Wang Ying, Shi Xuguang
College of Science, Beijing Forestry University, Beijing, 10083, People's Republic of China.
J Biol Phys. 2018 Mar;44(1):81-91. doi: 10.1007/s10867-017-9476-1. Epub 2017 Nov 13.
In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.
一般来说，DNA的几何结构是用弹性杆模型来表征的。朗道模型为我们研究DNA的几何结构提供了一种新理论。通过对DNA螺旋轴上弧单元的分解，我们发现DNA的自由能密度类似于双凝聚超导体的自由能密度。利用φ映射拓扑电流理论，证明了隐藏在DNA中的环面纽结孤子。我们展示了DNA的几何结构与自由能密度之间的关系，并考虑了微分几何理论中的弗伦内公式。因此，DNA的自由能密度可以用螺旋轴的曲率和挠率来表示。
