Disordered proteins are conformationally flexible proteins that are biologically important and have been implicated in devastating diseases such as Alzheimer’s disease and cancer. Unlike stably folded structured proteins, disordered proteins sample a range of different conformations that needs to be accounted for. Here, we treat disordered proteins as polymer chains, and compute a dimensionless quantity called instantaneous shape ratio (), as = , where is end-to-end distance and is radius of gyration. Extended protein conformations tend to have high compared with , and thus have high values, whereas compact conformations have smaller values. We use a scatter plot of (representing shape) against (representing size) as a simple map of conformational landscapes. We first examine the conformational landscape of simple polymer models such as Random Walk, Self-Avoiding Walk, and Gaussian Walk (GW), and we notice that all protein/polymer maps lie within the boundaries of the GW map. We thus use the GW map as a reference and, to assess conformational diversity, we compute the fraction of the GW conformations () covered by each protein/polymer. Disordered proteins all have high scores, consistent with their disordered nature. Each disordered protein accesses a different region of the reference map, revealing differences in their conformational ensembles. We additionally examine the conformational maps of the nonviral gene delivery vector polyethyleneimine at various protonation states, and find that they resemble disordered proteins, with coverage of the reference map decreasing with increasing protonation state, indicating decreasing conformational diversity. We propose that our method of combining and in a scatter plot generates a simple, meaningful map of the conformational landscape of a disordered protein, which in turn can be used to assess conformational diversity of disordered proteins.

中文翻译：

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用聚合物物理量绘制本质无序蛋白质的构象景观

无序蛋白质是构象灵活的蛋白质，具有重要的生物学意义，并与阿尔茨海默病和癌症等毁灭性疾病有关。与稳定折叠结构的蛋白质不同，无序蛋白质采样了一系列需要考虑的不同构象。在这里，我们将无序蛋白质视为聚合物链，并计算称为瞬时形状比 () 的无量纲量，如 = ，其中 是端到端距离， 是回转半径。与 相比，延伸的蛋白质构象往往具有较高的值，因此具有较高的值，而紧凑的构象具有较小的值。我们使用（代表形状）与（代表大小）的散点图作为构象景观的简单图。我们首先检查简单聚合物模型的构象景观，例如随机游走、自回避游走和高斯游走（GW），我们注意到所有蛋白质/聚合物图都位于 GW 图的边界内。因此，我们使用 GW 图作为参考，为了评估构象多样性，我们计算每个蛋白质/聚合物覆盖的 GW 构象的分数 ()。无序蛋白质都具有高分，与其无序性质一致。每个无序蛋白质访问参考图谱的不同区域，揭示其构象整体的差异。我们还检查了非病毒基因递送载体聚乙烯亚胺在各种质子化状态下的构象图，发现它们类似于无序蛋白质，参考图的覆盖范围随着质子化状态的增加而减少，表明构象多样性减少。我们提出，我们将 和 组合在散点图中的方法可以生成无序蛋白质构象景观的简单且有意义的图，该图反过来又可用于评估无序蛋白质的构象多样性。