A coordinate-free Lie-group formulation for generating ensembles of DNA conformations in solution is presented. In this formulation, stochastic differential equations define sample paths on the Euclidean motion group. The ensemble of these paths exhibits the same behavior as solutions of the Fokker-Planck equation for the stochastically forced elastica. Longer chains for which the effects of excluded volume become important are handled by piecing together shorter chains and modeling their interactions. It is assumed that the final chain lengths of interest are long enough for excluded volume effects to become important, but not so long that the semi-flexible nature of the chain is lost. The effect of excluded volume is then taken into account by grouping short self-avoiding conformations into 'bundles' with common end constraints and computing average interaction effects between bundles. The accuracy of this approximation is shown to be good when using a numerically generated ensemble of self-avoiding sample paths as the baseline for comparison.

中文翻译：

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DNA构象集合体的随机弹性和排除体积的扰动。

提出了用于在溶液中产生DNA构象集合的无坐标Lie-基配方。在此公式中，随机微分方程定义了欧几里得运动组上的样本路径。这些路径的集合表现出与Fokker-Planck方程针对随机受力弹性波的解相同的行为。对于较长的链（排除体积的影响变得重要），可以通过将较短的链拼接在一起并对其相互作用进行建模来处理。假定感兴趣的最终链长足够长，以至于排除的体积效应变得很重要，但不会太长以至于失去链的半柔韧性。然后通过将简短的自我规避构象分组为“捆绑”来考虑排除体积的影响 具有共同的最终约束条件并计算束之间的平均交互作用。当使用数字生成的自避免样本路径的集合作为比较基准时，此近似值的精度显示为良好。