When many noisy genes optimize information flow

It is often emphasized that the control of gene expression is noisy. A seemingly contradictory view is that control mechanisms have been optimized to transmit as much information as possible with a limited number of molecules. Here, we revisit a simple model where a single transcription factor species (TF) controls a large number of target genes. We include only the physically required noise sources—random arrival of TFs at their targets and counting noise in the synthesis and degradation of mRNA. By deriving a scaling law for the information capacity of the network under the constraint of finite mRNA resources, we show that the information transmitted about TF concentration is maximized when these resources are distributed across the largest possible number of target genes. To realize this capacity, the distribution of TF concentrations must be biased toward smaller values. Thus, in some limits, information transmission is optimized when individual expression levels are noisy. We explore other notable features of the optimal networks, including a dominance of weak binding interactions and emergent sloppy modes of the parameters. Our results connect to the surprising observation that many critical genes operate at very low concentrations.