In Silico Evidence for Gluconeogenesis from Fatty Acids in Humans

The question whether fatty acids can be converted into glucose in humans has a long standing tradition in biochemistry, and the expected answer is “No”. Using recent advances in Systems Biology in the form of large-scale metabolic reconstructions, we reassessed this question by performing a global investigation of a genome-scale human metabolic network, which had been reconstructed on the basis of experimental results. By elementary flux pattern analysis, we found numerous pathways on which gluconeogenesis from fatty acids is feasible in humans. On these pathways, four moles of acetyl-CoA are converted into one mole of glucose and two moles of CO2. Analyzing the detected pathways in detail we found that their energetic requirements potentially limit their capacity. This study has many other biochemical implications: effect of starvation, sports physiology, practically carbohydrate-free diets of inuit, as well as survival of hibernating animals and embryos of egg-laying animals. Moreover, the energetic loss associated to the usage of gluconeogenesis from fatty acids can help explain the efficiency of carbohydrate reduced and ketogenic diets such as the Atkins diet.


Model modifications
Besides the modifications described in the main document we added several reactions to the network. These reactions concern the degradation of propionyl-CoA into succinyl-CoA which are known to occur in humans [2,3,4], but were not present in the reconstruction. They are required for the degradation of methionine as well as threonine. The first reaction, catalyzed by propionyl-CoA carboxylase, converts propionyl-CoA to S-methylmalonyl-CoA. This reaction was present in the model, but only in the reverse direction. Thus, we added the following reaction (in the notation of the model) In two subsequent steps, catalyzed by methylmanoyl-CoA epimerase and methylmanoyl-CoA mutase, Smethylmalonyl-CoA is converted into succinyl-CoA. Thus, we added an additional reaction of the form Moreover, we found that there exist several sets of reactions in the model that allow the unconstrained conversion of ADP and Pi to ATP without consumption of any energy source. These are mainly transport reactions and the ATP synthase. We remedied this problem by blocking the reactions with the IDs (fforward reaction blocked, b-backward direction blocked) "R BILGLCURte"(b), "R BILDGLCURte"(b), "R ACOAO7p"(f), "R RDH1a"(f) and "R ATPS4m"(f). The last reaction corresponds to ATP synthase, the final step in the respiratory chain. Thus, we added two reactions to represent the respiratory chain (all metabolites in the mitochondrial form):

Determining reactions essential for a pathway
In order to determine which reactions are essential on a pathway a linear program can be used. It consists in checking whether there still exists a steady-state flux through the final reaction of the pathway, if the flux through each reaction of an initial pathway is individually constrained to zero. If we find no steady-state flux, the corresponding reaction is essential for the pathway. We use the same notation like in the main document. Thus, N corresponds to the m × n stoichiometric matrix of a reaction network of m metabolites and n reactions. Given an initial pathway of length l, that is, a set of indices of reactions, i 1 , ..., i l with 1 ≤ i 1 , ..., i l ≤ n we assume that i l is the index of the final reaction r i l of the pathway. In order to determine the essential reactions of the pathway we check for each with the variables v is feasible. Thus, we check if there still exists a steady-state flux through r i l if constraining the flux through r ip , v ip , to zero. In consequence, if the linear program in infeasible for a reaction i p , r ip is an essential reaction. Note that we split reversible reactions into irreversible forward and backward direction. Hence, equation (2) corresponds to an irreversibility constraint.

