Forming superhelix of double stranded DNA from local deformation

TL;DR

This paper derives geometric constraints on DNA superhelix formation from elasticity and validates the model with molecular dynamics simulations, highlighting the role of curvature constraints over topology.

Contribution

It introduces a novel geometric framework for understanding DNA superhelix formation based on differential geometry and elasticity, independent of topological considerations.

Findings

Geometrical constraints influence DNA bend-twist ratio.

Kurtosis from geometric constraints affects superhelix height.

Simulation confirms the curvature formation model.

Abstract

The formation of 1.7 turns of the superhelix of DNA strands is the quintessential step in DNA packaging, which is accompanied by superhelix formation around the core structure. In contrast to the sequence dependent elasticity of the DNA strand, which is revealed as nonlocal and nonlinear, the geometric constraints derived by differential geometry have not been fully elaborated in DNA strand dynamics, even though these constraints contribute independently to the quantification of related energetics. In this paper, the geometrical constraints on the base pair wise resolution in a curved DNA strand are derived separately from its elasticity, addressing the deformation characteristics during superhelix formation around a simplified core structure. The constraints that base pairs impose due to their inherent helicity characterize the conditional affinity for curvature formation, thereby specifying the bend-twist ratio. The result of the derivation indicates that the kurtosis derived from the geometrical constraints of an open-ended strand can be the factor that decides the height of the superhelix, rather than the topological properties of a circular chain or the binding conformation with the obstacles. Coarse-grained molecular dynamics simulation validates the description of the curvature formation process.