Here we present a new, manually curated metabolic model of the mitochondrion present in human heart tissue, called iAS253 (Additional File 4). It contains 229 mitochondrial matrix reactions, 24 cytosolic reactions, 89 compartment transport steps and 73 boundary conditions. Each reaction was manually evaluated in conjunction with the principle of metabolite availability before incorporation into the model, using 33 mitochondrial proteomic datasets from the MitoMiner database, combined with annotation from public resources and the literature. The model includes directionality constraints based upon general rules of irreversibility, thermodynamics and information from public resources and the literature. The resultant model contains no orphan metabolites and its directionality constraints allow every reaction in model to potentially possess a flux, while all flux loops have been eliminated. It is encoded in SBML format , and uses KEGG  identifiers where possible. Therefore, this model should be readily adaptable for use by other modellers either in isolation or with its addition to models of cellular metabolism. We believe it is the most refined model of the mitochondrion currently available as demonstrated by simulations of normal conditions, which closely correspond with experimentally determined flux figures and metabolic observations of heart. For example, fluxes though the TCA cycle and fatty acid oxidation pathway while using the objective function of maximum ATP production corresponded with measurements in rat heart (7.05 vs. 7.5 and 0.41 vs. 0.35 μmol/min/gDW respectively). The similarities between the model and the results of experiments in vivo suggest that the modelled flux distribution of core metabolism is biologically relevant. The minor discrepancies between the flux figures may be due to imprecise boundary constraints, the biological objective in vivo for core metabolism not being described accurately by the model's objective function of maximum ATP production, or difficulties in measuring these values experimentally.
These results are in contrast to those of previous mitochondrial FBA models [2, 3] where a much higher uptake of oxygen (about 40 nmol/min/gDW) was permitted, while maximum ATP production was 60% lower when this was set as the objective function. This discrepancy may be due to the use of capacity constraints on the transport steps between the cytosol and mitochondrion in these models. These constraints were derived from uptake rates determined experimentally in vitro, on isolated carrier proteins in liposomes, so are unlikely to reflect the uptake rates in vivo for the mitochondrion. Our model does not use capacity constraints on these transport steps and instead constrains the system at the boundary conditions.
The constraints placed on the boundary conditions of the system critically affected the behaviour of the model. These constraints reflect the imports and exports of the system and were chosen carefully from the primary literature (Additional File 3). There is some uncertainty in these figures as often the only data available are not from human and in one case not from heart tissue. In addition many of these experiments were conducted on isolated hearts, which may display significant metabolic differences to hearts in situ . Therefore these figures may not correspond to the maximum possible uptake values, which are necessary to set the upper bound of the constraint. Previous reconstructions have tried to account for this experimental uncertainty by increasing these figures by an arbitrary amount, such as 25% . This is problematic because no data exists on what scale of increase is appropriate whereas the uptake of some compounds, such as oxygen, are a critical limiting factor to the system under most circumstances, and will usually be at the maximum allowable rate. Therefore in the absence of more relevant data it was decided to use experimental figures without modification. Further experiments to determine and verify the uptake rates used would be beneficial for further refinement of the model and in particular to aid simulations of perturbed states where uptakes can have a large impact on model behaviour. In addition we included directionality constraints on the transport steps between the cytosol and the mitochondrial compartments to prevent flux loops, while reflecting the biological role of the underlying carrier and allowing normal metabolism. However, it is possible that under disease conditions the accumulation of metabolites may affect the direction of transport. In the metabolic disorders investigated here all metabolites that were experimentally reported as accumulating could be effluxed without the need to alter these constraints. The only exception was fumarate, which is known to accumulate in fumarase deficiency, where an extra transport step was included to allow its efflux.
