Genetically-identical cells can show remarkable intercellular variability in the level of a given protein which is commonly known as the gene expression noise. Besides intrinsic fluctuations that arise from the inherent stochasticity of the biochemical processes, a significant source of expression noise is extrinsic. Such extrinsic noise in gene expression arises from cell-to-cell differences in expression machinery, transcription factors, cell size, and cell cycle stage. Here, we consider the synthesis of a transcription factor (TF) whose production is impacted by a dynamic extrinsic disturbance, and systematically investigate the regulation of expression noise by decoy sites that can sequester the protein. Our analysis shows that increasing decoy numbers reduce noise in the level of the free (unbound) TF with noise levels approaching the Poisson limit for large number of decoys. Interestingly, the suppression of expression noise compared to no-decoy levels is maximized at intermediate disturbance timescales. Finally, we quantify the noise propagation from the TF to a downstream target protein and find counterintuitive behaviors. More specifically, for nonlinear dose responses of target-protein activation, the noise in the target protein can increase with the inclusion of decoys, and this phenomenon is explained by smaller but more prolonged fluctuations in the TF level. In summary, our results illustrates the nontrivial effects of high-affinity decoys in shaping the stochastic dynamics of gene expression to alter cell fate and phenotype at the single-cell level.
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