Overall we detected nine possible pathways for the conversion of acetyl-CoA into mitochondrial acetoacetate (see Text S1). In acetone degradation we identified 58 possible pathways.

In addition to the work of [26] in which acetone metabolism was reviewed, we identified a new intermediate of acetone metabolism, D-lactaldehyde, which is used in 14 out of the 58 pathways. This metabolite can be produced from either methylglyoxal or lactoyl-glutathione, an intermediate in the conversion of methylglyoxal to D-lactate. The conversion of methylglyoxal to D-lactaldehyde is catalyzed by an aldo-keto reductase or by a glyoxylate reductase. Aldo-keto reductase is only weakly expressed in the liver [27]. Thus, this pathway might be of greater importance in other tissues. Another important point is the import of pyruvate into mitochondria. Pyruvate can be either directly imported into the mitochondrion or indirectly via a lactate shuttle [28] (Fig. 4). We will not consider the indirect import since its importance is disputed [29]. Therefore, only 22 pathways for the conversion of acetol into pyruvate remain (Text S1).

One important feature of the described pathways is that many of them involve the reduction of NAD⁺ or oxidation of NADPH. Overall, 1–3 moles of NADPH are oxidized and 0–4 moles of NAD⁺ are reduced during the conversion of one mole of acetone into pyruvate (see Text S1). Special emphasis can be put on the oxidation of methylglyoxal to pyruvate. In this case, one mole of NADP⁺ can be reduced leading to pathways in which the net balance in oxidized NADPH is only one (pathways 7 and 14, depicted in Fig. 3). Pathways not using this reaction have a net balance of at least two moles of NADPH oxidized. As discussed below, these requirements on the reduction potential impose constraints on the utilization of gluconeogenic routes from fatty acids.

Besides the concept of elementary flux patterns, other techniques to determine pathways in genome-scale metabolic networks exist. Among the most widely used techniques is flux balance analysis [30] that allows one to identify physiologically feasible fluxes within a metabolic network that optimize a certain objective function. While a single pathway for the conversion of fatty acids in gluconeogenesis can be obtained with this method, a systematic identification of all possible pathways is not possible.

Another frequently used tool is elementary flux mode analysis [17] that allows one to enumerate all physiological feasible flux distributions in a metabolic network. However, the number of extreme pathways [31], a subset of the elementary flux modes, is estimated to be 10²⁹ for the human genome-scale network [32], which makes the full enumeration of all the elementary flux modes impossible. Nevertheless, recently two approaches to enumerate subsets of elementary flux modes with increasing number of reactions have been developed [33], [34]. Here, we used the K-shortest EFM method to compute the 100 shortest elementary flux modes producing cytosolic glucose 6-phosphate from mitochondrial acetyl-CoA. Within these elementary flux modes only nine of the 22 pathways for the conversion of acetone to pyruvate were present (Text S1). Hence, the complete enumeration of all possible pathways for the conversion of acetone to pyruvate on the pathway of gluconeogenesis from fatty acids could not be achieved by this approach.

We performed a global survey of gluconeogenic routes from fatty acids in human metabolism using a genome-scale metabolic model and elementary flux pattern analysis. Even though prominent biochemistry textbook negate the existence of such a route in mammals and humans in particular [11], [12], [13], we were able to confirm several routes that have been proposed earlier [18], [19]. Additionally, we were able to identify 14 new pathways that proceed via a new intermediate in acetone metabolism, D-lactaldehyde. These results further underline the utility of elementary flux pattern analysis in assessing the metabolic capabilities of organisms.

Gluconeogenesis becomes important when the glucose level in the body cannot be sustained by the glycogen store in the liver, which is sufficient for up to one day in humans [16]. Such a situation arises, for instance, during starvation, fasting, prolonged physical exercise, upon carbohydrate-reduced and ketogenic diets like Atkins diet as well as in hibernating animals. In addition to glucogenic amino acids from proteins, the glycerol component of lipids can be converted into glucose while fatty acids serve as principal metabolites to fuel oxidative phosphorylation. In prolonged starvation, not only muscular protein but also proteins essential for the maintenance of principal body functions are broken down to serve for gluconeogenesis [16]. However, there is obviously a limit to such protein degradation.

