Abstract
In the present paper, we have studied a discrete version of the worm-like-chain (WLC) model, which incorporates the spatial constraints imposed by the magnetic tweezer, used in current micromanipulation experiments. These obstruction effects are relevant for double stranded DNA (dsDNA) 'short' molecules, involving about two thousand base pairs (kbp) or fewer. Two elements of the device have to be considered: first, the fixed plastic slab on which is stuck one molecule end; second, a magnetic bead which is used to pull (or twist) the attached molecule free end. We have developed quantitative arguments showing that the bead surface can be replaced by its tangent plane at the anchoring point, when it is close to the bead south pole relative to the pulling direction. We are, then, led to a confinement model involving two repulsive plates: first, the fixed anchoring plate; second, a fluctuating plate, simulating the bead, in thermal equilibrium with the attached molecule and the ambient fluid. The bead obstruction effect reduces to a slight upper shift of the elongation, about four times smaller than and with the same sign as the effect induced by the anchoring plate. This result, which may contradict naive expectations, has been qualitatively confirmed within the soluble 'Gaussian' model for flexible polymers. A study of the molecule elongation versus the contour length L exhibits a significant non-extensive behaviour. Although the curve for 'short' molecules is well fitted by a straight line, with its slope very close to the prediction of the standard WLC model, it does not pass through the origin, due to the presence of an offset term independent of L. This leads to a 15% upward shift of the elongation for a 2 kbp molecule. Finally, the need for thorough analysis of the spatial constraints in super-coiled dsDNA elasticity measurements is illustrated by 'hat' curves, giving the elongation versus the torque.