Pulling strings at finite temperature: Another force-extension formula for the Worm-Like Chain Model

The derivation of Marko and Siggia's interpolation formula for the force-extension relation of the Worm-Like Chain Model (C.Bustamante, J.F.Marko, E.D.Siggia, and S.Smith, Science Vol.265, p.1599 (1994); J.F.Marko and E.D.Siggia, Macromolecules Vol.28, p.8759 (1995)) is retraced. Isotropy of space, resulting in rotational invariance of the free energy, is invoked together with analyticity. A new interpolation formula results for the force-extension relationship. It is as simple as the old one, but twice as close to the exact force-extension relationship. Application of the same reasoning to the second-order perturbative result obtained at strong force (J.D.Moroz and P.Nelson, Proc.Natl.Acad.Sci. USA Vol.94, p.14418 (1997)) results in yet a new interpolation formula, good to 1% at all forces.