Finite element analysis of DNA supercoiling

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.

Circularization of small DNAs in the presence of ethidium: A theoretical analysis

“…The supercoiling free energy shows little sign of the tertiary structural transitions that are manifested in the minimum potential energy pathway. '5, [39][40][41] A quadratic dependence of the supercoiling free energy on linking difference follows from both the quadratic variation of the torsion energy with net twist and the practically gaussian distribution of the simulated writhe in large unconstrained (nicked) circular DNAs. Bauer and Vinograd '" recognized that binding an unwinding ligand, such as the intercalator ethidium, to a closed circular DNA changes the superhelical strain, which in turn alters the affinity of DNA for the ligand.…”

Resonant helical deformations in nonhomogeneous Kirchhoff filaments

“…The effects of nonhomogeneous mass distribution in the dynamics of unstable closed rods have been analyzed by Fonseca and de Aguiar [31]. Yang et al [8] have studied a particular case of nonhomogeneous Young's modulus for closed rods. Manning et al [32] have incorporated into the Kirchhoff model the sequence-dependent discrete data of the intrinsic curvature of DNA.…”

Dynamics of an electrostatically charged elastic rod in fluid

“…Le Bret 1979Benham 1989;Yang et al 1993;Tobias et al 1994;Coleman et al 1995Westcott et al 1995;Dichmann et al 1996 and also references in Swigon 2009). Schlick et al (1994) incorporated both elastic potential and electrostatic forces in a computational model of DNA that represented the molecule by cubic B-splines.…”