HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text (PDF) Supplemental Data All Versions of this Article: 18/6/746 03-0475fjev1    most recent Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by LI, Z. Articles by CHAN, C. Search for Related Content PubMed PubMed Citation Articles by LI, Z. Articles by CHAN, C.

Inferring pathways and networks with a Bayesian framework¹

Department of Chemical Engineering and Material Science, Michigan State University, East Lansing, Michigan, USA

²Correspondence: Michigan State University, Department of Chemical Engineering and Material Science, 1257 EB, East Lansing, MI 48824, USA. E-mail: krischan{at}egr.msu.edu

SPECIFIC AIMS

The goal of this study was to illustrate a Bayesian based framework capable of inferring hepatocellular networks from metabolic data. Reverse engineering of pathways and networks provides a framework for predictive modeling and hypotheses testing to gain deeper insight into biological systems. We developed a framework that combines data-driven reverse engineering and model-driven statistical testing methods to infer biochemical networks. Evaluating this methodology initially against the known biochemical network(s) provides confidence in novel networks that may be uncovered from the data using this framework.

PRINCIPAL FINDINGS

1. Sub-networks such as the tricarboxylic acid (TCA) and urea cycles were inferred from metabolic data
Using Bayesian network analysis we reverse-engineered metabolic subnetworks from the flux data, namely, the TCA (Fig. 1 A) and urea (Fig. 1C ) cycles_. The TCA cycle is important for producing cellular energy (ATP) from the oxidation of fuels and generating intermediates for the gluconeogenic pathway. The analysis was able to infer causal relationships (solid lines), but not links between pathways 10–11 and 12–13 (dashed lines) shown in Fig. 1B . The analysis identified the coupling between the TCA cycle and oxidative phosphorylation (flux nos. 51–53). This recognition is encouraging, since oxidative phosphorylation by which electron transfer from NADH and FADH₂ to O₂ forms ATP is coupled to the TCA cycle. It is noteworthy that in our model, pathway no. 10–11 combines two pathways, namely, citrate - isocitrate and isocitrate - -ketoglutarate; and likewise, citrate - -ketoglutarate combines with pathway no. 12–13. Another important hepatic function is removal of NH₄⁺ given that elevated levels of NH₄⁺ are toxic. NH₄⁺ (derived typically from protein and amino acid metabolism) is converted to urea by the liver through the urea cycle. Bayesian network analysis was able to "learn" most of the pathways in the urea cycle. The link between pathways 16 and 15 was not learned by Bayesian network analysis (Fig. 1D ).

View larger version (29K): [in this window] [in a new window]   Figure 1. Reverse Engineered TCA and urea cycles. A) Actual metabolic network of TCA cycle. Each node represents a metabolite and connections (arcs) between nodes represent the metabolic fluxes. B) TCA cycle inferred by Bayesian network analysis, Solid connections were learned and dashed connections were not learned by Bayesian network analysis. C) Actual metabolic network of urea cycle. Each node represents a metabolite and connections between nodes represent the metabolic fluxes. D) Urea cycle inferred by Bayesian network analysis. Solid connections were learned and dashed connections were not learned by Bayesian network analysis.

2. Intracellular TG sub-networks were postulated and compared with Bayesian metric score
Despite the significant amount of information known about the hepatic metabolic network, understanding is incomplete. Due to imperfect knowledge of the metabolic network, it is plausible that important latent variables not measured but revealed by the model may be linked to currently unassociated pathways and may indeed exist. The ability of Bayesian network analysis to infer the known metabolic subnetworks from the flux data lend credence to the latent relationships it may uncover. Previously, we found that intracellular triglyceride (TG) accumulation was not captured completely by the partial least squares (PLS) method. A possible explanation may be due to insufficient details of the metabolic pathways pertinent to intracellular TG.

