Exact Chemical Potentials for Prokaryotic Transcription Factors


Transcriptional regulation is the most ubiquitous mechanism for control of gene expression, motivating the development of quantitative models for the kinetics and evolutionary dynamics of transcription factors. Occupancy probabilities for transcription factor binding sites are Fermi- Dirac distributed; while it is commonly granted that the chemical potential of such a distribution is well-modeled by an ideal gas approximation, it is not difficult to solve for it numerically. We do so for 27 transcription factors in Escherichia coli and show that in many cases the ideal gas approximation can diverge sharply from the exact solution, leading to underestimation of site occupancies by orders of magnitude. We conclude that researchers may observe qualitatively different behaviors in models of transcriptional regulation which admit approximate versus exact chemical potentials.