Thermodynamic Metabolic Flux Analysis of E. coli
Comparison of the predicted regulatory sites of the E. coli metabolic network with gene expression data
The magnitude of free energy change of a biochemical reaction dictates if the reaction is subject to regulation. Typically, biochemical reactions that operate close to equilibrium are not transcriptionally regulated, while reactions that operate far from equilibrium are insensitive to perturbations in the metabolite concentrations and can therefore be subject to regulation as the flux through such reactions can be manipulated by enzyme regulation alone. In contrast, thermodynamic bottlenecks are reactions that operate close to equilibrium. Consequently, even minor perturbations in the concentration of the reactants or products can force the net flux through these reactions to zero, thereby blocking them or changing their directions. Reactions identified using TVA for which ΔrG' is strictly negative were classified as candidates for regulation as these reactions cannot reach equilibrium under the activity ranges studied. Thus, based on the above criteria, we used the TVA analysis to predict both bottleneck reactions and candidates for regulation based on the observation that reactions that are irreversible under most conditions are likely to be regulated [4, 7, 8].
Beard, Qian and co-workers were pioneers in conducting energy balance analysis using non linear optimization to eliminate flux cycles generated by FBA in E. coli[9–11]. Kummel et al. further refined this method to quantitatively analyze metabolomic data sets in E. coli and S. cerevisiae[7], while Henry and co-workers [4] extended the method further to the genome scale to identify feasible metabolite activity ranges, bottleneck reactions, and reactions subject to regulatory control in the genome-scale network of E. coli. However, we note that, in previous studies, the identified bottleneck reactions and regulatory sites were not compared against gene expression data and were not thus comprehensively validated. It is in this aspect that our present work differs significantly as we have analyzed microarray data from a central repository with over 800 experimental datasets.
In order to validate predicted regulatory targets and bottleneck reactions in E. coli, we identified the range of gene expression for those reactions that were previously predicted [4, 6] to be operating close to equilibrium (thermodynamic bottleneck reactions) and those reactions that operated far from equilibrium (reaction subject to regulatory control) in E. coli (Figure 1A & 1B and Additional File 2: Supplemental Tables S3 & S4). As bottleneck reactions operate close to thermodynamic equilibrium, they are not likely to be regulated at the transcript level and correspondingly, the range of the gene expression fold change is expected to be narrower relative to the putative regulatory sites. The results of the comparison of ranges of gene expression data for thermodynamic bottleneck reactions and putative regulatory sites are shown in Figure 1. It was observed that the expression fold change for genes corresponding to the thermodynamic bottleneck reactions (Figure 1B) were narrower when compared to the reactions subject to regulatory control (Figure 1A), thereby validating the claim that these reactions were subject to regulation in vivo in E. coli. To verify if these results were statistically significant, we performed a two sided wilcoxon rank sum test considering the ranges in the reported gene expression fold changes for these two classes of reactions. Our analysis indicated a p value of 3.9960e-04, thereby showing that the medians are statistically significant for the two sample sets.
Correlation of predicted bottleneck reactions with exchange coefficients from C13 isotope labeling studies
Since thermodynamic bottleneck reactions operate in the vicinity of equilibrium, they are highly reversible in nature and can consequently have significant forward and reverse fluxes. Thus, we can associate an exchange coefficient (defined as the ratio of the forward to reverse flux assuming the forward flux is greater than the reverse flux) with these reactions. C13 isotope labeling studies can be used to measure the intracellular metabolic fluxes as well as the exchange coefficients [12]. Also, the exchange coefficients represent a measure of reversibility of a reaction and are determined from the experimentally measured mass isotopomer fractions of the amino acids. Hence, for these thermodynamic bottleneck reactions, we decided to evaluate previously published exchange coefficients from C13 isotope labeling experiments in aerobically grown E. coli with glucose as the substrate [13]. We found that three of the predicted bottleneck reactions, namely, phosphoglucose isomerase (PGI), glyceraldehyde 3-phoshpate dehydrogenase (GAPD), and malate dehydrogenase (MDH) had statistically significant exchange coefficients (PGI: 0.761, GAPD:0.402, MDH: 0.02), suggesting there was a significant forward and reverse flux at these predicted bottleneck reactions and that these reactions operate close to equilibrium in vivo. Consequently, the utility of using TMFA for the prediction of regulatory sites and bottleneck reactions was validated for genome-scale metabolic network of E. coli.
Thermodynamic Metabolic Flux Analysis of G. sulfurreducens
Predicted reactions subject to regulatory control in G. sulfurreducens and the corresponding gene expression ranges
In order to evaluate the potential of the TMFA for the analysis of a relatively poorly characterized organism such as G. sulfurreducens compared to E. coli, we implemented the TMFA for the genome-scale metabolic network of G. sulfurreducens. We subsequently used the TVA to calculate the range of Gibbs free energy change for each reaction in the network resulting in the identification of thermodynamic bottlenecks and putative regulatory sites (Figure 2A and 2C). Furthermore, application of thermodynamic constraints identified three others reactions namely, CYSTL (Cystathionine b-lyase), PPS (Phosphoenol pyruvate synthase) and DXPS (1-deoxy-D-xylulose-5-phosphatesynthase), whose free energy ranges indicate that they were on the threshold of regulation (See Additional File 2: Supplemental Tables S5, S6 & S7).
There were several common reactions among the predicted regulatory and bottleneck reactions for both E. coli and G. sulfurreducens, suggesting that the flux through these reactions is perhaps regulated in a similar manner across different metabolic networks. For example, malate dehydrogenase (MDH) which was identified to be thermodynamically constrained in E. coli is similarly identified as a constrained reaction in the G. sulfurreducens. In addition, Cystathionine b-lyase (CYSTL), 4-aminobenzoate synthase (ADCL), acetolactate synthase (ACLS), dihydrodipicolinate synthase (DHDPS), citrate synthase (CS), malic enzyme (ME1x) were predicted to be regulated in E. coli and these reactions were identified by TVA to be subject to regulation in G. sulfurreducens as well. Of these reactions, CYSTL, DHDPS and ACLS form a linear pathway in both G. sulfurreducens and E. coli.
We then evaluated the range of gene expression fold changes for the predicted regulatory targets and bottleneck reactions based on previously published microarray data (See Additional File 3: Supplemental Table S8) for G. sulfurreducens (Figure 2). These results indicate that the genes corresponding to the predicted regulatory candidates appear to have a broader range of fold changes (Figure 2D) relative to the thermodynamic bottleneck reactions, while the predicted bottleneck reactions have the narrowest range of gene expression (Figure 2B). Furthermore, a two sample t-test assuming un-equal variance suggested a p value of 0.029 that is statistically significant at the 95% confidence level.
Prediction of Thermodynamic bottleneck reactions in G. sulfurreducens and the correlation with corresponding exchange coefficients
Thermodynamic variability analysis in the absence of uncertainty about the standard free energy changes identified seven reactions that participate as bottlenecks in the metabolic network of G. sulfurreducens (Figure 2A). The analysis was done in the absence of uncertainty as we wanted to focus our analysis on the ranges the free energies could assume when they were influenced by the activities of metabolites alone. In order to validate these predictions, we decided to investigate previously published C13 flux analysis data of G. sulfurreducens.
Analysis of C13 labeled flux analysis data revealed exchange coefficients associated with two of the seven identified bottleneck reactions. The exchange coefficient for MDH and FUM were 0.29 and 0.37 respectively [14]. These results show that reactions that have significant forward and reverse fluxes are highly reversible. This results in scrambling of the C13 label at this step. Hence, this observation validates the prediction that these reactions operate close to equilibrium in vivo.