Hi-C is a genome-wide 3C based technology introduced by Lieberman-Aiden et al. in 2009 [3]. Realizing a genome-wide quantification of interactions, it constitutes a major breakthrough in the study of chromatin architecture. The Hi-C protocol differs from the standard 3C protocol in that there is an extra step needed before ligation. It consists of filling in the restriction digest of the chromosome with biotin-labeled nucleotides. After purification and shearing/ fragmentation of the Hi-C library, the biotin labeled material is pulled down to ensure that only ligation junctions are selected for further analysis.
“Chromosome conformation capture carbon copy” (5C) captures interactions between all restriction fragments within a selected region [55]. For example, it was used to study the spatial organization of the bacterial Caulobacter crescentus genome [76], the regulatory landscape of mouse X inactivation [8] and the long-range interaction landscape of gene promoters in the human genome [40]. A technique similar to Hi-C, called genome confor- mation capture (GCC), has been applied for mapping yeast chromosome interactions [57] as well as for studying the spatial organization of the Escherichia coli nucleoid [58].
All 3C-based methods, contrary to microscopy-based techniques, allow for both a more systematic and quantitative characterization of genome topology and a higher resolution. The essential drawback, however, is that the conventionally ensemble 3C-based methods are mostly performed on large populations of cells, leading to loss of information at the single-cell level.
In this chapter, we give an overview of the data analysis involved in the framework of a Hi-C experiment. Moreover, we present and discuss publicly available Hi-C datasets of bacterial genomes and present possibilities to assess and compare them in terms of data quality.
4.2 Hi-C Data Processing
This section covers the main steps involved in the data processing of a genome-wide 3C- based study. Since the focus of this chapter is mainly on genome-wide methods, such as Hi-C or GCC, methods relevant for theses technologies are discussed in this section. Hi-C data processing can be subdivided into the following four main steps: (1) Mapping to the reference genome, (2) Quality control, (3) Binning and contact matrix generation, (4) Balancing (Fig. 4.1). Each of these steps is discussed in the following section.
4.2.1 Mapping to the Reference Genome
The first step of genome-wide 3C data analysis consists of mapping reads back to the reference genome. The Hi-C method quantifies an interaction by a ligation product formed between two restriction fragments. By using paired-end sequencing and mapping both ends of each paired sequence to the reference genome, the two restriction fragments in the ligation product can be determined. However, if the read length is bigger than the length of one of the restriction fragments, the mapping will not work. To solve this problem, the mapping procedure can be refined by means of an iterative mapping scheme that involves truncating reads to a smaller length prior to mapping [77]. Reads that are not aligned uniquely at both ends are then re-aligned by iteratively increasing their portions. This process is repeated until either all reads uniquely map or until the read is extended to its entirety. Only paired-end reads with both sides being uniquely mapped to the reference genome contribute to the set of Hi-C interactions. All other paired-end reads are discarded.
@SRR824846.1 HWI-ST333_0267_FC:7:1101:1410:2200 length=40 CGCCGAGGCGACGCAAAAGCAGTTTCACTCAGATCTCGTN +SRR824846.1 HWI-ST333_0267_FC:7:1101:1410:2200 length=40 ___`ccccgg^^cagdgad]ccfhhhgfdgf`_cbgdgbB @SRR824846.2 HWI-ST333_0267_FC:7:1101:1447:2213 length=40 CGCCTGCCTGGCCTTGGTCTGCGGCGATCCGGTAATCTGG +SRR824846.2 HWI-ST333_0267_FC:7:1101:1447:2213 length=40 _a_cceeegggggihhhhiiibghih_egedga`g`bffh
raw sequence reads
Mapping to the reference genome
Data quality control and filtering
genome position [Mbp]
Contact matrix generation and bias-correction
Binning (i.e. accumulation) of read counts
0 1 2 3 4 0 1 2 3 4 genome position [Mbp]
Figure 4.1: Schematic overview of the general workflow for analyzing genome-wide 3C data such as Hi-C. The input (at the top left) is raw sequencing data and as a typical output we illustrated a bias-corrected contact matrix (at the top right). The dataset used here for illustration purposes is that of the study of Le et al. [48] (SRR824846).
4.2.2 Quality Control
The next step is quality control to ensure that the aligned sequence reads are likely to be the result of proximity-based ligation of digested fragments, and that they are reflecting long-range chromatin interaction rather than just random collision. Self-circularized or un-ligated (dangling-end) products will result in reads that map with both ends on the same restriction fragment. These reads should be removed. Also reads from neighboring fragments that map to the same strand should be removed since they are likely the result of incomplete digestion. Furthermore, reads that map multiple times at the exact same location on the reference genome are often the result of biased PCR-amplification and should also be removed. Hi-C sequencing reads can be compared to randomly generated control sequencing reads, whereby the Hi-C reads should be significantly closer to the chosen restriction sites than random reads [78]. The Hi-C reads should also be in the correct orientation with respect to the restriction site.
