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Many transcription factors bind to DNA with a remarkable lack of specificity, so that regulatory binding sites compete with an enormous number of nonregulatory “decoy” sites. For an autoregulated gene, we show decoy sites decrease noise in the number of unbound proteins to a Poisson limit that results from binding and unbinding. This noise buffering is optimized for a given protein concentration when decoys have a 1/2 probability of being occupied. Decoys linearly increase the time to approach steady state and exponentially increase the time to switch epigenetically between bistable states.
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