Worm-like chain under an external force: A classical mechanical approach

Biomolecules, such as DNA, are often modelled by the inextensible Worm-Like Chain (WLC) model when pulled by an external force. We examine the classical mechanical solution of a WLC arbitrarily grafted at one end while stretched with an external force acting on the other end. Shape equations governing the configurations of the WLC can be derived. Detail chain configurations can be solved numerically for arbitrary contour lengths and grafting conditions. Analytic results for the case of low force (linear regime) limit as well as near the fully stretched limit (strong force) and long chain limit are also derived.