The Gaussian Genome

Abstract

Recent studies in biophysics suggest transcription factor interactions with non-regulatory DNA are sequence-dependent and vary along the DNA strand. This makes numerical calculation of the grand canonical partition function cumbersome and renders predictions of genetic activity a seemingly insurmountable task. Using the cumulant-generating function of the normal distribution, we derive the partition function and define an effective binding energy, a single quantity which accounts for the contributions from the whole spectrum of binding energies. Applying our approach to LacI and RNAP, two prominent lac operon transcription factors, we obtain theoretical results which are in good accord with the actual biophysical picture, namely, the standard deviations of their binding energy distributions, on one hand, and binding mode differentiation on the other.