README:

This README describes the various files and file formats that have been uploaded to GEO accession GSE63525 as part of the study “A 3D Map of the Human Genome at Kilobase Resolution Reveals Principles of Chromatin Looping” (Rao and Huntley, et al., Cell 2014).

As part of this study, we have uploaded data at various processing stages, including:
- raw sequence data (FASTQ format)
- data post-alignment and duplicate filtering (merged_nodups.txt format)
- contact matrices and associated normalization and 1-D expected vectors (tar archives)
- feature annotations (loop annotations, contact domain annotations, subcompartment annotation for GM12878, super loop annotation for GM12878, intersect SNP list for GM12878)

The various files and file formats associated with each processing stage will be described in more detail below.

Raw Data:

FASTQ data for all the experiments performed in this study are available through SRA under the Sample Record for each experiment. Each experiment is labeled with a unique identifier: “HIC” followed by a three digit number (for example, HIC001 or HIC100). Full details for each experiment (including, but not limited to: cell type, experimental variations, number of reads sequenced, etc.) as well as which experiments were combined together to create the high resolution maps for each cell type are available in Supplemental Table S1 of Rao, Huntley, et al., Cell, 2014. Some information about each experiment (such as cell type and a general description of the experimental protocol used) is also available in each individual sample record.

Post-alignment and Duplicate Filtering Data:

Under each Sample Record, there is a file available named GSM*_HIC*_merged_nodups.txt.gz, where GSM* is the GEO Sample ID and HIC* is the unique sample identifier from Supplemental Table S1 of Rao, Huntley, et al., Cell, 2014. This file contains post-alignment and post-duplicate filtering data for each HIC experiment. At this stage of processing, read pairs where one or both ends do not align to the reference genome have already been removed, as well as chimeric ambiguous reads (see Section II.a.2 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for a definition of chimeric ambiguous reads). In addition, duplicate reads (reads where both ends align to within +/- 4bp of each other) have been removed as well (see Section II.a.3 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for a full description of duplicate removal). Full details of the Hi-C processing pipeline used in this study are provided in Section II.a. of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014.

Each line of the merged_nodups file represents a single Hi-C read pair that has passed the alignment and duplicate removal stages. The format of each line of the file is:

read_name    strand1    chromosome1    position1    fragment-index1    strand2    chromosome2    position2    fragment-index2    mapq1    mapq2

where:
read_name = the name of the read pair as seen in the FASTQ files
strand = the strand that the read maps to (0=forward, 16=reverse)
chromosome = the chromosome that the read maps to ([1-22,X,Y,MT] for human (b37 reference genome) or [chr1-chr19,chrX,chrY,chrM] for mouse (mm9 reference genome))
position = the position on the chromosome that the read maps to
fragment-index = the index of the interval demarcated by restrictions sites in the genome, starting with 0 for the interval preceding the first restriction site
mapq = the mapping quality score returned by BWA (see Section II.a.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for full details about the alignment process)

Contact matrices and Associated Normalization and Expected Vectors:

Under the main series record (GSE63525), there are a set of tar archives that contain the raw observed intra-chromosomal or inter-chromosomal contact matrices for each cell type analyzed in our study as well as normalization vectors to transform the raw matrices into normalized matrices and 1-d expected vectors to transform the observed matrices into O/E matrices (see the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014 for details).

The intrachromosomal contact matrix archives contain intrachromosomal contact matrices at 8 (9 for GM12878_combined) different base pair delimited resolutions (1 Mb, 500kb, 250kb, 100kb, 50kb, 25kb, 10kb, 5kb [and 1kb for GM12878_combined]). At each resolution, files associated with each chromosome are provided in a separate subdirectory. Within, each chromosome subdirectory, there are two further subdirectories (MAPQG0 and MAPQGE30). The MAPQG0 subdirectory contains files associated with the contact matrices constructed from all read pairs that uniquely align to the genome (MAPQ>0). The MAPQGE30 subdirectory contains files associated with the contact matrices constructed from all read pairs that map to the genome with a MAPQ>=30.

