- Research article
- Open Access
A network perspective on metabolic inconsistency
© Sonnenschein et al.; licensee BioMed Central Ltd. 2012
- Received: 16 November 2011
- Accepted: 14 April 2012
- Published: 14 May 2012
Integrating gene expression profiles and metabolic pathways under different experimental conditions is essential for understanding the coherence of these two layers of cellular organization. The network character of metabolic systems can be instrumental in developing concepts of agreement between expression data and pathways. A network-driven interpretation of gene expression data has the potential of suggesting novel classifiers for pathological cellular states and of contributing to a general theoretical understanding of gene regulation.
Here, we analyze the coherence of gene expression patterns and a reconstruction of human metabolism, using consistency scores obtained from network and constraint-based analysis methods. We find a surprisingly strong correlation between the two measures, demonstrating that a substantial part of inconsistencies between metabolic processes and gene expression can be understood from a network perspective alone. Prompted by this finding, we investigate the topological context of the individual biochemical reactions responsible for the observed inconsistencies. On this basis, we are able to separate the differential contributions that bear physiological information about the system, from the unspecific contributions that unravel gaps in the metabolic reconstruction. We demonstrate the biological potential of our network-driven approach by analyzing transcriptome profiles of aldosterone producing adenomas that have been obtained from a cohort of Primary Aldosteronism patients. We unravel systematics in the data that could not have been resolved by conventional microarray data analysis. In particular, we discover two distinct metabolic states in the adenoma expression patterns.
The methodology presented here can help understand metabolic inconsistencies from a network perspective. It thus serves as a mediator between the topology of metabolic systems and their dynamical function. Finally, we demonstrate how physiologically relevant insights into the structure and dynamics of metabolic networks can be obtained using this novel approach.
- Primary Aldosteronism
- Flux Balance Analysis
- Metabolic Reconstruction
Genomic knowledge allows compiling an inventory of an organism’s enzymes and thus the subsequent reconstruction and simulation of its metabolic system using constraint-based modeling (CBM) techniques. Compensating the lack of detailed information on the systems parameters, e.g., enzyme kinetics, gene regulation etc., CBM has proven to be a valuable tool for genome-scale system analysis. For example, flux balance analysis (FBA) has been used to predict with high accuracy the lethality of gene deletions in unicellular organisms by taking only the metabolic system’s stoichiometry, the assumption of optimal growth (implicit gene regulation), and a specified growth medium into account (see e.g., for a study involving Escherichia coli or, for a study involving Saccharomyces cerevisiae).
Duarte et al., published a genome-scale representation of human metabolism based on genomic, bibliographic, and biochemical information. In contrast to metabolic representations of unicellular organisms, the following caveats play a role in the modeling of multicellular reconstructions, in general, and in particular for the human system: (i) it is difficult to define environmental conditions for a multicellular system, (ii) usually not enough information is available about the cell-type specificity of human metabolic pathways, and (iii) cellular objectives, a prerequisite for flux balance analysis, are hard to define and validate. The precision of CBM predictions increase with the availability and accuracy of constraints, as they aid narrowing down the potential solution space to the biologically meaningful system states. Thus, integrating experimental data can help overcome the previously mentioned limitations.
In the present work, we will integrate human transcriptome data from a cohort of healthy controls and aldosterone producing adenomas (APA) of adrenal glands from primary aldosteronism (PAL) patients with the metabolic reconstruction Human Recon 1. Primary aldosteronism is a common form of hypertension with hypokalemia and suppressed renin-angiotensin system caused by autonomous aldosterone production. This data, among other data sets covered in the supporting information, will serve us to demonstrate how the metabolic contextualization dramatically increases the resolution of our perception of the data.
