Date Published: April 7, 2016
Publisher: Public Library of Science
Author(s): Young-Joo Kim, Do-Nyun Kim, Claudine Mayer.
In this article, we investigate the principal structural features of the DNA double helix and their effects on its elastic mechanical properties. We develop, in the pursuit of this purpose, a helical continuum model consisting of a soft helical core and two stiff ribbons wrapping around it. The proposed model can reproduce the negative twist-stretch coupling of the helix successfully as well as its global stretching, bending, and torsional rigidities measured experimentally. Our parametric study of the model using the finite element method further reveals that the stiffness of phosphate backbones is a crucial factor for the counterintuitive overwinding behavior of the duplex and its extraordinarily high torsional rigidity, the major-minor grooves augment the twist-stretch coupling, and the change of the helicity might be responsible for the transition from a negative to a positive twist-stretching coupling when a tensile force is applied to the duplex.
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 [1–3]. 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 [4–6]. 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 [10, 11]. However, the structural origin of these intriguing duplex properties remains elusive.
In conclusion, we investigate the effect of principal structural features of the DNA double helix on its mechanical properties using the helical continuum model. The proposed model reproduces successfully the elastic mechanical properties of the B-form DNA measured experimentally. Our study suggests, in particular, that (1) the stiffness of phosphate backbones is essential to achieve the counterintuitive overwinding behavior of the helix under tension and contributes mostly to the extraordinarily high torsional rigidity of the duplex, (2) the major-minor grooves increase the magnitude of the twist-stretch coupling particularly at a low helicity, and (3) the twist-stretch coupling is highly sensitive to the helicity implying the possibility of its transition from the overtwisting phase to the undertwisting phase or vice versa when a sufficiently large amount of tensile force or torsional moment is applied. We anticipate that the proposed model offers a versatile tool to explore the mechanics of various helical structures in depth because, for example, it can be easily integrated with other refined modeling approaches including molecular dynamics simulations in multi-scale analysis framework, enabling us to link the local conformational changes due to external forces, base pair modifications, and binding molecules to the global structural properties.