  We examine the binding of transcription factors to DNA in terms of an
information transfer problem. The input of the noisy channel is the biophysical
signal of a factor bound to a DNA site, and the output is a distribution of
probable DNA sequences at this site. This task involves an inherent tradeoff
between the information gain and the energetics of the binding interaction -
high binding energies provide higher information gain but hinder the dynamics
of the system as factors are bound too tightly. We show that adaptation of the
binding interaction towards increasing information transfer under a general
energy constraint implies that the information gain per specific binding energy
at each base-pair is maximized. We analyze hundreds of prokaryote and eukaryote
transcription factors from various organisms to evaluate the discrimination
energies. We find that, in accordance with our theoretical argument, binding
energies nearly maximize the information gain per energy. This work suggests
the adaptation of information gain as a generic design principle of molecular
recognition systems.
