Biological networks are complex systems where the interactions between the components give rise to a variety of systems-level structures, functions, and regulatory features that govern these functions. Examples include transcriptional regulatory networks, protein networks, and metabolic networks. To understand and eventually design these functions and features, a useful first step is to study the intervening levels of organization between the global network and the individual components. These intermediate structures are often referred to as ‘modules' and generally consist of a large number of directly interacting components. In recent years, advances in genomics and proteomics have supported the development of a number of different modeling approaches to analyze gene and protein network modules. In this study, we develop a novel divisive algorithm for the identification and characterization of metabolic network modules. To consider the dynamic influences of biochemical activity on the modularity of metabolic networks, our algorithm integrates metabolic flux analysis with a combined graph theory-stoichiometric pathway space analysis. As model systems, we examined two mammalian metabolic systems, the rat liver and mouse fat cells, for which detailed metabolic profiles were available.

Briefly, directed graph models were constructed with metabolites as nodes and reaction involvement as edges. Metabolic fluxes were calculated from metabolic profile data using a previously reported optimization-based approach. Graph edges were scaled with corresponding reaction fluxes such that the shortest distance between a pair of nodes was inversely proportional to the magnitude of the fluxes of the intervening reactions. The directed and flux-scaled graphs were iteratively decomposed into smaller sub-networks, or modules, using a global connectivity index based on edge-betweenness centrality. At each level of decomposition, the putative modules were scored for their biochemical likelihood through projections onto an abstract pathway space. The pathway space was calculated as an inventory of elementary flux modes (EFMs) supported by the network. Optimality of network decomposition was determined as a function of the fractional match between the putative modules and the EFMs.

Our results indicate that node-to-node connection diversity, introduced through flux weights, significantly influences the calculation of metabolic network modules. Moreover, the impact of the connection diversity is cell-type specific. For example, the three characteristic metabolic modules of the liver were: (1) gluconeogenesis/pentose phosphate pathway (PPP), (2) amino acid metabolism/urea cycle, and (3) fatty acid metabolism. In comparison, the metabolism of fat cells was dominated by a single large module consisting of lipid synthesis and degradation reactions. By incorporating time-varying metabolic activity data, our analysis also found different patterns of modularity following physiological stresses. For example, the modularity of the fat cell network exhibited a significant change at day 4 following a chemical induction of adipogenic differentiation, which also coincided with observable changes to the cellular morphology. Taken together, our results suggest that the functional organization of metabolic pathways are time-variant, and reflect the shifting objectives of the cell.

In conclusion, our findings are consistent with the notion that larger metabolic networks are organized into smaller functional units. In this respect, the modularity analysis presented here should provide a useful framework for identifying key clusters of reactions that participate in a common metabolic function. While the model systems examined here involve on the order of ~ 100 reactions and metabolites, the computational methods used in this study are scalable and thus applicable to metabolomic data sets of very large sizes. Finally, our directed graph representation of the metabolic network also enables the trace of carbon fluxes between modules. Prospectively, outcomes of modularity analysis will aid in the efficient localization of the sites of actions of both targeted and non-targeted stimuli. For example, by comparing modularity patterns with and without treatment, a drug compound's bioactivity may be characterized for multiple modes of action and potentially toxic side effects.