Weak Transcription Factor Clustering at Binding Sites can Facilitate Information Transfer from Molecular Signals

Transcription factor concentrations provide signals to cells that allow them to regulate gene expression to make correct cell fate decisions. Calculations for noise bounds in gene regulation suggest that clustering or cooperative binding of transcription factors decreases signal-to-noise ratios at binding sites. However, clustering of transcription factor molecules around binding sites is frequently observed. We develop two complementary models for clustering transcription factors at binding site sensors that allow us to study information transfer from a signal, the morphogen Bicoid, to a variable relevant to development, namely, future cell fates. We find that weak cooperativity or clustering can allow for maximal information transfer, especially about the relevant variable. The timescale of measurement is crucial for predicting the optimal clustering strength: for short measurements, finite clustering is optimal because it allows for the implementation of a switch, while for long measurements, a range of weak clustering strengths allow binding site sensors to access near-maximal developmental information. Weak transcription factor clustering also helps binding site sensors achieve optimality consistent with the information bottleneck bound, which encodes an optimal trade-off between conveying relevant information and making costly measurements: changes in clustering in conjunction with changes in the binding energy can shift the binding site sensor along the optimal bound, and towards an optimal trade-off between obtaining information about the signal and obtaining relevant information.