The complete bending energy function for nicked DNA

Abstract

We derive an analytic expression for the bending elastic energy of short DNA molecules, valid in the entire range from low to high energies. The elastic energy depends on three parameters: the length of the molecule (2L), the bending modulus B, and a critical torque τc at which the molecule develops a kink. In the kinked state, the elastic energy is linear in the kink angle, i.e. the torque at the kink is constant (= τc). τc depends (weakly) on the sequence around the nick, but is about 27 pN × nm. We measure it for a specific sequence, through experiments where the elastic energy of constrained DNA molecules is directly measured.

Critical Torque for Kink Formation in Double-Stranded DNA

“…Using the construction of Fig. 1, we were able to obtain a complete characterization of the bending energy from the linear to the nonlinear (high bending) regime, for the case of nicked ds DNA [19,20]. Here we characterize the bending energy for the case of non-nicked (i.e.…”

“…(a) Sketch of the monomer-dimer equilibrium used to measure the elastic energy of the monomer in [20]. The monomer is stressed because the ds part of the molecule has to bend and the ss part has to stretch, but the stress is relaxed in the dimer.…”

“…The monomer is stressed because the ds part of the molecule has to bend and the ss part has to stretch, but the stress is relaxed in the dimer. (b) Example of a gel used to determine the concentrations of monomers and dimers in the dimerization equilibrium experiments [20]. All lanes were loaded with the same sample, at successive (10 min) intervals.…”

“…The band in front of the monomer band is ss DNA and arises because the stoichiometry of the two strands used for the monomer construction is not exactly 1:1. the energy curve shown in Fig. 3(a) (reproduced from [20]). This energy is the sum of the elastic energy of the bent ds DNA and the stretched ss DNA:…”

“…This behavior is captured (solid line in Fig. 3(a)] by introducing one microscopic parameter (in addition to the bending modulus B), namely, a critical torque c at which the ds DNA develops a kink [20]. This torque couples to DNA bending, not twist, i.e., the torque in question is perpendicular to the helix axis (not parallel to it).…”