While the principal fuel of the brain under normal conditions is glucose, in starvation, the brain starts using ketone bodies in addition to reduced consumption of glucose. The increase of the production of ketone bodies leads to rising levels of acetoacetate, which is constantly decarboxylated into acetone. For example, in 21 days fasted humans, 37% of the acetoacetate is converted into acetone [35]. The putative enzyme catalyzing this reaction, acetoacetate decarboxylase, has been characterized in terms of catalytic activity [36] and inhibitors [37], but has not yet been identified [26]. 2–30% of acetone is excreted via the urine and breath [35], while the remainder is metabolized further and could account for up to 11% of gluconeogenesis during starvation [35]. Glucose formation from acetone was indeed suggested as an explanation for the finding that common gluconeogenic precursors alone could not fully account for renal gluconeogenesis [16]. Additional supporting evidences come from the increased activity of cytochrome P450 (Cyp2e1), an enzyme essential in the presented pathways, during starvation [38] and the observation that increased survival time of obese rats during starvation correlates with the activity of acetone metabolism [39]. Moreover, increased levels of methylglyoxal, an intermediate of some of the gluconeogenic routes from fatty acids, have been observed in subjects on the carbohydrate reduced Atkins diet during which ketogenesis is particularly active [40]. Thus, these pathways play an important role in gluconeogenesis also in other situations like the ones mentioned in the Introduction in which ketogenesis is particular active. In hibernating animals, for example, protein may be saved by not using it as the only source for gluconeogenesis. This hypothesis is confirmed by recent results in which it was found that Cyp2e1 and phosphoenolpyruvate carboxykinase (Pck1), both enzymes within the described pathways, are significantly (p = 0.005) upregulated in the liver of hibernating black bears (FoldChange 5.990 and 13.17, respectively) [41]. In a more recent work, also Pck1 (FC = 10.7) and Pc (FC = 2.62) were found to be upregulated in the liver of the animals during hibernation [42].

Important aspects related to the presented pathways are energetic requirements that constrain their capacity. Experimental investigation of the gluconeogenic role of acetone showed differences in its utilization between species: the net synthesis of glucose from acetone as observed in murine hepatocytes [43] does not seem to occur in perfused rat liver [44]. Instead, net synthesis from acetone could be demonstrated in either case when also other gluconeogenic substrates were given [43]. This can be explained by the increased requirement for NADPH in the conversion of acetone to pyruvate. Each possible pathway requires the oxidation of at least two moles of NADPH (see Fig. 4). However, there are only two pathways which reduce the net balance in NADPH to-1 moles by the direct conversion of methylglyoxal to pyruvate (pathways 7 and 14, Fig. 3). During gluconeogenesis, cytosolic pathways for the replenishment of NADPH are impaired since they would further deplete gluconeogenic metabolites [45]. In fact, NADPH has to be supplied from mitochondrial sources and its availability represents the rate-limiting factor in acetone metabolism [39], [46].

There are two known pathways of NADPH replenishment from mitochondria [45](Fig. 5). One of them involves the transport of mitochondrial NADPH into the cytosol and the other the transfer of electrons from mitochondrial NADH to cytosolic NADP⁺. The direct transport from the mitochondrion involves a citrate∶oxoglutarate shuttle. Since both metabolites are intermediates of the TCA cycle, they would potentially reduce mitochondrial fatty acid oxidation when used for this shuttle system. The other pathway of NADPH replenishment uses a route via cytosolic malic enzyme, which decarboxylates malate to pyruvate. Both metabolites are intermediates of gluconeogenesis from acetone. Hence, each oxidized NADPH would require an additional cycle in the conversion of pyruvate to malate. Each of these cycles involves the hydrolysis of one ATP to ADP and the oxidation of one NADH. Especially pathways 7 and 14 in the conversion of acetol to pyruvate are of interest since they only require a net consumption of one mole of NADPH per mole of pyruvate produced. Thus, only a single pyruvate-malate cycle would be necessary to balance NADPH consumption. Since there are several possible pathways in acetone metabolism, there might be species differences in the principal pathways which are used for acetone degradation.