For example, the files associated with the contact matrix for chromosome 1 at 5 kb resolution using MAPQ>=30 read pairs are in the subdirectory:

CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/

There are 7 text files associated with each intrachromosomal contact matrix ([CHR] represents the chromosome number and [RES] represents the resolution):

[CHR]_[RES].RAWobserved
[CHR]_[RES].KRnorm
[CHR]_[RES].VCnorm
[CHR]_[RES].SQRTVCnorm
[CHR]_[RES].RAWexpected
[CHR]_[RES].KRexpected
[CHR]_[RES].VCexpected
[CHR]_[RES].SQRTVCexpected

For example, the files associated with the contact matrix for chromosome 1 at 5 kb resolution using MAPQ>=30 read pairs are:

CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.RAWobserved
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.KRnorm
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.VCnorm
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.SQRTVCnorm
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.RAWexpected
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.KRexpected
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.VCexpected
CELL_TYPE/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.SQRTVCexpected

*.RAWobserved is a text file with the raw observed contact matrix in sparse matrix notation. Each line has three fields: i, j, and M_i,j. (i and j are written as the left edge of the bin at a given resolution; for example, at 100 kb resolution, the entry corresponding to the first row and tenth column of the matrix would correspond to M_i,j, where i=0, j=900000). Only the upper triangle of the matrix is provided (i.e. i<=j), the matrix is symmetric, so M_i,j = M_j,i.

The three *norm files are normalization vectors that can be used to transform the raw contact matrices M into normalized matrices M*. (See the glossary below and section II.b of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014 for more information about the different types of normalizations. All analyses and results presented in the main text of Rao, Huntley, et al., Cell, 2014 were performed using KR normalized contact matrices.) Each file is ordered such that the first line of the normalization vector file is the norm factor for the first row/column of the corresponding raw contact matrix, the second line is the factor for the second row/column of the contact matrix, and so on. To normalize, an entry M_i,j in a *RAWobserved file, divide the entry by the corresponding norm factors for i and j.

For example, here is a line from the GM12878_combined 5kb chr1 MAPQGE30 raw observed contact matrix (GM12878_combined/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.RAWobserved):
40000000	40100000	59.0

To normalize this entry using the KR normalization vector, one would divide 59.0 by the 8001st line ((40000000/5000)+1=8001) and the 8021st line ((40100000/5000)+1=8021) of GM12878_combined/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.KRnorm. The 8001st line of the KR norm file is 1.2988778370674694;The 8021st line of the KR norm file is 1.6080499717941548. So the corresponding KR normalized entry for the entry above is 59.0/(1.2988778370674694*1.6080499717941548) or 28.24776973966101. There will be some entries in the KR vector files which are NaNs – these correspond to rows which were too sparse and were thrown out before normalization was performed (See Section II.b.4 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014). If the KR normalization vector file is completely empty or all NaNs, then the KR algorithm didn’t converge on that particular matrix (likely due to sparsity of the matrix). In that case, one can use either the VC or SQRTVC normalizations or check a different resolution.  

The four *expected files are expected vectors that can be used to construct O/E matrices that account for the increased number of contacts seen at short distances due to random polymer interactions driven by one-dimensional genome proximity (see the glossary below and section II.c of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014 for more information about the construction of these expected vectors and O/E matrices). Note that these expected vectors only account for random polymer interactions driven by one-dimensional genome proximity and do not control for other features such as compartmentalization or contact domain structure. As such, they are not appropriate expected models when seeking to identify focal looping interactions. In identifying focal looping interactions, one must use local expecteds (see Section VI.a.4.i, Section VI.a.5.i, and Figure 3 of Rao, Huntley, et al., Cell 2014). These expected files are ordered such that first line of the expected vector file is the expected number of contacts between two loci separated by 0*RES base pairs (0th diagonal of contact matrix), the second line of the file is the expected number of contacts between two loci separated by 1*RES base pairs (1st diagonal of contact matrix), and so on. So to create the O/E matrix, divide each entry M_i,j by the expected value corresponding to the distance j-i.

