Kim Jin Seob, Chirikjian Gregory S
Department of Mechanical Engineering, the Johns Hopkins University, Baltimore, Maryland 21218, USA.
Polymer (Guildf). 2005 Nov 28;46(25):11904. doi: 10.1016/j.polymer.2005.09.012.
We present a unified method to generate conformational statistics which can be applied to any of the classical discrete-chain polymer models. The proposed method employs the concepts of Fourier transform and generalized convolution for the group of rigid-body motions in order to obtain probability density functions of chain end-to-end distance. In this paper, we demonstrate the proposed method with three different cases: the freely-rotating model, independent energy model, and interdependent pairwise energy model (the last two are also well-known as the Rotational Isomeric State model). As for numerical examples, for simplicity, we assume homogeneous polymer chains. For the freely-rotating model, we verify the proposed method by comparing with well-known closed-form results for mean-squared end-to-end distance. In the interdependent pairwise energy case, we take polypeptide chains such as polyalanine and polyvaline as examples.
我们提出了一种统一的方法来生成构象统计数据，该方法可应用于任何经典的离散链聚合物模型。所提出的方法利用傅里叶变换和刚体运动群的广义卷积概念，以获得链端到端距离的概率密度函数。在本文中，我们用三种不同的情况演示了所提出的方法：自由旋转模型、独立能量模型和相互依赖的成对能量模型（后两种也被称为旋转异构体状态模型）。至于数值示例，为简单起见，我们假设聚合物链是均匀的。对于自由旋转模型，我们通过与著名的端到端距离均方的闭式结果进行比较来验证所提出的方法。在相互依赖的成对能量情况下，我们以聚丙氨酸和聚缬氨酸等多肽链为例。
