Predicted Effects of Local Conformational Coupling and External Restraints on the Torsional Properties of Single DNA Molecules

Abstract

A newly developed, coarse-grained treatment of the low-frequency normal modes of DNA has been adapted to study the torsional properties of fully extended, double-helical molecules. Each base pair is approximated in this scheme as a rigid body, and molecular structure is described in terms of the relative position and orientation of successive base pairs. The torsional modulus C is computed from the lowest-frequency normal twisting mode using expressions valid for a homogeneous, naturally straight elastic rod. Fluctuations of local dimeric structure, including the coupled variation of conformational parameters, are based on the observed arrangements of neighboring base pairs in high-resolution structures. Chain ends are restrained by an elastic energy term. The calculations show how the end-to-end constraints placed on a naturally straight DNA molecule, in combination with the natural conformational features of the double helix, can account for the substantially larger torsional moduli determined with state-of-the-art, single-molecule experiments compared to values extracted from solution measurements and/or incorporated into theories to account for the force-extension properties of single molecules. The computed normal-mode frequencies and torsional moduli increase substantially if base pairs are inclined with respect to the double-helical axis and the deformations of selected conformational variables follow known interdependent patterns. The changes are greatest if the fluctuations in dimeric twisting are coupled with parameters that directly alter the end-to-end displacement. Imposed restraints that mimic the end-to-end conditions of single-molecule experiments then impede the twisting of base pairs and increase the torsional modulus. The natural inclination of base pairs concomitantly softens the Young's modulus, i.e., ease of duplex stretching. The analysis of naturally curved DNA points to a drop in the torsional modulus upon imposed extension of the double-helical molecule.