最近开始hi-c为代表的三维转录组的学习。即由于染色体的高度折叠性，即使同一染色体一维上相距很远的elements，也有可能空间距离很近，而产生interaction。
hi-c是目前探索相关信息的主要方法之一，本篇文献首次提出hi-c method，并进一步发现了染色体compartment分域方法。

• 文献：Comprehensive mapping of long range interactions reveals folding principles of the human genome
• PubMed ID：19815776
• GEO：GSE18199
• 关键字：hi-c method；A/B compartment

1、构建 hi-c library

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如上基本步骤为

• （1）cells are crosslinked with formaldehyde;
  DNA与甲醇交联，固定DNA（如果DNA间发生interaction，会有相关蛋白将interaction 区域固定在一起）
• （2）DNA is digested with a restriction enzyme that leaves a 5′-overhang;
  使用限制内切酶切开DNA，产生黏性末端（一端有一段缺口），有interaction的DNA片段会形成一个H形；
• （3）the 5′-overhang is filled, including a biotinylated residue;
  粘性末端缺口补平（包含biotinylated，如上图是那个紫色的标记）
• （4）the resulting blunt-end fragments are ligated ;
  H两端分别连接，成θ形
• （5）A Hi-C library is created by shearing the DNA and selecting the biotin-containing fragments with streptavidin beads.
  DNA打断碎片，富集、纯化含有biotinylated的片段，最终形成Hi-c library，进行测序。
• （6）parallel DNA sequencing, producing a catalog of interacting fragments
  将上述文库进行双端测序，以biotin为分隔成一组read pairs（read1、read2）分别比对到基因组两个位置 A、B

位置A、B即是染色体上的一段区域。单位长度即为bin 或者说resolution
bin越短 可匹配的越精确，但同时匹配的reads 数就减少了；
bin越长 匹配到的就越宽泛，但能够匹配到更多的reads ；

• 测序结果表明共有8.4M read pairs total。其中6.7 million corresponded to long-range contacts between segments greater than >20Kb apart.即六百万+的read pairs 相隔20KB长度以上，说明许多一维相距很远的bin，但空间距离很近。

2、genome-wide contact matrix M Heatmap

• 目的：将上述测序比对结果可视化。
• 矩阵格子：人染色体长度一般有100~200Mb，文献中用到的chr14长度为104M，bin设置为1Mb。

• 横、纵轴为相同的染色体长度，以bin长度（1mb）为轴刻度单位。因此对应的contact matrix M就是104*104大小的矩阵。（如下图）

  
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• Mij to be the number of ligation products between locusi and locus j (SOM).
  举例来说，假如M(2,8)=10就表示reads pairs分别匹配到染色体第2个bin与第8个bin的数目为10；再转换为对应热图相应的颜色等级。
• This matrix reflects an ensemble average of the interactions present inthe original sample of cells;
• It can be visually represented as a heatmap, with intensity indicating contact frequency.
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如上讨论的情况是pairs 的read1，read2均比对到同一条染色体的情况，称为Cis interaction
。而Trans interaction就是指read pairs分别比对到不同染色体的情况。

3、average intrachromosomal contact probability

• 疑问：如何计算？（基于1D component？）
• 概念：I n(s) for pairs of loci separated by a genomic distance s onchromosome n.
  指在染色体n上，平均相距长度为s（一维距离）的两个position contact probability
• 结果，如下图：从上往下依次代表染色体1内部、染色体1与10、染色体与其余所有染色体平均、染色体1与21。

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• 结论
  （1）contact probability decreases monotonically on every chromosome；就是说一般距离近，contact probability（interaction）作用强
  （2）chromosome territories.即使一条染色体上相距很远（超过200mb），其contact probability也比两条染色体里的任意两个position 高得多

  
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4、compartment

4.1、observed contact matrix M Heatmap

就是我们在第二点讨论的内容

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4.2、nomalization：observed/expected

• 为了校正 sequence proximity strongly influences contact probability，将raw data进行标准化；
• 标准化方法：dividing each entry in the contact matrix by the genome-wide average contact probability for loci at that genomic distance （上述第三点）.

• 结果如下：分为两大类，红色的大于1，蓝色的小于1
  The normalized matrix shows many large blocks of enriched and depleted interactions generating a ‘plaid’ pattern（格子图案）

  
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4.3、correlation matrix C

• If two loci (here 1 Mb regions) are nearby in space, we reasoned that they will share neighbors and have correlated interaction profiles. （未太理解这句话）

• 转换为相关矩阵correlation matrix C
  Cij is the Person correlation between the i row and j column of M which dramatically sharpened the plaid pattern（如下图）

  
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• The plaid pattern suggests that each chromosome can be decomposed into two sets of loci(arbitrarily labeled A and B) such that contacts within each set are enriched and contacts between sets are depleted.
  即表示将染色体分为两个区域，区域内的bins interaction 明显高于 区域间的interacton

4.4、pca的第一pc

• 对相关矩阵进行主成分分析，一般来说, the first principal component (PC) clearly corresponded to the plaid pattern (positive values defining one set, negative values the other)

• The entries of the PC vector reflected the sharp transitions from compartment to compartment observed within the plaid heatmaps.

  
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4.5 compartment A B

• The Hi-C data imply that regions tend be closer in space if they belong to the same
  compartment.
• 但是如上G图以及文章其它证据表明 compartment A compartment A is more closely associated with open, accessible, actively transcribed chromatin. 相对来说compartment B closed chromatin domains ,相对来说表达不活跃。

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