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The core has a simple rectangular cross-section parameterized using the diagonal length (D) corresponding to the helix diameter and the aspect ratio (AR) that is the ratio of the width (W) to the height (H) ( Fig 1b). The core structure is generated via helical sweep of a cross-section along the helical axis with a constant pitch assuming the straight mean conformation by neglecting any intrinsic, sequence-dependent curvatures in reality. The helical continuum model consists of a soft core and two thin, stiff ribbons wrapping around the core ( Fig 1). Helical continuum model for the DNA double helix We perform a comprehensive computational analysis using this model constructed by varying the helicity, the stiffness of phosphate backbones, and the major-minor groove pattern systematically. Also, unlike the elastic rod model, arguably the most popular modeling approach to DNA mechanics and widely used to study highly nonlinear behaviors of the DNA duplex for given stiffness coefficients of stretching, bending and twisting, our helical model seeks to identify the primary structural features governing those stiffness values and understand how they are determined better. It is noteworthy that a simple isotropic cylinder model cannot reproduce the exceptionally high torsional rigidity and negative twist-stretch coupling.
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In this article, we study the principal structural features of the duplex and their plausible role on its elastic mechanical properties using a helical continuum model where DNA double helices are treated as elastic helical solids with a polygonal cross-section. However, the structural origin of these intriguing duplex properties remains elusive. Numerous experiments have also demonstrated that these elastic properties are closely related to the helical conformation such as the axial rise (the distance between neighboring base-pairs along the helical axis) and the helical repeat (the number of base-pairs per one helical turn) that may vary with, for example, specific base sequences, dinucleotide steps, neutral or charged modification of base-pairs, and binding of small molecules. In particular, the elastic response of DNA double strands has been extensively studied, revealing their unique mechanical properties including the extraordinarily high torsional rigidity (approximately twice the bending rigidity) and the counterintuitive overwinding behavior under tension. Recent advances in single-molecule experiments have thrown new light on the mechanics of the DNA double helix through direct manipulation of individual DNA molecules and characterization of their structural properties.