We will compare the inconsistency I to the metabolic coherence (MC) introduced previously, which is a purely topological quantity that measures the fragmentation of effective metabolic gene networks (see Figure1b). The coherence of metabolic gene network topology and expression patterns is quantified as follows (see also Materials and Methods): in order to extract effective subnetworks, we map genes with expression values above threshold directly onto a metabolic gene network of human metabolism. Then, we compute the ratio of connected nodes and overall nodes in the effective subnetwork. This ratio is then converted into a z-score, by using a random distribution of expression changes as a null model (effectively choosing the same amount of affected nodes). This z-score is our metabolic coherence (MC), which measures the amount of network coherence between gene expression profiles and metabolic pathways.
The comparison between these two indices is interesting, as they highlight different properties of the network dynamics. The inconsistency index I, on the one hand, measures the level of disagreement between expression data and anticipated network dynamics. The MC index, on the other hand, measures the amount of coordinated (connected) expressed reaction structure, which can only be observed after contextualization of the expression data.
Figure1d shows a flow diagram that describes the structure and necessary steps of our comparative analysis. Based on this quantitative comparison, we will conduct a topological characterization of the individual contributions to I and show that valuable information can be extracted from them.
Inconsistency and metabolic coherence uncover two types of metabolic behavior
How does the purely topological metabolic coherence method compare to the previously applied GIMME approach? Measuring the metabolic coherence for the adenoma transcript data reveals a similar pattern (see Figure2c). Although not quite as distinct as for the inconsistency measure (compare to Figure2a), two groups of high and low coherence are visible, which leads us to the following comparison of inconsistency and metabolic coherence.
Comparison of metabolic coherence and inconsistency
We have shown above, that GIMME, as well as the metabolic coherence, permit an interrogation of the transcriptome data in a metabolic context. Both provide biological meaningful insights, which could not have been obtained by classical means of microarray data analysis. But how does GIMME compare to the metabolic coherence in detail, which is a purely topological score that inquires far less parameters and assumptions?
In Figure3d the dependence of the correlation between inconsistency and the MC on the chosen growth medium is shown. The distribution of correlation coefficients is narrow (between −0.75 to −0.4 for r and −0.73 to −0.35 for ρ), regardless of which correlation measure is considered. This indicates that both inconsistency and MC and their correlation seem not be strongly dependent on the environmental conditions provided. Furthermore, the correlation values obtained for the reference medium (i.e. r=−0.64 and ρ=−0.68, see also above) seem to originate in the left tail of the distributions, suggesting a rather high correspondence with the in vivo situation.
We confirmed that the observed anticorrelation between both measures is not a feature of the adenoma data, but holds true for other transcriptome data as well (see Figure S1 and S2 in Supporting Information Additional file1: Text S1).
Inconsistency contributions in central human metabolism
Individual contributions to the inconsistency
The correlation between metabolic coherence and inconsistency suggests a connection between both measures, and thus the possibility of interpreting the inconsistency values from the perspective of network topology. In order to investigate this point, we will decompose the inconsistency value into a vector of individual contributions, i.e., reactions that have been reinserted during the optimization procedure in order to achieve the targeted flux-level of the objective function. We further define the contribution strength of a reaction as the number of contributions it makes to the inconsistencies of a data set divided by the size of the respective data set.
On the other hand, a group of reactions with very high contribution strengths seems to contribute non-specifically and independently from the gene expression data. In the following, we want to elaborate on this set of reactions, and will use certain categories and topological markers to characterize them.
A reaction is expressed in vivo but the measured gene expression intensity falls below the threshold t under most or all experimental conditions (just below threshold). This is a consequence of the rigid application of a universal threshold. Topologically, these contributions often disrupt a chain of otherwise expressed reactions (chain disruptor).
A reaction is expressed in vivo but, e.g., wrong GPR associations, missing isozymes, wrong gene annotations, erroneous data etc., make it invisible for the analysis. Again, these artifacts are often characterized by an interrupted chain of expressed reactions (chain disruptor).
The reaction is not expressed, but it has to be utilized by GIMME due to the following reasons:
The stated objective function does not reflect the situation present in the cell. Defining the objective functions as the output of the system, these reactions contributions should often lie close to it (close to output layer).
