Before revision:  We quantify the dependence of the strength of this effect on the different parameters in the problem. In addition, 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  .
After revision:  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 .