline of [FS] to concentrations below those required to maintain the matrix in an anaerobic state. The O 2 that penetrates the matrix under these conditions reacts with FM, causing its decline, as well as an increase in ROS and MP concentrations. The loss of FM slows the rate of FS production further, leading to the spiraling effect. The decline in [FS] also causes cytosolic and mitochondrial import valves to open (and the vacuolar iron import valve to close) such that iron rushes into the cytosol, out of the vacuole and into mitochondria where it accumulates as MP. Some FM is not consumed in the ISC diseased state, such that the steady state ratio of [FM]/[Fe mit ] is ϳ7%. This is similar to the Mössbauer spectral intensity of mitochondria isolated from ISC mutant cells, which exhibit features of NHHS Fe II in addition to the dominating nanoparticles (21,22). The origin of this NHHS Fe II as an expanded FM pool had been unexplained prior to this model.
The disease spiral is delayed and moderated under microerophilic conditions (RO2 ϭ 1 M) (Fig. 5A). When the system lacks O 2 , FM cannot convert into nanoparticles, and [FS] only declines marginally. At R isu Ͻ 40 M/h, low [FS] and an assumed low growth rate result in higher iron levels in the cell and mitochondria, such that [FM] increases dramatically, reaching 6 mM at R isu ϭ 20 M/h. Thus, the model predicts that the iron content of mitochondria isolated from ISC mutant cells grown under anaerobic condions will be dominated by NHHS Fe II rather than by nanoparticles. We are examining this prediction experimentally.
Most component traces of the C-Reg variant were similar to those of the Dual-Reg variant, but vacuolar iron in the C-Reg variant did not empty as [FS] declined in simulating the ISC mutant state (Fig. 5B). Cellular iron in C-Reg cells increased largely because the growth rate declined, and vacuoles imported that iron because they could not sense the decline of [FS] in mitochondria. There was also no increase in the rate of iron import into mitochondria during formation of the ISC diseased state (Fig. 5C), in contrast to what is observed.
The FS-Reg variant exhibited acceptable behavior overall except that [C] increased to exceedingly high (mM) levels under ISC mutant conditions (Fig. 5B). Such unrealistically high concentrations arise because there is no Reg ϪC valve to curtail the flow of iron in slowly growing cells in which the Reg ϪFS valve is fully opened.
We next examined the ability of the Dual-Reg variant to reproduce the phenotype of nine genetic strains including ⌬YFH1, ⌬MRS3/4, Mrs3/4 overexpression, ⌬CCC1, CCC1 overexpression, Aft1/2-1 UP , ⌬YFH1:⌬MRS3/4, ⌬YFH1: MRS3/4 overexpression, and ⌬CCC1:⌬MRS3/4 (supplemental Tables S1 and S2). We simulated each strain by only adjusting the rate(s) in our model that was(were) associated with the particular genetic modification. Rates for deletion strains were not assigned exactly to 0 because the cells contain secondary pathways that remain operational despite the deletion. The model implicitly includes all pathways of iron into the cytosol, into mitochondria and vacuoles, whereas the genetic strains perturb only a particular pathway.
The most unusual simulated behavior was that of CCC1-UP, which showed high [F2] and low [F3] under conditions where the WT strain is dominated by F3 (Fig. 5D). This shift was due to a down-regulation of k 23 in the simulated CCC1-UP strain, attributed to a more reducing vacuolar environment. In ϳ65% of all literature cases reported in supplemental Table S1, model simulations "trended" in the observed direction and had reasonable quantitative agreement. Model simulations fitted even better to the Mössbauer-based data of supplemental Table S2. This overall ability to reproduce observed behaviors from the literature and from previous studies in our lab, although not uniformly successful, suggests that many aspects of this simple model are correct.
Finally, we evaluated the sensitivity of model parameters (supplemental Table S3). The rate of iron import into mitochondria was the most sensitive parameter, followed by rate constants for O 2 reacting with FM, for respiration and for nanoparticle formation. The rate of ISC/heme biosynthesis was also sensitive. The model was sensitive to the set point concentrations of FS and to Michaelis-Menten K m terms involving the import of cytosolic iron into mitochondria, the conversion of FM into FS, and the reduction of O 2 in respiration.
The optimized setpoint concentration for FS, averaged for all four sites, was 170 Ϯ 30 M. This was comparable to the average concentrations of FS in mitochondria (ϳ200 M), and it suggests that the FS-Reg valves were opening and closing as designed. The average sen factor for FS-Reg functions was 8 Ϯ 2, indicating the need for sensitive regulation.
In contrast, the model was relatively insensitive to parameters associated with C regulation. Set point concentrations for C were highly variable, including values of 27, 80, 1.2, and 2 M for cytosolic iron import, mitochondrial iron import, vacuolar iron import, and vacuolar Fe II oxidation, respectively. Those for cytosolic and mitochondrial iron import differed from the simulated range of C concentrations (2-4 M). This means that under most circumstances, the C-Reg valves "controlling" import into the cytosol and mitochondria were fully opened such that these import rates were essentially controlled only by [FS]. C-regulation played a stronger role in vacuolar iron import and oxidation, especially with variations in [N].

