  Many transcription factors bind to DNA with a remarkable lack of specificity,
so that regulatory binding sites compete with an enormous number of
non-regulatory 'decoy' sites. For an auto-regulated 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.
