Finite element analysis of DNA supercoiling

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Abstract
A DNA polymer with hundreds or thousands of base pairs is modeled as a thin elastic rod. To find the equilibrium configurations and associated elastic energies as a function of linking number difference (ΔLk), a finite element scheme based on Kirchhoff’s rod theory is newly formulated so as to be able to treat self‐contact. The numerical results obtained here agree well with those already published, both analytical and numerical, but a much more detailed picture emerges of the several equilibrium states which can exist for a given ΔLk. Of particular interest is the discovery of interwound states having odd integral values of the writhing number and very small twist energy. The existence of a noncircular cross section, inhomogeneous elastic constants, intrinsic curvature, and sequence‐dependent bending and twisting can all be readily incorporated into the new formalism.

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