Chiral Gauge Potential in Conversions Between B- and Z-Type DNA and its Solutions Along Helix Axis
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GENERAL AND APPLIED PHYSICS
Chiral Gauge Potential in Conversions Between B- and Z-Type DNA and its Solutions Along Helix Axis Jingda Guo1 · Xuguang Shi1 Received: 18 April 2020 © Sociedade Brasileira de F´ısica 2020
Abstract The conversions between different DNA have been observed in many experiments due to the development of technological hicks. Especially, the transformations between B- and Z-type DNA have been found by applying torque on DNA. The elastic rod model can be used to explain the experiments. Different from the elastic rod model, these transformations can be seen as the phase transformation, and then the Landau model and gauge theory were proposed to explain the conversions. The gauge potential describes the inner local interaction of the base pair. We find the equation of the chiral gauge potential and solve the equation. Furthermore, there are two parameters in the solutions; one decides the values of the gauge potential and affects the potential energy of the DNA. The other parameter describes the position the torque applying to. Keywords DNA · Landau model · Chiral gauge potential · Elliptic sine function
1 Introduction DNA is genetic material constructed by base pairs and phosphate bone, which has a double helix structure. It also can form a super helix and more complex structures. By considering the geometrical structure, there are at least three kinds of DNA in nature, such as A-type DNA, B-type DNA, and Z-type DNA. As the development of technological hicks, such as FRET, more and more processes of dynamics of DNA have been observed in experiments [1, 2]. Among these experiments, it is impressive that the conversions between different kinds of DNA have been observed. For example Z-type DNA can transform to B-type DNA by applying an extra torsion torque [3]. In this transformation, a critical torque is found. When the extra torsion torque is a little bigger than the critical torque, Z-type DNA switches sharply to B-type DNA. When the extra torque is a little smaller than the critical torque, B-type DNA switches sharply to Z-type DNA too. In order to explain this phenomenon, several models have been proposed, such as the modified ZZO model [4, 5], Poland-Scheraga model [6–8], Peyrard-Bishop-Dauxois model [9, 10], and Landau Xuguang Shi
[email protected] 1
College of Science, Beijing Forestry University, Beijing, People’s Republic of China
model. The Landau model is a special model that can make a bridge between the local interaction of the base pair and the global geometrical structure of the DNA. In the model, it is novel that a chiral gauge potential is introduced to describe the local interactions of the base pairs in the free energy density of the DNA. Although, the conversions between Band Z-type DNA have been explained by combining the Landau model [11–13] and nucleation theory [16]. In order to understand the DNA well, some detailed information should be given too, for example, the solutions of the chiral gauge potential along the DNA. However, this interesting question has not ye
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