Information flow and the accuracy of concentration measurements in a genetic network*

Many genes are regulated by transcription factor (TF) proteins which bind to DNA and control the synthesis of messenger RNA (mRNA). The information which output mRNA or protein levels carry about input TF concentrations is a measure of regulatory power. All this information passes through a bottleneck, the occupancy of the relevant binding sites along the DNA, and random arrival of TFs at these sites sets an irreducible noise level, which in turn limits the information capacity. We explore these issues in the gap gene network of the early fly embryo, where recent work shows that the concentrations of these transcription factors carry enough information to specific cellular position to 1% precision along the length of the embryo. But how accurately would the system need to “measure” these concentrations in order to extract this information? We show that these measurements need to be more accurate than is plausible given the physical limits at a single binding site, suggesting that the complex array of multiple binding sites provides a solution to the problem of efficient information transmission.