Protein-Mediated DNA Loops: Effects of Protein Bridge Size and Kinks

TL;DR

This study examines how protein bridge size and kinks influence the likelihood of DNA looping, using the Worm-Like Chain model and numerical methods to quantify free energy changes.

Contribution

It introduces a detailed analysis of DNA looping probabilities considering protein bridge size and kinks, extending existing models with numerical and saddle point methods.

Findings

Looping free energy decreases with larger protein bridges.

Kinks significantly lower the free energy required for looping.

Quantitative estimates of free energy reductions for specific DNA and protein configurations.

Abstract

This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size r of a protein bridge and/or the presence of a kink at half DNA length. The DNA is modeled by the Worm-Like Chain model, and the probability of loop formation is calculated in two ways: exact numerical evaluation of the constrained path integral and the extension of the Shimada and Yamakawa saddle point approximation. For example, we find that the looping free energy of a 100 base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a protein of r = 10 nm length. It further decreases to 5 kT when the loop has a kink of 120 degrees at half-length.