Another reason for the limited capacity of the pathways in question is that several of their intermediates, such as methylglyoxal and acetone, are toxic in higher or even moderate concentrations. Thus, the organisms can use these pathways only to a limited extent. A further limiting factor may arise if the decarboxylation of acetoacetate indeed proceeds spontaneously. As it had been observed that Caucasian people can adapt to the diet of inuit within about three weeks [23], the limitation in capacity of these pathways is likely to get less severe over time, probably due to induction of specific enzymes along those pathways.

We investigated the energetic requirements of the presented pathways in terms of ATP consumption under the assumption that all other metabolites, including NADPH and NADH need to be balanced (Fig. 6A and Text S1). We found that the presented pathways consume 6–22 moles of ATP for the production of one mole of glucose and two moles of CO₂ from four moles of acetyl-CoA (requiring a flux of two through the described pathways). The most efficient pathway in terms of ATP consumption proceeds via the oxidation of methylglyoxal to pyruvate, oxidizes two moles of NADPH and reduces two moles of NADH (pathway 7, displayed in Fig. 3). However, since the mitochondrial NADH concentration is already high during ketogenesis [47], pathway 14 might be more favorable because even two moles of cytosolic NADH are reduced on this pathway. Using this pathway the cost for the synthesis of one mole of glucose is increased to 16 moles of ATP.

Moreover, we computed the Gibbs free energy change of the overall pathways to check whether they are thermodynamically feasible (Fig. 6A). We performed these computations for gluconeogenesis starting from acetyl-CoA and palmitate, respectively. Thus, we found that the overall Gibbs free energy change is in the range of −1162 to −1449 for gluconeogenesis from acetyl-CoA and in the range of −1345 to −1610 for gluconeogenesis from palmitate. Thus, the presented pathways are all thermodynamically feasible.

In order to analyze the role of the described pathways during prolonged starvation and fasting, we computed for amino acids, fatty acids, lactate and glycerol how much energy in form of ATP is regained in the net balance if they are used for gluconeogenesis and subsequently catabolized. This quantity, termed gluconeogenic energy efficiency, is defined as the ratio of the above mentioned net amount of energy and the energy that would be obtained by catabolizing the substrate directly (Fig. 7A). That quantity equals unity if both pathways provide the same amount of ATP. Furthermore, we determined how well amino acids, fatty acids, lactate and glycerol are suited for the storage of glucose. This measure, termed glucose storage efficiency, is defined as the relative amount of glucose regained if these compounds are produced from glucose and subsequently converted back into glucose (Fig. 7B). Details on the calculation are given in Text S1.

Gluconeogenic energy efficiency and glucose storage efficiencies of a selected list of compounds are displayed in Fig. 6B. We found that 53–74% of the energy remains if fatty acids are used for gluconeogenesis using the most efficient and most inefficient pathways, respectively (pathways 7 and 20). Thus, 26–47% of the energy contained in fatty acids is lost if they are used for gluconeogenesis. For glucogenic amino acids, in contrast, the energy loss is much smaller; the gluconeogenic energy efficiency is in the range from 73% (leucine)–96% (valine) with a value of 87% for the amino acid composition of a typical dietary protein. For glycerol, the gluconeogenic energy efficiency is 95%. These values can explain the particular efficiency of carbohydrate reduced and ketogenic diets like Atkins diet for weight reduction. The reason is likely to be the increased energy loss of gluconeogenesis from fatty acids and ketogenic amino acids in comparison to gluconeogenesis from glucogenic amino acids. Indeed, intermediates of the pathway for gluconeogenesis from fatty acids have been observed in subjects on the Atkins diet [40]. This is also supported by the observation that the traditional diet of inuit does not lead to obesity in spite of the high content in fat. In contrast, new dietary habits of inuit implying a higher consumption in carbohydrates often lead to obesity [48].