4.2.3 Binning and Contact Matrix Generation
After the alignment of the sequence reads and quality control the next step is the con- struction of contact matrices of the interaction data. To produce a contact matrix, the genome is divided into equally sized loci, so called bins. The result of this aggregation of read-counts across bins is a symmetric matrix composed of interaction frequencies between bins covering the entire genome. The size of these bins used to represent the meaning- ful contacts between pairs of genomic loci can be referred to as the resolution of a Hi-C experiment (see Fig. 4.2 for a comparison of a contact matrix depicted at different bin sizes).
A linear increase of resolution requires a quadratic increase in total sequencing depth; the size of the bins and effectively the resolution is limited by sequencing depth. Moreover, the resolution also depends on the restriction enzyme used for the Hi-C experiment (see
4.2. Hi-C Data Processing 51 0 800 1600 2400 3200 4000 genome position [kbp] 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0 800 1600 2400 3200 4000 genome position [kbp] 0 800 1600 2400 3200 4000 genome position [kbp] 0.0006 0.0012 0.0018 0.0024 0.0030 0.0036 0.0042 0.0048 0.0054 0.0060 A B
Figure 4.2: Hi-C contact map depicted at two different resolutions (A. 4kbp and B. 16kbp). The contact map of higher resolution reveals much more detailed structures, especially on the interactions within the domains along the diagonal. Data on B. subtilis from Marbouty [73] (SRR2772323).
section 4.3.4). To illustrate this relationship between resolution and the total number of collected read pairs, we want to highlight that for a resolution of 100 kbp in the first Hi-C study of the human genome 8.4 million reads were collected [3]. Increasing the resolution to 1 kbp required 4.9 billion reads [36]. Thus, increasing the resolution by two orders of magnitude required increasing the total number of reads by three orders of magnitudes.
4.2.4 Balancing
Besides the bias introduced by individual reads or restriction fragments, binning generates biases, as well. Yaffe and Tanay identified the origin of some of these biases, such as the non-uniform distribution of the length of restriction fragments with respect to ligation efficiency, the nucleotide composition of the genome under investigation and issues with uniquely mapping the interactions back onto the reference genome. They proposed an integrated probabilistic model [78] for eliminating these known systematic biases from the “raw” contact maps. This procedure is referred to as normalization.
Several other models for normalizing Hi-C contact maps have been proposed [77, 79, 80]. Though, these approaches do not explicitly incorporate the aforementioned biases on the grounds that it is not possible to know each and every bias. Since most of these approaches are based on the Sinkhorn-Knopp (SK) balancing algorithm [81], they can be more precisely referred to as balancing instead of normalization. Explicit bias correction and balancing yield comparable results [36].
In this section, we focus on the SK balancing algorithm [81] that transforms a symmet- ric non-negative matrix A = (aij) , A ∈ Rn×n+ , into a doubly stochastic matrix S = (sij),
that is, a matrix whose rows and columns sum up to 1, i.e.,
∑︂ i sij = ∑︂ j sij = 1 .
The SK algorithm is an iterative process that consists in solving
0 1000 2000 3000 4000 genome position [kbp] 0 1000 2000 3000 4000 genome position [kbp] 0 200 400 600 800 1000 1200 1400 1600 0 1000 2000 3000 4000 genome position [kbp] 0.000 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032 0 800 1600 2400 3200 4000 genome position [kbp] 0 800 1600 2400 3200 4000 genome position [kbp] 0 20 40 60 80 100 120 140 160 180 200 0 800 1600 2400 3200 4000 genome position [kbp] 0.0006 0.0012 0.0018 0.0024 0.0030 0.0036 0.0042 0.0048 0.0054 0.0060 A B C D
Figure 4.3: Comparison of “raw” Hi-C contact frequency matrices on the left and the respective balanced equivalents, i.e. contact probability matrices, on the right. A, B. Data on C. crescentus of the study of Le et al. [48] (SRR824846). C, D. Data on B. subtilis of the study of Marbouty et al. [73] (SRR2772323). We balanced the matrices by applying the Sinkhorn-Knopp (SK) algorithm. These two examples illustrate that the balancing procedure leads to very different results dependent on the input “raw” Hi-C contact frequency matrix. In the case of the upper matrix on C. crescentus, the coverage of reads is homogenous along the genome and the contact frequency matrix (A) already indicates a domain structure along the diagonal. In contrast, the coverage of reads is considerably more heterogeneous in the case of the lower matrix on B. subtilis (C). The region from 1.7 up to 2.3 Mbp lacks reads. Therefore the structure of the balanced contact map (D) in this region is rather an artifact of the balancing procedure than of biological relevance.
where D1and D2 are unique up to a scalar factor diagonal matrices with positive main diagonal. The matrices D1 and D2 are obtained by alternatingly normalizing columns and rows of A.
Applied to our situation, A constitutes the raw matrix of contact frequencies, and the diagonal matrices D1 and D2 contain the biases for the bins involved in the contacts between bins i and j. S is then the matrix of unbiased relative contact frequencies, which is defined such that each row and column of the upper triangular matrix sums to 1. The biases, and therefore S, can be found by using the SK algorithm that converges to the solution of equation 4.1.