Weighting schemes in metabolic graphs for identifying biochemical routes

Metabolism forms an integral part of all cells and its study is important to understand the functioning of the system, to understand alterations that occur in disease state and hence for subsequent applications in drug discovery. Reconstruction of genome-scale metabolic graphs from genomics and other molecular or biochemical data is now feasible. Few methods have also been reported for inferring biochemical pathways from these networks. However, given the large scale and complex inter-connections in the networks, the problem of identifying biochemical routes is not trivial and some questions still remain open. In particular, how a given path is altered in perturbed conditions remains a difficult problem, warranting development of improved methods. Here we report a comparison of 6 different weighting schemes to derive node and edge weights for a metabolic graph, weights reflecting various kinetic, thermodynamic parameters as well as abundances inferred from transcriptome data. Using a network of 50 nodes and 107 edges of carbohydrate metabolism, we show that kinetic parameter derived weighting schemes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left[ {\left( {\frac{{K_{M}^{S} }}{{ K_{M}^{P } }}} \right){\text{ and }}\left( { \frac{{K_{M} }}{{K_{cat} }} } \right)} \right]$$\end{document} fare best. However, these are limited by their extent of availability, highlighting the usefulness of omics data under such conditions. Interestingly, transcriptome derived weights yield paths with best scores, but are inadequate to discriminate the theoretical paths. The method is tested on a system of Escherichia coli stress response. The approach illustrated here is generic in nature and can be used in the analysis for metabolic network from any species and perhaps more importantly for comparing condition-specific networks.