Comparing the glucose storage efficiency of the described compounds (Fig. 6B), we find fatty acids, using pathway 7, at the lower end with a storage efficiency of 50% in comparison to 39% for glycine, 78% for alanine and 86% for glycerol. Hence, the conversion of glucose to fatty acids and gluconeogenesis from fatty acids results in a loss of half of the glucose. These values show that fatty acids are not very well suited as glucose storage since their use as such is associated to a higher loss of glucose equivalents of carbohydrates in comparison to glycerol and amino acids that are the major carbohydrate storage compounds besides glycogen. Nevertheless, as discussed above, the utilization of fatty acids as glucose storage gives the body additional flexibility in the utilization of its storage compounds and appears to be used as such in situations during which gluconeogenesis is active. Moreover, both quantities can be useful for examining the effect of caloric restriction on ageing which is known to extend life span in a large number of organisms [49].

Summarizing our findings, it can be concluded that a thorough, systematic and detailed in-silico investigation of the stoichiometrically feasible routes from fatty acids to glucose based on an experimentally corroborated genome-scale metabolic network provides new insight into human metabolism under glucose limitation. It confirms earlier, anecdotal evidence and hypotheses about gluconeogenesis from fatty acids via acetone and provides hitherto unrecognized pathways for that conversion. This provides a plausible explanation for the surprising independence from nutritional carbohydrates over certain periods (e.g. upon the low-carbohydrate diet of inuit, in hibernating animals and embryos of egg-laying animals). Moreover, we provided a detailed analysis of the energetic balance of these pathways, which explains their limited capacity and their contribution to the particular efficiency of carbohydrate reduced and ketogenic diets.

Elementary flux patterns have been introduced as a new theoretical tool for the analysis of metabolic pathways in genome-scale metabolic networks [21]. Within a subsystem of metabolism, that is, a set of reactions of interest, elementary flux patterns correspond to basic route through that subsystem that are compatible with steady-state fluxes through the entire network. Thus, every elementary flux pattern is associated to at least one steady-state flux of the entire system and corresponds to the set of reactions used by this steady-state flux in the subsystem. The property of elementarity in the definition of elementary flux pattern requires that no elementary flux pattern can be written as set union of other elementary flux patterns. A formal definition will be provided next.

Given the stoichiometric matrix of a reaction network we assume for simplicity that the first reactions make up the subsystem of interest. A flux pattern is defined as a set of reactions within the subsystem that is compatible with at least one steady-state flux of the entire system. Hence, a set of reaction indices is called a flux pattern if there exists at least one flux vector that fulfills the following conditions:

Furthermore, we call a flux pattern elementary if this set of reactions cannot be written as set union, of other flux patterns. For more details see Kaleta et al (2009).

Elementary flux patterns can be used to elucidate all possible pathways consuming a certain compound and producing another. This process builds upon a successive expansion of the subsystem under study to reactions that belong to alternative pathways. It will be outlined by way of a small example network comprising glycolysis and the pentose phosphate pathway (Fig. 8). Within this system we want to find all pathways producing ribose-5-phosphate (R5P), a precursor of histidine and nucleotide syntheses from glucose (Glc).

We start with a subsystem encompassing the inflow reaction of Glc and the outflow of R5P (Fig. 8A). Two elementary flux patterns are found. One of them only contains the inflow reaction of Glc and the other the inflow of Glc as well as the outflow of R5P. The first elementary flux pattern indicates the existence of a pathway consuming Glc at steady state without using the outflow of R5P. This corresponds to the glycolytic pathway producing glycerol-3-phosphate (G3P) which is subsequently drained from the system (Fig. 8C). The other flux pattern corresponds to a pathway producing R5P (Fig. 8B). Since we found no elementary flux pattern containing the outflow of R5P without the inflow of Glc we can conclude that the inflow reaction is required for the production of R5P. Otherwise we would have obtained a second elementary flux pattern containing only the outflow of R5P.

