The polymeric properties of DNA molecules, which are electrostatically boun
d to glass-supported cationic lipid membranes, are investigated. The electr
ostatic interaction is sufficiently strong to hold DNA flat onto the fluid
lipid surface but allows DNA to diffuse freely in-plane. The molecules are
fluorescently labeled, and fluorescence images are examined in terms of rea
l-space monomer distributions of polymer chains. The chain extension of sin
gle DNA fragments of restriction enzyme digests shows power law scaling wit
h number of base pairs in accordance with self-avoiding walks in two dimens
ions. Dynamic scaling is found for center-of-mass diffusion following Rouse
dynamics, D similar to 1/N, and for rotational relaxation times, tau(r) pr
oportional to N-mu with mu = 2.6 +/- 0.4. A crowded surface of monodisperse
lambda-DNA behaves like a two-dimensional semidilute solution with a measu
rable correlation length xi being smaller than for dilute preparations. Pol
ymer unbinding and the role of surface defects are discussed.