The chosen media composition does not reflect the in vivo environment in which the experimental data has been obtained. The preliminary FBA step in GIMME is naive about the in vivo medium composition and uses everything provided and suitable for the maximization of the objective function. As GIMME enforces a certain achievement of the objective flux predicted by FBA, many of the transport reactions used by FBA will also be used by GIMME. Topologically, these reaction contributions are characterized by lying close to the provided medium components (close to input layer).
Too many missing gene-protein-reaction associations (GPR), either due to non-enzymatic reaction steps or knowledge gaps, before and after the contributing reaction can lead to wrongly activated paths, as missing GPR information is not punished by GIMME (invisible path).
Alternative expressed routes to the objective function are available in vivo, but are not covered by the metabolic reconstruction. This leads to reaction contributions that are characterized by producing essential precursors for the objective function, and thus constitute bottlenecks in the system (bottleneck).
Table1 lists topological and biological classifications for a selection of the 11 unspecific contributions as well as 8 selected differentially contributing reactions (see Figure5; the full listing is provided in Supporting Additional file1: Text S1 Table S1). The topological characterization from the enumeration above have also been applied to the specific contributions.
2-Aminoadipate transaminase;one out of two 2-oxoadipate producing reactions; missing GPR assoc. in all precursors.
Proline dehydrogenase; participates in a cycle that converts nadh to fadh2 (Figure 6); not expressed (Figure S5b).
Diphosphomevalonate decarboxylase; essential step in the cholesterol biosynthesis pathway; not expressed; wrong or missing GPR assoc. (Figure S5c).
Glycerol kinase; not expressed in control and LIG, indicating that glycerol (provided in the in silico medium) might not be available as a in vivo medium component; slightly elevated expression levels in LIG (see Figure S5i).
Phenylalanine 4-monooxygenase; converts phenylalanine (provided in the in silico medium) into tyrosine (not provided in the in silico medium); the high unspecific contribution strength indicates that tyrosine might be available as an in vivo medium component.
4-Hydroxyphenylpyruvate dioxygenase; involed in tryosine to fumarate and acetoacetate conversion; not expressed (see Figure S5m).
Fumarate transport (cytosol/mitochondria); expression just below threshold (see Figure S5o).
Glutaryl-CoA dehydrogenase; involved in the 2-oxoadipate pathway (see Figure S5); elevated expression levels in LIG (see Figure S6a).
Pyruvate dehydrogenase; entry point to the TCA cycle; elevated expression levels in LIG (see Figure S6c).
Methylmalonyl-CoA epimerase; involved in isoleucine degradation; slightly elevated expression levels in LIG (see Figure S6d).
Mevalonate kinase; an essential step in cholesterol biosynthesis; decreased expression levels in LIG and HIG (see Figure S6e).
Glucose-6-phosphate dehydrogenase; slightly elevated expression levels in LIG (see Figure S6f).
7-Dehydrocholesterol reductase; involved in cholesterol biosynthesis; slightly elevated expression levels in LIG (see Figure S6g).
Hexokinase; first step in glycolysis; slightly elevated expression levels in LIG (see Figure S6h).
Squalene epoxidase; decreased expression levels in LIG and HIG (see Figure S6i).
