In this paper, we describe an analysis framework for characterizing the directed interactions between the enzymes of a metabolic network following a physiological perturbation. This framework combines modularity and Bayesian analysis to infer causality relationships within systematically detected metabolic sub-networks. This framework supports the use of prior biochemical knowledge and efficient heuristic search algorithms for structure learning; moreover, it avoids the limitations of models that only consider pair-wise correlations. The present framework uses binary data discretization, stochastic noise generation, and the greedy (hill climbing) search algorithm to calculate the candidate Bayesian networks as directed acyclic graphs (DAG). The analysis focused on the pyruvate flux node, which is a key junction between anaerobic glycolysis and the TCA cycle.

Applied to metabolic flux data describing the time course of inflammation-mediated liver hypermetabolism, our analysis discriminated between flexible, i.e. physiological state dependent, and conserved pathway structures. A similar result was obtained for adipocytes undergoing differentiation and subsequent lipid loading, where highly conserved and directed interactions were found for enzymes of both lipogenesis and lipolysis. The learned sequence of cause-and-effect relationships suggested that the pyruvate carboxylase reaction is subject to regulation by both lipolysis and lipogenesis, where the influence of lipogenesis is mediated though lipolysis. Interestingly, lipolysis was not only directly influenced by a step in lipogenesis, but also by the flux of pyruvate kinase, a key step in glycolysis. This finding may at least partially explain how the adipocyte achieves a dynamic balance between lipogenesis and/or lipolysis. When the flux of triglyceride (TG) synthesis is high and/or the flux of pyruvate (and hence glycerone phosphate) is high, the overaccumulation of fat in the cell could be prevented by the direct activation of lipolysis via pyruvate kinase before the pyruvate carbons become sequestered into TG. Indeed, maximum likelihood estimates of the node parameters predicted that lipolysis is active when either fatty acid esterification or glycolysis flux is high; on the other hand, lipolysis is low only when both fluxes are also low.

Taken together, these results suggest that it is feasible to use probabilistic, data-driven network inference to identify new and meaningful causal relations that are not predicted by knowledge of traditional pathway structures. For example, this study found that the activation of lipase has a direct influence on the activation of pyruvate carboxylase. Another example involves the regulation of lipase by pyruvate kinase. While further, molecular studies are needed for conclusive validation of these predictions, evidences in the published literature provides support for these causal relations. For example, acyltransferase and pyruvate kinase are both known to be activated by insulin, which is a lipogenic hormone that ultimately increases fat storage in the adipocyte. Recent studies suggest that energy homeostasis is regulated to defend against drastic weight gain, i.e. adipose tissue mass expansion. Therefore, lipolysis is proportional to the amount of stored fat, and hence should be triggered if lipogenesis exceeds some threshold.