Abstract
Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.