  Transcription regulation is largely governed by the profile and the dynamics
of transcription factors' binding to DNA. Stochastic effects are intrinsic to
this dynamics and the binding to functional sites must be controled with a
certain specificity for living organisms to be able to elicit specific cellular
responses. Specificity stems here from the interplay between binding affinity
and cellular abundancy of transcription factor proteins and the binding of such
proteins to DNA is thus controlled by their chemical potential.
  We combine large-scale protein abundance data in the budding yeast with
binding affinities for all transcription factors with known DNA binding site
sequences to assess the behavior of their chemical potentials. A sizable
fraction of transcription factors is apparently bound non-specifically to DNA
and the observed abundances are marginally sufficient to ensure high
occupations of the functional sites. We argue that a biological cause of this
feature is related to its noise-filtering consequences: abundances below
physiological levels do not yield significant binding of functional targets and
mis-expressions of regulated genes are thus tamed.
