On the asymmetric elasticity of twisted dsDNA

We present an analytical-based proof for the consistency of two asymmetric elastic models of the double-stranded DNA in the regime around the B-form. We derive the shape equations in terms of Euler angles for a uniform ribbon with noncircular cross section and spontaneous torsion. We study the conditions to form a helical ribbon for the model and find that the Euler angle ψ must be either 0 or π/2. We find that the helix is always stable or at least metastable for the model, and there is either a continuous or discontinuous transition of extension, from a twisted straight ribbon to a helical ribbon. An “over-collapse” phenomena of extension is observed for the ribbon under twisting. The stability of the helix and the intrinsic asymmetric elasticity under twisting are also studied.