  The Hill coefficient is often used as a direct measure of the cooperativity
of binding processes. It is an essential tool for probing properties of
reactions in many biochemical systems. Here we analyze existing experimental
data and demonstrate that the Hill coefficient characterizing the binding of
transcription factors to their cognate sites can in fact be larger than one --
the standard indication of cooperativity -- even in the absence of any standard
cooperative binding mechanism. By studying the problem analytically, we
demonstrate that this effect occurs due to the disordered binding energy of the
transcription factor to the DNA molecule and the steric interactions between
the different copies of the transcription factor. We show that the enhanced
Hill coefficient implies a significant reduction in the number of copies of the
transcription factors which is needed to occupy a cognate site and, in many
cases, can explain existing estimates for numbers of the transcription factors
in cells. The mechanism is general and should be applicable to other biological
recognition processes.
