When many noisy genes optimize information flow

Abstract

It often is emphasized that gene expression is noisy. A seemingly contradictory view is that control mechanisms have been optimized to squeeze as much information as possible out of a limited number of molecules. Here we revisit these issues in a simple model where a single transcription factor (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. If the cell has a limited total number of mRNA molecules, then the capacity to transmit information 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. In addition, the dependence of information transmission on the parameters of this multi-gene system has a "sloppy" spectrum, so that optimal performance can co-exist with substantial variability.