Equation of state of looped DNA

We calculate the equation of state of DNA under tension for the case that the DNA features loops. Such loops occur transiently during DNA condensation in the presence of multivalent ions or sliding cationic protein linkers. The force-extension relation of such looped DNA modelled as a wormlike chain is calculated via path integration in the semiclassical limit. This allows us to determine rigorously 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. That means that the experimentally extracted single molecule elasticity does not necessarily reflect the bare DNA stiffness only, but can also contain additional contributions that depend on the overall chain conformation and length.