Supercoiling and Denaturation of DNA Loops

We study the statistical mechanics of small DNA loops emphasizing the competition between elasticity, supercoiling, and denaturation. Motivated by recent experiments and atomistic molecular dynamics simulation, we propose a new coarse-grained phenomenological model of DNA. We extend the classical elastic rod models to include the possibility of denaturation and nonlinear twist elasticity. Using this coarse-grained model, we obtain a phase diagram in terms of fractional overtwist and loop size that can be used to rationalize a number of experimental results which have also been confirmed by atomistic simulations.

Figure 1

Phase diagrams for $A/K=1/2$ and $\gamma =0.7$ with lengths measured in units of $\ell =1/h$ (we have used $A=250\ell$) for (a) $P/(K\ell )=1.5$, (b) $P/(K\ell )=10$, with no negative supercoiled phase at these loop sizes, and (c) $P/(K\ell )=\frac{17}{2}$, showing the appearance of the negatively supercoiled phase. Inset: Typical configurations from MD simulations of all atom 90 bp homonucleotide DNA loop in circle, supercoiled, and denatured states.