For example, for the above entry of the GM12878_combined 5kb chr1 MAPQGE30 raw observed contact matrix, to get the corresponding entry of the O/E matrix divide by the 21st line (((41000000-40000000)/5000)+1=21) of GM12878_combined/5kb_resolution_intrachromosomal/chr1/MAPQGE30/chr1_5kb.RAWexpected. The 21st line of the raw expected file is 20.101675. So the corresponding raw O/E entry for the entry above is 59.0/20.101675 or 2.935078793185145. To create the normalized O/E files, first construct the normalized observed matrices as above and then divide by the corresponding line of the normalized expected file (i.e. *.KRexpected, *.VCexpected, or *.SQRTVCexpected). 

The interchromosomal contact matrix archives contain interchromosomal contact matrices at 8 different base pair delimited resolutions (1 Mb, 500kb, 250kb, 100kb, 50kb, 25kb, 10kb, 5kb). At each resolution, the files associated with each pair of chromosomes are provided in a separate subdirectory. Within each chromosome pair subdirectory, there are two further subdirectories (MAPQG0 and MAPQGE30). The MAPQG0 subdirectory contains files associated with the contact matrices constructed from all read pairs that uniquely align to the genome (MAPQ>0). The MAPQGE30 subdirectory contains files associated with the contact matrices constructed from all read pairs that map to the genome with a MAPQ>=30.

For example, the files associated with the contact matrix for chromosome 1 and chromosome 2 using MAPQ>=30 read pairs are in the subdirectory:

CELL_TYPE/100kb_resolution_interchromosomal/chr1_chr2/MAPQGE30/

There are 15 text files associated with each interchromosomal contact matrix ([CHR1] represents the first chromosome number, [CHR2] represents the second chromosome number, and [RES] represents the resolution):

[CHR1]_[CHR2]_[RES].RAWobserved
[CHR1]_[RES].KRnorm
[CHR1]_[RES].VCnorm
[CHR1]_[RES].SQRTVCnorm
[CHR1]_[RES].INTERKRnorm
[CHR1]_[RES].INTERVCnorm
[CHR1]_[RES].GWKRnorm
[CHR1]_[RES].GWVCnorm
[CHR2]_[RES].KRnorm
[CHR2]_[RES].VCnorm
[CHR2]_[RES].SQRTVCnorm
[CHR2]_[RES].INTERKRnorm
[CHR2]_[RES].INTERVCnorm
[CHR2]_[RES].GWKRnorm
[CHR2]_[RES].GWVCnorm

For example, the files associated with the contact matrix for chromosome 1 and chromosome 2 using MAPQ>=30 read pairs are:

chr1_2_100kb.RAWobserved
chr1_100kb.KRnorm
chr1_100kb.VCnorm
chr1_100kb.SQRTVCnorm
chr1_100kb.INTERKRnorm
chr1_100kb.INTERVCnorm
chr1_100kb.GWKRnorm
chr1_100kb.GWVCnorm
chr2_100kb.KRnorm
chr2_100kb.VCnorm
chr2_100kb.SQRTVCnorm
chr2_100kb.INTERKRnorm
chr2_100kb.INTERVCnorm
chr2_100kb.GWKRnorm
chr2_100kb.GWVCnorm

At higher resolutions and for some cell types, INTERKR/VC files and GWKR/VC files are not available, so only 9 text files are provided.

The *.RAWobserved files for the interchromosomal matrices are formatted the same way as the intrachromosomal matrices above except the i locus corresponds to CHR1 and the j locus corresponds to CHR2. One can create the normalized matrices as above except one should use the line corresponding to the i locus norm factor from the CHR1 normalization vector file and the line corresponding to the j locus norm factor from the CHR2 normalization vector file. (See the glossary below and section II.b of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014 for more information about the different types of normalizations.)

