It is useful to describe the deformation characteristics of long biological macromolecules, such as deoxyribonucleic acid (DNA), by means of terms such as “bending”, “stretching”, or “twisting”. These terms are borrowed from classical beam theory, a traditional and widely known subfield of continuum mechanics, whereas the standard numerical modeling procedure for macromolecules, which is molecular dynamics, does not allow for explicit introduction of the aforementioned deformation modes. This somehow puts some limit to the mechanical understanding of biological macromolecules. As a remedy, we here propose an upscaling (or homogenization) approach, spanning a new conceptual bridge from molecular dynamics to beam theory. Firstly, we apply the principle of virtual power (PVP) to classical continuum beams subjected to stretching and twisting, as well as to atomic compounds represented as discrete systems of mass points in the framework of molecular dynamics. Equating virtual power densities associated with continuum and discrete representations provides homogenization rules from the atomic compounds to the continuum beam line elements. Secondly, the forces acting on the aforementioned mass points are derived from energy potentials associated with bond stretching, valence and torsion angle variations, as well as electrostatic and van der Waals interactions. Application of this strategy to a specific DNA sequence consisting of 20 base pairs reveals deformation-dependent conformational changes, as well as paradox phenomena such as “stretching due to overwinding”, in line with known experimental observations.

用诸如“弯曲”，“拉伸”或“扭曲”之类的术语描述长生物大分子（如脱氧核糖核酸（DNA））的变形特征是有用的。这些术语是从经典束理论中借用的，经典束理论是传统的且广为人知的连续介质力学子领域，而大分子的标准数值建模程序（即分子动力学）不允许明确引入上述变形模式。这某种程度上限制了对生物大分子的机械理解。作为一种补救措施，我们在这里提出一种升级（或均质化）方法，它跨越了从分子动力学到束流理论的新概念桥梁。首先，我们将虚拟功率（PVP）原理应用于经过拉伸和扭曲的经典连续谱梁，以及在分子动力学框架内以离散质量点系统表示的原子化合物。等同于连续体和离散表示的虚拟功率密度提供了从原子化合物到连续体束线元素的均化规则。其次，作用在上述质量点上的力是从与键拉伸，化合价和扭转角变化以及静电和范德华相互作用相关的能势中得出的。将该策略应用于由20个碱基对组成的特定DNA序列时，揭示了变形相关的构象变化，以及一些悖论现象，例如“由于过度缠绕而引起的拉伸”，这与已知的实验观察一致。