Conformation and self-diffusion of single DNA molecules confined to two dimensions

The conformation of DNA molecules electrostatically bound to fluid cationic lipid bilayers is investigated by fluorescence microscopy. The DNA diffuses freely in the plane and follows Rouse dynamics, D similar to 1/N, with an increasing number of base pairs N. The chain extension scales as [R-2] - N-2 nu, with nu = 0.79 +/- 0.04 in good agreement with the exact exponent nu = 3/4 for a self-avoiding random walk in two dimensions. The structure factor of dilute and semidilute DNA solutions shows fractal scaling behavior, S(k) similar to k(-1/nu). In highly concentrated two-dimensional DNA solutions, the chains were found to segregate.