DNA as a one-dimensional chiral material: Application to the structural transition between B form and Z form

Abstract

A dynamical model is presented for chiral change in DNA molecules. The model is an extension of the conventional elastic model, which incorporates the structure of base pairs and uses a spinor representation for the DNA configuration together with a gauge principle. Motivated by a recent experiment reporting chiral transitions between right-handed B-DNA and left-handed Z-DNA [Lee et al., Proc. Natl. Acad. Sci. (USA) 107, 4985 (2010)], we analyze the free energy for the particular case of linear DNA with an externally applied torque. The model shows that there exists, at low temperature, a rapid structural change depending on the torque exerted on the DNA, which causes switching in B and Z domain sizes. This can explain the frequent switches of DNA extension observed in experiments.

Knot soliton in DNA and geometric structure of its free-energy density

“…The two-component spin wave function is introduced for describing DNA in Ref. [6]. The spin wave function is usually written as:…”

“…The first superposition ψ 1 describes the DNA conformation, and the second superposition ψ 2 describes the internal structure of the base pair connected by hydrogen bonds. According to the Landau model [6], the free-energy density of DNA can be given from the spin wave function:…”

“…where B 2 represents the isotropic elastic bending and C = k 1 +k 2 4 equates to torsional elasticity (when the DNA molecule satisfies the linear model, θ = 0, φ = 0). If one assumes that the twist persistence length is 75 nm, then C = 91 × 10 −20 J [6]. In (8), dθ ds , dφ ds and dχ ds are the spatial variation of the Euler angle with the rotation of the DNA helical axis.…”

“…This means there must be some relationships between the free-energy density and geometric structure of DNA. This interesting question has not yet been clarified [6].…”

“…In order to explain this transformation theoretically, some theories can be considered e.g., the modified ZZO model [2], Poland-Scheraga model [3], and Peyrard-Bishop-Dauxois model [4,5]. Especially, the authors [6] consider the Landau model in the study of DNA transformation. In this model, the free-energy density of B-and Z-DNA is obtained by introducing the two-component spin wave function.…”