How the DNA sequence affects the Hill curve of transcriptional response

TL;DR

This paper reveals that high Hill coefficients in transcription factor binding can occur without cooperativity, due to disordered binding energies and steric interactions, impacting interpretations of transcriptional regulation.

Contribution

It analytically demonstrates a non-cooperative mechanism leading to high Hill coefficients, challenging traditional interpretations in transcriptional response analysis.

Findings

High Hill coefficients can arise without cooperative binding.

Disordered binding energies and steric effects explain this phenomenon.

Implications for estimating transcription factor numbers in cells.

Abstract

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.