The small world inside large metabolic networks

Abstract

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics e¡orts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and ¢nd that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The smallworld architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.

Exploring the cell's network with molecular imaging

“…Food webs are described as "scale-free" networks (18). In mapping the metabolic network in E. coli, somewhat surprisingly, a scale-free network was identified (19). Subsequently, it was found that the cell's proteome exhibits a similar scale-free topology (20).…”

“…Three properties are of particular interest. One statistic is the network's characteristic path length, which is the shortest path length measured as the least number of links between two nodes averaged for all pairs of nodes in the network (19,24,26,30). This is a global measure of a network (24,26,30).…”

“…Another statistic is the clustering coefficient, which is the fraction of all neighboring nodes that are connected to each other (24,26,30). It describes the connectivity ("cliquishness") around a node (19). This fraction is averaged over all nodes in the network (30) and is a local measure of a network (19,24,26).…”

“…It describes the connectivity ("cliquishness") around a node (19). This fraction is averaged over all nodes in the network (30) and is a local measure of a network (19,24,26). The third is vertex degree, which measures the number of links a node uses to connect to other nodes (30).…”

“…While it is unusual for mathematics and physics to trail sociology, this term is derived from sociology jargon; these networks were first encountered in the now classic social psychology experiment by Milgram (31). These characteristics eventually resulted in the phrase "six degrees of separation" popularized by John Guare's play and movie, which describes the connectedness in social networks (19,24,26,31,32).…”