Solitonlike base pair opening in a helicoidal DNA: An analogy with a helimagnet and a cholesteric liquid crystal

We propose a model for DNA dynamics by introducing the helical structure through twist deformation in analogy with the structure of a helimagnet and a cholesteric liquid-crystal system. The dynamics in this case is found to be governed by the completely integrable sine Gordon equation, which admits kink-antikink solitons with increased width, representing a wide base-pair opening configuration in DNA. The results show that the helicity introduces a length-scale variation and thus provides a better representation of the base-pair opening in DNA.

Figure 1

A schematic representation of (a) a DNA double-helical chain, (b) a helimagnet, and (c) a cholesteric liquid-crystal system.

Figure 2

A horizontal projection of the $n\text{th}$ base pair in a DNA double helix (a) in the $x\text{−}y$ plane and (b) in the $x\text{−}z$ plane.

Figure 3

(a) Kink-antikink one-soliton solutions [Eq. (10)] of the sine Gordon equation when helicity is present $(h\ne 0)$. (b) A sketch of the formation of open-state configuration in terms of kink-antikink solitons in a DNA double helix when helicity is present $(h\ne 0)$. (c) Kink-antikink one-soliton solutions of the sine Gordon equation when helicity is absent [Eq. (10) when $h=0$]. (d) A sketch of the formation of open-state configuration in terms of kink-antikink solitons in DNA double helix when helicity is absent $(h=0)$.

Figure 4

(a) The kink one-soliton [Eq. (10)] representing base-pair opening at $t=1$ for different values of helicity. (b) Variation of width of the kink soliton against helicity.