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Abstract：
While undergoing structural deformation, DNA experiences changes in the interactions between its internal base pairs, presenting challenges to conventional elastic methods. To address this, we propose the Discrete Critical State (DCS) model in this paper. This model combines surface discrete frame theory with gauge theory and Landau phase transition theory to investigate DNA\'s structural deformation, phase transitions, and chirality. Notably, the DCS model considers both the internal interactions within DNA and formulates an overall equation using unified physical and geometric parameters. By employing the discrete frame, we derive the evolution of physical quantities along the helical axis of DNA, including geodesic curvature, geodesic torsion, and others. Our findings indicate that B-DNA has a significantly lower free energy density compared to Z-DNA, which is in agreement with experimental observations. This research reveals that the direction of base pairs is primarily governed by the geodesic curve within the helical plane, aligning closely with the orientation of the base pairs. Moreover, the geodesic curve has a profound influence on the arrangement of base pairs at the microscopic level and effectively regulates the configuration and geometry of DNA through macroscopic-level free energy considerations.
摘要：
在经历结构变形时，DNA经历其内部碱基对之间相互作用的变化，对传统的弹性方法提出了挑战。为了解决这个问题，本文提出了离散临界状态(DCS)模型。该模型将表面离散框架理论与规范理论和Landau相变理论相结合，以研究DNA的结构变形。相变,和手性。值得注意的是,DCS模型考虑了DNA内部的相互作用，并使用统一的物理和几何参数制定了一个整体方程。通过采用离散框架，我们推导出沿着DNA螺旋轴的物理量的进化，包括测地曲率，测地扭转,和其他人。我们的发现表明，与Z-DNA相比，B-DNA具有明显更低的自由能密度。这与实验观察一致。这项研究表明，碱基对的方向主要由螺旋平面内的测地曲线决定，与碱基对的方向紧密对齐。此外，测地曲线在微观水平上对碱基对的排列有深远的影响，并通过宏观水平的自由能考虑有效地调节DNA的构型和几何形状。
