Symmetries in metabolic networks of <i>Escherichia coli</i>

The over-representation of motifs was previously considered a viable definition of building blocks in biological networks. Here, we construct an alternative definition based on invariance properties of enzymes in metabolic networks of <i>Escherichia coli</i>. In particular, we consider input trees of each enzyme that bundle all metabolic reactions where information is transmitted. Isomorphisms of such input trees point to symmetric enzymes grouped in "fibers" of the metabolic network that process equivalent dynamics. Such groups of enzymes constitute an alternative concept of building blocks which can be systematically classified into topological types of input trees according to their complexity. In contrast to motifs and modules, enzymes in such fibers are not necessarily mutually connected but still can be functionally related. Our analysis finds novel varieties of building blocks that capture such symmetries in hitherto unknown "composite Fibonacci" fibers. Lending credence to their significance as fundamental building blocks, we observe that enzymes in fibers are functionally more homogeneous than their network motif and module counterparts, suggesting that fibers point to a novel way of building blocks that capture metabolic functionality on a topological level.