ATP consumption for gluconeogenesis from fatty acids
Here we want to discuss the requirements in terms of NADPH, NADH and ATP of the presented pathways. A similar analysis of energetic requirements in acetone metabolism can be found in [5]. In the following, when speaking of quantities of metabolites, we will refer to moles of each metabolite without specifically stating this. Overall, one glucose and two carbon dioxide are produced from four acetyl-CoA. The following considerations will focus on the production of one glyceraldehyde 3-phosphate from two acetyl-CoA. The following steps in gluconeogenesis produce glucose from two glyceraldehyde 3-phosphate without further NADH or ATP consumption. It is assumed that a gradient of ten protons from intermembrane space to the inner mitochondrion equals an amount of 2.5 ATP that can be produced from oxidation of one mitochondrial NADH [6].
The alternative pathways in ketone metabolism only yield energy in form of ATP or GTP, if acetoacetate is produced from acetoacetyl-CoA. In one case, via the 3-Oxoacid CoA transferase, one succinyl-CoA is produced from succinate and coenzyme A. Succinyl-CoA can be hydrolyzed via production of one ATP or one GTP. In the cytosol, acetoacetate can be produced directly from acetoacetyl-CoA accompanied with production of one ATP from AMP and pyrophosphate. When equaling the phosphorylation of AMP to ATP with two times the reaction of ADP to ATP, the production of acetoacetate can yield in between zero and two ATP. The primary site of production of ketone bodies is the mitochondrial matrix. Hence, we base our calculations on the pathway via 3-Oxoacid CoA transferase since it produces one ATP in contrast to the alternative pathway via the intermediate of hydroxymethylglutaryl-CoA in which no ATP is being produced.
In acetone metabolism there are large differences in terms of NADPH oxidized and NAD + reduced in the different pathways. The reduction of one ferricytochrome can be equaled with the reduction of one NAD + . Replenishing one NADPH using the described pathway via the malic enzyme costs an equivalent of 3 1 2 ATP (Fig. 5 in main document). One ATP is consumed in the carboxylation of pyruvate to oxaloacetate. The reduction of oxaloacetate to malate oxidizes one NADH. Consequently, the import of pyruvate and carboxylation to oxaloacetate costs an equivalent of one ATP and the reduction to malate with subsequent transport into the cytosol 2.5 ATP.
Further down in the pathway, the conversion of one cytosolic pyruvate to cytosolic phosphoenolpyruvate costs 2 1 2 ATP. This is the cost of the cycling pathway described above plus the hydrolization of one GTP to decarboxylate oxaloacetate. In the following, one ATP and one NADH are necessary to form glyceraldehyde 3-phosphate. This sums up to a cost of 3 ATP.
Overall the energy requirements of the pathways are mainly determined by the pathway used in ketogenesis and acetone metabolism. The most efficient pathway in acetone metabolism is pathway 7 (Table ) which has a netto-balance of one NADPH consumed and 2 NADH produced. Overall this would result in an investment of − 1 ATP (conversion of acetyl-CoA to acetone) Thus, the production of one glucose from 4 acetyl-CoA costs at least 6 ATP. Using palmitic acid as starting compound instead we additionally need to take into account ATP produced during β-oxidation of palmitic acid. Starting from 0.5 palmitic acid, 4 acetyl-CoA can be produced and 13 ADP are converted into ATP [6]. Thus, there is a net production of 13 − 6 = 7 ATP if producing one glucose from 0.5 palmitic acid.
Taking by contrast a pathway which is in favor of NADPH consumption over NADH production, the balance is (pathway 14, Table ) − 1 ATP (conversion of acetyl-CoA to acetone)

