Conformation of Circular DNA in 2 Dimensions

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 ν is topologically invariant and equal to the SAW value (in the present case ν = 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 ≈ 8 ℓp. Additionally, the bond correlation function scales with the molecular length L as predicted. For molecular lengths L ≤ 5 ℓp, circular DNA behaves like a stiff molecule with approximately elliptic shape. From a theoretical and experimental perspective, the physics of linear polymers is well-established [1] and its predictions were also confirmed for linear DNA [2, 3, 4, 5]. On the contrary, topologically constrained polymers, like circular or knotted DNA, are still challenging, and the topological effects on the static and dynamic properties are a matter of debate A convergence has been reached on the theoretical value of the critical exponent ν describing the divergence of the radius of gyration with the length of circular and knotted polymers [7, 13, 14], and fixes this value to the SAW exponent. Recently, experimental evidence has been found that the scaling exponent ν for knotted DNA in 3D corresponds to the 3D linear SAW value [15]. For circular DNA in 3D, diffusion measurements have pointed in the same direction [16]. Real polymers, like DNA, have a mechanical stiffness which strongly influences the scaling properties as well as the bond correlation function, making the theoretical treatment more complex. Semiflexible polymer models were put forward in order to include this into the theory [17, 18, 19], and showed the existence of a gaussian regime between the rigid and the self-avoiding regimes [4]. Many theoretical investigations concerning the properties of circular molecules were motivated by the observation of DNA in closed form [20, 21, 22, 23, 24]. These studies are relevant for biology because DNA frequently adopts circular form in vivo [25]. Furthermore, the large persistence length ℓ p of DNA permits to test semi-flexible polymer theories and the effect of correlation along the molecule. In this Letter, we present the first results for circular DNA in 2D spanning lengths from L/ℓ p = 2 up to 120, where L is the plasmid length. We show that the gaus-sian regime is suppressed in …