Loop Annotation Files:
Under the main Series Record (GSE63525), there are files named *_HiCCUPS_looplist.txt.gz or *_HiCCUPS_looplist_with_motifs.txt.gz, where * represents each of the cell types analyzed in this study (GM12878, HMEC, HUVEC, HeLa, IMR90, K562, KBM7, NHEK, CH12-LX), as well as biological replicate annotations for GM12878 (GM12878_primary and GM12878_replicate). These files contain Juicebox-loadable (www.aidenlab.org/juicebox) loop annotations returned by our loop calling algorithm, HiCCUPS (see Fig. 3, the Experimental Procedures, and Section VI.a.5 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014). These files contain a header line, followed by a line for every loop. The files named *_HiCCUPS_looplist.txt.gz contain 20 fields per line in the following format:

chromosome1    x1    x2    chromosome2    y1    y2    color    observed    expected_bottom_left    expected_donut    expected_horizontal    expected_vertical    fdr_bottom_left    fdr_donut    fdr_horizontal    fdr_vertical    number_collapsed    centroid1    centroid2    radius

Explanations of each field are as follows:
chromosome = the chromosome that the loop is located on
x1,x2 = the coordinates of the upstream locus corresponding to the peak pixel (see the Experimental Procedures and VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for a definition of the peak pixel)
y1,y2 = the coordinates of the downstream locus corresponding to the peak pixel (see the Experimental Procedures and VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for a definition of the peak pixel)
color = the color that the feature will be rendered as if loaded in Juicebox (www.aidenlab.org/juicebox)
observed = the raw observed counts at the peak pixel (see the Experimental Procedures and VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for a definition of the peak pixel)
expected_[bottom_left, donut, horizontal, vertical] = the expected counts calculated using the [bottom_left, donut, horizontal, vertical] filter (see Figure 3 and section VI.a.5.i of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
fdr_[bottom_left, donut, horizontal, vertical] = the q-value of the loop calculated using the [bottom_left, donut, horizontal, vertical] filter (see VI.a.5.ii of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
number_collapsed = the number of pixels that were clustered together as part of the loop call (see section VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
centroid1 = the upstream coordinate of the centroid of the cluster of pixels corresponding to the loop (see section VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
centroid2 = the downstream coordinate of the centroid of the cluster of pixels corresponding to the loop (see section VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
radius = the Euclidean distance from the centroid of the cluster of pixels to the farthest pixel in the cluster of pixels (see section VI.a.5.iv of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)

The files named *_HiCCUPS_looplist_with_motifs.txt.gz contain 30 fields per line. The first 20 are the same as above, followed by an additional 10 in the following format:

motif_x1    motif_x2    sequence1    orientation1    uniqueness1    motif_y1    motif_y2    sequence2    orientation2    uniqueness2

Explanations of each field are as follows:
motif_x1,x2 = the start and end coordinates of the localized CTCF motif within the upstream loop anchor (see Section VI.e.7 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014). 
sequence1 = the sequence of the localized CTCF motif within the upstream loop anchor
orientation1 = the orientation of the localized CTCF motif within the upstream loop anchor; p’ if the motif sequence is on the forward strand and ’n’ if the motif sequence is on the reverse strand
uniqueness1 = whether the localized CTCF motif within the upstream loop anchor was uniquely called (‘u’; see Section VI.e.7 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014) or inferred based on the convergent orientation principle (‘i’; see Section VI.e.8 of the  Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
motif_y1,y2; sequence2; orientation2; and uniqueness2 are the same as above except for the downstream loop anchor.