Next, we need to determine an elementary mode through the entire system using exactly the reactions of the elementary flux pattern in the subsystem. Such an elementary mode can be obtained using linear programming [21]. This elementary mode corresponds to a first pathway for the production of R5P from Glc. From this initial pathway it is possible to deduce reactions that are essential for the conversion of R5P to Glc (see Text S1 for more details). Thus, we find that in addition to the inflow of Glc, the conversion of Glc to glucose-6-phosphate (G6P) and the conversion of ribulose-5-phosphate (Ru5P) to R5P are required for production of R5P at steady state. The knowledge of essential reactions can simplify the analysis in two ways. First, we do not need to include essential reactions into the subsequent subsystems since every pathway producing R5P will use them anyway. Second, if we find several sequences of essential reactions the task of searching for pathways can be split into sub-tasks. Each sub-task then consists in the search for a pathway connecting a product of a sequence of essential reactions and the educt of the next sequence of essential reactions.

In order to determine reactions that belong to alternative pathways, we include the reactions of the first detected pathway into the subsystem of the next step. As noted above, we need not to add essential reactions and consequently, the subsystem of the second step comprises three reactions (Fig. 8D): the inflow of glucose, the conversion of G6P to Ru5P and the outflow of R5P. This subsystem gives rise to three elementary flux patterns. One of them contains the inflow of G6P and the outflow of R5P (Fig. 8E). This elementary flux pattern corresponds to a pathway for the production of R5P. This flux pattern is associated to an elementary mode that also uses reactions that do not belong to the subsystem (and are not essential reactions). Hence, we have identified reactions that belong to an alternative route. These reactions are subsequently added to the subsystem of the third step (Fig. 8F). In this subsystem we find eight elementary flux patterns, two of which contain the outflow of R5P (Figs. 8G and 8H). Determining the elementary modes associated to these elementary flux patterns, we find that both use only reactions that are either essential for the pathway or belong to the subsystem. Thus, we have identified all pathways producing R5P from Glc. These pathways correspond to the elementary modes associated to each of the two flux patterns containing the outflow of R5P.

We computed the 100 shortest elementary flux modes producing glucose 6-phosphate from acetyl-CoA using a previously described method [33]. This method allows one to enumerate elementary flux modes with increasing number of reactions. The entire set of elementary flux modes cannot be computed for the genome-scale metabolic network of humans since their number is too large [32]. For the computation we set the metabolites H₂O, CO₂, Pi, Ppi, protons, O₂, ATP, ADP, AMP, GTP, GDP, NADH, NAD⁺, NADPH, NADP⁺, coenzyme A and HCO₃⁺ to external status to obtain elementary flux modes differing in the underlying carbon conversion pathway rather than in co-factor balancing reactions.

We calculated the Gibbs free-energy changes of the described pathways. We performed these calculations for two scenarios: gluconeogenesis from acetyl-CoA and from palmitate. For the first scenario, we assumed that additionally to the energetic balance as depicted in Fig. 6 four moles of acetyl-CoA are converted into one mole of glucose, four moles of coenzyme A and two moles of carbon dioxide. For the second scenario, we assumed that biosynthesis starts from 0.5 moles of palmitate yielding an additional 3.5 moles of NADH as well as FADH and hydrolyzing one mole of ATP through β-oxidation of fatty acids. We calculated the Gibbs free energy change bywhere corresponds to the Gibbs free energy of formation, to the universal gas constant, to the temperature, to the stoichiometric coefficient of the th product and to the stoichiometric coefficient of the th substrate of the pathway. We assumed a pH-value of 7.2 and a temperature of 37°C. We used measured Gibbs free-energy of formation when available [50], [51] and estimated values otherwise [52]. For concentrations we used measured values if they were available. The corresponding values and references are given in Text S1.