非均匀Kirchhoff细丝中的共振螺旋形变
Resonant helical deformations in nonhomogeneous Kirchhoff filaments
摘要：
本文研究了具有周期性变化杨氏模量的非均匀基尔霍夫纤维的三维静态结构。这种类型的变异可能发生在DNA的长串联重复序列中。我们分析的杨氏模量的频闪映射中的振荡频率和振幅的影响，并在定期（非混沌）的空间配置的细丝。我们的分析表明，长丝的三维构象可能严重依赖于杨氏模量频率的情况下，与其他固有频率的长丝共振。正如所料，远离共振的解决方案的形状仍然非常接近的齐次情况。在生物分子的情况下，众所周知，除了序列依赖性效应之外，各种其他元素结合起来决定它们的构象，如自接触，盐浓度，热波动，各向异性和与蛋白质的相互作用。我们的研究结果表明，序列依赖性效应本身可能对这些分子（包括DNA）的形状产生重大影响。因此，这可能是“垃圾”序列的一种可能的机械功能。
英文摘要：
We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young's modulus. This type of variation may occur in long tandemly repeated sequences of DNA. We analyse the effects of the Young's modulus frequence and amplitude of oscillation in the stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. Our analysis shows that the tridimensional conformations of long filaments may depend critically on the Young's modulus frequence in case of resonance with other natural frequencies of the filament. As expected, far from resonance the shape of the solutions remain very close to that of the homogeneous case. In the case of biomolecules, it is well known that various other elements, besides sequence-dependent effects, combine to determine their conformation, like self-contact, salt concentration, thermal fluctuations, anisotropy and interaction with proteins. Our results show that sequence-dependent effects alone may have a significant influence on the shape of these molecules, including DNA. This could, therefore, be a possible mechanical function of the ``junk'' sequences.
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