The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

中文翻译：

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通过逆布朗动力学从接触概率图计算 3D 染色质配置


染色质的三维 (3D) 组织（在一些基因的长度范围内）对于确定染色质的功能状态（可及性和基因表达量）至关重要。染色体构象捕获实验的最新进展提供了细胞群中染色质组织的部分信息，即任何片段对之间的接触计数，但没有提供导致这些接触计数的相互作用强度。然而，给定接触矩阵，确定整个染色质聚合物的完整 3D 组织是一个逆问题。在这项工作中，提出了一种基于粗粒珠弹簧链模型的新型逆布朗动力学方法来计算染色质不同片段之间的最佳相互作用强度，从而满足实验测量的接触计数概率约束。将此方法应用于两种不同细胞类型中的 α-珠蛋白基因位点，我们预测了与该位点染色质的活跃和抑制状态相对应的 3D 组织。我们表明，该区域任意两段之间的平均距离具有广泛的分布，并且不能仅根据接触概率计算为简单的逆关系。多种归一化方法的结果表明，所有可测量的量可能在很大程度上取决于归一化的性质。我们认为，通过实验测量预测量，人们可以推断出适当的标准化形式。