Proline dehydrogenase (PROD2) emerges as one of the major unspecific inconsistency contributors (see Table1). Together with Δ1-pyrroline-5-carboxylate reductase (P5CRx), it is involved in a cycle that interconverts NADH into FADH2 (see Figure6), a necessary redox factor for the biosynthesis of cholesterol biosynthesis, the ultimate precursor for all steroid pathways and concomitantly aldosterone production. The cycle involves synthesis and degradation of L-proline, where Δ1-pyrroline-5-carboxylate (1pyr5c) acts as precursor as well as degradative product. In the cytosol, P5CRx seems to be expressed in most of the samples, whereas expression levels for PROD2 fall all below the GIMME threshold. It is intriguing that the gene expression profiles are almost reversed in the mitochondrion, where PROD2m (a mitochondrial version of PROD2) is expressed (at least in the control) and P5CRxm (a mitochondrial version of P5CRx) is not expressed. It is known that the distinct reaction steps of the Δ1-pyrroline-5-carboxylate-proline cycle are localized over different subcellular locations: (i) the dehydrogenation of proline to 1pyr5c takes place in the mitochondrion (i.e. by PROD2m), (ii) 1pyr5c emerges from the mitochondrion and (iii) is converted back to proline in the cytosol, (iv) which is then transported back into the mitochondrion, closing the cycle. In fact, these are also the steps suggested by the observed expression patterns. So why does GIMME predict the cycle to take place exclusively in the cytosol, although PROD2 expression is clearly absent in all samples? Checking the model revealed missing mitochondrial transporters for 1pyr5c (a transporter for proline is available), prohibiting its correct physiological operation and suggesting necessary amendments to the human model. Furthermore, the reduced expression of PROD2m in LIG and HIG constitutes an interesting deviation to metabolic signature of the control group.
2-Oxoadipate (2oxoadp) is one of the precursors for acetyl-CoA (see Figure7a), which is heavily utilized in cholesterol biosynthesis. Only two paths lead to 2-oxoadipate, i.e., L-tryptophan (Figure7a) and L-lysine degradation (Figure7b). The many missing GPR associations (Invisible pathway) on the path leading from lysine to 2-oxoadipate (Figure7b), surely promote the usage of this specific pathway versus the alternative pathway leading from tryptophan to 2-oxoadipate (Figure7a), explaining the high contribution strength of AATAi (see Figure5 and Table1). The expression data suggests the absence of both catabolic pathways. However, it is intriguing to see that all subsequent steps from 2-oxoadipate to acetyl-CoA seem to be expressed in the control and LIG (Figure7a), implying that 2-oxiadipate might still be metabolized in the samples. Further investigations in this direction might be promising, especially in the light of the elevated expression levels (LIG vs. control) found for glutaryl-CoA dehydrogenase (GLUTCOADHm) and acetyl-CoA C-acetyltransferase (ACACT1rm).
There is an ongoing interest in the generic and network-based properties of metabolic systems, though discussions of metabolic systems from a network perspective have frequently been criticized and are prone to artifacts, when one attempts to biologically interpret the observed topological properties. Table1 on the other hand shows, how a topological perspective can help guide the biological interpretation of experimental data and constraint-based analysis results. Classifying metabolic inconsistencies from a topological perspective allowed us to think of such inconsistencies in terms of bottlenecks, paths and branching ratios, etc. As an extension to this work we would like to formalize our approach in the future.
Comparing the contribution strengths of individual reactions among the different sample categories (control, LIG, HIG) revealed unspecific contributions to the inconsistency, as well as a group of reactions that differentially contribute in a specific fashion. We constructed a methodological framework for the topological classification of the inconsistency contributions. Therefore, topological markers were developed for the characterization of both, specific and unspecific contributions, thus enabling a thorough understanding of the context-specific flux-activity results. It turned out, that on the one hand, the specific contributions cast light on an unforeseen diversity of alterations in the physiology of adrenal gland adenomas and, on the other hand, the unspecific contributions provide entry points for the iterative refinement of the metabolic reconstruction.
We have presented a sequence of three results on the network-mediated correspondence between gene expression patterns and metabolic systems: (1) We have shown the general agreement between GIMME and a purely topological method from, both of them capable to detect distinct physiological behaviors in the adrenal gland tumors. (2) We have extended the GIMME approach by moving from the inconsistency score to the inconsistency vector that contains the various contributions to the metabolic inconsistency. (3) We have been able to formulate biological hypotheses for these vector components based on comparison with network topology.
An extended “Methods” section is provided in the Supporting Information.
Model of human metabolism
All flux balance simulations were conducted using the metabolic reconstruction Recon 1, a genome-scale compartmentalized representation of human metabolism, which is available in SBML format via the BIGG database.
