Twisting and bending stress in DNA minicircles

Abstract

The interplay between bending of the molecule axis and appearance of disruptions in circular DNA molecules, with ∼100 base pairs, is addressed. Three minicircles with different radii and almost equal contents of AT and GC pairs are investigated. The DNA sequences are modeled by a mesoscopic Hamiltonian which describes the essential interactions in the helix at the level of the base pair and incorporates twisting and bending degrees of freedom. Helix unwinding and bubble formation patterns are consistently computed by a path integral method that sums over a large number of molecule configurations compatible with the model potential. The path ensembles are determined, as a function of temperature, by minimizing the free energy of the system. Fluctuational openings appear along the helix to release the stress due to the bending of the molecule backbone. In agreement with the experimental findings, base pair disruptions are found with larger probability in the smallest minicircle of 66 bps whose bending angle is ∼6°. For this minicircle, a sizeable untwisting is obtained with the helical repeat showing a step-like increase at T = 315 K. The method can be generalized to determine the bubble probability profiles of open ends linear sequences.

Entropic penalties in circular DNA assembly

“…[44]. While the latter work found, at room temperature, the free energy minima in the range h ∈ [∼ 10, 11], it did not however capture the minima for large h which instead appear in Fig.…”

“…[43]. These circles have been recently studied to test the effects of the bending and torsional stress on the stability of the helix [44]. Their thermodynamical properties are now examined at the light of the new computational approach.…”

“…Then, by virtue of its nonlinear structure, the potential in Eq. (9) is adequate to account for those cooperative effects which may propagate along the molecule stack and cause even large fluctuational openings at high temperature [44].…”

Helical Disruptions in Small Loops of DNA

“…The measure Dx i is a multiple integral over the path Fourier coefficients while indicates that the paths x i (τ ) are closed trajectories. The integration over the two particles potential greatly enhances the computational times with respect to the previous method [10] but it offers a more realistic model for the base stacking in sequences of any length.…”

“…My previous path integral analysis of DNA [2,3,4,5,6,7,8,9,10] were based on the ansatz that the bps displacements could be treated as one dimensional paths x(τ i ), |r i | → x(τ i ), with the imaginary time τ i ∈ [0, β] and β being the inverse the temperature.…”