A common objective function used with models of microorganisms is the production of biomass. Biomass represents all the metabolites that are required for growth of that particular organism, with the assumption that the organism is biologically optimised for maximum growth. The relative proportions of each metabolite in the biomass are derived from experimental figures measured from cellular biomass. However, a single biomass objective function cannot currently be devised for the mitochondrion, as no experimental figures exist for its composition. It is also unlikely that the biological objective in vivo is maximum growth as one of the main roles of the mitochondrion is to produce ATP and so this would also have to be incorporated in the objective function to make it biologically relevant. This would require the ratios between ATP production and growth and maintenance of the mitochondrion to be experimentally verified and this is not currently available, and is likely to be extremely difficult if not impossible to determine. Therefore to represent the different aspects of mitochondrial metabolism, six separate pseudo reactions were devised, encompassing growth and maintenance as well as haem and ATP production. Although maximum ATP production is most likely to be the closest to the biological objective (as shown with the close correspondence to experimentally measured figures), the inclusion of the other pseudo reactions ensures the model can produce metabolites known to be required by the mitochondrion. However the flux distributions found when using these other pseudo reactions individually as objective functions are unlikely to be realistic, as no one objective function in isolation will match the biological objective of the system in vivo. The pseudo reactions that are used for these objective functions have been included in the model for convenience and to allow other researchers to easily replicate our results.
To demonstrate the predictive abilities of the model we simulated and analysed the complicated phenotypes of three disorders of the TCA cycle using the iAS253 model.
The mechanism of fumarase deficiency
Patients with the most severe symptoms of the disorder often have residual fumarase activities near zero . This would equate to near zero flux through the fumarase reaction in the model. Under these conditions both lactate and fumarate were effluxed from the system, matching the phenotype. Initial simulations would predict that such a reduction would result in a very large decrease in maximum ATP production in heart (Figure 1), which would seem likely to have catastrophic effects. However, heart defects in patients have not been reported , which would imply that the predicted reduction in ATP production must be compensated. In a series of simulations the boundary constraints were removed one by one to determine if increased metabolite uptake could counteract the decrease. This identified the uptake of valine, aspartate, malate, proline, bicarbonate, oxoaloacetate, arginine, glutamine, serine and glucose as having a positive effect on ATP production (Figure 2).
The effect of aspartate on the system supports the hypothesis of Bourgeron et al. , which suggests a reaction in the malate-aspartate shuttle is used to convert aspartate and oxoglutarate into oxaloacetate and glutamate, acting as a metabolic bypass and allowing the impaired part of the TCA cycle to be circumvented. They suggest the low level of aspartate found in the blood plasma of two patients in their study supports the existence of such a bypass. The iAS253 model predicts that if aspartate is available, this bypass is used. A relatively small uptake resulted in a large difference in maximum ATP production, which suggests it could be biologically relevant.
Oxaloacetate and malate also had a large effect by using the reactions of the malate-aspartate shuttle. In the simulations oxaloacetate was converted to malate before being transported to the matrix using the oxoglutarate transporter. Malate was then converted back into oxaloacetate to complete the TCA cycle. As a consequence of the transport step oxoglutarate was counter-exchanged from the matrix into the cytosol and then effluxed from the system. Such a mechanism in vivo may explain the oxoglutarate observed in urine of patients with fumarase deficiency.
The import of proline, arginine, glutamate and valine caused a large increase in ATP production due to the degradation of these metabolites into oxoglutarate, increasing the flux through part of the TCA cycle, and leading to an increase in fumarate efflux. The model predicts that a corresponding increase in the efflux of glutamine and alanine should also be observed. The production of glutamine was required to remove the ammonia produced during the deamination of these metabolites, whereas alanine efflux was involved in the glucose-alanine cycle, where pyruvate is converted into oxoglutarate (Figure 3). However, both of these metabolites are further metabolised in the kidney and liver respectively, so it is not clear whether they would accumulate to a sufficient degree to be elevated in a patient metabolite profile.
The uptake of bicarbonate had a large impact on ATP production by allowing the direct conversion of pyruvate to oxaloacetate. However, due to the production of lactate, and bicarbonate acting as a cellular buffer, it may not be available at sufficient levels to have a significant affect in vivo.
Serine had an effect on increasing ATP production, but only from its degradation to glycine, producing NADH and NADPH in the process. It did not directly contribute to the TCA cycle, which explains why even at high uptakes its effect on maximum ATP production is lower than the other metabolites except glucose.
Although increased glucose uptake did increase ATP production the effect was small, while dramatically increasing lactate efflux. Therefore, although increasing glucose levels may be easily achieved physiologically, a low glucose diet, while increasing the levels of the other metabolites may be more beneficial to maintain ATP production, while minimising lactic acidosis.
