The radial distribution function of worm-like chains

Thermal conformations of semiflexible macromolecules are generically described by the worm-like chain model. The end-to-end distance distribution, a fundamental quantity of the model, is not yet known in closed form. We provide a solution to the practical problem of choosing an appropriate approximation. First, a comprehensive review of existing approximations and exact limiting results is given. We then propose an explicit expression which interpolates between all relevant limiting cases. We show that it accurately reproduces, at no computational cost, high-precision Monte Carlo data, covering a wide range from stiff to flexible chains and from looped to fully stretched configurations. Using this result we quantify the enhancement of short worm-like loop formation by (protein) bridges.