Discussion
Immediately following the discovery of Aft1-dependent regulation in 1995, cytosolic iron was commonly assumed to be the sensor of a classic homeostatic regulatory system for controlling iron import and trafficking in yeast cells. This assumption was based on the response of healthy WT cells to changes in the iron concentration of the growth medium. Starting in the early 2000s, cellular iron overload caused by defects in mitochondrial ISC activity revealed the importance of this activity in cellular iron regulation. The classic model predicted that the massive import of iron into ISC-defective mitochondria resulted from an iron-deficient cytosol, which stimulated iron import by activating the iron regulon. Unexpectedly, evidence suggested that the cytosol in ISC mutant cells is iron-replete.
Once it was established that events in the mitochondria impacted those in the nucleus, focus shifted to how such information was transferred from mitochondria to nucleus. In the last decade, many details regarding this mitochondrial 3 nuclear signal transduction pathway have been established.
Included in this intellectual journey was the conclusion that cytosolic iron is NOT sensed in regulation. However, our study suggests that both cytosolic iron and mitochondrial ISC activity are sensed. Fe cyt -sensing plays an important regulatory role when healthy cells are grown in iron-deficient, iron-sufficient, and iron excess medium (especially with regard to vacuolar iron import and oxidation). In these cases, the level of ISC assembly is relatively constant, such that the rates of iron import into the cytosol and mitochondria are largely invariant. This leads to the observed relative invariance of iron content in mitochondria. On the other hand, when mitochondrial ISC activity is attenuated or halted, FS-based regulation controls these iron import rates.
Both Fe cyt and mitochondrial ISC activity could be regulatory sensors if both were required to generate a single downstream signal for the mitochondrial-nuclear signal transduction pathway. This requirement would be fulfilled if Fe cyt reacted in the cytosol with X-S that had been exported from the mitochondria to generate the Fe 2 S 2 cluster in the Grx⅐Fe 2 S 2c Grx homodimer (see red star in Fig. 2). When Fe cyt is limiting and X-S abundant, [Grx⅐Fe 2 S 2 ⅐Grx] would be limited, which would activate the iron regulon. In this circumstance, Fe cyt would play the dominant regulatory role. On the other hand, when X-S is limiting and Fe cyt is abundant, [Grx⅐Fe 2 S 2 ⅐Grx] would also be limiting, and the iron regulon would again be activated. However, [X-S] would play the dominant regulatory role. It is only when Fe cyt AND X-S are both abundant (relative to the amount of Grx available) that the iron regulon would not be activated. This is the situation found in healthy WT cells grown on iron-sufficient (or iron excess) conditions. These considerations were assumed in deriving the product function used in the Dual-Reg variant.
Remarkably, dual regulation was proposed in 2003 by Mühlenhoff et al. (10) based on their perceptive observation that both deletion and overexpression of Mrs3/4 activated the iron regulon. They posited that deleting Mrs3/4 caused low levels of ISC biosynthesis (thereby stimulating the iron regulon), whereas overexpressing Mrs3/4 caused low levels of Fe cyt (also stimulating the iron regulon). Kaplan and co-workers (11,12,36) also interpreted particular experiments assuming that both cytosolic iron and ISC activity regulate iron traffic in yeast.
ISC biosynthesis activity might regulate iron trafficking to help mitochondria import more iron when cells transition from fermentation to respiration. In the late 1980s, Raguzzi, Lesuisse, and Crichton (44) hypothesized that vacuolar iron is mobilized during this metabolic transition. Respiring cells contain approximately three times the concentration of mitochondria as fermenting cells, indicating that the metabolic shift involves mitochondriogenesis (45). Some of the iron for this process comes from mobilized vacuolar iron. The trigger for mitochondriogenesis (perhaps low glucose levels) may not be perfectly coordinated to an increase in the rate of iron import into mitochondria. In this case, growing and dividing mitochondria might experience a transitory period in which insufficient ISCs are made. This might be sensed by a lower than set point concentration of X-S in the cytosol, which might stimulate the ISC mutant phenotype (importing more iron into the cell, exporting vacuolar iron into the cytosol, and importing more Fe cyt into mitochondria). The essential difference is that in healthy respiring cells, the imported iron can be used to make ISCs, whereas in ISC mutant cells, it cannot. Accordingly, the up-regulation of iron import, which generates nanoparticle iron in ISC mutant cells, is "earmarked" for ISC biosynthesis in healthy cells. In healthy cells, once sufficient ISCs are made, the signal (X-S) indicating this would attenuate further iron import and allow vacuolar iron stores to be replenished. In contrast, ISC mutant cells cannot use that iron to make ISCs, and so X-S is not made in sufficient amounts to shut down the coordinated import of iron into mitochondria; thus, vacuoles remain devoid of iron, whereas excessive iron pours into mitochondria, generating large amounts of nanoparticles and ROS as it reacts with O 2 . This leads to the iron accumulation phenotype that defines ISC-associated diseases.
Mathematical models of biochemical processes in cells become increasingly insightful as the complexity of such processes and the amount of relevant information increases. Such models have the unique ability to integrate the pieces of the puzzle and allow the entire process to be viewed from a systems' level perspective. Modeling the progression from healthy to diseased states is a powerful way to understand the mechanism of diseases and to evaluate the efficacy of different treatments. We hope that further developments of this model will clarify the complex chemical relationships that collectively cause Friedreich's ataxia and other iron accumulation diseases and that such models might promote more effective treatments.
Author Contributions-J. D. W. helped develop the model, wrote the software code, and executed all simulations. P. A. L. designed the model, provided advice, and wrote most of the paper. Both authors reviewed and approved the final version of the manuscript.