Computation of storage efficiencies
Computation of gluconeogenic energy efficiencies The gluconeogenic energy efficiency relates the amount of ATP that can be produced by directly oxidizing a compound c to the amount of ATP that can be obtained by oxidizing the amount of glucose that can be produced from c. For the computations we added an inflow reaction of c to the metabolic network used in the main manuscript: → c.
Additionally, we added a reaction of the form: that mimics ATP hydrolyzing reactions. Then we computed the gluconeogenic energy efficiency e energy (c) of a compound c as follows. First, we computed the maximum amount of ATP that can be produced from completely oxidizing c, max (1) AT P (c). This we did by optimizing the following linear program where N (1) represents the stoichiometric matrix with the two previously mentioned reactions added (v inf lowc -flux through inflow reaction of c, v AT P -flux through ATP hydrolysis reaction): The optimal value of the objective function corresponds to the maximum amount of ATP, max (1) AT P (c), that can be produced from oxidizing c. Please note that this includes cases in which c cannot be completely oxidized by the metabolic network but some derivative of c is excreted.
Second, we computed the maximum amount of glucose that can be produced from each compound c, max Glc (c), by adding an outflow reaction of glucose Glucose → and solving the following linear program in which N (2) corresponds to N (1) with the outflow of glucose added ((v outf low G lc -flux through outflow reaction of glucose): The optimal value of the objective function corresponds to the maximum amount of glucose, max Glc (c), that can be obtained from c. If gluconeogenesis from a particular compound c is not possible, max Glc (c) is zero.
Third, in some cases gluconeogenesis starting from a compound can yield additional ATP. Thus, we computed the maximum amount of ATP that can be obtained during gluconeogenesis from a particular compound c, assuming a maximum of glucose produced, max (2) AT P (c). This we did by fixing the outflow of glucose to the maximum, max Glc (c), and maximizing the flux through the ATP hydrolysis reaction: The optimal value of the objective function corresponds to the maximum amount of ATP, max (2) AT P (c), that can be obtained during gluconeogenesis from c assuming the maximum of glucose produced. If gluconeogenesis from a particular compound c is not possible the linear program is infeasible.
Multiplying max Glc (c) with the 32 ATP that can be produced by completely oxidizing one glucose in humans [6] and adding max (2) AT P (c) we obtain the maximum amount of ATP that can be produced during and after gluconeogenesis from c. Relating this value to the amount of ATP that can be produced by directly oxidizing c we obtain the gluconeogenic energy efficiency e energy (c) by e energy (c) = max Glc (c) · 32 + max (2) AT P (c) max (1) AT P (c) . (5)

Computation of glucose storage efficiencies
The glucose storage efficiency of a particular compound c, e storage (c), relates the amount of glucose that can be produced from one c to the amount of glucose that is required to produce one c. From the last subsection we have already obtained the maximum amount of glucose that can be produced from compound c, max Glc (c). Thus, we additionally require the minimal amount of glucose that is required for the production of one c, min Glc prod c (c). This value can be obtained by adding an inflow reaction of glucose → Glucose and an outflow reaction of c c → to the original metabolic network. Then we optimize the following linear program in which N (3) corresponds to the initial stoichiometric matrix to which the two above reactions have been added (v inf low Glcflux through inflow reaction of Glc, v outf lowc -flux through outflow reaction of c): The optimal value of the objective function corresponds to the minimal amount of glucose, min Glc prod c (c), that is required for the production of one c. If the biosynthesis of a particular compound c from glucose is not possible the linear program is infeasible. Thus, we obtain the glucose storage efficiency of c, e storage (c), by e storage (c) = max Glc (c) min Glc prod c (c) .

Storage efficiencies in humans and Escherichia coli
We computed gluconeogenic energy efficiencies and glucose storage efficiencies for important storage compounds in humans. We also computed these values for E. coli, which possesses a native glyoxylate shunt, for comparison. For E. coli we used the genome-scale metabolic model of Feist et al. [7]. For amino acids we modified Eq. 6 by additionally subtracting 4 ATP in the numerator to take into account the storage of amino acids in proteins (cost of amino acid polymerization into proteins). The results are listed in the following table. For palmitic acid we give values for the most efficient pathway (for humans, pathway 7 in Tab. ) and the most inefficient pathway (for humans, pathways 15, 16, 19 or 20 in Tab. and no ATP production in ketogenesis). Compounds for which "-" is given lack a degradation pathway in case of the gluconeogenic energy efficiency, and either a biosynthetic or degradation pathway in case of the glucose storage efficiency.

∆G-values and concentrations of compounds
For the calculation of the ∆G-values of the presented pathways, Gibbs free energies of formation and concentrations of the converted metabolites are required. Where possible, measured Gibbs free energies of formation from [8] as well as [9] and otherwise estimated values from [10] were used. For ATP, ADP and Pi we used the difference of the ∆G-values between the substrates and products of ATP hydrolization instead of the individual values. As concentrations we used data from rat hepatocyte, the primary site of gluconeogenesis, where possible and a standard concentration of 10 −3 mol l otherwise. There were no principal changes in the resulting ∆Gvalues when varying this value. Total NADH/NADH+ and NADPH/NADP+ concentrations in rat liver were measured in [11]. The relative fraction of the reduced to the oxidized state for NADH/NADH+ as well as NADPH/NADP+ in mitochondria and cytosol of rat liver were taken from [12].