(570e) Metabolic Flux-Based Modularity Using Shortest Retroactive Distances

Modularity analysis offers a route to better understand the organization of cellular biochemical networks as well as to derive practically useful, simplified models of these complex systems. While there is general agreement regarding the qualitative properties of a biochemical module, there is no clear consensus on the quantitative criteria that may be used to systematically derive these modules. Recently, we proposed a round trip distance metric, termed Shortest Retroactive Distance (ShReD), to characterize the cyclical interaction between any two reactions in a biochemical network and to group together network components that mutually influence each other [1]. Applied to a liver metabolic network, the ShReD partitions found hierarchically arranged modules, many of which contained reactions that were cyclically related by the shared consumption and production of cofactors. One limitation of this analysis was that it relied on uniform edge weights, implicitly assuming that all the reactions in the network are equally engaged.  In this work, we update the ShReD-base partitioning algorithm with a novel edge-weighting scheme that enables the use of metabolic flux data for metabolic state-dependent modularity analysis.

In a reaction-centric graph model of a metabolic network, a quantitative measure of the interaction between a pair of connected reaction nodes can be obtained from the flux of the intermediary metabolite. We define the weight of an edge between a connected pair of reaction nodes as the inverse of the fraction of the intermediate metabolite production flux that is directed towards the destination node. This definition is consistent with the intuitive notion that a large metabolite flux from one reaction to another corresponds to a strong interaction, and thus is represented by a relatively short edge, whereas a weak interaction is represented by a long edge. To examine the impact of the flux weights, we applied the modified partitioning algorithm to flux data describing adipocyte differentiation and enzyme inhibition [2]. Our results indicate that the metabolic state of the adipocyte significantly impacts the modular assignment of two key upstream reactions in fatty acid synthesis and glycerogenesis, pyruvate carboxylase (PCX), and phosphoenolpyruvate carboxykinase  (PEPCK), which connect carbohydrate metabolism to lipogenesis. Our analysis also identifies several robust reaction pairs that consistently partition together into the same module regardless of metabolic state. Examples include reaction pairs that couple the pentose phosphate shunt and palmitate synthesis through the production and consumption of NADPH. Lastly, we show that the modular organization of adipocyte metabolism is relatively stable with respect to the inhibition of an enzyme compared to a major physiological change such as cellular differentiation.  

[1] Sridharan GV, Hassoun S, Lee K (2011) Identification of Biochemical Network Modules Based on Shortest Retroactive Distances. PLoS Comput Biol 7(11): e1002262. doi:10.1371/journal.pcbi.1002262

[2] Si, Yaguang, Hai Shi, and Kyongbum Lee. “Impact of perturbed pyruvate metabolism on adipocyte triglyceride accumulation.” Metabolic engineering 11, no. 6 (November 2009): 382-90.