Forming superhelix of double stranded DNA from local deformation

Abstract

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, which is the quintessential step in DNA packaging. The constraints derived from the given helicity of DNA strand characterize the conditional affinity for curvature formation, thereby specifying the bend-twist ratio required for superhelix formation. The result includes the conditional kurtosis, which is the deformation perpendicular to the plane defined by the curved strand, determining the height of the superhelix. Coarse-grained molecular dynamics simulation validates the description of the curvature formation process and its sequence dependent affinity.