Conformation of Circular DNA in 2 Dimensions

TL;DR

This study investigates the 2D conformations of circular DNA on mica, confirming the invariance of the critical exponent and revealing how topology and dimensionality influence DNA behavior across different length scales.

Contribution

It provides experimental validation that the critical exponent for 2D circular DNA is topologically invariant and explores the crossover between rigid and self-avoiding regimes.

Findings

Critical exponent $ u$ equals 3/4, invariant to topology.

Crossover between rigid and self-avoiding regimes at $L oughly 8 \, ext{ell}_p$.

Circular DNA behaves as a stiff, elliptic shape for $L \, extless \, 5 \, ext{ell}_p$.

Abstract

The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent $\nu$ is topologically invariant and equal to the SAW value (in the present case $\nu=3/4$), and that the topology and dimensionality of the system strongly influences the cross-over between the rigid regime and the self-avoiding regime at a scale $L\approx 8 \ell_p$. Additionally, the bond correlation function scales with the molecular length $L$ as predicted. For molecular lengths $L\leq5 \ell_p$, circular DNA behaves like a stiff molecule with approximately elliptic shape.