School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, 5005, Australia,
Eur Biophys J. 2014 Jan;43(1):25-33. doi: 10.1007/s00249-013-0936-7. Epub 2013 Nov 8.
Nanotechnology is a rapidly expanding research area, and it is believed that the unique properties of molecules at the nano-scale will prove to be of substantial benefit to mankind, especially so in medicine and electronics. Here we use applied mathematical modelling exploiting the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider the equilibrium offset positions for both single-strand and double-strand DNA molecules inside a single-walled carbon nanotube, and we predict offset positions with reference to the cross-section of the carbon nanotube. For the double-strand DNA, the potential energy is determined for the general case for any helical phase angle ϕ, but we also consider a special case when ϕ = π, which leads to a substantial simplification in the analytical expression for the energy. As might be expected, our results confirm that the global minimum energy positions for a single-strand DNA molecule and a double-strand DNA molecule will lie off axis and they become closer to the tube wall as the radius of the tube increases.
纳米技术是一个快速发展的研究领域,人们相信分子在纳米尺度上的独特性质将对人类产生实质性的益处,特别是在医学和电子学方面。在这里,我们使用应用数学建模方法,利用力学的基本原理和 6-12 Lennard-Jones 势能函数以及连续体近似,假设分子间相互作用可以用平均原子表面密度来近似。我们考虑了单链和双链 DNA 分子在单壁碳纳米管内的平衡偏移位置,并参考碳纳米管的横截面来预测偏移位置。对于双链 DNA,我们确定了任意螺旋相位角 ϕ 的一般情况下的势能,但我们也考虑了一个特殊情况,即 ϕ = π,这导致能量的解析表达式大大简化。正如预期的那样,我们的结果证实,单链 DNA 分子和双链 DNA 分子的全局最小能量位置将偏离轴线,并且随着管半径的增加,它们会更接近管壁。