Bend-Twist Coupling and its Design from Geometrical Constraints in Double Stranded DNA

Abstract

The versatility of helical structures in nature, such as DNA strands, tendrils, actin filaments, and more, across various life forms and molecular systems, indicates their readiness to manifest useful functionality that can conserve, spread, and assemble. However, it remains unclear precisely why these geometric forms benefit their functions. The structural features of the B-DNA strand, particularly the major and minor grooves and their relation to bend-twist coupling and associated dynamics, serve as a compelling example. Uncovering the direct connection between molecular geometry and its induced dynamics is fundamental to bridging the related energetics and functionality, while unlocking the design principles of various helical nanoscale applications. In this paper, we use geometrical constraints from helicity to derive an ansatz for bend-twist coupling within the Darboux frame and the Frenet-Serret formula. This approch models the conditional deformation of a curved strand wrapping around a simplified core, a structural motif quintessential to DNA packaging. Constraints from differential geometry for B-DNA strands specify the bend-twist ratio required to form an open-ended superhelix, while the related ansatz explains how the major and minor grooves shape these structural characteristics, imparting robust stability to the curved strand. Coarse-grained molecular dynamics simulations validate the results from the ansatz and their sequence-dependent preferences during the wrapping process.