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arXiv · 2307.04597

Geometrically Given Constraints in Double Helical Strand

Heeyuen Koh·Jae Young Lee·Jae Gyung Lee
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Abstract

The versatility of helical structures in nature, such as DNA strands, tendrils, actin filaments, and more, in similar shapes across various life forms and molecular systems, indicates their readiness to manifest useful functionality that can conserve, spread, and assemble. However, it has not been fully explained why being in such structural forms is beneficial for developing their functionalities, which is crucial for designing an artificial system with helicity or molecular shape. For instance, the energetics of the bend-twist coupling of DNA strands has been studied and evaluated in various simulations and theoretical works. Yet it has not fully elucidated the structural features of the DNA strand, such as the roles of the major and minor grooves, which are related to its proneness to bend-twist coupling and associated dynamics. In this paper, the geometrical constraints from helicity yield an ansatz for the bend-twist coupling in the Darboux frame and the Frenet-Serret formula, addressing the conditional characteristics of deformation in a curved strand during wrapping around a simplified core structure, which is the quintessential step in DNA packaging. The constraints derived from differential geometry for B-DNA strands specify the bend-twist ratio required to form a superhelix in an open-ended strand, thereby offering free energy affinity preferences along sequence-dependent elasticity. The result of the ansatz shows conditional kurtosis, which is the deformation perpendicular to the plane defined by the curvature of the strand, determining the height of the superhelix and the role of the major-minor groove in forming these structural characteristics of the curved strand. Coarse-grained molecular dynamics simulation validates the derivation and sequence-dependent preferences during the wrapping process.

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Heeyuen Koh, Jae Young Lee, Jae Gyung Lee. 2023-07-10. Geometrically Given Constraints in Double Helical Strand. https://arxiv.org/abs/2307.04597

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