It is easy to imagine that the transcription factors (TFs) are superfast regulators of gene expression, but in reality it might take several minutes before a TF finds and binds its target sequence. As a result, negative feed-back (where the expression of a TF is inhibited by the TF itself) cannot at the same time be fast and strong.
If the TF binds strongly to the repressor site, most proteins are necessarily produced immediately after cell replication and if the binding is very week, the protein production is essentially linear; in both cases the negative-feedback is virtually nonexistent. In a study recently published in Nature Communications, we show that there is an optimal TF binding strength, where the time the binding site is free is not dependent on TF concentration. An important implication is that the TF binding strength is not necessarily correlated to its functional importance as a gene regulator.