Defect-Facilitated Buckling in Supercoiled Double-Helix DNA

Abstract

We present a statistical-mechanical model for stretched twisted double-helix DNA, where thermal fluctuations are treated explicitly from a Hamiltonian without using any scaling hypotheses. Our model applied to defect-free supercoiled DNA describes coexistence of multiple plectoneme domains in long DNA molecules at physiological salt concentrations (≈ 0.1 M Na + ) and stretching forces (≈ 1 pN). We find higher (lower) number of domains at lower (higher) ionic strengths and stretching forces, in accord with experimental observations. We use our model to study the effect of an immobile point defect on the DNA contour that allows a localized kink. The degree of the kink is controlled by the defect size, such that a larger defect further reduces the bending energy of the defect-facilitated kinked end loop. We find that a defect can spatially pin a plectoneme domain via nucleation of a kinked end loop, in accord with experiments and simulations. Our model explains previously-reported magnetic tweezer experiments [1] showing two buckling signatures: buckling and 'rebuckling' in supercoiled DNA with a base-unpaired region. Comparing with experiments, we find that under 1 pN force, a kinked end loop nucleated at a base-mismatched site reduces the bending energy by ≈ 0.7 kBT per unpaired base. Our model predicts coexistence of three states at the buckling and rebuckling transitions that warrants new experiments.

Coarse-Grained Modelling of DNA Plectoneme Pinning in the Presence of Base-Pair Mismatches

“…This data, establishing the effect of mismatch size on bending energy, is consistent with results from previous studies 18,31,35 and suggests that the mismatch model is feasible for investigating DNA plectoneme formation in the presence of mismatches through coarse-grained approaches.…”

“…2 c]. This result, which has been predicted theoretically 31 , is described in detail below. The finite probability of buckling at the mismatch for the low salt and low force conditions leads to a bifurcation of the end loop angle: the end loop angle is constant, independent of the mismatch size, when the mismatch is not located at the tip of the plectoneme but decreases significantly with increasing mismatch size when the mismatch coincides with the tip of the plectoneme ( Fig.…”

“…To verify the results of the MD simulations, we compared them with results obtained from a previously published theoretical model 31 in the end loop and this reduction is incorporated through a defect size parameter. A significant limitation of a purely free energy based approach to modeling the effect of bp mismatches is its inability to quantitatively map the number of mismatches to an overall free energy penalty or the defect-size parameter.…”

“…A significant limitation of a purely free energy based approach to modeling the effect of bp mismatches is its inability to quantitatively map the number of mismatches to an overall free energy penalty or the defect-size parameter. Brahmachari et al 31 were able to provide rough estimates for the relation between the number of mismatches and the defect size parameter or the decrease in bending energy through comparisons with experimental measurements of defect facilitated DNA buckling 18 .…”

“…However, in genomic DNA that contains millions of base pairs, it is possible that thermal fluctuations and entropic effects could mask the influence of the defect. Alternatively, depending on the type and the size of the defect, the enthalpic gain of buckling at the defect could result in preferential buckling and plectoneme formation at the defect 18,31 . Furthermore, the type and the size of the defect could significantly alter the structure of the end loop containing the defect; for example, localizing the defect at the sharply kinked tip of a plectoneme may promote the flipping out of the base at the mismatch 32 .…”