Spatial Constraint Corrections to the Elasticity of dsDNA Measured with Magnetic Tweezers

Abstract

In this paper, we have studied, within a discrete WLC model, the spatial constraints in magnetic tweezers used in single molecule experiments. Two elements are involved: first, the fixed plastic slab on which is stuck the initial strand, second, the magnetic bead which pulls (or twists) the attached molecule free end. We have shown 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 force. We are led to a model with two parallel repulsive plates: the fixed anchoring plate and a fluctuating plate, simulating the bead, in thermal equilibrium with the system. The bead effect is a slight upper shift of the elongation, about four times smaller than the similar effect induced by the fixed plate. This rather unexpected result, has been qualitatively confirmed within the soluble Gaussian model. A study of the molecule elongation versus the countour length exhibits a significant non-extensive behaviour. The curve for short molecules (with less than 2 kbp) is well fitted by a straight line, with a slope given by the WLC model, but it does not go through the origin. The non-extensive offset gives a 15% upward shift to the elongation of a 2 kbp molecule stretched by a 0.3 pN force.