Applying a constraint-based algorithm to infer a sub-network containing pathways linked to TG, we found that intracellular TG (flux no. 76) was influenced most by ß-hydroxybutyrate (BOH) dehydrogenase (flux no. 50), glutaminase (flux no. 38), and glutamate dehydrogenase I (flux no. 36); while extracellular TG (flux no. 70) was affected by lactate dehydrogenase (LDH) (flux no. 8), glyceraldehyde-3-P (G3P) (flux no. 5), free fatty acid uptake (flux no. 72), glutamate dehydrogenase I (flux no. 36), and asparaginase (flux no. 45). Latent variable detection algorithm was applied to the aforementioned pathways, along with several other pathways (flux nos. 2,26,54,61,64,73,74,75) and results suggest that latent variables may exist which influence intracellular TG and the glutamate related pathways (flux nos. 36 and 38). From currently known pathways related to TG metabolism and inferred connections, we postulated several alternative networks, shown in Fig. 2 . We tested the hypothesis that flux no. 50 may be a latent variable between flux no. 76 and flux no. 36 (Fig. 2A ) and between flux no. 76 and flux no. 38 (Fig. 2C ). Similarly, we tested the hypothesis that flux no. 36 was a latent variable between flux nos. 76 and 38 (Fig. 2B ) and flux no. 38 was a latent variable between flux nos. 76 and 36 (not shown, but will be denoted as 2B alternate). Finally, in Fig. 2D , we tested the possibility that flux no. 50 was the latent variable influencing flux nos. 76 and 38, in combination with flux no. 38 as the latent variable for flux nos. 76 and 36. We evaluated the likelihood of these models with a Bayesian metric score and prediction accuracy of the postulated model. With the help of a metric score and the model’s prediction accuracy the model illustrated in Fig. 2D is the most likely of the several hypothetical models postulated. As an indirect confirmation of the model in Fig. 2D , we applied the Markov Chain Monte Carlo (MCMC) algorithm, which is a search and score method, to pathways illustrated in Fig. 2 . Since this is a computationally expensive method, application is not feasible for the entire metabolic network. On the other hand, we were able to obtain a solution for the sub-network after 500 iterations. This search and score method identified the connection between flux nos. 38 and 76, which we postulated as being the latent variable between flux nos. 36 and 76. This indirectly lends support to our hypothesis that flux no. 38 may be the latent variable linking flux no. 36 with flux no. 76.

View larger version (38K): [in this window] [in a new window]   Figure 2. Postulated sub-networks for intracellular TG accumulation, learned with IC* algorithm. A) Postulated network that assumes ß-hydroxybutyrate as the latent variable regulating intracellular TG accumulation and glutamate dehydrogenase pathways. The network’s Bayesian metric score is -168. B) Postulated network that assumes glutamate dehydrogenase pathway as the latent variable between intracellular TG accumulation and glutaminase. The network’s Bayesian metric score is –158. C) Postulated network that assumes ß-hydroxybutyrate as latent variable regulating intracellular TG accumulation and glutaminase pathways. The network’s Bayesian metric score is -155. D) Postulated network that assumes ß-hydroxybutyrate as the latent variable regulating intracellular TG accumulation and glutaminase pathways while glutaminase influences intracellular TG accumulation and glutamate dehydrogenase pathways. The network’s Bayesian metric score is –152.

3. Sensitivity analysis of Bayesian network identifies the important pathways in a network
A sensitivity analysis was applied to the intracellular TG sub-network, with intracellular TG (flux no. 76) as the response variable. The results indicate that the intracellular TG level is most sensitive to ß-hydroxybutyrate (flux no. 50) and glutaminase (flux no. 38), and least sensitive to glutamate dehydrogenase (flux no. 36) and cholesterol ester uptake (flux no. 75). Although the sensitivity coefficients are all small, the coefficients for ß-hydroxybutyrate (flux no. 50) and glutaminase (flux no. 38) are generally an order of magnitude larger than the other pathways, indicating that they have more impact on TG storage. Thus, changing flux nos. 50 and 38 will more likely alter the level of intracellular TG accumulation as oppose to altering other pathways.

