Protein-mediated DNA loops: Effects of protein bridge size and kinks

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 wormlike 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 k(B)T to 13 k(B)T when the loop is closed by a protein of r=10 nm length. It further decreases to 5 k(B)T when the loop has a kink of 120 degrees at half-length.