If the fields are ‘NA’ that indicates that we were unable to localize the anchor to a single CTCF motif. Motifs were called using STORM (Schones, et al., 2007) using the following CTCF position weight matrix from Kim, et al., 2007:

P0       A       C       G       T
00      60      47      69      53
01       0      82      40     107
02      46      41     103      39
03      77       0     152       0
04       0     229       0       0
05       0     229       0       0
06     171       0      30      28
07      18     112      99       0
08      27     144      19      39
09     229       0       0       0
10       0       0     229       0
11     111       0     118       0
12       0       0     142      87
13       0       0     229       0
14       0       0     229       0
15      36     171       0      22
16      88       0     127      14
17       0     135      94       0
18      37      96      32      64
19      72      74      70      13

Contact Domain Annotation Files:
Under the main Series Record (GSE63525), there are files named *_Arrowhead_domainlist.txt.gz where * represents each of the cell types analyzed in this study (GM12878, HMEC, HUVEC, HeLa, IMR90, K562, KBM7, NHEK, CH12-LX). These files contain Juicebox-loadable (www.aidenlab.org/juicebox) domain annotations returned by our domain calling algorithm, Arrowhead (see Fig. 2, the Experimental Procedures, and Section IV.a. of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014). These files contain a header line, followed by a line for every domain. These files contain 12 fields per line in the following format:

chromosome1    x1    x2    chromosome2    y1    y2    color    corner_score    Uvar    Lvar    Usign    Lsign

Explanations of each field are as follows:
chromosome = the chromosome that the domain is located on
x1,x2/y1,y2 = the interval spanned by the domain (contact domains manifest as squares on the diagonal of a Hi-C matrix and as such: x1=y1, x2=y2)
color = the color that the feature will be rendered as if loaded in Juicebox (www.aidenlab.org/juicebox)
corner_score = the corner score, a score indicating the likelihood that a pixel is at the corner of a contact domain. Higher values indicate a greater likelihood of being at the corner of a domain (see Section IV.a.3 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014)
Uvar  = the variance of the upper triangle
Lvar = the variance of the lower triangle
Usign = -1*(sum of the sign of the entries in the upper triangle)
Lsign = sum of the sign of the entries in the lower triangle

Corner pixels which had both their left and right edges match to within 5 bins were merged to a single block call. In this case, the scores – given by the last 5 columns -  are the mean of the all the corner pixels in the merged group, and the edges are given by the largest (in bp) values called for each edge. (See Section IV.a.3 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for details about these scores.)

Subcompartment Annotation File:
GSE63525_GM12878_subcompartments.bed.gz contains the GM12878 annotation of the locations of the six subcompartments (A1, A2, B1, B2, B3, B4) identified in this study (see Section V.a.2 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 for details regarding the clustering algorithm). The file is a bed file; the name of the subcompartment (A1, A2, B1, B2, B3, B4) is provided in the name field of the bed file for each entry. NA is used in the name field for loci that could not be assigned to a subcompartment. An annotation of the six subcompartments is only provided for GM12878 as our other maps were too sparse to reliably annotate subcompartments.

Superloop Annotation File:
GSE63525_GM12878_HiCCUPS_chrX_superloop_list.txt.gz contains the GM12878 annotation of super loops on chromosome X. The file is in the same format as the loop annotations (20 fields per line) above.

SNP File:
GSE63525_GM12878_SNPs.txt.gz contains the GM12878 SNPs used to generate the diploid Hi-C maps produced in this study (see VII.a. for details about how this SNP list was generated).  Each row of the text file represents one SNP and contains three fields:

chr:position paternal_nucleotide maternal_nucleotide

For example, the first line is 1:63697 C T indicating that this is the SNP on chromosome 1, position 63697, and that the paternal chromosome will have the nucleotide “C” at this position, and the maternal chromosome will have the nucleotide “T” at this position. Contact matrices for GM12878 maternal and paternal homologs generated using this SNP list are provided in the tar archive ‘GSE63525_GM12878_diploid_intrachromosomal_contact_matrices.tar.gz’. Contact matrices are provided in the format specified above.
 
