Upon the Joyeux-Buyukdagli model of DNA, the helicoidal interactions are introduced, and their effects on the dynamical behaviors of the molecule investigated. A theoretical framework for the analysis is presented in an external force field, taking into account Stokes and hydrodynamics viscous forces. In the semi-discrete approximation, the dynamics of the molecule is found governed by the cubic complex Ginzburg-Landau (CGL) equation. By choosing an appropriate decoupling ansatz, the cubic CGL equation is transformed into a nonlinear differential equation whose analytical solitary wave-like solutions can be explored by means of the direct method, which is more tractable in case where the form of soliton solutions is known. Based on this, a dissipative bright-like soliton solution is obtained. Numerical experiments have been done, and relevant results were brought out, such as the quantitative and qualitative influences of the helical interactions on the parameters of the traveling bubble. The important role-played by these interactions in the DNA biological processes is brought out, showing that depending on the wave number, their effects can increase, decrease, or keep constant the bubble angular frequency, velocity, amplitude, and width, as well as the energy involved by enzymes in the initiation of DNA biological processes. This can prevent some coding or reading errors and resulting genetic damages. Analytical predictions and numerical experiments were in good agreement.

中文翻译：

---

外力场中DNA阻尼螺旋Joyeux-Buyukdagli模型中的碱基对开口

在 DNA 的 Joyeux-Buyukdagli 模型上，引入了螺旋相互作用，并研究了它们对分子动力学行为的影响。分析的理论框架在外力场中提出，考虑到斯托克斯和流体动力学粘性力。在半离散近似中，分子的动力学由三次复数 Ginzburg-Landau (CGL) 方程控制。通过选择合适的解耦 ansatz，三次 CGL 方程转化为非线性微分方程，其解析孤立波状解可以通过直接方法探索，这在孤立子解形式已知的情况下更易于处理。在此基础上，得到了耗散的类亮孤子解。已经做了数值实验，并得出了相关结果，如螺旋相互作用对行进气泡参数的定量和定性影响。揭示了这些相互作用在 DNA 生物过程中所起的重要作用，表明根据波数的不同，它们的作用可以增加、减少或保持恒定的气泡角频率、速度、幅度和宽度，以及酶在启动 DNA 生物过程中所涉及的能量。这可以防止一些编码或阅读错误以及由此产生的遗传损伤。分析预测和数值实验非常吻合。揭示了这些相互作用在 DNA 生物过程中所起的重要作用，表明根据波数的不同，它们的作用可以增加、减少或保持恒定的气泡角频率、速度、幅度和宽度，以及酶在启动 DNA 生物过程中所涉及的能量。这可以防止一些编码或阅读错误以及由此产生的遗传损伤。分析预测和数值实验非常吻合。揭示了这些相互作用在 DNA 生物过程中所起的重要作用，表明根据波数的不同，它们的作用可以增加、减少或保持恒定的气泡角频率、速度、幅度和宽度，以及酶在启动 DNA 生物过程中所涉及的能量。这可以防止一些编码或阅读错误以及由此产生的遗传损伤。分析预测和数值实验非常吻合。