4. Noise in the data and omitted measurements are two possible reasons for the missing relationships
In the reversed Bayesian network, several causal relations were missed, for example, pathways 12–13 in Fig. 1B and 15–16 in Fig. 1D . Two possible explanations could account for this, either noise in the data or omitted measurements. We tested the first hypothesis by adding noise to our data and examining its effect on the resulting network structure. We added 3 levels of noise (5%, 10%, and 20%) to the data. When 5% noise was added, the pathway 16–17 disappeared and pathway 15–16 was learned. This indicated the possibility that pathway 15–16 may have been missed due to noise in the data. Adding 10% noise to the data resulted in pathway 17–18 being replaced by a new pathway 16–18; and adding 20% noise eliminated both pathways 15–16 and 17–18. Results suggested that Bayesian network analysis could tolerate a certain degree (5%10%) of noise within the data to provide a satisfactory level of performance, represented by the number of causal relation inferred. Although when noise was increased to a higher level (e.g., 20%), the performance of Bayesian network approach decreased as reflected in the higher number of missed causal relations. We tested the second explanation by omitting one measurement from the data and examining the pathways inferred. To illustrate this idea, we removed the lactate measurement from the dataset, which resulted in the omission of two additional pathways, pathways 87 and 7–9 in Fig. 1B , which were no longer inferred by the Bayesian network analysis. Therefore, both noise and missing measurements could contribute to an incomplete or incorrect reversed Bayesian network.

CONCLUSIONS

We developed a Bayesian-based framework, schematically shown in Fig. 3 , to infer network structures from metabolic data. From the resulting network, we can identify the relevant variables that most affect target function(s), thereby providing a framework to optimize target function(s) and insight into the underlying mechanisms that govern the metabolic state. Finally, the ability of this methodology to infer well-known metabolic structures from experimental data provides confidence in the ability of this methodology to infer other networks, such as, genetic regulatory networks from gene data.

View larger version (16K): [in this window] [in a new window]   Figure 3. Bayesian network based framework. Mutual information based Bayesian network structure learning algorithm was first applied to the metabolic profile to infer the regulatory network. Incorporating known biological knowledge into the formulation of the hypothetical networks further refined the structures. Bayesian metric score identified the mostly likely network structure.

FOOTNOTES

¹ To read the full text of this article, go to http://www.fasebj.org/cgi/doi/10.1096/fj.03-0475fje; doi: 10.1096/fj.03-0475fje

This article has been cited by other articles:

				D. R. Boverhof and T. R. Zacharewski Toxicogenomics in Risk Assessment: Applications and Needs Toxicol. Sci., February 1, 2006; 89(2): 352 - 360. [Abstract] [Full Text] [PDF]

				G. V. HarshaRani, S. J. Vayttaden, and U. S. Bhalla Electronic Data Sources for Kinetic Models of Cell Signaling J. Biochem., June 1, 2005; 137(6): 653 - 657. [Abstract] [Full Text] [PDF]

				H. Li, L. Lu, K. F. Manly, E. J. Chesler, L. Bao, J. Wang, M. Zhou, R. W. Williams, and Y. Cui Inferring gene transcriptional modulatory relations: a genetical genomics approach Hum. Mol. Genet., May 1, 2005; 14(9): 1119 - 1125. [Abstract] [Full Text] [PDF]

				Z. Li and C. Chan Integrating Gene Expression and Metabolic Profiles J. Biol. Chem., June 25, 2004; 279(26): 27124 - 27137. [Abstract] [Full Text] [PDF]

This Article Full Text (PDF) Supplemental Data All Versions of this Article: 18/6/746 03-0475fjev1    most recent Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by LI, Z. Articles by CHAN, C. Search for Related Content PubMed PubMed Citation Articles by LI, Z. Articles by CHAN, C.