Equation of State of Looped DNA

We derive the equation of state of DNA under tension that features a loop. Such loops occur transiently during DNA condensation in the presence of multivalent ions or permanently through sliding protein linkers such as condensin. The force-extension relation of such looped-DNA modeled as a wormlike chain is calculated via path integration in the semiclassical limit. This allows us to rigorously determine the high stretching asymptotics. Notably the functional form of the force-extension curve resembles that of straight DNA, yet with a strongly renormalized apparent persistence length. We also present analogous results for DNA under tension with several protein-induced kinks and/or loops. That means that the experimentally extracted single-molecule elasticity does not necessarily only reflect the bare DNA stiffness, but can also contain additional contributions that depend on the overall chain conformation and length.