Stochasticity in protein levels drives colinearity of gene order in metabolic operons of Escherichia coli

In bacterial genomes, gene order is not random. This is most evident when looking at operons, these often encoding enzymes involved in the same metabolic pathway or proteins from the same complex. Is gene order within operons nonrandom, however, and if so why? We examine this issue using metabolic operons as a case study. Using the metabolic network of Escherichia coli, we define the temporal order of reactions. We find a pronounced trend for genes to appear in operons in the same order as they are needed in metabolism (colinearity). This is paradoxical as, at steady state, enzymes abundance should be independent of order within the operon. We consider three extensions of the steady-state model that could potentially account for colinearity: (1) increased productivity associated with higher expression levels of the most 59 genes, (2) a faster metabolic processing immediately after up-regulation, and (3) metabolic stalling owing to stochastic protein loss. We establish the validity of these hypotheses by employing deterministic and stochastic models of enzyme kinetics. The stochastic stalling hypothesis correctly and uniquely predicts that colinearity is more pronounced both for lowly expressed operons and for genes that are not physically adjacent. The alternative models fail to find any support. These results support the view that stochasticity is a pervasive problem to a cell and that gene order evolution can be driven by the selective consequences of fluctuations in protein levels.