It is not apparent if in vivo the uptakes of any of these metabolites are increased beyond normal limits and have a significant impact on ATP production. Although it may be unlikely that any one metabolite could sustain a high uptake flux under physiological conditions, it may be feasible that all of these metabolites contribute collectively to increasing ATP production. Further experimental data would be required to test these predictions and to further refine the model.
A common occurrence throughout these simulations was fatty acid metabolism was restricted, as acetyl-CoA could not enter the TCA cycle. If this occurs in vivo, these excess fatty acids may be stored in adipocytes or alternatively be expressed as an increase in the production of ketone bodies (directionality constraints prevent this in the current model as only liver produces ketones while the heart consumes them), a known cellular method to use excess acetyl-CoA, rather than a reduction in fatty acid metabolism. This would be supported by the elevated levels of acetoacetate in the blood plasma of two patients with the disorder (0.07 and 0.08 mmol/l) in comparison to controls (0.016 - 0.04 mmol/l), although levels of hydroxybutanoate appeared to be within the normal range . Additional data from fumarase deficient patients are needed to verify if these predictions are correct.
The mechanism of succinate dehydrogenase deficiency
The simulations of succinate dehydrogenase deficiency were very similar to fumarase deficiency in both the reduction in ATP production (Figure 1 and Figure S1, Additional File 5) and the effect of increasing certain metabolite uptake rates (Figure 2 and Figures S2 and S3, Additional File 5). The metabolites that had a positive effect on maximum ATP production were shared between the two deficiencies and used the same degradation pathways and entry points into the TCA cycle (Figure 3 and Figure S4, Additional File 5). The main difference was the efflux of succinate rather than fumarate as found in fumarase deficiency and a slightly lower level of ATP production, as complex II could no longer contribute to the electron transport chain. The similarities between the disorders are unsurprising as the enzymes are adjacent in the TCA cycle. The main physiological difference between them is that many patients with succinate dehydrogenase deficiency have residual enzyme activity in the range of 10-50% whereas many patients with fumarase deficiency have 0% activity . However, it is not possible to predict what level of succinate dehydrogenase flux this will correspond with, as residual enzyme activity and enzyme flux are not directly correlated . However, even low levels of enzyme flux result in a dramatic increase in maximum ATP production (Figure S1, Additional File 5). This has the effect that the uptake rates of metabolites that impact ATP production can be much lower while returning production to normal levels (Figure S2, Additional File 5), which may make these interventions more physiologically feasible.
The mechanism of α-ketoglutarate dehydrogenase deficiency
The effect of α-ketoglutarate dehydrogenase deficiency on maximum ATP production was minor even when no flux was allowed through the reaction representing the enzyme. This was the result of a bypass known as the GABA shunt , which converts oxoglutarate to succinate using succinate semialdehyde and GABA as intermediates, circumventing the impaired reaction. Although the GABA shunt is usually associated with brain, there is evidence in MitoMiner, and the literature  that it is present in heart. Oxoglutarate was only effluxed from the system if the flux through the GABA shunt was limited so that not all the flux could proceed through it. If the bypass in vivo is unable to sustain the large flux required for the TCA cycle to function at full capacity, this could explain the phenotype of oxoglutarate excretion. Gene expression data for patients with the disorder may give some indication whether the enzymes that constitute the GABA shunt are up-regulated in heart to allow the bypass to function. GABA also acts as an inhibitory neurotransmitter and its involvement in the bypass may begin to explain the encephalopathy reported in patients.
An efflux of lactate was never observed when only α-ketoglutarate dehydrogenase was constrained. Therefore to determine whether a defect in subunit E3 of the enzyme complex, which is also shared with pyruvate dehydrogenase and ketoacid dehydrogenase complexes, was responsible, the reactions representing the latter were also restricted. Only when pyruvate dehydrogenase was constrained was lactate produced, as not all pyruvate from glycolysis could enter the TCA cycle. This suggests that a lactic acidosis phenotype is the result of a defect in the E3 subunit, and isolated α-ketoglutarate dehydrogenase deficiency can be discounted.