Gene expression data
Aldosterone producing adenomas were obtained through the COMETE network from patients who had undergone surgery for lateralized PAL at the Hôpital Européen Georges Pompidou between 2002 and 2006. Methods for screening and criteria for diagnosing PAL were in accordance with institutional guidelines and have been described recently. The clinical and biological characteristics of the patients are resumed in Boulkroun et al.. Here, logarithmized transcript levels from 58 adenomas and 11 control tissue samples were mapped onto the GPR (gene-protein-reaction) associations included in the Human Recon 1 model. Therefore, it was necessary to replace logical AND and OR by min and max functions, respectively, following the protocol described in. The eleven control normal adrenals (CA) were obtained from enlarged nephrectomies (kindly provided by the department of Pathology of the University Hospital of Rouen, Hôpital Tenon as described previously). The EBER2 gene expression has been published in.
Context-specific flux balance analysis
Context-specific flux balance analysis of human expression data was conducted using the GIMME algorithm as described in and in the introduction to this work. ATP-production was implemented as a cellular objective by introducing an artificial reaction that consumes cytosolic ATP. The aldosterone objective was implemented as the maximization of flux through aldosterone synthase (model ID: P45011B21m). The pathway to aldosterone was initially blocked in the metabolic reconstruction. Further analysis revealed 4-Methylpentanal as a dead-end metabolite inhibiting steady-state flux to the aldosterone synthase reaction. The introduction of an artificial drain for 4-Methylpentanal restored the functionality of the whole pathway. Furthermore, the same conservative approach was chosen regarding missing GPR: reactions without GPR associations were assumed to be expressed, i.e., having expression values above t. The aldosterone objective and the parameters t=2 and l=0.8 were used throughout the study, if not stated otherwise.
The growth medium was defined as in (see Table S1 in Supporting Information Additional file1: Text S1). It contains both glucose and glycerol as carbon sources, the amino acids L-arginine, L-histidine, L-isoleucine, L-leucine, L-lysine, L-Methionine, L-phenylalanine, L-threonine and L-tryptophane, as well as the fatty acids palmitic and linoleic acid. Aerobic conditions were assumed by leaving oxygen consumption unconstrained. Random media conditions were constructed by picking randomly between 4% (approx. the number of enabled exchange reactions in the reference medium) to 100% of all available exchange reactions in the model and assigning random upper and lower boundaries in the intervals and to them. Oxygen, protons, sulfate, phosphate, water were assumed to be always available. In case of random media sampling, inconsistency values I have been normalized by the objective function’s flux in order to make them comparable.
Before constructing the gene network out of the bipartite representation, overly abundant currency metabolites, e.g., ATP, H2O, NADH etc., have been excluded by removal of 4% of the highest connected compounds from each compartment in the network. The presented results, e.g., the strong anti-correlation between MC and inconsistency, are not particularly sensitive to this parameter (see Additional file1: Text S1 Supplementary Figure S7).
The authors wish to thank Pr. H. Lefebvre and Dr. E. Louiset (University Hospital and University of Rouen, France) for kindly providing tissue samples from control adrenal glands, and Pr. PF. Plouin (Hôpital Européen George Pompidou, Paris, France) and the COMETE network for providing adrenal tumor samples. Furthermore, the authors would like to thank Martin Sigurdsson for providing us with the growth medium conditions.
This work was supported in part by PHRC grant AOM 06 179 and by grants from INSERM and Ministère Délégué à la Recherche et des Nouvelles Technologies for the COMETE Network. This work was furthermore funded by the Agence Nationale pour la Recherche (ANR Physio 2007, No.: 013-01, to: MCZ, AB), the Fondation pour la Recherche sur l’Hypertension Artérielle (AO 2007, to: MCZ, AB), and the Genopole Evry (to: AB), and by Deutsche Forschungsgemeinschaft (grant HU-937/8-1 to MTH) JFGD is a recipient of a CoNaCyT Ph.D. fellowship from the Mexican government (No.: 207676/302245). NS was supported by a Jacobs University scholarship. All authors have read and approved the manuscript.
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