GLOSSARY:

KRnorm = normalization vector obtained using the matrix balancing procedure of Knight and Ruiz on the intrachromosomal contact matrix, as reimplemented by us in Java. See Knight & Ruiz, IMA Journal of Numerical Analysis, 2012; section II.b.4 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

GWKRnorm = normalization vector obtained using the matrix balancing procedure of Knight and Ruiz on the entire genome-wide contact matrix (i.e. all intrachromosomal and interchromosomal contact matrices), as reimplemented by us in Java. See Knight & Ruiz, IMA Journal of Numerical Analysis, 2012; section II.b.4 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

INTERKRnorm = normalization vector obtained using the matrix balancing procedure of Knight and Ruiz on the entire genome-wide contact matrix without intrachromosomal contact matrices (i.e. only interchromosomal contact matrices), as reimplemented by us in Java. See Knight & Ruiz, IMA Journal of Numerical Analysis, 2012; section II.b.4 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

VCnorm = normalization vector obtained by calculating coverages (row-sums of the intrachromosomal contact matrix) for each locus as performed in Lieberman-Aiden, van Berkum, et al. See Lieberman-Aiden, van Berkum, et al., Science 2009; section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Note that these values are not the reciprocals of the row-sums as written in section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 but rather are proportional to the row sums themselves, hence why one must divide the raw observed matrix entries by the normalization factors rather than multiplying. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

GWVCnorm = normalization vector obtained by calculating genome-wide coverages (row-sums of the genome-wide contact matrix, i.e. both intra- and inter-chromosomal contact matrices) for each locus as performed in Lieberman-Aiden, van Berkum, et al. See Lieberman-Aiden, van Berkum, et al., Science 2009; section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Note that these values are not the reciprocals of the row-sums as written in section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 but rather are proportional to the row sums themselves, hence why one must divide the raw observed matrix entries by the normalization factors rather than multiplying. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

INTERVCnorm = normalization vector obtained by calculating interchromosomal coverages (row-sums across interchromosomal contact matrices) for each locus as performed in Lieberman-Aiden, van Berkum, et al. See Lieberman-Aiden, van Berkum, et al., Science 2009; section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Note that these values are not the reciprocals of the row-sums as written in section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell 2014 but rather are proportional to the row sums themselves, hence why one must divide the raw observed matrix entries by the normalization factors rather than multiplying. Normalization factors are scaled such that the sum of the entries in the normalized contact matrix is equal to the sum of the entries in the raw contact matrix.

SQRTVCnorm = normalization vector obtained by taking the square root of the VCnorm vector. See section II.b.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014.

RAWexpected = a genome-wide model of interaction probability as a function of 1-dimensional genomic distance as introduced in Lieberman-Aiden, van Berkum, et al. and refined by us. See Lieberman-Aiden, van Berkum, et al., Science 2009; section II.c.1 of the Extended Experimental Procedures of Rao, Huntley, et al., Cell, 2014. Note that while the expected vector is calculated by taking averages over all matrix entries at a fixed distance genome-wide, the vectors are independently scaled for each chromosome such that the sum of the entries for a given intrachromosomal expected matrix is equal to the sum of the entries for the intrachromosomal observed matrix.

KRexpected = the same model of interaction probability as a function of 1-dimensional genomic distance as RAWexpected except calculated from the KR normalized contact matrix. Note that while the expected vector is calculated by taking averages over all matrix entries at a fixed distance genome-wide, the vectors are independently scaled for each chromosome such that the sum of the entries for a given intrachromosomal expected matrix is equal to the sum of the entries for the intrachromosomal observed matrix.

VCexpected = the same model of interaction probability as a function of 1-dimensional genomic distance as RAWexpected except calculated from the VC normalized contact matrix. Note that while the expected vector is calculated by taking averages over all matrix entries at a fixed distance genome-wide, the vectors are independently scaled for each chromosome such that the sum of the entries for a given intrachromosomal expected matrix is equal to the sum of the entries for the intrachromosomal observed matrix.

SQRTVCexpected = the same model of interaction probability as a function of 1-dimensional genomic distance as RAWexpected except calculated from the SQRTVC normalized contact matrix. Note that while the expected vector is calculated by taking averages over all matrix entries at a fixed distance genome-wide, the vectors are independently scaled for each chromosome such that the sum of the entries for a given intrachromosomal expected matrix is equal to the sum of the entries for the intrachromosomal observed matrix.