Molecular Sequestration Enhances Precision in Timing of Intracellular Events

Abstract

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. Binding of transcription factors (TFs) to decoys is shown to be an indirect but crucial way to control the dynamics and stochasticity in gene regulation. Here, we explore how such decoys impact 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 first passage time (FPT). As binding introduces nonlinearity, an exact mathematical analysis is challenging. However, assuming quasi-static equilibrium (QSE) for binding/unbinding reactions, we can analytically discern the impact of decoys on FPT statistics by using small noise approximation (SNA) and reformulating the FPT question in terms of a suitable variable whose dynamics is linear. The stability of the decoy-bound TFs influences the impact of decoys on FPT statistics. The presence of decoys makes the mean FPT long and even longer for unstable bound TFs. 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, the noise in FPT is not directly influenced by the number of decoys or their binding affinities. 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.